Chapter 5 Sampling-Based Motion Planning

[1]  H. Weyl Über die Gleichverteilung von Zahlen mod. Eins , 1916 .

[2]  P. Moran,et al.  Mathematics of Statistics , 1948, Nature.

[3]  J. Halton On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[4]  R. A. Silverman,et al.  Introductory Real Analysis , 1972 .

[5]  A. G. Sukharev Optimal strategies of the search for an extremum , 1971 .

[6]  Donald W. Kahn,et al.  Topology: An introduction to the point-set and algebraic areas , 1975 .

[7]  Jon Louis Bentley,et al.  An Algorithm for Finding Best Matches in Logarithmic Expected Time , 1977, TOMS.

[8]  Michael O. Rabin,et al.  Transaction Protection by Beacons , 1983, J. Comput. Syst. Sci..

[9]  Gerald B. Folland,et al.  Real Analysis: Modern Techniques and Their Applications , 1984 .

[10]  Bernard Faverjon,et al.  Obstacle avoidance using an octree in the configuration space of a manipulator , 1984, ICRA.

[11]  B. Donald Motion Planning with Six Degrees of Freedom , 1984 .

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

[13]  Elmer G. Gilbert,et al.  Distance functions and their application to robot path planning in the presence of obstacles , 1985, IEEE J. Robotics Autom..

[14]  Tomas Lozano-Perez A simple motion-planning algorithm for general robot manipulators , 1986, IEEE J. Robotics Autom..

[15]  Bruce Randall Donald,et al.  A Search Algorithm for Motion Planning with Six Degrees of Freedom , 1987, Artif. Intell..

[16]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..

[17]  Bernard Faverjon,et al.  Hierarchical object models for efficient anti-collision algorithms , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[18]  Brad E. Paden,et al.  Path planning using a Jacobian-based freespace generation algorithm , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[19]  Bernhard Glavina,et al.  Solving findpath by combination of goal-directed and randomized search , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[20]  Bruce Randall Donald,et al.  Real-time robot motion planning using rasterizing computer graphics hardware , 1990, SIGGRAPH.

[21]  W. Fischer,et al.  Sphere Packings, Lattices and Groups , 1990 .

[22]  Jean-Claude Latombe,et al.  A Monte-Carlo algorithm for path planning with many degrees of freedom , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[23]  Franz Aurenhammer,et al.  Voronoi diagrams—a survey of a fundamental geometric data structure , 1991, CSUR.

[24]  Koichi Kondo,et al.  Motion planning with six degrees of freedom by multistrategic bidirectional heuristic free-space enumeration , 1991, IEEE Trans. Robotics Autom..

[25]  Jean-Claude Latombe,et al.  Robot Motion Planning: A Distributed Representation Approach , 1991, Int. J. Robotics Res..

[26]  James Arvo,et al.  Fast Random Rotation matrices , 1992, Graphics Gems III.

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

[28]  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.

[29]  Narendra Ahuja,et al.  Gross motion planning—a survey , 1992, CSUR.

[30]  Ken Shoemake,et al.  Uniform Random Rotations , 1992, Graphics Gems III.

[31]  Peter N. Yianilos,et al.  Data structures and algorithms for nearest neighbor search in general metric spaces , 1993, SODA '93.

[32]  Sunil Arya,et al.  Approximate nearest neighbor queries in fixed dimensions , 1993, SODA '93.

[33]  Sunil Arya,et al.  Algorithms for fast vector quantization , 1993, [Proceedings] DCC `93: Data Compression Conference.

[34]  Henning Tolle,et al.  Motion planning with many degrees of freedom-random reflections at C-space obstacles , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[35]  Sean Quinlan,et al.  Efficient distance computation between non-convex objects , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[36]  Jean-Claude Latombe,et al.  Planning motions with intentions , 1994, SIGGRAPH.

[37]  I. Sloan Lattice Methods for Multiple Integration , 1994 .

[38]  Kamal K. Gupta,et al.  Practical global motion planning for many degrees of freedom: a novel approach within sequential framework , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[39]  Vipin Kumar,et al.  A parallel formulation of informed randomized search for robot motion planning problems , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[40]  S. Tezuka Uniform Random Numbers: Theory and Practice , 1995 .

[41]  Kamal K. Gupta,et al.  Motion planning for many degrees of freedom: sequential search with backtracking , 1995, IEEE Trans. Robotics Autom..

[42]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[43]  Dinesh Manocha,et al.  Collision Detection: Algorithms and Applications , 1996 .

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

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

[46]  Boris Baginski,et al.  The Z^3-Method for Fast Path Planning in Dynamic Environments , 1996 .

[47]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

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

[49]  Stephen Cameron,et al.  A comparison of two fast algorithms for computing the distance between convex polyhedra , 1997, IEEE Trans. Robotics Autom..

[50]  Brian Mirtich,et al.  Efficient Algorithms for Two-Phase Collision Detection , 1997 .

[51]  Jon M. Kleinberg,et al.  Two algorithms for nearest-neighbor search in high dimensions , 1997, STOC '97.

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

[53]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[54]  F. J. Hickernell Lattice rules: how well do they measure up? in random and quasi-random point sets , 1998 .

[55]  Piotr Indyk,et al.  Approximate nearest neighbors: towards removing the curse of dimensionality , 1998, STOC '98.

[56]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[57]  Pierre Bessière,et al.  The Ariadne's Clew Algorithm , 1993, J. Artif. Intell. Res..

[58]  P. Hellekalek,et al.  Random and Quasi-Random Point Sets , 1998 .

[59]  Yong Yu,et al.  On sensor-based roadmap: a framework for motion planning for a manipulator arm in unknown environments , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[60]  Brian Mirtich,et al.  V-Clip: fast and robust polyhedral collision detection , 1998, TOGS.

[61]  Daniel Vallejo,et al.  OBPRM: an obstacle-based PRM for 3D workspaces , 1998 .

[62]  M. Mackey,et al.  Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics , 1998 .

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

[64]  Bernard Chazelle,et al.  The Discrepancy Method , 1998, ISAAC.

[65]  Carme Torras,et al.  Collision detection algorithms for motion planning , 1998 .

[66]  H. Niederreiter,et al.  Nets, ( t, s )-Sequences, and Algebraic Geometry , 1998 .

[67]  Leonidas J. Guibas,et al.  H-Walk: hierarchical distance computation for moving convex bodies , 1999, SCG '99.

[68]  Dinesh Manocha,et al.  Randomized Path Planning for a Rigid Body Based on Hardware Accelerated Voronoi Sampling , 1999 .

[69]  Mark H. Overmars,et al.  The Gaussian sampling strategy for probabilistic roadmap planners , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[70]  Nancy M. Amato,et al.  Probabilistic roadmap methods are embarrassingly parallel , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

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

[72]  Boris Baginski,et al.  Motion planning for manipulators with many degrees of freedom - the BB-method , 1999, DISKI.

[73]  Nancy M. Amato,et al.  MAPRM: a probabilistic roadmap planner with sampling on the medial axis of the free space , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

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

[75]  Lydia E. Kavraki,et al.  A framework for using the workspace medial axis in PRM planners , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[76]  Stefano Caselli,et al.  ERPP: An experience-based randomized path planner , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[77]  Nancy M. Amato,et al.  Choosing good distance metrics and local planners for probabilistic roadmap methods , 2000, IEEE Trans. Robotics Autom..

[78]  Fred J. Hickernell,et al.  Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature , 2000, SIAM J. Sci. Comput..

[79]  Lydia E. Kavraki,et al.  Path planning using lazy PRM , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

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

[81]  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).

[82]  Leonidas J. Guibas,et al.  Disconnection proofs for motion planning , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[83]  Nancy M. Amato,et al.  Using motion planning to study protein folding pathways , 2001, J. Comput. Biol..

[84]  Ming C. Lin,et al.  Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition , 2001, Comput. Graph. Forum.

[85]  Jean-Claude Latombe,et al.  A Single-Query Bi-Directional Probabilistic Roadmap Planner with Lazy Collision Checking , 2001, ISRR.

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

[87]  M. Coutinho Dynamic Simulations of Multibody Systems , 2001, Springer New York.

[88]  Lydia E. Kavraki,et al.  Randomized path planning for linkages with closed kinematic chains , 2001, IEEE Trans. Robotics Autom..

[89]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[90]  Dinesh Manocha,et al.  A Voronoi-based hybrid motion planner , 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).

[91]  Y. Wang,et al.  An Historical Overview of Lattice Point Sets , 2002 .

[92]  Seth Hutchinson,et al.  A Framework for Real-time Path Planning in Changing Environments , 2002, Int. J. Robotics Res..

[93]  Pekka Isto,et al.  Constructing probabilistic roadmaps with powerful local planning and path optimization , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[94]  Enrico Pagello,et al.  On Parallel RRTs for Multi-robot Systems , 2002 .

[95]  Mitul Saha,et al.  Exact Collision Checking of Robot Paths , 2002, WAFR.

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

[97]  Seth Hutchinson,et al.  Using manipulability to bias sampling during the construction of probabilistic roadmaps , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[98]  Jean-Claude Latombe,et al.  Efficient maintenance and self-collision testing for Kinematic Chains , 2002, SCG '02.

[99]  Steven M. LaValle,et al.  Efficient nearest neighbor searching for motion planning , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[100]  Steven M. LaValle,et al.  Resolution complete rapidly-exploring random trees , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[101]  Manuela M. Veloso,et al.  Real-time randomized path planning for robot navigation , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[102]  K. Clarkson Nearest Neighbor Searching in Metric Spaces : Experimental Results for sb ( S ) , 2002 .

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

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

[105]  Tsai-Yen Li,et al.  An incremental learning approach to motion planning with roadmap management , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[106]  David Hsu,et al.  The bridge test for sampling narrow passages with probabilistic roadmap planners , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[107]  Steven M. LaValle,et al.  Current Issues in Sampling-Based Motion Planning , 2005, ISRR.

[108]  James P. Ostrowski,et al.  Motion planning a aerial robot using rapidly-exploring random trees with dynamic constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[109]  Masayuki Inaba,et al.  Humanoid arm motion planning using stereo vision and RRT search , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[110]  Nancy M. Amato,et al.  A general framework for sampling on the medial axis of the free space , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[111]  Juan Cortés,et al.  Motion Planning Algorithms for General Closed-Chain Mechanisms , 2003 .

[112]  Reid G. Simmons,et al.  Approaches for heuristically biasing RRT growth , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[113]  Michael M. Curtiss,et al.  RRTs for nonlinear, discrete, and hybrid planning and control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[114]  Mark H. Overmars,et al.  Sampling Techniques for Probabilistic Roadmap Planners , 2003 .

[115]  Thierry Siméon,et al.  Eurographics/siggraph Symposium on Computer Animation (2003) Visual Simulation of Ice Crystal Growth , 2022 .

[116]  Stefano Carpin,et al.  Robot motion planning using adaptive random walks , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[117]  Steven M. LaValle,et al.  Incremental low-discrepancy lattice methods for motion planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[118]  Lydia E. Kavraki,et al.  Measure theoretic analysis of probabilistic path planning , 2004, IEEE Transactions on Robotics and Automation.

[119]  Morten Strandberg,et al.  Robot path planning : an object-oriented approach , 2004 .

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

[121]  M. Strandberg,et al.  Augmenting RRT-planners with local trees , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[122]  Steven M. LaValle,et al.  Steps toward derandomizing RRTs , 2004, Proceedings of the Fourth International Workshop on Robot Motion and Control (IEEE Cat. No.04EX891).

[123]  Maja J. Mataric,et al.  Motion planning using dynamic roadmaps , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[124]  Steven M. LaValle,et al.  Deterministic sampling methods for spheres and SO(3) , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[125]  James J. Kuffner,et al.  Effective sampling and distance metrics for 3D rigid body path planning , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[126]  Jan van Leeuwen,et al.  Dynamic multi-dimensional data structures based on quad- and k—d trees , 1982, Acta Informatica.

[127]  Steven M. LaValle,et al.  Incrementally reducing dispersion by increasing Voronoi bias in RRTs , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[128]  Mark H. Overmars,et al.  Useful cycles in probabilistic roadmap graphs , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[129]  Steven M. LaValle,et al.  Incremental Grid Sampling Strategies in Robotics , 2004, WAFR.

[130]  James J. Kuffner,et al.  Autonomous behaviors for interactive vehicle animations , 2004, SCA '04.

[131]  Piotr Indyk,et al.  Nearest Neighbors in High-Dimensional Spaces , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[132]  Dinesh Manocha,et al.  Collision and Proximity Queries , 2004, Handbook of Discrete and Computational Geometry, 2nd Ed..

[133]  Danica Kragic,et al.  Artificial potential biased probabilistic roadmap method , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[134]  Jean-Claude Latombe,et al.  Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles , 2005, Algorithmica.

[135]  Lydia E. Kavraki,et al.  Distributed Sampling-Based Roadmap of Trees for Large-Scale Motion Planning , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[136]  Robert F. Sproull,et al.  Refinements to nearest-neighbor searching ink-dimensional trees , 1991, Algorithmica.

[137]  Thierry Siméon,et al.  Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[138]  Oliver Brock,et al.  Sampling-Based Motion Planning Using Predictive Models , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[139]  Mark H. Overmars,et al.  Roadmap-based motion planning in dynamic environments , 2004, IEEE Transactions on Robotics.

[140]  Stefano Carpin,et al.  Merging the adaptive random walks planner with the randomized potential field planner , 2005, Proceedings of the Fifth International Workshop on Robot Motion and Control, 2005. RoMoCo '05..

[141]  P. Atzberger The Monte-Carlo Method , 2006 .

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

[143]  J. K. Hunter,et al.  Measure Theory , 2007 .

[144]  Harry Chia-Hung Hsu,et al.  Robot Path Planning , 2009, Wiley Encyclopedia of Computer Science and Engineering.

[145]  D. Thalmann,et al.  Planning collision-free reaching motions for interactive object manipulation and grasping , 2008, SIGGRAPH '08.