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Energy-Economical Heuristically Based Control of Compass Gait Walking on Stochastically Varying Terrain Christian Hubicki Bucknell University

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Energy-Economical Heuristically Based Control of Compass Gait Walking on Stochastically Varying Terrain Christian Hubicki Bucknell University Bucknell University Bucknell Digital Commons Master’s Theses Student Theses 2011 Energy-Economical Heuristically Based Control of Compass Gait Walking on Stochastically Varying Terrain Christian Hubicki Bucknell University Follow this and additional works at: https://digitalcommons.bucknell.edu/masters_theses Part of the Mechanical Engineering Commons Recommended Citation Hubicki, Christian, "Energy-Economical Heuristically Based Control of Compass Gait Walking on Stochastically Varying Terrain" (2011). Master’s Theses. 26. https://digitalcommons.bucknell.edu/masters_theses/26 This Masters Thesis is brought to you for free and open access by the Student Theses at Bucknell Digital Commons. It has been accepted for inclusion in Master’s Theses by an authorized administrator of Bucknell Digital Commons. For more information, please contact [email protected]. I, Christian Hubicki, do grant permission for my thesis to be copied. ACKNOWLEDGEMENTS To Mom, Dad, and Alexa, who have always supported me in all my pursuits, Who always lend a caring ear and never miss an opportunity to feed me, Who sacrifice routinely for their family in ways I can never repay. To Keith, who took a chance on an overly confident student five years ago, Who always made room in his daunting schedule if I needed help, Who never failed to prove that he was looking out for me. To Emily, who always makes a rainy day a joy, Who has dinner cooked when I come back from the lab, Who could not possibly know how happy she makes me every day. Thank you all. ii Table of Contents Page Acknowledgements ..........................................................................................................i Table of Contents .............................................................................................................ii List of Tables ...................................................................................................................vi List of Figures ..................................................................................................................vii Abstract ............................................................................................................................xi Chapter 1: Introduction ................................................................................................1 .... Controlling Walking Robots .....................................................................................2 Zero-Moment Point Control .....................................................................................2 Passive-Dynamic Walking ........................................................................................3 Underactuated Systems .............................................................................................4 Limit-Cycle Stability and Robustness ................................................................6...... Robust Biped Control ...............................................................................................7 Metastability .............................................................................................................9 Performance Tradeoffs .............................................................................................11 Goal Statement ..........................................................................................................12 Chapter 2: Simulation Model ...........................................................................................13 Hybrid Continuous/Discrete Dynamics ................................................................13.... Poincare Section .......................................................................................................14 Terrain-Crossing Conditions ....................................................................................15 iii Compass Gait Continuous Dynamics .......................................................................17 Collisions ..................................................................................................................21 Impulse .....................................................................................................................23 Stochastic Terrain Model ..........................................................................................24 Validation .................................................................................................................27 Actuation and Control ...............................................................................................27 Chapter 3: Genetically Optimized Gain Scheduled Control ............................................29 Proportional-Derivative Control ...............................................................................29 Gain-Scheduled Control ...........................................................................................31 Control Parameter Set ...............................................................................................34 Genetic Optimization ................................................................................................34 “Methinks it is like a weasel” ...................................................................................35 Mutation ....................................................................................................................36 Fitness Function ........................................................................................................37 Robustness Cost Function.........................................................................................38 Failure Modes ...........................................................................................................39 Energy-Speed Weighting Factor ...............................................................................41 Reproduction .............................................................................................................42 Convergence .............................................................................................................43 Data Collection .........................................................................................................44 Genetic Algorithm Results .......................................................................................47 iv Conclusions...............................................................................................................48 Chapter 4: Heuristic Control ............................................................................................50 Optimization-Inspired Heuristic ...............................................................................50 Selection Pressures ................................................................................................54... Random Walk ...........................................................................................................54 Impulse Selection Pressures .....................................................................................56 Gain Schedule Selection Pressures ...........................................................................59 Mean Gain Schedule ................................................................................................62 . Tradeoff-Conducive Control Heuristic ................................................................64..... Heuristic Bounding Parameters ................................................................................66 Heuristic Parameter Tuning ......................................................................................67 Gradient-Descent Algorithm ....................................................................................68 Tradeoff Curve Metrics ............................................................................................69 Approximated Gradient ............................................................................................71 Heuristic Tradeoff Curve Results .............................................................................73 Conclusions...............................................................................................................79 Chapter 5: Reinforcement Learning.................................................................................80 Artificial Intelligence ................................................................................................81 Machine Learning ................................................................................................81..... Reinforcement Learning ...........................................................................................82 State and Action Value Functions ............................................................................82 v Value Iteration ..........................................................................................................84 Mean First-Passage Time .........................................................................................88 Approximate Optimal Robustness ............................................................................89 Value-Iteration Robustness Results ..........................................................................90 Chapter 6: Simulated Walking Experiment ................................................................93..... Value-Iteration Cost Function ..................................................................................93
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