A Lie algebraic method of motion planning for driftless nonholonomic systems

Abstract

In this paper a Lie algebraic method is proposed to steer driftless nonholonomic systems. It uses the special instance of the generalized Campbell-Baker-Hausdorff-Dynkin formula for driftless nonholonomic systems to establish a mapping between controls and a resulting direction of motion. Then, locally, a motion planning task is to find the inverse of this mapping. Usually, it can be supported by analytic computations.