Motion Planning

Here, we give the Part II of the two-part tutorial. Part I emphasized the basic problem formulation, mathematical concepts, and the most common solutions. The goal of Part II is to help you understand current robotics challenges from a motion planning perspective.

[1]  Anthony N. Michel,et al.  Applied Algebra and Functional Analysis , 2011 .

[2]  Steven M. LaValle,et al.  Simple and Efficient Algorithms for Computing Smooth, Collision-free Feedback Laws Over Given Cell Decompositions , 2009, Int. J. Robotics Res..

[3]  Steven M. LaValle,et al.  Distance-Optimal Navigation in an Unknown Environment Without Sensing Distances , 2007, IEEE Transactions on Robotics.

[4]  John Langford,et al.  Cover trees for nearest neighbor , 2006, ICML.

[5]  Hugh F. Durrant-Whyte,et al.  Simultaneous localization and mapping: part I , 2006, IEEE Robotics & Automation Magazine.

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

[7]  Alonzo Kelly,et al.  Generating near minimal spanning control sets for constrained motion planning in discrete state spaces , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[9]  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..

[10]  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.

[11]  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.

[12]  Stefano Carpin,et al.  Motion planning using adaptive random walks , 2005, IEEE Transactions on Robotics.

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

[14]  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.

[15]  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.

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

[17]  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.

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

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

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

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

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

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

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

[25]  Hajime Asama,et al.  Inevitable collision states — a step towards safer robots? , 2004, Adv. Robotics.

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

[27]  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).

[28]  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).

[29]  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).

[30]  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).

[31]  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).

[32]  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).

[33]  Kostas E. Bekris,et al.  Multiple query probabilistic roadmap planning using single query planning primitives , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[34]  Daniel Thalmann,et al.  Planning Collision‐Free Reaching Motions for Interactive Object Manipulation and Grasping , 2003, Comput. Graph. Forum.

[35]  M. 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).

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

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

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

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

[40]  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).

[41]  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).

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

[43]  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).

[44]  Devin J. Balkcom,et al.  Time Optimal Trajectories for Bounded Velocity Differential Drive Vehicles , 2002, Int. J. Robotics Res..

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

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

[47]  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).

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

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

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

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

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

[53]  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).

[54]  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).

[55]  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).

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

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

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

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

[60]  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).

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

[62]  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).

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

[64]  B. Mirtich.  V-Clip: fast and robust polyhedral collision detection , 1998, TOGS.

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

[66]  Lucia K. Dale,et al.  Choosing Good Distance Metrics and Local Planners for Probabilistic Roadmap Methods , 1998, ICRA.

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

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

[69]  R. Wasserstein.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

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

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

[72]  Lydia E. Kavraki,et al.  Probabilistic roadmaps for path planning in high-dimensional configuration spaces , 1996, IEEE Trans. Robotics Autom..

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

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

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

[76]  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.

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

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

[79]  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.

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

[81]  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.

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

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

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

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

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

[87]  Kamal Kant Gupta,et al.  Motion planning for many degrees of freedom: sequential search with backtracking , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[88]  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.

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

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

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

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

[93]  Jean-Claude Latombe,et al.  Nonholonomic multibody mobile robots: Controllability and motion planning in the presence of obstacles , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

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

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

[96]  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.

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

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

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

[100]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[101]  B. Faverjon,et al.  A local based approach for path planning of manipulators with a high number of degrees of freedom , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

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

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

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

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

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

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

[108]  E. Angel,et al.  Principles of dynamic programming part 1 , 1980, Proceedings of the IEEE.

[109]  Manuel Blum,et al.  On the power of the compass (or, why mazes are easier to search than graphs) , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

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

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

[112]  Donald Ervin Knuth,et al.  The Art of Computer Programming, Volume II: Seminumerical Algorithms , 1970 .

[113]  P. B. Coaker,et al.  Applied Dynamic Programming , 1964 .

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

[115]  J. Hammersley.  MONTE CARLO METHODS FOR SOLVING MULTIVARIABLE PROBLEMS , 1960 .

[116]  N. Metropolis,et al.  The Monte Carlo method. , 1949, Journal of the American Statistical Association.

[117]  Steven M. LaValle,et al.  Filtering and Planning in Information Spaces , 2009 .

[118]  Dimitri P. Bertsekas,et al.  Neuro-Dynamic Programming , 2009, Encyclopedia of Optimization.

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

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

[121]  Robert Bohlin,et al.  Robot Path Planning , 2002 .

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

[123]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[124]  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).

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

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

[127]  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).

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

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

[130]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

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

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

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

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

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

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

[137]  H. Sagan.  Space-filling curves , 1994 .

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

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

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

[141]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[142]  A. Nijenhuis.  Combinatorial algorithms , 1975 .

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

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