Kinematic Trajectory Planning for Dynamically Unconstrained Nonprehensile Joints

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.