Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Systems

Abstract

This paper describes the application of differential flatness techniques from nonlinear control theory to mechanical (Lagrangian) systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. For the special case of mechanical control systems, much more geometric information is present and the purpose of this paper is to explore the implications and features of that class of systems. We concentrate on several worked examples which illustrate the general theory and present a detailed catalog of known examples of differentially flat mechanical systems. Keywords: nonlinear control, mechanical systems, trajectory generation, differential flatness. 1 Introduction An emerging paradigm in nonlinear control is the use of two degree of freedom design techniques to generate nonlinear controllers for mechanical systems performing motion control tasks. The basic approach of two degree of freedo..