A Non-Holonomic Dynamic Interpolation Problem

Abstract

The tracking problem in which certain dynamic variables of a control system are forced to follow a desired path, is a major problem in theory and practice. Another way of attaching the problem is to specify the trajectory in terms of a discrete, ordered set of points through which the dynamic variables must pass. It is natural to impose smoothness constraints on the trajectories. We call this the dynamic interpolation problem. A number of authors have considered the problem, in conjunction with applications to flight paths of aircraft, [6], [7], [8], and path planning for robots [3], [15]. The main emphasis in this work has been to satisfy the many constraints on the state variables to be met in these applications, whilst minimizing natural costs associated with the control. However, the underlying geometry of the resulting trajectories is obscured and not dealt with specifically.