Benoit Pigneur and Kartik Ariyur School of Mechanical Engineering Purdue University June 2013 Inexpensive Sensing For Full State Estimation of Spacecraft

Benoit Pigneur and Kartik Ariyur

School of Mechanical Engineering

Purdue University

June 2013

Inexpensive Sensing For Full State Estimation of Spacecraft

Benoit Pigneur - Purdue University 2

Outline

• Background & Motivation

• Methodology

• Test Cases

• Conclusion & Future Work


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)



• 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)



• Next generation/future missions– Reduce operational costs– Improve autonomous GNC

normal nav-igation

Mars Odyssey

01234567

full-time-equivalent navigators



• 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



• 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



• 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


Outline


• Methodology

• Test Cases



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


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 r

dt dt dt


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 IM

I I

M I I

I I

I IM

I I

( sin cos ) tan

cos sin

1( sin cos )

cos

x y z

y z

y z

13

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

Benoit Pigneur - Purdue University

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


Outline


• Methodology

• Test Cases



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


• Circular 2D orbit:– Simulation conditions:

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

Test Cases


Test Cases

• Entry, descent and landing:– Simulation conditions:

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


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


Outline


• Methodology

• Test Cases



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…


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


Questions ?

Authors: Benoit Pigneur (speaker): [email protected] Kartik Ariyur

Thanks!

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Benoit Pigneur and Kartik Ariyur School of Mechanical Engineering Purdue University June 2013 Inexpensive Sensing For Full State Estimation of Spacecraft