Motion planning by the homotopy continuation method for control-affine systems

The subject of this paper is the homotopy continuation method (HCM) for solving basic motion planning problems. The validity of the HCM has been demonstrated for driftless control-affine systems belonging to a special class. In this paper, we study the validity of the HCM for control-affine systems with drift. The two crucial steps in the validation process are (1) to minimize the set of singular controls, and (2) to establish a certain sublinear growth condition. Here we give general conditions which ensure that the set of singular controls is empty, and that the sublinear growth condition holds. The results are illustrated by a simple example.