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Safe, Scalable, and Complete Motion Planning of Large Teams of Interchangeable Robots University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2014 Safe, Scalable, and Complete Motion Planning of Large Teams of Interchangeable Robots Matthew Turpin University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Computer Sciences Commons, Mechanical Engineering Commons, and the Robotics Commons Recommended Citation Turpin, Matthew, "Safe, Scalable, and Complete Motion Planning of Large Teams of Interchangeable Robots" (2014). Publicly Accessible Penn Dissertations. 1478. https://repository.upenn.edu/edissertations/1478 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/1478 For more information, please contact [email protected]. Safe, Scalable, and Complete Motion Planning of Large Teams of Interchangeable Robots Abstract Large teams of mobile robots have an unprecedented potential to assist humans in a number of roles ranging from humanitarian efforts to e-commerce order fulfillment. Utilizing a team of obotsr provides an inherent parallelism in computation and task completion while providing redundancy to isolated robot failures. Whether a mission requires all robots to stay close to each other in a formation, navigate to a preselected set of goal locations, or to actively try to spread out to gain as much information as possible, the team must be able to successfully navigate the robots to desired locations. While there is a rich literature on motion planning for teams of robots, the problem is sufficiently challenging that in general all methods trade off one of the following properties: completeness, computational scalability, safety, or optimality. This dissertation proposes robot interchangeability as an additional trade-off consideration. Specifically, the work presented here leverages the total interchangeability of robots and develops a series of novel, complete, computationally tractable algorithms to control a team of robots and avoid collisions while retaining a notion of optimality. This dissertation begins by presenting a robust decentralized formation control algorithm for control of robots operating in tight proximity to one another. Next, a series of complete, computationally tractable multiple robot planning algorithms are presented. These planners preserve optimality, completeness, and computationally tractability by leveraging robot interchangeability. Finally, a polynomial time approximation algorithm is proposed that routes teams of robots to visit a large number of specified locations while bounding the suboptimality of total mission completion time. Each algorithm is verified in simulation and when applicable, on a team of dynamic aerial robots. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Mechanical Engineering & Applied Mechanics First Advisor Vijay Kumar Second Advisor Nathan Michael Keywords Approximation Algorithm, Completeness, Formation Control, Multi-Robot Planning, Task Assignment, Trajectory Generation Subject Categories Computer Sciences | Mechanical Engineering | Robotics This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/1478 SAFE, SCALABLE, AND COMPLETE MOTION PLANNING OF LARGE TEAMS OF INTERCHANGEABLE ROBOTS Matthew Turpin A DISSERTATION in Mechanical Engineering and Applied Mechanics Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2014 Vijay Kumar, Supervisor of Dissertation UPS Foundation Professor of Mechanical Engineering and Applied Mechanics Nathan Michael, Co-Supervisor of Dissertation Assistant Research Professor of Robotics Prashant Purohit, Graduate Group Chairperson Associate Professor of Mechanical Engineering and Applied Mechanics Dissertation Committee: Mark Yim, Professor of Mechanical Engineering and Applied Mechanics Vijay Kumar, Professor of Mechanical Engineering and Applied Mechanics Nathan Michael, Assistant Research Professor of Robotics Howie Choset, Professor of Robotics Camillo J. Taylor, Professor of Computer and Information Science Acknowledgments Over the course writing this dissertation, I have had the pleasure of working with many wonderful people on a number of very interesting projects. I would especially like to thank my advisors Vijay Kumar and Nathan Michael for their support over the course of my Ph.D. They have continually shown interest and enthusiasm in my work and given me a great deal of support. I thank my committee members, who were extremely helpful in the dissertation writing process and have provided excellent feedback on improving the quality of this work and its presentation. My NSF graduate research fellowship has given me a tremendous amount of flexibility in choosing research direction. I thank my undergraduate mentors Kevin Lynch and Tom Vose for helping me define and produce my own research at such an early stage in my career that led to my NSF award. I would like to thank all of my lab mates in the MRSL for providing a fun community where there is always someone willing to offer a hand. Most of all, I thank my partner Kristen. She is a tremendous inspiration and I could not have made it without her help and support. ii ABSTRACT SAFE, SCALABLE, AND COMPLETE MOTION PLANNING OF LARGE TEAMS OF INTERCHANGEABLE ROBOTS Matthew Turpin Vijay Kumar Nathan Michael Large teams of mobile robots have an unprecedented potential to assist humans in a number of roles ranging from humanitarian efforts to e-commerce order fulfillment. Utiliz- ing a team of robots provides an inherent parallelism in computation and task completion while providing redundancy to isolated robot failures. Whether a mission requires all robots to stay close to each other in a formation, navigate to a preselected set of goal locations, or to actively try to spread out to gain as much information as possible, the team must be able to successfully navigate the robots to desired locations. While there is a rich literature on motion planning for teams of robots, the prob- lem is sufficiently challenging that in general all methods trade off one of the following four attributes: completeness, computational scalability, safety, or optimality. This dis- sertation proposes robot interchangeability as an additional attribute for consideration. Specifically, the work presented here leverages the total interchangeability of robots and develops a series of novel, complete, computationally tractable algorithms to control a team of robots and avoid collisions while retaining a notion of optimality. This dissertation begins by presenting a robust decentralized formation control algo- iii rithm for control of robots operating in tight proximity to one another. Next, a series of complete, computationally tractable multiple robot planning algorithms are presented. These planners exploit the interchangeability property to achieve optimality, complete- ness, and computational tractability. Finally, a polynomial time approximation algorithm is proposed that routes teams of robots to visit a large number of specified locations while bounding the suboptimality of total mission completion time. Each algorithm is verified in simulation and empirically evaluated on an experimental testbed consisting of a team of dynamic aerial robots. iv Contents Acknowledgements ii Abstract iii 1 Introduction1 2 Scientific Background6 2.1 Single Agent Trajectory Planning Review..................6 2.2 Planning for Multiple Robots......................... 10 2.3 Formation Control............................... 16 2.4 Robot Interchangeability............................ 18 2.5 Vehicle Routing................................. 20 3 Formation Control 23 3.1 Modeling the Robot Formation........................ 26 3.2 Formation Control............................... 29 3.3 Consensus on Trajectories........................... 32 3.4 Simulations Results............................... 37 3.5 Experimental Results.............................. 39 3.5.1 Performance with Variable Maximum Velocity and Acceleration.. 41 3.5.2 Performance with Degraded Network Communication....... 43 3.5.3 Performance with Critical Robot Failures.............. 44 3.6 Chapter Summary............................... 45 4 Concurrent Assignment and Planning of Trajectories Capt 48 4.1 Preliminaries.................................. 51 4.2 c-Capt: a Centralized Obstacle-Free Capt Solution........... 54 4.2.1 Minimum Sum of Distances Trajectories............... 55 4.2.2 Minimum Velocity Squared Trajectories............... 57 4.2.3 c-Capt Definition........................... 63 4.3 c-Capt for Fewer Robots than Goals.................... 64 4.4 c-Capt for Dynamic Robots......................... 65 4.5 d-Capt: a Decentralized Algorithm for Obstacle-Free Capt ........ 66 4.6 Simulation Results............................... 70 4.7 Experimental Verification........................... 72 4.8 Pathological Case for d-Capt and Resolution................ 73 4.9 Chapter Summary............................... 74 v 5 Goal Assignment and Planning Gap 83 5.1 Preliminaries.................................. 84 5.2 Algorithm.................................... 85 5.2.1 Graph Generation........................... 86 5.2.2 Computing Individual Trajectories.................. 89 5.2.3 Assignment............................... 90 5.2.4 Prioritization.............................. 91 5.2.5 Parameterization and Collision Avoidance............. 95 5.2.6 Optional
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