Approximate steering of a plate-ball system under bounded model perturbation using ensemble control

In this paper we revisit the classical plate-ball system and prove this system remains controllable under model perturbation that scales the ball radius by an unknown but bounded constant. We present an algorithm for approximate steering and validate the algorithm with hardware experiments. To perform these experiments, we introduce a new version of the plate-ball system based on magnetic actuation. This system is easy to implement and, with our steering algorithm, enables simultaneous manipulation of multiple balls with different radii.