Passivity-Based Control for a Rolling-Balancing System: The Nonprehensile Disk-on-Disk

In this brief, we propose a passivity-based control design for a rolling-balancing system called the disk-on-disk (DoD). The stabilization of the desired equilibrium is obtained via energy shaping and damping injection. The DoD is an underactuated mechanical system composed of two disks arranged one on top of the other. The top disk, which we call the object, is free to roll without slipping on the lower disk, which we call the hand. The hand is actuated by a controlled torque, while the object is unactuated. The control objective is to balance the object at the upright position and drive the hand to a desired angle. We design an energy shaping controller without solving the partial differential equations, which rise from the matching equation. We assess the performance of the controller by both simulations and experiment results, which also verify the practical applicability of the design approach.