Motion planning by the homotopy continuation method for control-affine systems: Sublinear growth conditions

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. A crucial step in the validation process is to establish a certain sublinear growth condition. Here we derive a set of general conditions which ensure that such a growth condition holds.