On the control of complementary-slackness juggling mechanical systems

This paper studies the feedback control of a class of complementary-slackne ss hybrid mechanical systems. Roughly, the systems we study are composed of an uncontrollable part (the "object") and a controlled one (the "robot"),l inked by a unilateral constraint and an impact rule. A systematic and gener al control design method for this class of systems is proposed. The approac h is a nontrivial extension of the one degree-of-freedom (DOF) juggler cont rol design. In addition to the robot control, it is also useful to study so me intermediate controllability properties of the object's impact Poincare mapping, which generally takes the form of a nonlinear discrete-time system . The force input mainly consists of a family of dead-beat feedback control laws, introduced via a recursive procedure, and exploiting the underlying discrete-time structure of the system. The main goal of this paper is to hi ghlight the role of various physical and control properties characteristic of the system on its stabilizability properties and to propose solutions in certain cases.