Control of Underactuated Mechanical Systems Using Switching and Saturation

In this paper we present some ideas on the control of underactuated mechanical systems using switching and saturation. We focus on the swingup control problem for a class of \gymnast" robots and also for the classical cart{pole system. The design methodology is based on partial feedback linearization in a rst stage to linearize the actuated degrees of freedom followed by the control of the transfer of energy from the actuated to the unactuated degrees of freedom in a second stage. In a typical swingup control the desired equilibrium is unstable in the closed loop system as a consequence of the non-minimum phase behavior of the system. For this reason it is necessary to switch controllers at the appropriate time to a controller which renders the equilibrium stable. The successful implementation of the switching control has proved to be nontrivial, both in simulation and in experiment. We discuss both local and global design methods and present some simulation results.