Optimal feedback control for route tracking with a bounded-curvature vehicle

The problem of driving a vehicle along a given path is considered. The vehicle is supposed to move forward only, with a given velocity profile, and to have a bounded turning radius. Such a model, also known as 'Dubins' vehicle', is relevant to the kinematics of road vehicles as well as aircraft cruising at constant altitude, or sea vessels. We consider the optimal control problem consisting of minimizing the length travelled by the vehicle starting from a generic configuration to connect to a specified route. A feedback law is proposed, such that straight routes can be approached optimally, while the system is asymptotically stabilized. Experimental results are reported showing real-time feasibility of the proposed approach.

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

[2]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

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

[4]  Jean-Jacques E. Slotine,et al.  Tracking control of nonlinear systems using sliding surfaces , 1983 .

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

[6]  J. Sussmann,et al.  SHORTEST PATHS FOR THE REEDS-SHEPP CAR: A WORKED OUT EXAMPLE OF THE USE OF GEOMETRIC TECHNIQUES IN NONLINEAR OPTIMAL CONTROL. 1 , 1991 .

[7]  Carlos Canudas de Wit,et al.  Exponential control law for a mobile robot: extension to path following , 1992, ICRA.

[8]  Georges Bastin,et al.  Dynamic feedback linearization of nonholonomic wheeled mobile robots , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[9]  Jean-Daniel Boissonnat,et al.  Shortest paths of bounded curvature in the plane , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[10]  S. Shankar Sastry,et al.  Stabilization of trajectories for systems with nonholonomic constraints , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[11]  Alessandro De Luca,et al.  Control of nonholonomic systems via dynamic compensation , 1993, Kybernetika.

[12]  P. Souéres,et al.  The Shortest path synthesis for non-holonomic robots moving forwards , 1994 .

[13]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  V. I. Utkin,et al.  Sliding Mode Control of Mobile Robots. , 1994 .

[15]  Vijay Kumar,et al.  Control of Mechanical Systems With Rolling Constraints , 1994, Int. J. Robotics Res..

[16]  C. Samson.  Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

[17]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[18]  Alessandro Astolfi,et al.  Exponential stabilization of a car-like vehicle , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[19]  Antonio Bicchi,et al.  Closed loop steering of unicycle like vehicles via Lyapunov techniques , 1995, IEEE Robotics Autom. Mag..

[20]  Mitsuji Sampei,et al.  Arbitrary path tracking control of articulated vehicles using nonlinear control theory , 1995, IEEE Trans. Control. Syst. Technol..

[21]  P. Souéres,et al.  Shortest paths synthesis for a car-like robot , 1996, IEEE Trans. Autom. Control..

[22]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[23]  B. Piccoli,et al.  A Generic Classification of Time-Optimal Planar Stabilizing Feedbacks , 1998 .

[24]  Héctor J. Sussmann,et al.  Regular Synthesis and Sufficiency Conditions for Optimality , 2000, SIAM J. Control. Optim..

[25]  Mark R. Greenstreet,et al.  Hybrid Systems: Computation and Control , 2002, Lecture Notes in Computer Science.