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

2. Outline Background & Motivation Methodology Test Cases Conclusion & Future Work Benoit Pigneur - Purdue University2

3. Background & Motivation Next generation/future missions – Increase landing mass (ex: human mission) Benoit Pigneur - Purdue University3

4. Background & Motivation Next generation/future missions – Increase precision landing Benoit Pigneur - Purdue University4

5. Background & Motivation Next generation/future missions – Reduce operational costs – Improve autonomous GNC Benoit Pigneur - Purdue University5

6. Background & Motivation State of the art of GNC algorithms for EDLS Benoit Pigneur - Purdue University6 19602010 MSL: Convex optimization of power-descent 2000 Terminal point controller (Apollo) Numerical Predictor-Corrector Analytical Predictor-Corrector Gravity Turn Profile Tracking

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 University7

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 University8

9. Outline Background & Motivation Methodology Test Cases Conclusion & Future Work Benoit Pigneur - Purdue University9

10. Methodology Multiple distributed sensors: Geometric configuration – Low SWAP sensors – Large distribution – Exclude outlier measurement – Combine measurements with geometric configuration Benoit Pigneur - Purdue University10 Center of mass MEMS accelerometers x z y x’ z’ y’ R r’ r

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 Benoit Pigneur - Purdue University11

12. Methodology Mathematical model: change of inertia – Inertia -> angular acceleration – Angular velocity -> attitude (Euler angles) 1.Euler equations of motion 2.Kinematic equations Benoit Pigneur - Purdue University12

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 University13

14. Outline Background & Motivation Methodology Test Cases Conclusion & Future Work Benoit Pigneur - Purdue University14

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 University15

16. Circular 2D orbit: – Simulation conditions: circular orbit at 95 km altitude around the Moon no external force Test Cases Benoit Pigneur - Purdue University16

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 University17

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 University18

19. Outline Background & Motivation Methodology Test Cases Conclusion & Future Work Benoit Pigneur - Purdue University19

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 University20

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 University21

22. Questions ? Authors: Benoit Pigneur (speaker): bpigneur@purdue.edu Kartik Ariyur Thanks! Benoit Pigneur - Purdue University22