Robust Ballistic Catching: A Hybrid System Stabilization Problem

Abstract

This paper addresses a remaining gap between today's academic catching robots and their future in industrial applications: reliable task execution. A novel parameterization is derived to reduce the three-dimensional (3-D) catching problem to 1-D on the ballistic flight path. Vice versa, an efficient dynamical system formulation allows reconstruction of solutions from 1-D to 3-D. Hence, the body of the work in hybrid dynamical systems theory, in particular on the 1-D bouncing ball problem, becomes available for robotic catching. Uniform Zeno asymptotic stability from bouncing ball literature is adapted, as an example, and extended to fit the catching problem. A quantitative stability measure and the importance of the initial relative state between the object and end-effector are discussed. As a result, constrained dynamic optimization maximizes convergence speed while satisfying all kinematic and dynamic limits. Thus, for the first time, a quantitative success-oriented comparison of catching motions becomes available. The feasible and optimal solution is then validated on two symmetric robots autonomously playing throw and catch.