21. Space Robotics MAE 342 2016 - Princeton University · 2020-02-12 · 2/12/20 3 Elements of Intelligent Control Intelligent Control System 5 Declarative Functions Expert Systems,

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Space RoboticsSpace System Design, MAE 342, Princeton University

Robert Stengel

Copyright 2016 by Robert Stengel. All rights reserved. For educational use only.http://www.princeton.edu/~stengel/MAE342.html 1

§ Robots and Robotics§ Autonomous Spacecraft§ Planetary and Lunar Rovers§ Path Planning§ Robotic Arms§ Robonauts§ Deep Impact 1

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Robots and Robotics

• Design, manufacture, control, and programming of robots

• Use of robots to solve problems• Study of control processes, sensors, and

algorithms used in humans, animals, and machines• Application of control processes and algorithms to

designing robots

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Biomimetics (Bionics)• Understanding biological principles

and applying them to system design– Configuration– Structure– Behavior– Dynamics– Control

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Autonomous Robots • Self control• Self maintenance• Awareness of

environment• Task orientation• Mission specificity

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• Power source• Cooperation and

collaboration• = Intelligence?• Self replication?• Ethical issues

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Elements of Intelligent Control

Intelligent Control System

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Declarative Functions Expert Systems, Decision TreesProcedural Functions Estimation and Control "Circuits"Reflexive Functions Control Laws, Neural Networks

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Robotic Vehicles

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Expendable (Rocket) Launch Vehicles

Current space launch vehicles are largely autonomous

Atlas Vhttp://www.youtube.com/watch?v=K

xQbex7LJwg

Delta 4

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• Reusable experimental/operational vehicle

• Unmanned “mini-Space Shuttle”

• Highly classified project

• 1st 3 missions: 224, 469, & 675 days in orbit

• 4th mission on-going

X-37B

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http://www.youtube.com/watch%3Fv=KxQbex7LJwg

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Orbital Express: ASTRO and NEXTSat• DARPA, 2007

–Automatic rendezvous, docking, and undocking

–On-orbit transfer of replaceable units

–6DOF robot arm–Video guidance sensor–Atlas 5 launch

9https://en.m.wikipedia.org/wiki/Robotic_spacecraft

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Mars Science Laboratory(Curiosity)

• Transport science payload over Martian surface– Rocker-bogie suspension

• Communications with Earth• Guidance, navigation, and

control• Power supply• Support for deployable

devices• Size ~ Mini-Cooper• Landed, 8/6/12, and

operational

Curiosity Trailerhttp://www.jpl.nasa.gov/video/details.php?id=1014

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Curiosity Rocker-Bogie Suspension

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Curiosity Robotic Arms

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Curiosity Preparation, Spacecraft, and Aeroshell

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Curiosity Approach and Landing

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Mars Opportunity Rover Navigation

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Google LunarX Prize

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Astrobotic Lunar Lander

Express MX-1

Lunar XPrize India

SpaceIL Lander

https://en.m.wikipedia.org/wiki/Google_Lunar_X_Prize

1st privately funded spacecraft to land on Moon, travel 500m, and stream live TV

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Path Planning on Occupancy Grid

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Admissible and Inadmissible Blocks

• Identify feasible paths from Start to Goal• Chose path that best satisfies criteria, e.g.,

– Simplicity of calculation– Lowest cost– Highest performance

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1) Identify shortest unconstrained path from Start to Goal2) Chose path that navigates the boundary

1) Stays as close as to possible to unconstrained path2) Satisfies constraint3) Follows simple rule, e.g., “stay to the left”

Bug Path Planning

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D* or A* Path Planning

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• Determine occupancy cost of each block• Chose path from Start to Goal that minimizes

occupancy cost with each step

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Probabilistic Road Map

• Construction Phase: Random configuration of admissible points• Connect admissible points to nearest neighbors

• Assessment Phase: Assess incremental cost of traveling along each “edge” between points

• Query Phase: Find all feasible paths from Start to Goal and select lowest cost path

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Note that this approach would miss the lowest cost path found on the previous slide

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Rapidly Exploring Random Trees (RRT, RRT*)

§ RRT§ Space-filling tree evolves from Start§ Open-loop trajectories with state constraints§ Initially feasible solution converges to

optimal solution through searching§ RRT*

§ “Committed trajectories”§ Branch-and-bound tree adaptation§ Provable convergence

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Interpolation

• Piecewise polynomials (linear -> quintic)• End-point discontinuities• End-point constraints

• Single polynomial through all points• Polynomial degree = # of points – 1• Sensitivity to high-degree terms (e.g., ct6)• Possibility of large excursions between points

• Polynomials through adjacent points• e.g., cubic B splines

Connect the Dots

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Path Planning with Potential Fields

Features attract or repel path from Start to Goal, e.g., +/– gravity fields

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Simultaneous Location and Mapping (SLAM)

• Build or update a local map within an unknown environment– Stochastic map, defined by mean and

covariance of many points– Landmark, terrain, and target tracking– Multi-sensor integration– SLAM Algorithm = Bank of state

estimators

Durrant- Whyte et al

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Mars Aerial Regional-Scale Environmental Survey (ARES)

Research Airplane Concept, ~2008

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https://www.youtube.com/watch?v=wAOTOmGFs5M

https://www.youtube.com/watch?v=8YutbpJuFiI

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ARES System Layout

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Articulated Robot Arms

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Robot Arms for SpaceDEXTRE Manipulator, ISS

Canadarm2, ISS

Curiosity Robot Arm

Kibo Arm, ISS

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DEXTRE

28https://en.m.wikipedia.org/wiki/Dextre

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Manipulator Redundancy and Degeneracy

• More than one link configuration may provide a given end point if dim(xJ) ≥ dim(xE) ≥ dim(xT)

• Redundancy: Finite number of joint vectors provide the same task-dependent vector

• Degeneracy: Infinite number of joint vectors provide the same task-dependent vector

• Co-linear joint axes are degenerate

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Space Robot Arms are Highly Redundant

Why?

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Robot Arm Configurations

McKerrow, 1991

CartesianCylindrical

Polar Articulated Revolute

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Robot Arm Workspaces

McKerrow, 1991

Cylindrical

ArticulatedRevolute

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Serial Robotic Manipulators

• Serial chain of robotic links and joints– Large workspace– Low stiffness– Cumulative errors from link

to link– Proximal links carry the

weight and load of distal links

– Actuation of proximal joints affects distal links

– Limited load-carrying capability at end effecter

Proximal link: closer to the baseDistal link: farther from the base

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NASA/GM Robonaut R2

Robonauthttp://www.youtube.com/watch?v=g3u48T4Vx7k

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http://www.youtube.com/watch%3Fv=g3u48T4Vx7k

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Robonaut 2 Structure

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Robonaut 2 Hand

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Robonaut 2 Fingers

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• Control by tendons and four-bar linkages

• Linear actuators in forearm

Index Finger

Thumb

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Four-Bar Linkage

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• Closed-loop structure

• Rotational joints• Planar motion• Proportions of link

lengths determine pattern of motion

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Robonaut 2 Wrist and Forearm

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Revolute Robotic JointsRotation about a single axis

Parallel to Link

Perpendicular to Link

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Prismatic Robotic JointsSliding along a single axis

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Other Robotic Joints

Cylindrical (sliding and turning composite)

Roller ScrewFlexible

Spherical (or ball)

Planar (sliding and turning composite)

Universal Constant-Velocity

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Characteristic Transformation of a Link

• Each link type has a characteristic transformation matrixrelating the proximal joint to the distal joint

• Link n has– Proximal end: Joint n,

coordinate frame n – 1– Distal end: Joint n + 1,

coordinate frame n

Link: solid structure between two joints

McKerrow, 1991

Proximal

Distal

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Links Between Revolute Joints• Link: solid structure between two

joints– Proximal end: closer to the base– Distal end: farther from the base

• 4 Link Parameters– Length of the link between rotational

axes, l, along the common normal– Twist angle between axes, α– Angle between 2 links, θ (revolute)– Offset between links, d (prismatic)

• Joint Variable: single link parameterthat is free to vary

Type 1 LinkTwo parallel revolute joints

Type 2 LinkTwo non-parallel revolute joints

McKerrow, 1991 44

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Homogeneous TransformationMatrix

snew =

RotationMatrix

⎛⎝⎜

⎞⎠⎟ old

new Locationof OldOrigin

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟new

0 0 0( ) 1

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

sold = Aoldnew sold

4 ×1( )new =3× 3( ) 3×1( )1× 3( ) 1×1( )

⎡

⎣⎢⎢

⎤

⎦⎥⎥4 ×1( )old = 4 × 4( )⎡⎣ ⎤⎦ 4 ×1( )old

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Express rotation and translation in a single transformation

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Homogeneous Transformation• Rotation and translation can be expressed in terms

of homogeneous coordinates– Single matrix-vector product produces rotation and

transformation

• or

snew =Hold

new roldnew

0 0 0( ) 1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥sold = A sold

xyx1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥new

=

h11 h12 h13 xoh21 h22 h23 yoh31 h32 h33 zo0 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

xyz1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥old

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Equivalent Scalar Equations for Homogeneous Transformation

xyx1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥new

=

h11 h12 h13 xoh21 h22 h23 yoh31 h32 h33 zo0 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

xyz1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥old

�

snew =A oldnew sold

Matrix-Vector Multiplication

Individual Operations

xnew = h11xold + h12yold + h13zold + xoynew = h21xold + h22yold + h23zold + yoznew = h31xold + h32yold + h33zold + zo− − − −1= 1

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Series of Homogeneous Transformations

s2 = A12A0

1 s0 = A02 s0

Two serial transformations can be combined in a single transformation

Four transformations for SCARA robot

s4 = A34A2

3A12A0

1 s0 = A04 s0

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Transformation for a Single Robotic Joint

• Each joint requires four sequentialtransformations:– Rotation about α– Translation along d– Translation along l– Rotation about θ

Type 2 Link

sn+1 = A3n+1A2

3A12An

1 sn = Ann+1 sn

= AθAdAlAα sn = Ann+1 sn

• ... axes for each transformation (along or around) must be specified

sn+1 = A zn−1,θn( )A zn−1,dn( )A xn−1,ln( )A xn−1,αn( ) sn = Ann+1 sn

1st2nd3rd4th

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Denavit-HartenbergRepresentation of Joint-

Link-Joint Transformation

An =

cosθn − sinθn 0 0sinθn cosθn 0 00 0 1 00 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

1 0 0 00 1 0 00 0 1 dn0 0 0 1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

1 0 0 ln0 1 0 00 0 1 00 0 0 1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

1 0 0 00 cosαn − sinαn 00 sinαn cosαn 00 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

An =

cosθn −sinθn cosα n sinθn sinα n ln cosθn

sinθn cosθn cosα n −cosθn sinα n ln sinθn

0 sinα n cosα n dn0 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

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FirstThenThenThen

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Forward and Inverse TransformationsForward transformation through links requires pre-multiplication of matrices

s1 = A01s0 ; s2 = A1

2s1 = A12A0

1s0 = A02s0

Reverse transformation uses the matrix inverse

s0 = A02( )−1 s2 = A2

0s2 = A10A2

1s2

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Homogeneous Transformation Matrix is not Orthonormal

A20 = A0

2( )−1 ≠ A02( )T

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…but a useful identity makes inversion simple

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Matrix Inverse IdentityForward transformation

A1 A2

A3 A4

⎡

⎣⎢⎢

⎤

⎦⎥⎥=

Holdnew ro

0 0 0( ) 1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

Inverse

A1 A2

A3 A4

⎡

⎣⎢⎢

⎤

⎦⎥⎥

−1

=Hnew

old −Hnewold ro

0 0 0( ) 1

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

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Manipulator Maneuvering Spaces

Joint space: Vector of joint variables, e.g.,

rJ = θwaist θshoulder θelbow θwrist−bend θ flange θwrist− twist⎡⎣

⎤⎦T

End-effecter space: Vector of end-effecter positions, e.g.,

rE = xtool ytool ztool ψ tool θtool φtool⎡⎣

⎤⎦T

Task space: Vector of task-dependent positions, e.g., locating a symmetric grinding tool above a horizontal surface:

rT = xtool ytool ztool ψ tool θtool⎡⎣

⎤⎦T

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Forward and Inverse Transformations of a Robotic Assembly

Forward TransformationTransforms homogeneous coordinates from tool frame to

reference frame coordinates

Inverse TransformationTransform homogeneous coordinate from reference frame to

tool frame coordinates

sbase = Atoolbasestool

= AwaistAshoulderAelbowAwrist−bendA flangeAwrist−twiststool

stool = Abasetool sbase

= A−1wrist−twistA

−1flangeA

−1wrist−bendA

−1elbowA

−1shoulderA

−1waistsbase

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Deep Impact 1

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Deep Space 1 Flyby and ImpactorSpacecraft

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Deep Space 1 Encounter Scenario

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• Impactor mass = 370 kg

• Impact velocity = 10 km/s+

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Impactor Characteristics

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§ Image data volume: § 17 MB (~35 images)

§ Pointing accuracy: § 3σ = 2 mrad

§ Energy storage for 24-hr mission: § 28 KWh

§ Propulsion/RCS:§ 25 m/s divert, 1750 N-s impulse

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Deep Space 1 Autonomous Navigation and Targeting

• Flyby spacecraft comes within 500 km of Tempel 1comet, observes impact event for 800 s

• Impactor guided toward comet nucleus by AutoNav software (s/w)

• Identical attitude determination and control (ADCS) s/w in Flyby and Impactor

• Impactor Targeting Sensor (ITS) commands images every 15 sec

• “Scripted Autonomy”

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Mastrodemos, Kubitschek, Synnott, JPL, 2005

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Flyby Flight Control System§ Two RAD750 computers§ Medium Resolution Imager (MRI) for autonomous

navigation during encounter§ High Resolution Imager (HRI) for approach phase

optical navigation§ Power to both s/c while attached§ High-gain antenna for data return§ S-band antenna for communication with Impactor§ 3-axis momentum wheel attitude control§ 4 RCS thrusters for divert and momentum dumps§ Star Tracker/Inertial Reference Unit (SSIRU)

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Impactor Flight Control System• Battery power for 24-hr operation• One RAD750 computer• SSIRU• Simple ITS• Divert/RCS thrusters• AutoNav components– Image processing– Orbit determination– Maneuver computation

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Impactor Targeting Strategy• Options

– Proportional Navigation• Measurement of closing velocity

and line-of-sight angular rates• “Reduced dynamic approach”

– Predictive Guidance• Equations of motion for target

and interceptor• State estimation (“filtering”), like

SLAM

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• Selected: Predictive, Pulsed Guidance to desired location on target

• Best quality observations obtained during non-thrusting periods

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Impactor Targeting Strategy• Large uncertainty in knowledge of prior

position reduced via optical navigation• Nucleus rotation rate and solar phase angle

induce motion in center of brightness (CB)

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• Mitigated by batch filtering process and selection of 20-min data arc length


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Autonomous Navigation• AutoNav modes

– Star-relative mode– Star-less mode based on ADCS only and camera alignment

• Autonomous guidance process1) Timpact – 2 hr: Acquire comet nucleus images every 15 sec2) Compute pixel/line location of CB3) Compute measurement error4) Perform trajectory observation (OD) updates every min5) Perform 3 Impactor targeting maneuvers (ITM), at Timpact –

100 min, Timpact – 35 min, Timpact – 7.5 min6) Compute scene-analysis-based offset prior to 3rd ITM7) Timpact – 4 min: Point ITS along estimated comet-relative

velocity vector8) Flyby maintains tracking of impact point

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Trajectory Determination• Updated once per minute for last 2 hr• Sequential batch processing updates

position, velocity, navigation line-of-sight attitude bias drift errors

• 80 observations in each 20-min arc• Time series of Impactor position relative to

the nucleus predicted with Chebyshevpolynomial (i.e., smooth extrapolation of prior position estimates)

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Impactor Targeting Maneuvers (ITM)• Initiated via AutoNav sequence command• Required impulsive maneuver ΔV magnitude and

direction calculated• Finite-burn start time computed, tstart• Integration of accelerometer data indicates when ΔV

has been reached, and burn is terminated, tfinish• ITM-1 removes Flyby pre-release delivery errors (~6

km), requiring ΔV ~ 1 m/s• ITM-2 improves targeting, requiring ΔV ~ 11 cm/s• ITM-3 refines fine targeting of illuminated nucleus

based on CB observations, requiring ΔV ~ 7m/s– B-plane correction of as much as 4 km– Accurate to ~ 54 m

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Expected Targeting Error

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Expected Targeting Error

69Mastrodemos, Kubitschek, Synnott, JPL, 2005

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Next Time:Human Factors of

Spaceflight

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Supplemental Material

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MSL Descent

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ARES Data Handling and Processing System

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Links Involving Prismatic JointsType 6 LinkIntersecting revolute and prismatic joints

McKerrow, 1991

Type 5 Link Intersecting prismatic joints

• Link n extends along zn-1 axis• ln = 0, along xn-1• dn = length, along zn-1 (variable)• θn = 0, about zn-1• αn = fixed orientation of n + 1

prismatic axis about xn-1

• Link n extends along zn-1 axis• ln = 0, along xn-1• dn = length, along zn-1 (fixed)• θn = variable joint angle n

about zn-1

• αn = fixed orientation of n + 1prismatic axis about xn-1

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Two-Link/Three-Joint Manipulator

Assignment of coordinate frames

Manipulator in zero position

Parameters and Variables for 2-link manipulator

McKerrow, 1991

• Link lengths (fixed)• Joint angles (variable)

Parallel Rotation Axes

Workspace

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Denavit-Hartenberg Representation of Joint-Link-Joint Transformation

• Like Euler angle rotation, transformational effects of the 4 link parameters are defined in a specific application sequence(right to left): {θ, d, l, α }

• 4 link parameters– Angle between 2 links, θ (revolute)– Distance (offset) between links, d

(prismatic)– Length of the link between rotational

axes, l, along the common normal (prismatic)

– Twist angle between axes, α (revolute)

An = A zn−1,θn( )A zn−1,dn( )A xn−1,ln( )A xn−1,α n( )= Rot(zn−1,θn ) Trans(zn−1,dn ) Trans(xn−1,ln ) Rot(xn−1,α n )! nTn+1 in some references (e.g., McKerrow, 1991)

Denavit-Hartenberg Demohttp://www.youtube.com/watch?v=10mUtjfGmzw

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Four Transformations from One Joint to the Next

(Single Link)

�

Rot(zn−1,θn ) =

cosθn −sinθn 0 0sinθn cosθn 0 00 0 1 00 0 0 1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

Trans(zn−1,dn ) =

1 0 0 00 1 0 00 0 1 dn0 0 0 1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

�

Trans(xn−1,ln ) =

1 0 0 ln0 1 0 00 0 1 00 0 0 1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

�

Rot(xn−1,αn ) =

1 0 0 00 cosαn −sinαn 00 sinαn cosαn 00 0 0 1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

Rotation of θn about the zn-1 axis

Rotation of αn about the xn-1 axisTranslation of ln along the xn-1 axis

Translation of dn along the zn-1 axis

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Example: Denavit-HartenbergRepresentation of Joint-Link-Joint

Transformation for Type 1 Link

An =

cosθn − sinθn cosαn sinθn sinαn ln cosθn

sinθn cosθn cosαn − cosθn sinαn ln sinθn

0 sinαn cosαn dn0 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

θ 30 degd = 0 ml = 0.25 mα = 90 deg

Joint Variable = θn

An =

cosθn 0 sinθn 0.25cosθn

sinθn 0 − cosθn 0.25sinθn

0 1 0 00 0 0 1

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

θ = variabled = 0 ml = 0.25 mα = 90 deg

An =

0.866 0 0.5 0.2170.5 0 −0.866 0.1250 1 0 00 0 0 1

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

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Matrix Inverse Identity Given: a square matrix, A, and its inverse, B

A =A1m×m

A2m×n

A3n×m

A4n×n

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥; B A−1 =

B1 B2B3 B4

⎡

⎣⎢⎢

⎤

⎦⎥⎥

AB = AA−1 = Im+n

=Im 00 In

⎡

⎣⎢⎢

⎤

⎦⎥⎥=

A1B1 +A2B3( ) A1B2 +A2B4( )A3B1 +A4B3( ) A3B2 +A4B4( )

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

Then

Equating like parts, and solving for Bi

B1 B2B3 B4

⎡

⎣⎢⎢

⎤

⎦⎥⎥=

A1 − A2A4−1A3( )−1 −A1

−1A2 A4 − A3A1−1A2( )−1

−A4−1A3 A1 − A2A4

−1A3( )−1 A4 − A3A1−1A2( )−1

⎡

⎣

⎢⎢⎢

⎤

⎦

⎥⎥⎥

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Forward and Inverse Kinematics Between Joints, Tool Position, and Tool Orientation

Forward Kinematic Problem: Compute the position of the tool in the reference frame that corresponds to a given joint vector (i.e., vector of link variables)

Inverse Kinematic Problem: Find the vector of link variablesthat corresponds to a desired task-dependent position

sbase = AwaistAshoulderAelbowAwrist−bendA flangeAwrist−twiststool = Atoolbasestool

To Be Determined ⇐Given

AwaistAshoulderAelbowAwrist−bendA flangeAwrist−twiststool = Atoolbases0 = sbase

To Be Determined ⇐ Given80

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21. Space Robotics MAE 342 2016 - Princeton University · 2020-02-12 · 2/12/20 3 Elements of Intelligent Control Intelligent Control System 5 Declarative Functions Expert Systems,