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.

On-line frequency adaptation and movement imitation for rhythmic robotic tasks

“…Both joints have the same motion pattern (sinusoidal) with a phase difference between them at φ l = π/2. Therefore, the device was travelling in a circle, which satisfies the required kinematic criteria for accelerating the gyroscopic device (Petrič et al 2010).…”

“…In this case the precession speed is proportional to the spin speed ω. According to Petrič et al (2010) the ratio between these speeds is 32.…”

“…Such tasks include swinging of different pendulums (Spong 1995;Furuta 2003), playing with different toys, i.e. the yo-yo (Hashimoto and Noritsugu 1996;Jin and Zacksenhouse 2003;Žlajpah 2006;Jin et al 2009) or a gyroscopic device called the Powerball (Heyda 2002;Gams et al 2007;Cafuta and Curk 2008;Petrič et al 2010), juggling (Schaal and Atkeson 1993;Buehler et al 1994;Williamson 1999;Ronsse et al 2007) and locomotion (Ilg et al 1999;Ijspeert 2008;Morimoto et al 2008). Rhythmic tasks are also handshaking (Kasuga and Hashimoto 2005;Sato et al 2007;Jindai and Watanabe 2007) and even handwriting (Hollerbach 1981;Gangadhar et al 2007).…”

Performing Periodic Tasks: On-Line Learning, Adaptation and Synchronization with External Signals

“…Such robotic tasks include swinging of different pendulums (Furuta, 2003;Spong, 1995), playing with different toys, i.e. the yo-yo (Hashimoto & Noritsugu, 1996;Jin et al, 2009;Jin & Zacksenhouse, 2003;Žlajpah, 2006) or a gyroscopic device called the Powerball (Cafuta & Curk, 2008;Gams et al, 2007;Heyda, 2002;Petrič et al, 2010), juggling (Buehler et al, 1994;Ronsse et al, 2007;Schaal & Atkeson, 1993;Williamson, 1999) and locomotion (Ijspeert, 2008b;Ilg et al, 1999;Morimoto et al, 2008). Rhythmic tasks are also handshaking (Jindai & Watanabe, 2007;Kasuga & Hashimoto, 2005;Sato et al, 2007) and even handwriting (Gangadhar et al, 2007;Hollerbach, 1981).…”

Compliant movement primitives in a bimanual setting

“…However, this requires the correct dynamic model of not only the robot, but also of each task and task variation. Models of the task dynamics are often not available or hard to obtain [6].…”