  We define "robotic contact juggling" to be the purposeful control of the
motion of a three-dimensional 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 paper we provide the
first general formulation and solution method for the case of an arbitrary
smooth object in single-point rolling contact on an arbitrary smooth hand. Our
formulation splits the problem into four subproblems: (1) deriving the
second-order rolling kinematics; (2) deriving the three-dimensional rolling
dynamics; (3) planning rolling motions that satisfy the rolling dynamics; and
(4) feedback stabilization of planned rolling trajectories. The theoretical
results are demonstrated in simulation and experiment using feedback from a
high-speed vision system.
