A Lagrangian Formulation of Nonholonomic Path Following

Abstract

We address the problem of following an unknown planar contour with a nonholonomic vehicle based on visual feedback. The control task is to keep a point of the vehicle as close as possible to the contour for a choice of norm. A camera mounted on-board the vehicle provides measurements of the contour. We formulate the problem and compute the control law in a moving reference frame modeling the evolution of the contour as seen by an observer sitting on the vehicle. The result is an on-line path planning strategy and a predictive control law which leads the vehicle to land softly on the unknown curve. Depending on the choice of the tracking criterion, the controller can exhibit non-trivial behaviors including automatic manouvering. 1 Introduction In this paper we consider the problem of tracking an unknown contour by a nonholonomic vehicle, using visual feedback. This is a fundamental problem in autonomous navigation. The contour to be followed may be the boundary of some unknown obstacle..