Discrete abstractions for robot motion planning and control in polygonal environments

In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems, specified in terms of triangles, to computationally inexpensive problems on finite-state-transition systems. In this framework, discrete planning algorithms in complex environments can be seamlessly linked to automatic generation of feedback control laws for robots with underactuation constraints and control bounds. We focus on fully actuated kinematic robots with velocity bounds and (underactuated) unicycles with forward and turning speed bounds.

[1]  Gerardo Lafferriere,et al.  A Differential Geometric Approach to Motion Planning , 1993 .

[2]  D. Koditschek,et al.  The construction of analytic diffeomorphisms for exact robot navigation on star worlds , 1991 .

[3]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[4]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[5]  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.

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

[7]  Daniel E. Koditschek,et al.  Sequential Composition of Dynamically Dexterous Robot Behaviors , 1999, Int. J. Robotics Res..

[8]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[9]  Sampath Kannan,et al.  Locating and Capturing an Evader in a Polygonal Environment , 2004, WAFR.

[10]  A. Isidori.  Nonlinear Control Systems , 1985 .

[11]  M. Fliess,et al.  Flatness, motion planning and trailer systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[12]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[13]  Dawn M. Tilbury,et al.  Steering a Three-Input Nonholonomic System using Multi-rate Controls , 1992 .

[14]  Paulo Tabuada,et al.  Bisimulation Relations for Dynamical and Control Systems , 2003, CTCS.

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

[16]  P. Cheng,et al.  RRT-based trajectory design for autonomous automobiles and spacecraft , 2001 .

[17]  Paulo Tabuada,et al.  Model Checking LTL over Controllable Linear Systems Is Decidable , 2003, HSCC.

[18]  Eduardo Sontag,et al.  Remarks on control Lyapunov functions for discontinuous stabilizing feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[19]  Sampath Kannan,et al.  Randomized pursuit-evasion with limited visibility , 2004, SODA '04.

[20]  David H. Bailey,et al.  Algorithms and applications , 1988 .

[21]  A. Astolfi.  Discontinuous control of nonholonomic systems , 1996 .

[22]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[23]  D. Manocha,et al.  Fast Polygon Triangulation Based on Seidel's Algorithm , 1995 .

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

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

[26]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[27]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[28]  Reuven Bar-Yehuda,et al.  Triangulating disjoint Jordan chains , 1994, Int. J. Comput. Geom. Appl..

[29]  Alfred A. Rizzi.  Hybrid control as a method for robot motion programming , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[30]  Kostas J. Kyriakopoulos,et al.  Nonholonomic navigation and control of cooperating mobile manipulators , 2003, IEEE Trans. Robotics Autom..

[31]  O. J. Sordalen,et al.  Exponential stabilization of mobile robots with nonholonomic constraints , 1992 .

[32]  J. O´Rourke,et al.  Computational Geometry in C: Arrangements , 1998 .

[33]  Pascal Morin,et al.  Control of nonlinear chained systems: from the Routh-Hurwitz stability criterion to time-varying exponential stabilizers , 2000, IEEE Trans. Autom. Control..

[34]  Bernard Chazelle.  Triangulating a simple polygon in linear time , 1991, Discret. Comput. Geom..

[35]  R. Murray,et al.  Trajectory generation for the N-trailer problem using Goursat normal form , 1995 .

[36]  Javier González,et al.  Multihierarchical Graph Search , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  Howie Choset,et al.  Composition of local potential functions for global robot control and navigation , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[38]  L. Seneviratne,et al.  Triangulation-based path planning for a mobile robot , 1997 .

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

[40]  George J. Pappas.  Bisimilar linear systems , 2003, Autom..

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

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

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

[44]  Howie Choset,et al.  Construction and automated deployment of local potential functions for global robot control and navigation , 2003 .

[45]  C. Belta,et al.  Constructing decidable hybrid systems with velocity bounds , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[46]  Alfred A. Rizzi,et al.  Robust and efficient motion planning for a planar robot using hybrid control , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[47]  Nick Barnes,et al.  Towards an efficient optimal trajectory planner for multiple mobile robots , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[48]  Cipriano Galindo,et al.  Improving efficiency in mobile robot task planning through world abstraction , 2004, IEEE Transactions on Robotics.

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

[50]  Daniel E. Koditschek.  The Control of Natural Motion in Mechanical Systems , 1991 .

[51]  Jan H. van Schuppen,et al.  A control problem for affine dynamical systems on a full-dimensional polytope , 2004, Autom..

[52]  Bernard Chazelle,et al.  Triangulating a simple polygon in linear time , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[53]  Calin Belta,et al.  Hybrid control for visibility-based pursuit-evasion games , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

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

[55]  Vijay Kumar,et al.  Controlling formations of multiple mobile robots , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).