A visibility-based approach to computing non-deterministic bouncing strategies

Inspired by motion patterns of some commercially available mobile robots, we investigate the power of robots that move forward in straight lines until colliding with an environment boundary, at which point they can rotate in place and move forward again; we visualize this as the robot “bouncing” off boundaries. We define bounce rules governing how the robot should reorient after reaching a boundary, such as reorienting relative to its heading prior to collision, or relative to the normal of the boundary. We then generate plans as sequences of rules, using the bounce visibility graph generated from a polygonal environment definition, while assuming we have unavoidable non-determinism in our actuation. Our planner can be queried to determine the feasibility of tasks such as reaching goal sets and patrolling (repeatedly visiting a sequence of goals). If the task is found feasible, the planner provides a sequence of non-deterministic interaction rules, which also provide information on how precisely the robot must execute the plan to succeed. We also show how to compute stable cyclic trajectories and use these to limit uncertainty in the robot’s position.

[1]  Michael A. Erdmann,et al.  Using Backprojections for Fine Motion Planning with Uncertainty , 1986 .

[2]  Serge Tabachnikov,et al.  Geometry and billiards , 2005 .

[3]  Steven M. LaValle,et al.  Periodic trajectories of mobile robots , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[4]  Matthew T. Mason,et al.  The mechanics of manipulation , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[5]  Subhash Suri,et al.  Simple Robots with Minimal Sensing: From Local Visibility to Global Geometry , 2007, Int. J. Robotics Res..

[6]  Boris Aronov,et al.  Visibility with Multiple Reflections , 1998, Discret. Comput. Geom..

[7]  Daniel E. Koditschek,et al.  Sequential Composition of Dynamically Dexterous Robot Behaviors , 1999, Int. J. Robotics Res..

[8]  Tamal K. Dey,et al.  Visibility with multiple diffuse reflections , 1998, Comput. Geom..

[9]  L. Guvenc,et al.  Household robotics: autonomous devices for vacuuming and lawn mowing [Applications of control] , 2007, IEEE Control Systems.

[10]  Daniel E. Whitney,et al.  Force Feedback Control of Manipulator Fine Motions , 1977 .

[11]  Ileana Streinu,et al.  The vertex-edge visibility graph of a polygon , 1998, Comput. Geom..

[12]  James Dugundji,et al.  Elementary Fixed Point Theorems , 2003 .

[13]  Kevin M. Lynch,et al.  Pulling by Pushing, Slip With Infinite Friction, and Perfectly Rough Surfaces , 1995, Int. J. Robotics Res..

[14]  Jean-Luc Thiffeault,et al.  Microorganism Billiards , 2015, 1502.01478.

[15]  Thierry Siméon,et al.  Visibility-based probabilistic roadmaps for motion planning , 2000, Adv. Robotics.

[16]  Steven M. LaValle,et al.  A visibility-based approach to computing non-deterministic bouncing strategies , 2021, WAFR.

[17]  Jason M. O'Kane,et al.  Guaranteed Coverage with a Blind Unreliable Robot , 2018, 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[18]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[19]  László Szirmay-Kalos,et al.  Worst-case versus average case complexity of ray-shooting , 1998, Computing.

[20]  Subir Kumar Ghosh,et al.  Visibility Algorithms in the Plane , 2007 .

[21]  Subhash Suri,et al.  Simple Robots in Polygonal Environments: A Hierarchy , 2008, ALGOSENSORS.

[22]  Pedro Duarte,et al.  SRB Measures for Polygonal Billiards with Contracting Reflection Laws , 2014 .

[23]  Hazel Everett,et al.  The Aquarium Keeper's Problem , 1991, SODA '91.

[24]  Jason M. O'Kane,et al.  Planning for provably reliable navigation using an unreliable, nearly sensorless robot , 2013, Int. J. Robotics Res..

[25]  Yoshihiko Nakamura,et al.  The chaotic mobile robot , 2001, IEEE Trans. Robotics Autom..

[26]  Steven M. LaValle,et al.  Toward the design and analysis of blind, bouncing robots , 2013, 2013 IEEE International Conference on Robotics and Automation.

[27]  Gaojin Li,et al.  Hydrodynamic interaction of microswimmers near a wall. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Leslie Pack Kaelbling,et al.  Reliably Arranging Objects in Uncertain Domains , 2018, 2018 IEEE International Conference on Robotics and Automation (ICRA).

[29]  David Avis,et al.  A Linear Algorithm for Computing the Visibility Polygon from a Point , 1981, J. Algorithms.

[30]  Russell H. Taylor,et al.  Automatic Synthesis of Fine-Motion Strategies for Robots , 1984 .

[31]  Todd D. Murphey,et al.  Ergodic Exploration of Distributed Information , 2016, IEEE Transactions on Robotics.

[32]  Roberto Markarian,et al.  Pinball billiards with dominated splitting , 2009, Ergodic Theory and Dynamical Systems.

[33]  Gert Vegter,et al.  In handbook of discrete and computational geometry , 1997 .

[34]  Dylan A. Shell,et al.  Space-Efficient Filters for Mobile Robot Localization from Discrete Limit Cycles , 2018, IEEE Robotics and Automation Letters.

[35]  Joel W. Burdick,et al.  Two-Finger Caging of Polygonal Objects Using Contact Space Search , 2015, IEEE Transactions on Robotics.

[36]  Kevin M. Lynch,et al.  Pulling by Pushing, Slip With Infinite Friction, and Perfectly Rough Surfaces , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[37]  Kenneth Y. Goldberg,et al.  Orienting polygonal parts without sensors , 1993, Algorithmica.

[38]  Dylan A. Shell,et al.  Minimalist Robot Navigation and Coverage Using a Dynamical System Approach , 2017, 2017 First IEEE International Conference on Robotic Computing (IRC).

[39]  Siddharth Mayya,et al.  Localization in Densely Packed Swarms Using Interrobot Collisions as a Sensing Modality , 2019, IEEE Transactions on Robotics.