Decoupling and feedback linearization of robots with mixed rigid/elastic joints

Abstract

We consider some theoretical aspects of the control problem for rigid link robots having some joints rigid and some with non-negligible elasticity. We start from the reduced model of robots with all joints elastic introduced by Spong, which is linearizable by static feedback. For the mixed rigid/elastic joint case, we give structural necessary and sufficient conditions for input–output decoupling and full-state linearization via static state feedback. These turn out to be very restrictive. However, when a robot fails to satisfy these conditions, we show that a physically motivated dynamic state feedback will always guarantee the same result. The analysis is performed without resorting to the state-space equation format. As a result, the explicit form of the exact linearizing and input–output decoupling controllers is provided directly in terms of the robot dynamic model terms. © 1998 John Wiley & Sons, Ltd.