Control of the motion of nonholonomic systems

Abstract

This dissertation deals with the control, guidance and stabilisation of nonlinear, non¬holonomic systems. It is shown that the kinematics of the system can be separated from the dynamics of the system by using successively two inverse dynamics type of transformations. This leads to a linear decoupled kinematical system, control strategies can then be developed that directly control the motion of the system. The method is applied to a system which is composed of a disk rolling on a plane, a controlled slender rod that is pivoted through its center of mass about the disk's center and two overhead rotors with their axes fixed in the upper part of the rod. Control strategies are designed under which the disk's inclination is stabilised about its vertical position and the disk's motion is able to asymptotically track any given smooth ground trajectory. The control strategy is shown to be stable in the presence parametric uncertainties. It was furthermore shown that the system is path controllable. Finally an extended inverse dynamics control law is introduced which deals directly with underactuated systems. An example of an articulated crane is solved using extended inverse dynamics control. Feasible control is used to ensure that the internal dynamics of the system remains bounded and that the crane reach its desired final position in a given time interval [O, tƒ].