On the Hamiltonian Approach to the Collocated Virtual Holonomic Constraints in the Underactuated Mechanical Systems

Abstract

In this paper, the collocated virtual holonomic constraints for the underactuated mechanical system are represented in a special canonical form using its Hamiltonian description. This form is used to provide an alternative, backstepping based, algorithm how to impose these constraints. Its robustness is illustrated by simulated swinging up the mechanical four link chain with precisely unknown masses of its links.