Energy shaping based controllers for rigid and elastic joint robots: analysis via passivity theorems

In this paper we present in a simple and unified framework, the asymptotic stability analysis for energy shaping plus damping injection based set-point controllers for rigid and elastic joint robot manipulators by involving passivity theorems. Such an analysis is made for both cases: when position and velocity measurements are available for feedback purposes, and when only position measurements are available. To this end we use a particular case of a theorem introduced by Byrnes et al. (1991) and we present an adaptation, for asymptotic stability purposes, of a passivity theorem given by Canudas de Wit et al. (1996) and Khalil (1996)