A multisteering trailer system: conversion into chained form using dynamic feedback

This paper examines the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, linked together with rigid bars. The state space and kinematic equations of the system are defined, and it is shown how these kinematic equations may be converted into a multiinput chained form. The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization; some of these methods are discussed here. Dynamic state feedback is used to convert the system to this multiinput chained form. It is shown how the dynamic state feedback that is used in this paper corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers. Two different example systems are also presented, along with simulation results for a parallel-parking maneuver.

[1]  Philippe Martin,et al.  Flatness and motion planning : the car with n trailers. , 1992 .

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

[3]  S. Sastry,et al.  Extended Goursat normal forms with applications to nonholonomic motion planning , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[4]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

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

[6]  D. Normand-Cyrot,et al.  An introduction to motion planning under multirate digital control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[7]  J. C. Alexander,et al.  MANEUVERING OF VEHICLES , 1987 .

[8]  S. Sastry,et al.  Trajectory generation for the N-trailer problem using Goursat normal form , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

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

[11]  J. Descusse,et al.  Decoupling with Dynamic Compensation for Strong Invertible Affine Non Linear Systems , 1985 .

[12]  D. Taghirad.  Ieee Transactions on Robotics and Automation 1 Robust Torque Control of Harmonic Drive Systems , 1997 .

[13]  Linda Bushnell,et al.  Stabilization of multiple input chained form control systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[15]  R. Gardner,et al.  The GS algorithm for exact linearization to Brunovsky normal form , 1992 .

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

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

[18]  Linda Bushnell,et al.  Steering Three-Input Chained Form Nonholonomic Systems Using Sinusoids: The Fire Truck Example , 1993 .

[19]  S. Shankar Sastry,et al.  Steering Three-Input Nonholonomic Systems: The Fire Truck Example , 1995, Int. J. Robotics Res..

[20]  Richard M. Murray,et al.  Nonholonomic control systems: from steering to stabilization with sinusoids , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[21]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[22]  Richard M. Murray,et al.  STABILIZATION AND TRACKING FOR NONHOLONOMIC CONTROL SYSTEMS USING TIME-VARYING STATE FEEDBACK , 1992 .

[23]  Jean-Paul Laumond,et al.  Controllability of a multibody mobile robot , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[24]  Richard M. Murray,et al.  Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems , 1994, Math. Control. Signals Syst..

[25]  Ole Jakob Sørdalen,et al.  Conversion of the kinematics of a car with n trailers into a chained form , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.