Smooth Feedback for Car-Like Vehicles in Polygonal Environments

We introduce a method for constructing provably safe smooth feedback laws for car-like robots in obstacle-cluttered polygonal environments. The robot is taken to be a point with motion that must satisfy bounded path curvature constraints. We construct a global feedback plan (or control policy) by partitioning the environment into convex cells, computing a discrete plan on the resulting cell complex, and generating local control laws on the state space that are safe, consistent with the high level plan, and satisfy smoothness conditions. The trajectories of the resulting global feedback plan are smooth and stabilize the position of the robot in the plane, neglecting the orientation.

[1]  J. Tsitsiklis,et al.  Efficient algorithms for globally optimal trajectories , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[2]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[3]  Steven M. LaValle,et al.  Computing Smooth Feedback Plans Over Cylindrical Algebraic Decompositions , 2006, Robotics: Science and Systems.

[4]  Calin Belta,et al.  Discrete abstractions for robot motion planning and control in polygonal environments , 2005, IEEE Transactions on Robotics.

[5]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[6]  I.I. Hussein,et al.  Real Time Feedback Control for Nonholonomic Mobile Robots With Obstacles , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[8]  Raimund Seidel,et al.  A Simple and Fast Incremental Randomized Algorithm for Computing Trapezoidal Decompositions and for Triangulating Polygons , 1991, Comput. Geom..

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

[10]  H. Zhang,et al.  Simple Mechanical Control Systems with Constraints and Symmetry , 2002, SIAM J. Control. Optim..

[11]  S. LaValle,et al.  Smoothly Blending Vector Fields for Global Robot Navigation , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  J. Mark Keil,et al.  Decomposing a Polygon into Simpler Components , 1985, SIAM J. Comput..

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

[14]  K. Lynch.  Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[15]  Steven M. LaValle,et al.  Algorithms for Computing Numerical Optimal Feedback Motion Strategies , 2001, Int. J. Robotics Res..

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

[17]  Kostas J. Kyriakopoulos,et al.  Nonholonomic stabilization with collision avoidance for mobile robots , 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).

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

[19]  Giuseppe Oriolo,et al.  Feedback control of a nonholonomic car-like robot , 1998 .

[20]  J.H. van Schuppen,et al.  Control to facet problems for affine systems on simplices and polytopes – With applications to control of hybrid systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[21]  Claude Samson,et al.  Time-varying Feedback Stabilization of Car-like Wheeled Mobile Robots , 1993, Int. J. Robotics Res..

[22]  Rodney A. Brooks,et al.  Solving the find-path problem by good representation of free space , 1982, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  M. Egerstedt,et al.  Control of a car-like robot using a virtual vehicle approach , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

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

[26]  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).

[27]  Steven M. LaValle,et al.  Multiresolution approach for motion planning under differential constraints , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

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

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

[30]  Mireille E. Broucke,et al.  Necessary and Sufficient Conditions for Reachability on a Simplex , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.