Abstract
In this paper, we consider the problem of stabilizing the kinematic model of a car to a general path in the plane, subject to very mild restrictions. The car model, although rather simplified, contains some of the most relevant limitations that make application of existing results in the literature impossible: namely, the car can only move forward, and turn with a bounded steering radius; also, only limited sensory information is available.
The approach we follow to stabilization is to adapt to the present general case an optimal synthesis approach successfully applied in our previous work to tracking rectilinear paths. Due to both the nature of the problem, and the solution technique used, the analysis of the controlled system involves a rather complex switching logic. Hybrid formalism and verification techniques prove extremely useful in this context to formally proof stability of the resulting system, and are described in detail in the paper.
The work has been conducted with partial support of PARADES, a Cadence, Magneti-Marelli and ST-microelectronics E.E.I.G, by CNR PF MADESSII SP3.1.2.
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References
E. Asarin, T. Dang, O. Maler, and O. Bournez. Approximate reachability analysis of piecewise-linear dynamical systems. In Nancy Lynch and Bruce H. Krogh, editors, Third International Workshop, HSCC2000, Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science, pages 20–31. Springer-Verlag, New York, U.S.A., 2000.
A. Balluchi, L. Benvenuti, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. Automotive engine control and hybrid systems: Challenges and opportunities. Proceedings of the IEEE, 88, “Special Issue on Hybrid Systems” (invited paper)(7):888–912, July 2000.
A. Balluchi, L. Benvenuti, H. Wong-Toi, T. Villa, and A. L. Sangiovanni-Vincentelli. Controller synthesis for hybrid systems with lower bounds on event separation. In Proc. 38th IEEE Conference on Decision and Control, pages 3984–3989, Phoenix, Arizona, USA, December 1999.
L. E. Dubins. On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents. American Journal of Mathematics, 79:497–516, 1957.
Thomas A. Henzinger. Hybrid automata with finite bisimulations. In Z. Fülöp and F. Gécseg, editors, ICALP’95: Automata, Languages, and Programming, pages 324–335. Springer-Verlag, 1995.
J.P. Laumond, S. Sekhavat, and F. Lamiraux. Robot motion planning and control. Springer-Verlag, Berlin, Germany, 1998.
J. Lygeros, C. Tomlin, and S. Sastry. Controllers for reachability specifications for hybrid systems. Automatica, 35(3), March 1999.
A. Olivero, J. Sifakis, and S. Yovine. Using abstractions for the verification of linear hybrid systems. In Proceedings of Sixth International Conference on Computer-Aided Verification (CAV-94), pages 81–94. Springer-Verlag, 1994. Lecture Notes in Computer Science 818.
C. Samson. Control of chained systems application to path following and time-varying point-stabilization of mobile robots. IEEE Transaction on Automatic Control, 40(1):64–77, January 1995.
O.J. Sordalen and C. Canudas de Wit. Exponential control law for a mobile robot: Extension to path following. IEEE Transactions on Robotics and Automation, 9(6):837–842,, 1993.
P. Souères, A. Balluchi, and A. Bicchi. Optimal feedback control for line tracking with a bounded-curvature vehicle. to appear in International Journal of Control, 2000.
D. Tilbury, O.J. Sordalen, L. Bushnell, and S.S. Sastry. A multi-steering trailer system: conversion into chained form using dynamic feedback. IEEE Transactions on Robotics and Automation, 11(6):807–18, December 1995.
V.I. Utkin. Variable structure systems with sliding modes: a survey. IEEE Transations on Automatic Control, 22:212–222, 1977.
J. Zhang, K. H. Johansson, J. Lygeros, and S. Sastry. Dynamical systems revisited: Hybrid systems with zeno executions. In Nancy Lynch and Bruce H. Krogh, editors, Third International Workshop, HSCC2000, Hybrid Systems: Computation and Control, volume 1790 of Lecture Notes in Computer Science, pages 451–464. Springer-Verlag, New York, U.S.A., 2000.
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Balluchi, A., Souéres, P., Bicchi, A. (2001). Hybrid Feedback Control for Path Tracking by a Bounded—Curbature Vehicle. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2001. Lecture Notes in Computer Science, vol 2034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45351-2_14
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DOI: https://doi.org/10.1007/3-540-45351-2_14
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