Robotic Contact Juggling

In this article, we define "robotic contact juggling" to be the purposeful control of the motion of a 3-D smooth object as it rolls freely on a motion-controlled robot manipulator, or "hand." While specific examples of robotic contact juggling have been studied before, in this article, we provide the first general formulation and solution method for the case of an arbitrary smooth object in a single-point rolling contact on an arbitrary smooth hand. Our formulation splits the problem into four subproblems: deriving the second-order rolling kinematics; deriving the 3-D rolling dynamics; planning rolling motions that satisfy the rolling dynamics and achieve the desired goal; and stabilization of planned rolling trajectories. The theoretical results are demonstrated in 3-D simulations and 2-D experiments using feedback from a high-speed vision system.