Overcoming the Dissipation Condition in Passivity-Based Control for a Class of Mechanical Systems

A well-known problem in the application of the Interconnection and Damping Assignment technique for the stabilization of underactuated mechanical systems is dissipation in unactuated coordinates, since it may impede the definiteness requirements for the closed-loop system. Recently, the expansion of the closed-loop Hamiltonian function by a cross term between coordinates and momenta has been explored showing promising results. However, the large number of free parameters is an issue for the tuning of the closed-loop system, and the solution of the matching partial differential equations (PDEs) remains a difficult task. In this work, we aim at giving the closed-loop augmented Hamiltonian more structure in order to simplify the controller parametrization. The result is desired behavior at the equilibrium avoiding the solution of PDEs. Simulations and experiments demonstrate the applicability of the method.      «

A well-known problem in the application of the Interconnection and Damping Assignment technique for the stabilization of underactuated mechanical systems is dissipation in unactuated coordinates, since it may impede the definiteness requirements for the closed-loop system. Recently, the expansion of the closed-loop Hamiltonian function by a cross term between coordinates and momenta has been explored showing promising results. However, the large number of free parameters is an issue for the tuni...     »