Motion Planning With Dynamics by a Synergistic Combination of Layers of Planning

To efficiently solve challenges related to motion-planning problems with dynamics, this paper proposes treating motion planning not just as a search problem in a continuous space but as a search problem in a hybrid space consisting of discrete and continuous components. A multilayered framework is presented which combines discrete search and sampling-based motion planning. This framework is called synergistic combination of layers of planning ( SyCLoP) hereafter. Discrete search uses a workspace decomposition to compute leads, i.e., sequences of regions in the neighborhood that guide sampling-based motion planning during the state-space exploration. In return, information gathered by motion planning, such as progress made, is fed back to the discrete search. This combination allows SyCLoP to identify new directions to lead the exploration toward the goal, making it possible to efficiently find solutions, even when other planners get stuck. Simulation experiments with dynamical models of ground and flying vehicles demonstrate that the combination of discrete search and motion planning in SyCLoP offers significant advantages. In fact, speedups of up to two orders of magnitude were obtained for all the sampling-based motion planners used as the continuous layer of SyCLoP.

[1]  Jean-Claude Latombe,et al.  Multi-modal Motion Planning in Non-expansive Spaces , 2010, Int. J. Robotics Res..

[2]  Rajeev Motwani,et al.  Path planning in expansive configuration spaces , 1997, Proceedings of International Conference on Robotics and Automation.

[3]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[4]  Lydia E. Kavraki,et al.  On the performance of random linear projections for sampling-based motion planning , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[5]  Mark de Berg,et al.  Computational geometry: algorithms and applications, 3rd Edition , 1997 .

[6]  James J. Kuffner,et al.  Planning Among Movable Obstacles with Artificial Constraints , 2008, WAFR.

[7]  John Canny,et al.  The complexity of robot motion planning , 1988 .

[8]  Oliver Brock,et al.  Efficient Motion Planning Based on Disassembly , 2005, Robotics: Science and Systems.

[9]  Lydia E. Kavraki,et al.  Motion Planning in the Presence of Drift, Underactuation and Discrete System Changes , 2005, Robotics: Science and Systems.

[10]  Jean-Paul Laumond,et al.  Control of Probabilistic Diffusion in Motion Planning , 2008, WAFR.

[11]  Siddhartha S. Srinivasa,et al.  Manipulation planning with Workspace Goal Regions , 2009, 2009 IEEE International Conference on Robotics and Automation.

[12]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[13]  Micha Sharir,et al.  A Survey of Motion Planning and Related Geometric Algorithms , 1988, Artificial Intelligence.

[14]  Jonathan Richard Shewchuk,et al.  General-Dimensional Constrained Delaunay and Constrained Regular Triangulations, I: Combinatorial Properties , 2008, Discret. Comput. Geom..

[15]  Robert F. Tichy,et al.  Sequences, Discrepancies and Applications , 1997 .

[16]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[17]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[18]  Michiel van de Panne,et al.  RRT-blossom: RRT with a local flood-fill behavior , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[19]  Lynne E. Parker,et al.  Multi-Robot Systems: From Swarms to Intelligent Automata , 2002, Springer Netherlands.

[20]  Jean-Claude Latombe,et al.  Randomized Kinodynamic Motion Planning with Moving Obstacles , 2002, Int. J. Robotics Res..

[21]  Steven M. LaValle,et al.  On the Relationship between Classical Grid Search and Probabilistic Roadmaps , 2004, Int. J. Robotics Res..

[22]  Anthony Stentz,et al.  Mission-level path planning and re-planning for rover exploration , 2006, Robotics Auton. Syst..

[23]  Alexandre M. Bayen,et al.  Computational Techniques for the Verification and Control of Hybrid Systems , 2005 .

[24]  Weixiong Zhang State-space search - algorithms, complexity, extensions, and applications , 1999 .

[25]  M. Spong,et al.  Robot Modeling and Control , 2005 .

[26]  Oliver Brock,et al.  Decomposition-based motion planning: a framework for real-time motion planning in high-dimensional configuration spaces , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[27]  S. LaValle,et al.  Motion Planning , 2008, Springer Handbook of Robotics.

[28]  Manuela Veloso,et al.  Real-Time Multi-Robot Motion Planning with Safe Dynamics , 2005 .

[29]  Mark H. Overmars,et al.  Using Workspace Information as a Guide to Non-uniform Sampling in Probabilistic Roadmap Planners , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[30]  Jean-Claude Latombe,et al.  On Delaying Collision Checking in PRM Planning: Application to Multi-Robot Coordination , 2002, Int. J. Robotics Res..

[31]  Munther A. Dahleh,et al.  Maneuver-based motion planning for nonlinear systems with symmetries , 2005, IEEE Transactions on Robotics.

[32]  Timothy Bretl,et al.  Motion Planning of Multi-Limbed Robots Subject to Equilibrium Constraints: The Free-Climbing Robot Problem , 2006, Int. J. Robotics Res..

[33]  G. Fairweather,et al.  Numerical Methods for Two – Point Boundary Value Problems , 2008 .

[34]  Robert Bohlin,et al.  Path planning in practice; lazy evaluation on a multi-resolution grid , 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).

[35]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[36]  Mark H. Overmars,et al.  Dynamic Motion Planning in Low Obstacle Density Environments , 1997, WADS.

[37]  Lydia E. Kavraki,et al.  Sampling-based robot motion planning: Towards realistic applications , 2007, Comput. Sci. Rev..

[38]  Mark H. Overmars,et al.  A Comparative Study of Probabilistic Roadmap Planners , 2002, WAFR.

[39]  Kostas E. Bekris,et al.  Greedy but Safe Replanning under Kinodynamic Constraints , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[40]  Oliver Brock,et al.  Single-Query Motion Planning with Utility-Guided Random Trees , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[41]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[42]  Nancy M. Amato,et al.  RESAMPL: A Region-Sensitive Adaptive Motion Planner , 2008, WAFR.

[43]  Yong K. Hwang,et al.  SANDROS: a motion planner with performance proportional to task difficulty , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[44]  Timothy Bretl,et al.  Motion Planning for Legged Robots on Varied Terrain , 2008, Int. J. Robotics Res..

[45]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[46]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[47]  Jean-Claude Latombe,et al.  New heuristic algorithms for efficient hierarchical path planning , 1991, IEEE Trans. Robotics Autom..

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

[49]  Thierry Siméon,et al.  Transition-based RRT for path planning in continuous cost spaces , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[50]  Lydia E. Kavraki,et al.  Hybrid systems: from verification to falsification by combining motion planning and discrete search , 2007, CAV.

[51]  Vijay Kumar,et al.  Decidability of Motion Planning with Differential Constraints , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[52]  Steven M. LaValle,et al.  Survivability: Measuring and ensuring path diversity , 2009, 2009 IEEE International Conference on Robotics and Automation.

[53]  Jean-Paul Laumond,et al.  Controllability of a multibody mobile robot , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[54]  Kostas E. Bekris,et al.  Sampling-based roadmap of trees for parallel motion planning , 2005, IEEE Transactions on Robotics.

[55]  Jean-Claude Latombe,et al.  Multi-modal Motion Planning in Non-expansive Spaces , 2010, Int. J. Robotics Res..

[56]  Antonio Bicchi,et al.  On optimal cooperative conflict resolution for air traffic management systems , 2000, IEEE Trans. Intell. Transp. Syst..

[57]  Dinesh Manocha,et al.  An efficient retraction-based RRT planner , 2008, 2008 IEEE International Conference on Robotics and Automation.

[58]  Rodney A. Brooks,et al.  A subdivision algorithm in configuration space for findpath with rotation , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[59]  Jonathan Richard Shewchuk,et al.  Delaunay refinement algorithms for triangular mesh generation , 2002, Comput. Geom..

[60]  Ahmad A. Masoud,et al.  Kinodynamic Motion Planning , 2010, IEEE Robotics & Automation Magazine.

[61]  John H. Reif,et al.  Complexity of the mover's problem and generalizations , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[62]  Rachid Alami,et al.  Two manipulation planning algorithms , 1995 .

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

[64]  Thierry Siméon,et al.  The Stochastic Motion Roadmap: A Sampling Framework for Planning with Markov Motion Uncertainty , 2007, Robotics: Science and Systems.

[65]  Jeffrey C. Trinkle,et al.  Complementarity-based dynamic simulation for kinodynamic motion planning , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[66]  Steven M. LaValle,et al.  Improving Motion-Planning Algorithms by Efficient Nearest-Neighbor Searching , 2007, IEEE Transactions on Robotics.

[67]  Lydia E. Kavraki,et al.  Replanning: A powerful planning strategy for hard kinodynamic problems , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[68]  Lydia E. Kavraki,et al.  Discrete Search Leading Continuous Exploration for Kinodynamic Motion Planning , 2007, Robotics: Science and Systems.

[69]  Lucia Pallottino,et al.  On Optimal Cooperative Con ict Resolution for Air Tra c Management Systems , 2000 .

[70]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[71]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[72]  Vijay Kumar,et al.  Adaptive RRTs for Validating Hybrid Robotic Control Systems , 2004, WAFR.

[73]  Sanjiv Singh,et al.  An efficient on-line path planner for outdoor mobile robots , 2000, Robotics Auton. Syst..

[74]  Frank Lingelbach,et al.  Path planning using probabilistic cell decomposition , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[75]  Howie Choset,et al.  Principles of Robot Motion: Theory, Algorithms, and Implementation ERRATA!!!! 1 , 2007 .

[76]  David Hsu,et al.  Workspace-Based Connectivity Oracle: An Adaptive Sampling Strategy for PRM Planning , 2006, WAFR.

[77]  Siddhartha S. Srinivasa,et al.  BiSpace Planning: Concurrent Multi-Space Exploration , 2008, Robotics: Science and Systems.

[78]  Ross A. Knepper,et al.  Path and trajectory diversity: Theory and algorithms , 2008, 2008 IEEE International Conference on Robotics and Automation.

[79]  Lydia E. Kavraki,et al.  Fast Tree-Based Exploration of State Space for Robots with Dynamics , 2004, WAFR.

[80]  Wolfram Burgard,et al.  Discrete Search Leading Continuous Exploration for Kinodynamic Motion Planning , 2008 .

[81]  Lydia E. Kavraki,et al.  Quantitative Analysis of Nearest-Neighbors Search in High-Dimensional Sampling-Based Motion Planning , 2006, WAFR.

[82]  Thierry Siméon,et al.  Adaptive tuning of the sampling domain for dynamic-domain RRTs , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[83]  Lydia E. Kavraki,et al.  Impact of workspace decompositions on discrete search leading continuous exploration (DSLX) motion planning , 2008, 2008 IEEE International Conference on Robotics and Automation.

[84]  Frank L. Lewis,et al.  Autonomous Mobile Robots : Sensing, Control, Decision Making and Applications , 2006 .

[85]  Matthew R. Walter,et al.  Reachability-guided sampling for planning under differential constraints , 2009, 2009 IEEE International Conference on Robotics and Automation.

[86]  Anthony Stentz,et al.  Optimal and efficient path planning for partially-known environments , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[87]  Tarik Nahhal,et al.  Test Coverage for Continuous and Hybrid Systems , 2007, CAV.

[88]  Lydia E. Kavraki,et al.  Kinodynamic Motion Planning by Interior-Exterior Cell Exploration , 2008, WAFR.

[89]  Jean-Jacques Risler,et al.  Nonholonomic Systems: Controllability and Complexity , 1996, Theor. Comput. Sci..

[90]  E. Feron,et al.  Real-time motion planning for agile autonomous vehicles , 2000, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[91]  Emilio Frazzoli,et al.  Improving the Performance of Sampling-Based Motion Planning With Symmetry-Based Gap Reduction , 2008, IEEE Transactions on Robotics.

[92]  Mark Yim,et al.  Kinodynamic motion planning with hardware demonstrations , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[93]  Kostas E. Bekris,et al.  OOPS for Motion Planning: An Online, Open-source, Programming System , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[94]  Lydia E. Kavraki,et al.  A two level fuzzy PRM for manipulation planning , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[95]  Russ Tedrake,et al.  Path planning in 1000+ dimensions using a task-space Voronoi bias , 2009, 2009 IEEE International Conference on Robotics and Automation.

[96]  Florent Lamiraux,et al.  Smooth motion planning for car-like vehicles , 2001, IEEE Trans. Robotics Autom..

[97]  Oliver Brock,et al.  Balancing exploration and exploitation in motion planning , 2008, 2008 IEEE International Conference on Robotics and Automation.

[98]  Mark H. Overmars,et al.  An Effective Framework for Path Planning Amidst Movable Obstacles , 2006, WAFR.

[99]  Richard M. Murray,et al.  A motion planner for nonholonomic mobile robots , 1994, IEEE Trans. Robotics Autom..