Abstract

A simple numerical technique for path-planning is presented, which relies upon recent developments regarding the existence of universal nonsingular controls. It is based on the use of \generic loops " which provide rst-order controllability along trajectories. The method can be applied in principle to any analytic system having no drift term. The basic theoretical framework is reviewed, and a convergence result is established.

Citations

286	Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition - Sontag - 1998
124	Asymptotic stability and feedback stabilization - Brockett - 1983
65	Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift - Pomet - 1992
62	Global asymptotic stabilization for controllable systems without drift - Coron - 1991
57	Controllability of Non-Linear systems - Jurdjevic, Sussmann
23	A continuation method for nonholonomic path-finding problems - Sussmann, Chitour - 1993
18	Single-input observability of continuous-time systems - Sussmann - 1979
17	Steering nonholonomic systems in chained form - Murray, Sastry - 1991
14	Orders of input/output differential equations and state space dimensions - Wang, Sontag - 1995
12	Gradient optimization and nonlinear control - Hasdorff - 1976
11	On the observability of polynomial systems - Sontag - 1979
11	Pattern generation and feedback control of nonholonomic systems - Brockett - 1993
10	A global approach to nonholonomic motion planning - Divelbiss, Wen - 1992
10	General Strategy for Computing Steering Controls of Systems Without Drift - Lafferriere, “A - 1991
9	Finite dimensional open-loop control generators for nonlinear systems - Sontag - 1988
8	Linearized control systems and applications to smooth stabilization - Coron - 1994
8	An existence theorem for observers of bilinear systems - Grasselli, Isidori - 1981
6	Control and stabilization of nonholonomic caplygin dynamic systems - Bloch, McClamroch, et al. - 1991
6	Averaging approach to nonholonomic motion planning - Gurvits - 1992
4	Controllability and linearized regulation - Sontag
3	On the preservation of certain controllability properties under sampling,” in Developpement et Utilization d’Outiles et Modèles Mathématiques pour l’Automatique, l’Analyse de Systèmes et le Traitement du Signal - Sontag - 1983
3	I�o equations for nonlinear systems and observation spaces - Sontag, Wang - 1991
3	Gradient Optimization and Nonlinear Control - Hasdor - 1976
3	Universal nonsingular controls, in "Systems and - SONTAG - 1992
1	Universal nonsingular controls," Systems and Control Letters 19(1992 - Sontag
1	A General Strategy for Computing Steering Controls of Systems Without Drift - G - 1991