Direct adaptive control design for one-degree-of-freedom complementary-slackness jugglers

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 some 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. The dynamics of a simple 1-dof hopper is shown to be controllable by the proposed control algorithm. Numerical simulations support the theoretical results. (C) 2001 Elsevier Science Ltd. All rights reserved.