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Attitude Stabilization of an Unknown and Spinning Target Spacecraft using a Visco-Elastic Tether Kirk Hovell and Steve Ulrich Department of Mechanical and Aerospace Engineering Carleton University Ottawa Canada
13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
2 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Context Space debris becoming a major problem
23000 pieces larger than 10 cm Only 1000 operational satellites
Space debris is growing
250 in-orbit fragmentation events since 1961 Chinese Anti-Satellite test +25 IridiumCosmos collision +2200 70+ launches per year
carletoncaspacecraft
[Source ESA]
3 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
4 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Critical Density Reached Kessler Syndrome -1978 Cascading collisions Exponential growth in space debris Currently 1 collision per 10 years
5 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Solution Active removal of the highest risk debris is required
Highest Risk Debris High mass Densely populated orbits High altitudes
6 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
2 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Context Space debris becoming a major problem
23000 pieces larger than 10 cm Only 1000 operational satellites
Space debris is growing
250 in-orbit fragmentation events since 1961 Chinese Anti-Satellite test +25 IridiumCosmos collision +2200 70+ launches per year
carletoncaspacecraft
[Source ESA]
3 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
4 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Critical Density Reached Kessler Syndrome -1978 Cascading collisions Exponential growth in space debris Currently 1 collision per 10 years
5 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Solution Active removal of the highest risk debris is required
Highest Risk Debris High mass Densely populated orbits High altitudes
6 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
3 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
4 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Critical Density Reached Kessler Syndrome -1978 Cascading collisions Exponential growth in space debris Currently 1 collision per 10 years
5 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Solution Active removal of the highest risk debris is required
Highest Risk Debris High mass Densely populated orbits High altitudes
6 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
4 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Critical Density Reached Kessler Syndrome -1978 Cascading collisions Exponential growth in space debris Currently 1 collision per 10 years
5 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Solution Active removal of the highest risk debris is required
Highest Risk Debris High mass Densely populated orbits High altitudes
6 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
5 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Solution Active removal of the highest risk debris is required
Highest Risk Debris High mass Densely populated orbits High altitudes
6 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
6 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
[Source ESA]
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
7 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Possible Capture Strategy Tethered Spacecraft System (TSS)
Lower collision risk than physically attaching to target Mechanically simpler than using a grappling arm Does not require a specific attachment point on target
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
8 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Source Bruce Burlton
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
9 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation carletoncaspacecraft
Tethered Spacecraft System (TSS) Technical Challenges
Stable Target is Required
Scope of this presentation
Controlling tumbling target To avoid collision with chaser To reduce forces transmitted to chaser For predictable orbital maneuvers
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
10 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Literature Review Dynamics of tethered space systems [Alpatov et al (2010)]
Extensive analysis of the motion of point masses connected via tether
Target attitude motion [Aslanov et al (2013)] Newtonian approach to use tether to damp angular momentum of debris using single tether and thrust from chaser Found that safe transportation is achieved using thrust
carletoncaspacecraft
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
11 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Motivation
Original Contributions
A novel TSS with 4 sub-tethers is presented to improve stabilization ability of the system Only chaser is treated as a point mass
To safely stabilize a spinning space debris immediately after capture
carletoncaspacecraft
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
12 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Tether
Uncooperative Target
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
13 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Approach carletoncaspacecraft
Chaser
Main Tether
Uncooperative Target
Sub-Tethers
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
14 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
15 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Attitude Dynamics of Target
Translational Motion of Target Chaser and Junction
carletoncaspacecraft
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
16 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation carletoncaspacecraft
Chaser Tether
Junction
Uncooperative Debris
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
17 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Vector Definition In Inertial reference frame In Target-fixed reference frame
carletoncaspacecraft
Target position components Junction position components Chaser position components The ith sub-tether components
The ith sub-tether attachment point on target components
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
18 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Vector
carletoncaspacecraft
Tether vector is Where Is the rotation matrix from target frame to inertial frame obtained from the quaternion
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
19 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Modeling Force magnitude in ith tether
Where and are spring and damping constants of tether is magnitude of tether stretch is magnitude of tether stretch rate
carletoncaspacecraft
Massless spring-damper is assumed
When stretched
When un-stretched
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
20 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Tether Stretch
Tether Stretch Rate
carletoncaspacecraft
Where and are the velocities of the junction and target respectively
Where is the un-stretched length
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
21 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net force vector on target
Net torque vector on target
carletoncaspacecraft
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
22 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Net Force Vector on Junction
Net Force Vector on Chaser
carletoncaspacecraft
4 sub tethers and main tether contribute
Only main tether contributes
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
23 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Dynamics Formulation
Assumptions
carletoncaspacecraft
Chaser Junction are point masses Tether segments are massless Tether torsion and bending are ignored Sub-tethers are perfectly attached to target
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
24 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
25 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
Objective Determine possible control modes through proof-of-concept
simulations
Three simulations presented 1 Stationary chaser 2 Simple thrust 3 Spinning TSS
carletoncaspacecraft
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
26 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
1 Stationary chaser Spinning target captured at t = 0 Chaser mass very large such that it remains stationary All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass Large Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
1 Nsm
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
27 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
28 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
29 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
30 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
2 Simple thrust Spinning target captured at t = 0 Chaser thrusts away from target All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 100 Nm
Junction mass 5 mg Damping Coefficient
10 Nsm
Chaser Thrust 150 N
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
31 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
32 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
33 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation
3 Spinning TSS Spinning target captured at t = 0 TSS is rotated such that centrifugal force maintains tension in
tether All tethers initially under 0 N of tension
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 350 kg Target angular rates
[05 05 05] rads
Chaser mass 350 kg Spring Constant 1000 Nm
Junction mass 5 mg Damping Coefficient
100 Nsm
TSS Spin Rate 05 rads
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
34 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
35 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
36 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Deep Space Simulation carletoncaspacecraft
Results Tension in tethers is important Ensures collision avoidance and is necessary to stabilize target
Cannot remove angular momentum along main tether axis Due to the lack of a moment arm and the flexible nature of the material Should approach target such that this effect is minimized
Novel TSS is a feasible solution
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
37 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Outline
1 Dynamics Formulation
2 Deep Space Simulation
3 In-Orbit Simulation
carletoncaspacecraft
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
38 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Motivation Orbital motion causes relative motion between chaser and
target May be possible to exploit this motion ie utilize the relative motion to generate TSS spin
carletoncaspacecraft
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
39 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
Formulation Newtonrsquos Law of Gravitation incorporated for each body
Three scenarios 1 Long-term stability of pre-stabilized target 2 Stabilizing ability of orbital motion 3 Deorbiting thrust on target attitude
carletoncaspacecraft
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
40 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
1 Long-term stability Target has no angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[0 0 0] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
41 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
42 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
2 Stabilizing ability of orbital motion Target has 100 Nms of angular momentum at t = 0 Chaser is connected to target from lagging orbit Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
43 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
44 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation
3 Deorbiting thrust on target attitude Target has 100 Nms angular momentum at t = 0 Chaser is connected to target from lagging orbit and thrusts
with 5 N retrograde Orbit of RADARSAT-1 selected
carletoncaspacecraft
Parameter Value Parameter Value
Target mass 2500 kg Target angular rates
[000500050004] rads
Chaser mass 3000 kg Spring Constant 1000 Nm
Junction mass 1 kg Damping Coefficient
10 Nsm
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
45 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
In-Orbit Simulation carletoncaspacecraft
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
46 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Conclusions
Summary The dynamics of a novel TSS with 4 sub-tethers attached to a
tumbling target was derived
Numerical simulations demonstrate stabilization of target is achievable through chaser input Attitude cannot be regulated along main tether axis
In-orbit simulations demonstrate target may be passively controlled in the long term
carletoncaspacecraft
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
47 13th Symposium on Advanced Space Technologies in Robotics and Automation Noordwijk The Netherlands 11-13 May 2015
Thank You
![Constrained Geometric Attitude Control on SO 3 · 2017. 11. 28. · attitude stabilization using continuous time-invariant feedback [3]. Attitude control is typically studied using](https://img.pdfslide.us/doc/110x75/60a4eb0ae410a9227605d582/constrained-geometric-attitude-control-on-so-3-2017-11-28-attitude-stabilization.jpg)
