Benoit Pigneur and Kartik AriyurSchool of Mechanical Engineering

Purdue University

June 2013

Inexpensive Sensing For Full State Estimation of Spacecraft

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Outline• Background & Motivation

• Methodology

• Test Cases

• Conclusion & Future Work

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Background & Motivation• Next generation/future missions

– Increase landing mass (ex: human mission)

MPF MER-A MER-B MSL0

500

1000

1500

2000

2500

3000

3500

entry mass (kg)mass landed (kg)

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Background & Motivation• Next generation/future missions

– Increase precision landing

MPF MER-A MER-B MSL0

50

100

150

200

250

300

350

landing ellipse semimajor axis(km)landing ellipse semiminor axis (km)

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Background & Motivation• Next generation/future missions

– Reduce operational costs– Improve autonomous GNC

normal nav-igation

Mars Odyssey

01234567

full-time-equivalent navigators

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Background & Motivation• State of the art of GNC algorithms for EDLS

1960 2010MSL: Convex optimization of power-descent

2000

Terminal point controller (Apollo)

Numerical Predictor-CorrectorAnalytical Predictor-Corrector

Gravity Turn

Profile Tracking

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Background & Motivation• Current 2 main directions in development in

sensing and state estimation

– Development of better sensor accuracy• Ex: Hubble’s Fine Guidance Sensors

– Improvement in processing inertial measurement unit data• Ex: Mars Odyssey aerobraking maneuver

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Background & Motivation• Improve sensing and state estimation

– Develop next generation of autonomous GNC algorithms– Answer some of the challenges for future missions

• Reduce costs– Reduce operational cost during spacecraft operational

life by increasing the autonomy – Reduce cost by using low SWAP (size weight and power)

sensors

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Outline• Background & Motivation

• Methodology

• Test Cases

• Conclusion & Future Work

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Methodology• Multiple distributed sensors: Geometric

configuration– Low SWAP sensors– Large distribution– Exclude outlier measurement– Combine measurements with geometric configuration

Center of mass

MEMS accelerometers

x

z

y

x’

z’

y’R

r’r

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Methodology• Mathematical model: rigid body with constant mass

– Acceleration equation with inertial to non-inertial frame conversion formula

– R is the distance in the inertial frame– r’ is the distance in the non-inertial frame (rotating frame)– ω is the angular velocity– is the angular acceleration

2 2

2 2

'' 2 'd r d R drr rdt dt dt

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Methodology• Mathematical model: change of inertia

– Inertia -> angular acceleration – Angular velocity -> attitude (Euler angles)

1.Euler equations of motion 2.Kinematic equations( )

( )

( )

z yxx y z

x x

y x zy x z

y y

y xzz x y

z z

I IMI IM I II I

I IMI I

( sin cos ) tan

cos sin

1( sin cos )cos

x y z

y z

y z

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Methodology• Mathematical model:

– Assuming r’ is constant for a rigid body (accelerometers are fixed in the body frame)

– The subscript represents the index of the measurement units– a : linear acceleration of the body in the inertial frame– is the accelerometer position– ω is the angular velocity– is the angular acceleration– is the accelerometer measurement

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ir thi

iA thi

i

2 2

2 2

2 2

( )

( )

( )

xi x y z xi x y yi x z zi y zi z yi

yi y x z yi x y xi y z zi z xi x zi

zi z x y zi x z xi y z yi x yi y xi

A a r r r r r

A a r r r r r

A a r r r r r

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Outline• Background & Motivation

• Methodology

• Test Cases

• Conclusion & Future Work

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Test Cases• 3 different cases:

– Circular 2D orbit– Entry, descent and landing– Change of inertia during descent phase

• Comparison between nominal trajectory, standard IMU simulation and distributed multi-accelerometers simulation

• Uncertainty in measurement of acceleration – Error ratio of 1/5 between the standard IMU and the

distributed multi-accelerometers

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• Circular 2D orbit:– Simulation conditions:

• circular orbit at 95 km altitude around the Moon• no external force

Test Cases

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Test Cases• Entry, descent and landing:

– Simulation conditions: • Moon • Starting altitude at 95 km • Velocity: 1670 m/s• Flight path angle: -10°

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Test Cases• Entry, descent and landing: change of inertia

– Simulation conditions: • Thrusters time: ON at 200s, OFF at 270s• single-axis stabilization along thrust direction

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Outline• Background & Motivation

• Methodology

• Test Cases

• Conclusion & Future Work

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Conclusion & Future Work• Advantages of the proposed method

– Low SWAP sensors reduce the cost

– Optimal geometric configuration and algorithm improve the state estimation

– Distributed sensors (accelerometers) give useful information about flexible and moving parts

– The methodology is applicable to different sensors: MEMS accelerometers, CMOS imagers…

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Conclusion & Future Work• Future Work

– Improve estimation algorithm by development of optimal geometric configuration

– Develop the technique for more challenging environment (atmospheric disturbances, gravity gradient, magnetic field, solar pressure, ionic winds…)

– Develop autonomous GNC based on the improvement of the state estimation

– Develop this method for other sensors

– Improve the attitude estimation for 3-axis stabilized spacecraft

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Questions ?

Authors: Benoit Pigneur (speaker): bpigneur@purdue.edu Kartik Ariyur

Thanks!