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

We consider the theoretical aspects of the control problem for robots with rigid links which consist of some rigid joints and some non-negligible elastic joints. We start from the reduced model of robots with all elastic joints introduced by Spong, which is linearizable by static feedback (as for the rigid robot model). For the mixed rigid/elastic joints, we give the 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 dynamic state feedback always guarantees the same result. This implies that, for the mixed rigid/elastic joint case, the role of dynamic feedback is essential. The explicit forms of the needed nonlinear controllers are provided in terms of the dynamic model elements