State feedback control of the spacehawk earth based lunar hopper
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State-Feedback Control of the SpaceHawk Earth-Based Lunar Hopper. Andrew Abraham, May 2013. Background. Researching the dynamics and controls associated with a ‘hopping’ spacecraft trajectory. OBSTACLE. Location A. Location B. Background.

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State feedback control of the spacehawk earth based lunar hopper

State-Feedback Control of the SpaceHawk Earth-Based Lunar Hopper

Andrew Abraham, May 2013


Background
Background

  • Researching the dynamics and controls associated with a ‘hopping’ spacecraft trajectory

OBSTACLE

Location A

Location B


Background1
Background

  • 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

Mars Exploration Rover

Surveyor 6


Specifications
Specifications

  • 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


  • Specifications1
    Specifications

    • Arduino Mega for control computer

    • MEMS IMU

    • 4 LiPoly Batteries: 2.25lbs each

    • ICE 80amp Electronic Speed Controller

    • Project funded by NASA

    Arduino Mega

    6 DOF Analog IMU

    1 of 4 LiPo Batteries







    Feedback linearization position
    Feedback Linearization(Position)

    Exact Linearization Control Law

    Plug Into Equations of Motion

    Now, linear control laws can be used with r as the virtual input


    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


    Approximate Feedback Linearization(Angles)

    Exact Linearization Control Law

    (highly nonlinear)

    Near δ = 0

    &

    Approximate Linearization Control Law (linear)


    Critically damped pd controller
    Critically-DampedPD Controller



    Control implementation
    Control Implementation

    Over-Actuated System Without Following Two Additional Constraints

    PWM

    Time


    Simulation
    Simulation

    3m

    10m

    A

    B


    Definitions1
    Definitions

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


    Acknowledgements
    Acknowledgements

    Authors:

    Anthony Dzaba, Andrew Abraham, Evan Mucasey, Terry Hart, and Eugenio Schuster

    Funding Agencies:

    NASA PA Space Grant




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