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

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

Background 3 Surveyor 6 Mars Exploration Rover 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

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

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

Testing 6

7

Axis and Forces 8

Definitions 9

Equations of Motion 10

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

Critically-Damped PD Controller 14

Control Strategy 15

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

Simulation 17 A B 3m 10m

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

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

Thank You! 20

Definitions 21