Singularities and Topological Aspects in Nonholonomic Motion Planning

Motion planning is an already old and classical problem in Robotics. A few years ago a new instance of this problem has appeared in the literature : motion planning for nonholonomic systems. While useful tools in motion planning come from Computer Science and Mathematics (Computational Geometry, Real Algebraic Geometry), nonholonomic motion planning needs some Control Theory and more Mathematics (Differential Geometry).

[1]  Wei-Liang Chow.  Über Systeme von liearren partiellen Differentialgleichungen erster Ordnung , 1940 .

[2]  R. Sternberg.  Variational methods and non-oscillation theorems for systems of differential equations , 1952 .

[3]  L. Dubins.  On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[4]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[5]  S. Sternberg.  Lectures on Differential Geometry , 1964 .

[6]  C. Lobry.  Contr^olabilite des systemes non lineaires , 1970 .

[7]  David M. Auslander,et al.  Control and dynamic systems , 1970 .

[8]  H. Sussmann,et al.  Controllability of nonlinear systems , 1972 .

[9]  M. Spivak.  A comprehensive introduction to differential geometry , 1979 .

[10]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[11]  G. Viennot.  Algèbres de Lie Libres et Monoïdes Libres , 1978 .

[12]  C. Desoer,et al.  Linear Time-Invariant Robust Servomechanism Problem: A Self-Contained Exposition , 1980 .

[13]  R. Brockett.  Control Theory and Singular Riemannian Geometry , 1982 .

[14]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[15]  Peter Hilton,et al.  New Directions in Applied Mathematics , 1982 .

[16]  H. Hermes,et al.  Nilpotent bases for distributions and control systems , 1984 .

[17]  Richard P. Paul,et al.  Robotics research : the First International Symposium , 1984 .

[18]  J. Mitchell.  On Carnot-Carathéodory metrics , 1985 .

[19]  P. Schönemann.  On artificial intelligence , 1985, Behavioral and Brain Sciences.

[20]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1986 .

[21]  Jean-Paul Laumond,et al.  Feasible Trajectories for Mobile Robots with Kinematic and Environment Constraints , 1986, IAS.

[22]  Georges Giralt,et al.  Robotics research : the third international symposium , 1986 .

[23]  Frank L. Lewis,et al.  Optimal Control , 1986 .

[24]  R. Strichartz.  Sub-Riemannian geometry , 1986 .

[25]  Chee Yap,et al.  Algorithmic motion planning , 1987 .

[26]  R. Strichartz.  The Campbell-Baker-Hausdorff-Dynkin formula and solutions of differential equations , 1987 .

[27]  Jean-Paul Laumond,et al.  Finding Collision-Free Smooth Trajectories for a Non-Holonomic Mobile Robot , 1987, IJCAI.

[28]  Pierre Tournassoud.  Motion planning for a mobile robot with a kinematic constraint , 1988, Geometry and Robotics.

[29]  Bruce Randall Donald,et al.  On the complexity of kinodynamic planning , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[30]  Jean-Daniel Boissonnat,et al.  A practical exact motion planning algorithm for polygonal object amidst polygonal obstacles , 1988, Geometry and Robotics.

[31]  Gordon T. Wilfong,et al.  Planning constrained motion , 1988, STOC '88.

[32]  A. Vershik,et al.  Nonholonomic problems and the theory of distributions , 1988 .

[33]  Thierry Siméon,et al.  Trajectory planning and motion control for mobile robots , 1988, Geometry and Robotics.

[34]  J. Latombe,et al.  On nonholonomic mobile robots and optimal maneuvering , 1989, Proceedings. IEEE International Symposium on Intelligent Control 1989.

[35]  Bruce H. Krogh,et al.  Dynamic generation of subgoals for autonomous mobile robots using local feedback information , 1989 .

[36]  Micha Sharir,et al.  Algorithmic motion planning in robotics , 1991, Computer.

[37]  Daniel E. Koditschek,et al.  The construction of analytic diffeomorphisms for exact robot navigation on star worlds , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[38]  John F. Canny,et al.  Planning smooth paths for mobile robots , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[39]  John F. Canny,et al.  An exact algorithm for kinodynamic planning in the plane , 1990, SCG '90.

[40]  J. Latombe,et al.  Controllability of Mobile Robots with Kinematic Constraints. , 1990 .

[41]  Georges Giralt,et al.  An Integrated Navigation and Motion Control System for Autonomous Multisensory Mobile Robots , 1990, Autonomous Robot Vehicles.

[42]  Zexiang Li,et al.  Motion of two rigid bodies with rolling constraint , 1990, IEEE Trans. Robotics Autom..

[43]  Jean-Paul Laumond,et al.  A motion planner for car-like robots based on a mixed global/local approach , 1990, EEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications.

[44]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[45]  John F. Canny,et al.  Robust motion planning for mobile robots , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[46]  Steven Dubowsky,et al.  On the nature of control algorithms for space manipulators , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[47]  Micha Sharir,et al.  An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space , 1990, Discret. Comput. Geom..

[48]  Yoshihiko Nakamura,et al.  Nonholonomic path planning of space robots via bi-directional approach , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[49]  Gordon Wilfong.  Motion Planning for an Autonomous Vehicle , 1990, Autonomous Robot Vehicles.

[50]  Mark Yim,et al.  Indoor automation with many mobile robots , 1990, EEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications.

[51]  J. Laumond.  Nonholonomic motion planning versus controllability via the multibody car system example , 1990 .

[52]  Christian Laugier,et al.  Robot motion planning: the case of nonholonomic mobiles in a dynamic world , 1990, EEE International Workshop on Intelligent Robots and Systems, Towards a New Frontier of Applications.

[53]  Claude Samson,et al.  Feedback control of a nonholonomic wheeled cart in Cartesian space , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[54]  Zexiang Li,et al.  A variational approach to optimal nonholonomic motion planning , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

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

[56]  Jean-Daniel Boissonnat,et al.  Shortest paths of Bounded Curvature in the Plane , 1991, Geometric Reasoning for Perception and Action.

[57]  Michel Taïx,et al.  Efficient motion planners for nonholonomic mobile robots , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[58]  Takeo Kanade,et al.  Intelligent Autonomous Systems , 1991, Robotics Auton. Syst..

[59]  H. Sussmann,et al.  Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[60]  Georges Bastin,et al.  Modelling and control of non-holonomic wheeled mobile robots , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[61]  J. Laumond.  Controllability of a multibody mobile robot , 1991 .

[62]  Carlos Canudas de Wit,et al.  Path following of a 2-DOF wheeled mobile robot under path and input torque constraints , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[63]  Jean-Claude Latombe.  A Fast Path Planner for a Car-Like Indoor Mobile Robot , 1991, AAAI.

[64]  S. Shankar Sastry,et al.  Steering car-like systems with trailers using sinusoids , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.