A path following problem for a class of non-holonomic control systems with noise

This paper deals with a path following problem for a system affected by noise and proposes a dynamic inversion-based controller that makes use of the error between the real position and a suitable path location. An estimate of such error is given in terms of the noise bounds, showing the practical stability of the closed loop system. The results presented in this article apply to a subclass of Chaplygin control systems which includes several common mechanical systems. As an example the developed strategy has been applied to maneuver a kinematic model of a system moving in a 3-dimensional space in such a way that a point located at a positive distance from its center of geometry is driven towards a given path.