Ball dribbling with an underactuated continuous-time control phase

Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motions of the ball. This task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. The ball can be only controlled during ball-manipulator contact and moves freely otherwise. We propose a manipulator equipped with a spring that gets compressed when the ball bounces against it. Hence, we can have continuous-time control over this underactuated Ball-Spring-Manipulator system until the spring releases its accumulated energy back to the ball. This paper illustrates a systematic way of planning such a modified dribbling motion, computing an analytical transverse linearization and achieving orbital stabilization.