benoit pigneur and kartik ariyur school of mechanical engineering purdue university june 2013...
TRANSCRIPT
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
Benoit Pigneur - Purdue University 3
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)
Benoit Pigneur - Purdue University 4
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)
Benoit Pigneur - Purdue University 5
Background & Motivation
• Next generation/future missions– Reduce operational costs– Improve autonomous GNC
normal nav-igation
Mars Odyssey
01234567
full-time-equivalent navigators
Benoit Pigneur - Purdue University 6
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
Benoit Pigneur - Purdue University 7
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
Benoit Pigneur - Purdue University 8
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
Benoit Pigneur - Purdue University 9
Outline
• Background & Motivation
• Methodology
• Test Cases
• Conclusion & Future Work
Benoit Pigneur - Purdue University 10
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
Benoit Pigneur - Purdue University 11
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
Benoit Pigneur - Purdue University 12
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
Benoit Pigneur - Purdue University 14
Outline
• Background & Motivation
• Methodology
• Test Cases
• Conclusion & Future Work
Benoit Pigneur - Purdue University 15
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
Benoit Pigneur - Purdue University 16
• Circular 2D orbit:– Simulation conditions:
• circular orbit at 95 km altitude around the Moon• no external force
Test Cases
Benoit Pigneur - Purdue University 17
Test Cases
• Entry, descent and landing:– Simulation conditions:
• Moon • Starting altitude at 95 km • Velocity: 1670 m/s• Flight path angle: -10°
Benoit Pigneur - Purdue University 18
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
Benoit Pigneur - Purdue University 19
Outline
• Background & Motivation
• Methodology
• Test Cases
• Conclusion & Future Work
Benoit Pigneur - Purdue University 20
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…
Benoit Pigneur - Purdue University 21
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
Benoit Pigneur - Purdue University 22
Questions ?
Authors: Benoit Pigneur (speaker): [email protected] Kartik Ariyur
Thanks!