| Two New Methods for Motion Planning for Controllable Systems without Drift (1991) | |||||||||||||||||
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| Introduction The purpose of this note is to describe two new general procedures for constructing (open-loop) control functions for systems without drift, i.e. for solving the Motion Planning Problem (MPP) for nonholonomic systems without drift. 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 and Li. In this note we outline some results, described in more detail in [9], [10], [16], [17], [18], that provide a new approach to the problem. Consider a control system \Sigma : x = m X i=1 u i f i (x); (1) where f 1 ; f 2 ; : : : ; f m are smooth vector fields in IR n . An admissible control for System (1) is a Lebesgue integrable function t | |||||||||||||||||
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