No abstract

This letter considers an augmented kinematic formulation for nonprehensile manipulation through intermittent contacts as occurring in catching, batting, or juggling. In such scenarios, the contact point with an end-effector is variable, which we propose to model with additional virtual joints at the end of the kinematic chain. While not in contact with the manipulated part, these new joints are unconstrained in terms of velocity and acceleration. An optimization based and, thus, tuning-free comparison of differential inverse kinematic approaches is carried out, given path or trajectory of the manipulation task is known. Simulations and an experiment show that the proposed augmentation enables dynamically feasible acceleration variations at high velocities on and close to a given path.

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.