Modelling of the robotic Powerball®: a nonholonomic, underactuated and variable structure-type system

Abstract

The Powerball® is the commercial name for a gyroscopic device that is marketed as a wrist exerciser. The device has a rotor with two underactuated degrees of freedom, which can be actuated by the appropriate motion of human or robot wrist axes. After the initial spin, applying the appropriate motion and torques to the housing leads to a spin-up of the rotor. Finding these torques intuitively is an easy task for human operators, but a complex task for a technical consideration, for example, in robotics. This article's main contribution is a novel dynamic model that considers friction effects. The presented model includes all three working principles of the device: free rotor mode and both modes of rotor rolling in the housing. The work introduces models with one and two degrees of freedom actuation, both of which are suitable for laboratory control experiments. An estimation of the friction is discussed, and both the simulation and the experimental results are presented to evaluate the models.