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.

One of the key challenges in dynamic manipulation is to establish continuous contact between a moving object and a manipulator. Direct robotic catching is a benchmark in this context, especially without grasping devices. In this paper, we explain why it is unrewarding to aim for an ideal initial dynamic contact if only imprecise knowledge of the object states is available. Robust initial contacts are proposed such that a successful quasi-direct catch can be predicted. The proposed robustness originates in a negative relative acceleration between object and catching end-effector. Sets, for which an upper negative relative acceleration bound holds, are evaluated throughout an exemplary catching motion. Reachable set computations allow to express and visualize these sets of successful object states at any point in time before contact. The paper closes with a robot-robot experiment that shows successful quasi-direct catches without feedback on the object states for a robotic throw.