On the feedback control of a simple juggling robot

Abstract

In this note we focus on the design of controllers for one degree-of-freedom juggling robots. These systems belong to a class of convex conical systems, i.e. dynamical systems of the form x = Ax+Bu, Cx ≥ 0. The derived family of force control inputs permits the stabilization of the object at arbitrary periodic trajectories. The robustness of the proposed schemes with respect to various types of disturbances is also analyzed. Contrarily to previous studies on the subject, we do not assume that the mass of the robot is infinitely large compared to that of the object. The analyzed open-loop system is thus 4-dimension al, i.e. x ∊ R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> Hence the controller really represents the force input to be applied to the robot. Numerical simulations illustrate the theoretical investigations.