Controlled Lagrangians and the stabilization of Euler-Poincare mechanical systems

In this paper we develop a constructive approach to the determination of st abilizing control laws for a class of Lagrangian mechanical systems with sy mmetry - systems whose underlying dynamics are governed by the Euler-Poinca re equations. This work extends our previous work on the stabilization of m echanical control systems using the method of controlled Lagrangians. 7:he guiding principle behind our methodology is to develop a class of stabilizi ng feedback control laws which yield closed-loop dynamics that remain in La grangian form. Using the methodology for Euler-Poincare systems, we analyse stabilization of a satellite and an underwater vehicle controlled with mom entum wheels. Copyright (C) 2001 John Wiley & Sons, Ltd.