| Motion Planning and Approximate Tracking for Controllable Systems without Drift (1991) | |||||||||||||||
Abstract | |||||||||||||||
| We describe an approach for motion planning for nonholonomic systems without drift based on a combination of (a) earlier work of Sussmann and Lafferriere and (b) some recent results on approximation of trajectories, based on extensions of theorems of Kurzweil and Jarnik about limits of trajectories for highly oscillatory inputs. 1. Introduction Recently there has been a great deal of interest in the Motion Planning Problem (MPP) for nonholonomic systems. Following the early work of Brockett and Sastry, cf. [3], [11], many methods have been proposed for solving this problem, e.g. by Sastry, Hauser, Murray, Li, Lafferriere and Sussmann. The purpose of this note is to present a new general procedure for constructing the control functions for systems without drift. Using the theorems in our paper [16], Lie brackets of vector fields and Lie algebraic properties, we can explicitly construct a sequence of control functions whose corresponding solutions converge uniformly to a desired path. ... | |||||||||||||||
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