Trajectory Tracking for Nonholonomic Vehicles

For many years, the control of nonholonomic vehicles has been a very active research field. At least two reasons account for this fact. On one hand, wheeled-vehicles constitute a major and ever more ubiquitous transportation system. Previously restricted to research laboratories and factories, automated wheeled-vehicles are now envisioned in everyday life (e.g. through car-platooning applications or urban transportation services), not to mention the military domain. These novel applications, which require coordination between multiple agents, give rise to new control problems. On the other hand, the kinematic equations of nonholonomic systems are highly nonlinear, and thus of particular interest for the development of nonlinear control theory and practice. Furthermore, some of the control methods initially developed for nonholonomic systems have proven to be applicable to other physical systems (e.g. underactuated mechanical systems), as well as to more general classes of nonlinear systems.

[1]  P. Krishnaprasad,et al.  Nonholonomic mechanical systems with symmetry , 1996 .

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

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

[4]  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..

[5]  Eduardo Sontag Universal nonsingular controls , 1993 .

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

[7]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[8]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems using homogeneous feedback , 1997, IEEE Trans. Autom. Control..

[9]  Henry Hermes,et al.  Nilpotent and High-Order Approximations of Vector Field Systems , 1991, SIAM Rev..

[10]  J. Zabczyk Some comments on stabilizability , 1989 .

[11]  G. Campion,et al.  Modelling and state feedback control of nonholonomic mechanical systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[12]  David A. Lizárraga,et al.  Obstructions to the Existence of Universal Stabilizers for Smooth Control Systems , 2004, Math. Control. Signals Syst..

[13]  Warren E. Dixon,et al.  Robust tracking and regulation control for mobile robots , 2000 .

[14]  A. Yu. Khapalov Optimal measurement trajectories for distributed parameter systems , 1992 .

[15]  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.

[16]  E. Ryan On Brockett's Condition for Smooth Stabilizability and its Necessity in a Context of Nonsmooth Feedback , 1994 .

[17]  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.

[18]  Pascal Morin,et al.  Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems Via Oscillatory Approximation of Lie Brackets in Closed Loop , 1999, SIAM J. Control. Optim..

[19]  Richard M. Murray,et al.  Steering nonholonomic systems in chained form , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[20]  P. Morin,et al.  Non-robustness of continuous homogeneous stabilizers for affine control systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[21]  C. Samson,et al.  EXPONENTIAL STABILIZATION OF NONLINEAR DRIFTLESS SYSTEMS WITH ROBUSTNESS TO UNMODELED DYNAMICS , 1999 .

[22]  Pascal Morin,et al.  A Characterization of the Lie Algebra Rank Condition by Transverse Periodic Functions , 2002, SIAM J. Control. Optim..

[23]  Carlos Canudas de Wit,et al.  Theory of Robot Control , 1996 .

[24]  Pascal Morin,et al.  Trajectory tracking for non-holonomic vehicles: overview and case study , 2004, Proceedings of the Fourth International Workshop on Robot Motion and Control (IEEE Cat. No.04EX891).

[25]  R. Murray,et al.  Nonholonomic systems and exponential convergence: some analysis tools , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[26]  Pascal Morin,et al.  Practical stabilization of driftless systems on Lie groups: the transverse function approach , 2003, IEEE Trans. Autom. Control..

[27]  Claude Samson,et al.  Control of a Maneuvering Mobile Robot by Transverse Functions , 2004 .

[28]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[29]  Claude Samson,et al.  Velocity and torque feedback control of a nonholonomic cart , 1991 .

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

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

[32]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .