Nonholonomic motion planning: a polynomial fitting approach

Nonholonomic systems are governed by constraints of motion that are nonintegrable differential expressions. The mathematical tools commonly used for investigating such a nonholonomic system are Stroke's theorem, nonlinear control theory and Lie Algebras, and the flatness of the system. In this paper, we show that the problem of steering systems with nonholonomic constraints between any two arbitrary configurations for the two typical nonholonomic systems, a hopping robot and a car-like robot considered by Murray-Sastry (1993), can be converted into a polynomial fitting problem. Therefore, the complicated nonholonomic motion planning problem can be dealt with easily using the standard techniques available in numerical analysis and has a good physical insight. Simulation results of a typical manoeuvring, a lane-change manoeuvring for a car-like robot are presented.