Direct adaptive control of a one-degree-of-freedom complementary-slackness juggler

This note deals with the problem of controlling a simple one-degree-of-freedom (1-dof) juggling robot (a system that belongs to the class of nonsmooth hybrid complementary-slackness dynamical systems), when the physical parameters such as the object mass and the restitution coefficient are not exactly known. The proposed adaptive controller is based on so-called dead-beat viable controllers previously studied, in which the sequence of desired "robot" pre-impact velocities is suitably modified. Before introducing the adaptive scheme, it is shown that a more general criterion about controllability of complementary-slackness juggling systems applies to the 1-dof juggler.