Permissible control of general constrained mechanical systems

Abstract

This paper develops a unified approach for modeling and controlling mechanical systems that are constrained with general holonomic and nonholonomic constraints. The approach conceptually distinguishes and separates constraints that are imposed on the mechanical system for developing its physical structure between constraints that may be used for control purposes. This gives way to a general class of nonlinear control systems for constrained mechanical systems in which the control inputs are viewed as the permissible control forces. In light of this view, a new and simple technique for designing nonlinear state feedback controllers for constrained mechanical systems is presented. The general applicability of the approach is demonstrated by considering the nonlinear control of an underactuated system.