Control of nonholonomic robotic load

Powerball^reg is a commercial name for gyroscopic device that is marketed as a wrist exerciser. The device has rotor with two unactuated degrees of freedom and can be actuated with suitable rotational motion of human or robot wrist axis [1]. After substantial initial rotor´s spin, the properly applied torque and motion about two wrist axis lead to spin-up of the rotor. Finding this torque intuitively is easy job for most peoples, but not so easy for technical consideration for example in robotics. In the paper, a modeling of different modes of the device is presented first. A dynamic model with nonholonomic rolling connection which appear in normal operational mode is discussed. With the rotor and housing connection the additional friction effect is observed. When the nutation reaction torque is to low, only dissipation of energy is observed and rotor stops. But when the reaction torque causes normal forces on a connection in a degree that the friction is high enough, the rotor shaft begins to roll. The connection with the housing takes place in a gap so two connecting pairs are possible. One is up-down for left precession and another is down-up for opposite precession rotation. Developed models are used as a basis for control structure in the second part when the experiments are performed with the robot. The control strategy is oriented towards underactuated system, active and passive robots degrees of freedom.