New developments in the dynamics of constrained systems and applications to tracking control

Abstract

This paper deals with the development of the explicit equations of motion for nonlinear mechanical and structural systems, which are holonomically and/or nonholonomically constrained. Based on these new results from analytical dynamics, the paper goes on to develop a class of tracking controllers for controlling general, nonlinear, mechanical systems. Unlike most control methods that perform some kind of linearization and/or cancellation, the methodology developed here obtains a class of control forces that 'exactly' maintain the system along a certain trajectory, which in general, may be described by a set of differential equations in the observations/measurements. While having the ability to control general nonlinear mechanical systems so that the trajectory requirements as 'exactly' satisfied, the method involves very little computation compared to standard approaches. This therefore makes the approach useful for the on-line real-time control of highly nonlinear systems.