Multi-robot motion planning via optimal transport theory

In this work we establish a simple yet effective strategy, based on optimal transport theory, for enabling a group of robots to accomplish complex tasks, such as shape formation and assembly. We demonstrate the feasibility of this approach and rigorously prove collision avoidance and convergence properties of the proposed algorithms.

[1]  L. Kantorovitch,et al.  On the Translocation of Masses , 1958 .

[2]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[3]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[4]  Charles W. Warren,et al.  Global path planning using artificial potential fields , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[5]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Autonomous Robot Vehicles.

[6]  Charles W. Warren,et al.  Multiple robot path coordination using artificial potential fields , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[7]  Yoram Koren,et al.  Potential field methods and their inherent limitations for mobile robot navigation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[9]  Mark H. Overmars,et al.  A random approach to motion planning , 1992 .

[10]  Lydia E. Kavraki,et al.  Randomized preprocessing of configuration for fast path planning , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[11]  Anthony Stentz,et al.  The Focussed D* Algorithm for Real-Time Replanning , 1995, IJCAI.

[12]  Nancy M. Amato,et al.  A randomized roadmap method for path and manipulation planning , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[13]  Annie Luciani,et al.  Global and local path planning in natural environment by physical modeling , 1996, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems. IROS '96.

[14]  Andrew B. Kahng,et al.  Cooperative Mobile Robotics: Antecedents and Directions , 1997, Auton. Robots.

[15]  Paolo Fiorini,et al.  Motion Planning in Dynamic Environments Using Velocity Obstacles , 1998, Int. J. Robotics Res..

[16]  S. LaValle.  Rapidly-exploring random trees : a new tool for path planning , 1998 .

[17]  Steven M. LaValle,et al.  Rapidly-Exploring Random Trees: Progress and Prospects , 2000 .

[18]  Petter Ögren,et al.  A control Lyapunov function approach to multi-agent coordination , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[19]  Bernhard Nebel,et al.  Decentralized collision avoidance, deadlock detection, and deadlock resolution for multiple mobile robots , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[20]  Min Cheol Lee,et al.  Obstacle avoidance for mobile robots using artificial potential field approach with simulated annealing , 2001, ISIE 2001. 2001 IEEE International Symposium on Industrial Electronics Proceedings (Cat. No.01TH8570).

[21]  Shuzhi Sam Ge,et al.  Dynamic Motion Planning for Mobile Robots Using Potential Field Method , 2002, Auton. Robots.

[22]  Maxim Likhachev,et al.  D*lite , 2002, AAAI/IAAI.

[23]  Yi Guo,et al.  A distributed and optimal motion planning approach for multiple mobile robots , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[24]  Min Cheol Lee,et al.  Artificial potential field based path planning for mobile robots using a virtual obstacle concept , 2003, Proceedings 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2003).

[25]  Howie Choset,et al.  Limited communication, multi-robot team based coverage , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[26]  Brian P. Gerkey,et al.  Are ( explicit ) multi-robot coordination and multi-agent coordination really so different ? , 2004 .

[27]  David Furcy,et al.  Lifelong Planning A , 2004, Artif. Intell..

[28]  Andrea L. Bertozzi,et al.  Determining Environmental Boundaries: Asynchronous Communication and Physical Scales , 2005 .

[29]  Nidhi Kalra,et al.  Market-Based Multirobot Coordination: A Comprehensive Survey and Analysis , 2005 .

[30]  Sven Koenig,et al.  Fast replanning for navigation in unknown terrain , 2005, IEEE Transactions on Robotics.

[31]  Anthony Stentz,et al.  A Guide to Heuristic-based Path Planning , 2005 .

[32]  L. Kantorovich.  On the Translocation of Masses , 2006 .

[33]  G. Swaminathan.  Robot Motion Planning , 2006 .

[34]  Yong Yu,et al.  Optimal transport on wireless networks , 2007, physics/0703261.

[35]  M. Ani Hsieh,et al.  Decentralized controllers for shape generation with robotic swarms , 2008, Robotica.

[36]  Sebastian Thrun,et al.  Anytime search in dynamic graphs , 2008, Artif. Intell..

[37]  C. Villani.  Optimal Transport: Old and New , 2008 .

[38]  Bernard Kin Lup. Wong.  Swarming robots (A) , 2009 .

[39]  Leandro Soriano Marcolino,et al.  Traffic control for a swarm of robots: Avoiding group conflicts , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[40]  Sarit Kraus,et al.  Adaptive multi-robot coordination: A game-theoretic perspective , 2010, 2010 IEEE International Conference on Robotics and Automation.

[41]  Kostas E. Bekris,et al.  Efficient and complete centralized multi-robot path planning , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[42]  Emilio Frazzoli,et al.  Sampling-based algorithms for optimal motion planning , 2011, Int. J. Robotics Res..

[43]  Quentin Mérigot,et al.  A Multiscale Approach to Optimal Transport , 2011, Comput. Graph. Forum.

[44]  Christine Julien,et al.  On coordination in practical multi-robot patrol , 2012, 2012 IEEE International Conference on Robotics and Automation.

[45]  Shui-Nee Chow,et al.  Global Optimizations by Intermittent Diffusion , 2013 .

[46]  L. Ambrosio,et al.  A User’s Guide to Optimal Transport , 2013 .

[47]  Nicolas Jouandeau,et al.  A Survey and Analysis of Multi-Robot Coordination , 2013 .

[48]  Chonhyon Park,et al.  Real-time optimization-based planning in dynamic environments using GPUs , 2013, 2013 IEEE International Conference on Robotics and Automation.

[49]  A. Matveev,et al.  Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey , 2014, Robotica.

[50]  Jun Lu.  Method of evolving junctions: a new approach to path planning and optimal control , 2014 .

[51]  Magnus Egerstedt,et al.  Shortest paths through 3-dimensional cluttered environments , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[52]  Saptarshi Bandyopadhyay,et al.  Probabilistic swarm guidance using optimal transport , 2014, 2014 IEEE Conference on Control Applications (CCA).

[53]  Sung G. Lee,et al.  Multirobot Control Using Time-Varying Density Functions , 2014, IEEE Transactions on Robotics.

[54]  Silvia Ferrari,et al.  Distributed Optimal Control of Multiscale Dynamical Systems: A Tutorial , 2016, IEEE Control Systems.

[55]  Brittany D. Froese,et al.  Freeform illumination optics construction following an optimal transport map. , 2016, Applied optics.

[56]  Jun Lu,et al.  Method of evolving junctions: A new approach to optimal control with constraints , 2017, Autom..

[57]  Spring Berman,et al.  Decentralized stochastic control of robotic swarm density: Theory, simulation, and experiment , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[58]  Alfred Galichon,et al.  A Survey of Some Recent Applications of Optimal Transport Methods to Econometrics , 2017, 2102.01716.

[59]  Vijay Kumar,et al.  A Survey on Aerial Swarm Robotics , 2018, IEEE Transactions on Robotics.

[60]  Spring Berman,et al.  Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms , 2016, IEEE Transactions on Automatic Control.

[61]  Fei Ren,et al.  Quantitative Assessment of Robotic Swarm Coverage , 2018, ICINCO.

[62]  Michael Wolf,et al.  Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy , 2018, ArXiv.

[63]  Sonia Martínez,et al.  Distributed Optimal Transport for the Deployment of Swarms , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[64]  Magnus Egerstedt,et al.  Coverage Control for Multirobot Teams With Heterogeneous Sensing Capabilities , 2018, IEEE Robotics and Automation Letters.