A Survey for Controlled Lagrangian Method

Abstract

The method of controlled Lagrangian (CL) has been developed to stabilize simple mechanical systems based on energy shaping. Since the introduction of this controller design methodology in 1997, many theoretical developments and practical applications have been reported in the literature. The theoretical developments include a series of criteria for its applicability, special shortcuts that are useful when dealing with particular classes of systems, and the incorporation of additional features to handle control scenarios other than just stabilization. On the application side, the method has been applied to a wide variety of practical mechanical control systems, especially under actuated systems. The purpose of this survey is to review the fundamental idea and theory of this controller design methodology, research developments achieved by different research groups, as well as to discuss the current open problems and future research directions.