© 2020 Alexandra Q. Nilles DESIGNING BOUNDARY INTERACTIONS FOR SIMPLE MOBILE ROBOTS BY ALEXANDRA Q. NILLES DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate College of the University of Illinois at Urbana-Champaign, 2020 Urbana, Illinois Doctoral Committee: Professor Steven M. LaValle, Chair Professor Nancy M. Amato Professor Sayan Mitra Professor Todd D. Murphey, Northwestern University Abstract Mobile robots are becoming increasingly common for applications such as logistics and delivery. While most research for mobile robots focuses on generating collision-free paths, however, an environment may be so crowded with obstacles that allowing contact with environment boundaries makes our robot more efficient or our plans more robust. The robot may be so small or in a remote environment such that traditional sensing and communication is impossible, and contact with boundaries can help reduce uncertainty in the robot's state while navigating. These novel scenarios call for novel system designs, and novel system design tools. To address this gap, this thesis presents a general approach to modelling and planning over interactions between a robot and boundaries of its environment, and presents prototypes or simulations of such systems for solving high-level tasks such as object manipulation. One major contribution of this thesis is the derivation of necessary and sufficient conditions of stable, periodic trajectories for \bouncing robots," a particular model of point robots that move in straight lines between boundary interactions. Another major contribution is the description and implementation of an exact geometric planner for bouncing robots. We demonstrate the planner on traditional trajectory generation from start to goal states, as well as how to specify and generate stable periodic trajectories. In addition, we demonstrate the utility of the planner for environment geometry analysis, with respect to the role of environment geometry and system design constraints on the reachability and stability of bouncing robot trajectories. We propose a general approach for the design of bouncing robot systems, as well as more general classes of wild robots. We start by identifying useful, robust open-loop motion strategies, then integrate sensors and information space reasoning to determine conditions for switching between these open-loop behaviors. This approach is demonstrated on the task of \cart-on-track" object manipulation, motivated by design constraints for robots at the micrometer length scale. We identify the parts of this approach most amenable to automation, and provide a collection of supporting software tools. The final contribution of the thesis is a chapter including qualitative design principles for automated robot design systems, as well as an example of a live-coding interface for the design of mobile robot motion patterns demonstrating some of these principles. We conclude with an outline of our vision for this area of research in the future. ii To my parents, and all my teachers. iii Acknowledgments They say a Ph.D. is a marathon, not a sprint; although I've never ran that far in one go, I'd say it's an accurate analogy. However, I think a more appropriate cliche is the one about how it takes a village - certainly, this thesis would never have been completed without a large village of incredibly supportive people. Of course I must thank my parents, who were \blessed" with two extremely precocious and stubborn children. Thank you for all your love and support, and for always encouraging me to “finish strong." Thank you to my brother Andrew, for all the laughs and for getting me out into the wilderness when I needed a break from the robots. I must also thank my friends and chosen family, especially Leah Moldauer, Alex Phillips, Halie Kastle, Lucy Orsi, Simona Mara Smith, Jacob Dixon, Ted Kim, and Eric Jones. Your love kept me sane through the toughest times. Special thanks to Jordan Hall, for your incredible patience through the emotional rollercoaster of 2020, and for always being able to make me laugh. I would also like to remember Maria Schmidt and David Vargas, two friends that I lost during the Ph.D. May they rest in power. I owe an immeasurable debt to my advisor, Professor Steve LaValle. From the beginning Steve has treated me (and all his students and collaborators) with deep respect. He has taught me a great deal about math, motion planning, and technical writing; he has also been a great teacher in how to stay honest, kind, and humble under pressure. His love of learning is infectious and inspirational, whether focused on technology, business, language, or new cuisines. Thank you to Steve, Anna, and your family for your grace over the years and for being incredible hosts. I hope to be able to visit Oulu again soon! Thank you to all the people in the Motion Strategy Lab that I have worked with over the years - no matter how brief our collaboration, I have learned something from everyone I have worked with. Israel Becerra visited as a postdoc and provided some much-needed structure to my project management when I was just starting out. Thanks to Samara Ren for all the delightful conversations, lovely illustrations, mathematical insights, and for helping me navigate the maze of research directions over several years of collaboration. I have been lucky to work with many undergraduate students over the years, many of which are better researchers than I and are constant inspirations to me. I wish to thank Justin Wasserman, Austin Born, John Born, Chris Horn, Thomas Driscoll, and Jon Park in particular for sticking with me on the weaselballs project, even when it seemed a wild goose chase. Deep thanks to Dr. Amy LaViers and the entire Robotics, Automation, and Dance (RAD) iv Lab, especially Umer Huzaifa, Ishaan Pakrasi, Catie Cuan, Anum Jang Sher, and everyone else in Amy's 598 class. The RAD Lab is a wonderfully self-aware community and helped me feel less alone for caring about what I care about. On a related note, thank you to Dance at Illinois for allowing me into your spaces; even though the credits didn't count toward my degree they were some of the most valuable classes I have ever taken. Thank you to the Department of Computer Science, especially Kathy Runck, Viveka Ku- daligama, Maggie Metzger Chappell, Julie Owens, and all of the administrative staff that helped me with the surprisingly difficult logistics of being a graduate student. Thanks to everyone who helped me resurrect the nearly-defunct graduate student organization, espe- cially Zane Ma, Deepak Kumar, Helen Wauck, Patrick Lin, and Shant Boodaghians; that was fun, and Chez Tom will live on forever in my heart. Thanks to the theory group in particular for being friendly and welcoming despite my relative lack of rigor! I must thank all my teachers and professors over the years. I would like to especially thank Yuliy Baryshnikov for extending support several times when I was in need, and for his patience with my still-ongoing progress toward publishable results. I would also like to acknowledge the late Dr. Alfred Hubler, who managed to reignite my love of experiments, as well as gave me a much-needed kick in the pants to start publishing. His loss was deeply felt. I would also like to extend thanks to Leonardo Bobadilla, Jason O'Kane, Andrea Censi, Dylan Shell, and Seth Hutchinson for your mentorship and support over the years, as well as everyone who has kindly welcomed me to the robotics community and made conferences a highly entertaining experience. Finally, my deepest gratitude to my committee { Nancy Amato, Sayan Mitra, and Todd Murphey { for your extra support in Steve's absence, your help with talk preparation, and all the constructive feedback and ideas for future work. Several local Champaign-Urbana institutions were instrumental to the completion of this work, including Golden Wok, Ozu Ramen, Aroma Cafe, Watson's Shack and Rail, Clark Bar, and 25 O'Clock Brewing Company. When I moved to the middle of Illinois, I never expected to find such a vibrant community of lovely people, and so much art, activism, and cooperative spirit. CU will always have a special place in my heart. Finally, I must give my love and appreciation to my co-op, the Community of Urbana- Champaign Cooperative Housing (COUCH), which housed and fed me for the entirety of my time in graduate school. I also found some of my closest friends there. While helping manage a cooperative business may have been somewhat distracting from my Ph.D. work, I would not trade the experience for anything. Living in community with many different people taught me how to be a dramatically more kind, responsible, communicative person. COUCH also taught me quite a lot about anti-racism and equity work, lessons I hope will benefit my communities for the rest of my life. v Table of Contents Chapter 1 Introduction . 1 1.1 Roadmap: Moving Up the Abstraction \Stack" . .2 1.2 Contributions . .4 Chapter 2 Background and Related Work . 6 2.1 Handling Uncertainty in Robotics, Control Theory and Artificial Intelligence6 2.2 Formal Methods in Robotics . .7 2.3 Mobile Robots . 10 2.4 Micro-Robotics . 13 2.5 Related Mathematical Problems . 15 2.6 Conclusion . 16 Chapter 3 Modelling . 17 3.1 Bouncing Robots . 18 3.2 Wild Bodies . 22 Chapter 4 Trajectories as Dynamical Systems . 25 4.1 What Behaviors are Useful? . 25 4.2 Trajectories in Regular Polygons . 26 4.3 Nondeterministic Trajectories . 37 4.4 Trajectories in Nonconvex Polygons . 44 4.5 Ergodic and Chaotic Trajectories . 45 Chapter 5 Motion Planning for Bouncing Robots . 46 5.1 Planning for a Perfect Robot .