Control of a class of underactuated mechanical systems obviating matching conditions

Abstract

The presently established techniques for control of underactuated mechanical systems are dependent on solving partial differential equations (PDEs) arising out of matching conditions. In this brief a novel controller design methodology for (asymptotic) stabilization of nonlinear systems is proposed that obviates the need of solving PDEs to obtain the control laws. The geometry based energy shaping methodology forms the fully constructive procedure for control of underactuated mechanical systems. The control methodology is based on manipulating symmetric structure of the system such that the power flow is established between the controller and unactuated part of the system. The modifications leads to identification of the two new passive outputs which are further utilized for kinetic and potential shaping and the desired controller is obtained using passivity based techniques. The theory is illustrated with two benchmark examples.