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Signature Redacted a Uthor Toward Optimal Motion Planning for Dynamic Robots: Applications On-Orbit by Keenan Eugene Sumner Albee Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2019 o Massachusetts Institute of Technology 2019. All rights reserved. Signature redacted A uthor .............................. Department of Aeronautics and Astronautics May 23, 2019 Signature redacted C ertified by ........................ .... David W. Miller Professor, Aeronautics and Astronautics Thesis Supervisor Signature redacted A ccepted by .......................... Sertac Karaman Chairman, Department Committee on Graduate Theses MASSACHUSEITS INSTUTE OF TECHNMWY JUL 012019 L1 IRIES ARCHIVES Toward Optimal Motion Planning for Dynamic Robots: Applications On-Orbit by Keenan Eugene Sumner Albee Submitted to the Department of Aeronautics and Astronautics on May 23, 2019, in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering Abstract Robotic motion planning is a well-studied field at the intersection of optimal control, artificial intelligence, and applied mechanics. Methods for robots without dynamics are well-studied and are often practical for real-time deployment on current systems. However, robots that have dynamics, operate with uncertainty, or navigate difficult environments are at the edge of what is deployable today. While one may be able to develop a kinematic trajectory for a stationary fully-actuated robotic manipulator with modest degrees of freedom, developing strategies for underactuated systems of nearly any dimensionality remains a formidable challenge. This thesis addresses two primary corners of this problem, with specific focus on a use case of microgravity robotics: (1) how can one develop trajectories-ideally optimally and in real-time- for systems with high dimensionality and challenging environmental/dynamical con- straints and (2) how can uncertain parameters be dealt with explicitly via motion planning. These methods are placed in context with discussion of the on-orbit as- sembly and servicing scenarios in which they might be used. A launch manifesting strategy for future missions requiring a large number of components on a mix of rock- ets is presented. These tools are a step in the direction of greater autonomy on-orbit, with wider applicability to robotic systems at large. Thesis Supervisor: David W. Miller Title: Professor, Aeronautics and Astronautics 3 4 Acknowledgments This work was performed primarily under the NASA Space Technology Research Fellowship program, grant number 80NSSC17K0077. Additional support was pro- vided by the NASA Jet Propulsion Laboratory's iSAT investigation, subcontract number 1613399. The author gratefully acknowledges these sponsors for enabling this research. I wouldn't have been able to piece two words together let alone write this thesis if it weren't for my family. Thanks mom and dad, for making countless sacrifices for me, Cyril, and Miranda, and always supporting our choices in life. Kristina, you are amazing and I enjoy every minute we have together in Cambridge. My research advisor, Professor Miller, got me started in the lab and has always offered useful feedback and occasional scary plane rides-thank you for your support. Thanks to the SPHERES team for onboarding the final SPHERES generation, especially Will and Tonio for endless support and advice. Sorry Tonio for almost letting you freeze to death in Montana. Thanks Danilo for saving us many times. The rest of the SSL team has kept the lab going and made MIT a better place: Charlotte, Alex, Hailee, Daniel, Michael, and everyone else. Thanks to Bobby and other AeroAstro friends for being great colleagues and sometimes better hockey teammates. Thanks to Professor Mike for helping me get through quals and always offering advice. Thanks In Won and Brian for your advice and support, especially over the summer. Finally, many past mentors taught me to be a better engineer and for that I am forever grateful. Recalling just some of them, thank you to Al Bowers, Oscar Murillo, Tom Andrews, Kim Harrison, Darwin Chang, Kirk Svartstrom, Jason Graham, John O'Neil, Doug Adams, Prof. Marc Donohue, Prof. Sunil Agrawal, Haohan Zhang, and Adrian Stoica. I would also like to acknowledge research collaborators that I worked with directly The title of this thesis was partially inspired by the title of an ICRA 2019 workshop, "Toward Online Optimal Control of Dynamic Robots," which happened to combine multiple buzzwords the author was floating around in a sensible way. 5 on portions of this work. Particularly, Monica Ekal, Ryan de Freitas Bart, Hailee Hettrick, Oliver Jia-Richards, Alex Steighner, and the iSAT team. 6 Contents 1 Introduction 15 1.1 M otivation ............ ............. ........ 15 1.1.1 Robotic Motion Planning .................... 15 1.1.2 Microgravity Space Robotics ................... 17 1.2 Simulators and Testbeds .................... ..... 17 1.2.1 SPHERES ................ ............. 17 1.2.2 A strobee ............ .................. 18 1.3 Thesis Organization and Approach ................... 20 2 Background and Research Gap 21 2.1 Robotic Space Systems ................ .......... 21 2.1.1 Microgravity Robotics ......... ............. 21 2.1.2 Planetary Surface Robotics . .................. 26 2.2 Motion Planning ............................. 26 2.2.1 Discrete Planning ..................... .... 30 2.2.2 Classical Robotic Motion Planning ............ ... 31 2.2.3 Control and Dynamical Systems Theory ............ 31 2.2.4 Optimal Control: Optimization for Controlling Dynamical Sys- tem s ... ..................... ........ 32 2.2.5 Trajectory Optimization: Adapting Mathematical Optimiza- tion for Dynamical Systems .. .......... ....... 34 2.2.6 Planning under Uncertainty ............... .... 36 2.3 Research Gap for Microgravity Robotics ...... .......... 37 7 3 Dynamical Systems of Interest 39 3.1 Dynamics Preliminaries .......................... 39 3.1.1 Attitude Representation ....... .......... ... 39 3.1.2 Attitude Kinematics and Dynamics ..... ......... 43 3.1.3 Translation Kinematics and Dynamics ......... ... 44 3.2 M odel System s ........ ........... .......... 44 3.2.1 Double Integrator ......... .......... ..... 45 3.2.2 3 DoF Rigid Body ... ........... ......... 45 3.2.3 Rigid Body Satellite (6 DoF Rigid Body) .. ........ 46 3.2.4 Robotic Manipulator Systems (Free-Flying and Free-Floating) 46 3.2.5 C hallenges .......... ........... ....... 48 3.2.6 Demonstrations in Simulation ...... ........... 49 4 Motion Planning for Challenging Dynamical Robots 53 4.1 Constraints ....... ...... ... .... ... ... .. 5 3 4.1.1 Dynamics Constraints .. ... .. .... ... ... .... 5 3 4.1.2 Environmental Constraints .. ..... ..... ..... 5 5 4.2 Underlying Scenario ...... .... .. .... ... 55 4.2.1 Planning for Complex Dynamics. ... .... .. 56 4.2.2 Systems of Interest . ...... ... .... .. 56 4.3 Sampling-Based Planning (SBP) ... .. .... ... 57 4.3.1 Optimal SBP .. ....... .... ... ... 58 4.3.2 Dynamics-Aware SBP ..... .. ... ... .. 60 4.3.3 Dynamics-Aware Optimal SBP ... ... .... 63 4.4 SBP for Satellite Dynamics ..... ....... .. 64 4.5 Results for Satellite Dynamics ..... .. ... ... .. 66 5 Planning for Information Gain 75 5.1 Background on Probability .. .... .... .... .... .... 76 5.2 Underlying Scenario .. ..... .... ..... ..... .... 76 5.2.1 Planning with Uncertain Parameters . ..... .... ... 77 8 5.2.2 System of Interest ................ ........ 77 5.3 Relevant Methods . ......... .......... ...... 79 5.3.1 Real-Time Motion Planning ...... .... ........ 79 5.3.2 Adaptive and Robust Control ....... .. .. ...... 80 5.3.3 Estimation Methods and Parameter Estimation ... ..... 81 5.4 Real-time Planning for Information Gain ... .... .... .... 81 5.4.1 The Fisher Information Matrix . ....... ........ 82 5.4.2 Nonlinear Model Predictive Control ...... ........ 85 5.4.3 Implementation Details .. ..... ...... ...... 86 5.5 Algorithm Results . .... ..... ..... .... .. ...... 88 5.5.1 Demonstration of Updating Parameters .... ........ 88 5.5.2 Results on a 6 DoF System ...... .... .. ...... 89 5.5.3 Summary of Framework .... ...... .. ........ 92 6 Systems Considerations and Launch Manifesting Optimization 95 6.1 Scenarios for On-Orbit Motion Planning ..... ..... ..... 95 6.2 Case Study: Launch Manifesting Optimization . ..... ...... 98 6.2.1 Large-Aperture Assembled Telescope Background .... .. 98 6.2.2 Problem Formulation ..... ....... ....... ... 99 6.2.3 Existing Approaches and Challenges ..... ..... ... 101 6.2.4 Integer Optimization Approach .. ...... ..... ... 102 6.2.5 Greedy Packing Approach ..... ....... ....... 104 6.2.6 R epacking ...... ..... ..... ...... ..... 106 6.2.7 Test Cases and Results .... ....... ....... ... 108 6.3 Summary and Contrast to Motion Planning Optimization . ..... 110 7 Conclusions and Future Work 111 7.1 Conclusions and Contributions .... ...... ..... ...... 111 7.2 Future Work ..... ....... ........ ........ ... 112 9 A Launch Vehicle and Component Tables 115 A.1 20 m In-Space Assembled Telescope ..... ................... 115 A .2 Launch Vehicles .... .... ..... .... .... .... .... 116 B Robust Optimization for Satellite Control 117 B.1 Robust Optimization Primer .... ...... ....... ...... 117 B.2 Robust Receding Horizon Control for 3 DoF Dynamics ..... ... 118 B.2.1 Problem Formulation ... ...... ...... .....
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