Generalized Canonical Transformations and Passivity-based Control for Nonholonomic Hamiltonian Systems with Affine Constraints

Abstract

This paper is devoted to control of nonholonomic Hamiltonian systems with affine constraints (NHSAC). We first sum up some concepts on nonholonomic affine constraints and the HNSAC. Next, we derive two versions of generalized canonical transformations for the NHSAC; the one transforms the NHSAC into a simpler system that has the structure of the extended chained form, the other changes the Hamiltonian of the NHSAC in order to make the NHSAC satisfy passivity. We then design a control algorithm based on passivity for a physical example, a coin on a rotating table. Finally, some simulations are carried out to verify the proposed method.