1. State-Feedback Control of the SpaceHawk Earth-Based Lunar Hopper Andrew Abraham, May 2013

2. Background 2 OBSTACLE Location ALocation B Researching the dynamics and controls associated with a ‘hopping’ spacecraft trajectory

3. Background 3 Surveyor 6 Mars Exploration Rover 1967- Surveyor 6 has been the only spacecraft to ‘hop’ - Travelled 8 ft. Conventional landers are designed to be rovers constrained to the ground - Disadvantageous for exploring

4. Specifications 4 4 ducted fans; each with 10lbs of thrust @ full throttle Fans Produce ZERO torque @ 75% Gimbaled in 1 direction Frame made from aluminum Easy to construct Total weight: 32lbs 26” From end to end

5. Arduino Mega for control computer MEMS IMU 4 LiPoly Batteries: 2.25lbs each ICE 80amp Electronic Speed Controller Project funded by NASA Specifications 5 6 DOF Analog IMU Arduino Mega 1 of 4 LiPo Batteries

6. Testing 6

7. 7

8. Axis and Forces 8

9. Definitions 9

10. Equations of Motion 10

11. Feedback Linearization (Position) 11 Exact Linearization Control Law Plug Into Equations of Motion Now, linear control laws can be used with r as the virtual input

12. 12 Exact Feedback Linearization (Angles) Exact Linearization Control Law Plug Into Equations of Motion Now, linear control laws can be used with r as the virtual input

13. 13 Approximate Feedback Linearization (Angles) Exact Linearization Control Law (highly nonlinear) Near δ = 0 Approximate Linearization Control Law (linear) &

14. Critically-Damped PD Controller 14

15. Control Strategy 15

16. Control Implementation 16 Over-Actuated System Without Following Two Additional Constraints Time PWM

17. Simulation 17 A B 3m 10m

18. Definitions 18 Red = Reference Signal, Blue = Exact, Green = Approximate

19. Acknowledgements 19 Authors: Anthony Dzaba, Andrew Abraham, Evan Mucasey, Terry Hart, and Eugenio Schuster Funding Agencies: NASA PA Space Grant

20. Thank You! 20

21. Definitions 21