Details

Steady uncontrolled robot motion can be the basiс dynamics of control modes [1–4]. In [3], the families of steady motion of a robot-gyrostat consisting of a disk with a rotating flywheel were found and conditions for their stability were obtained. This Demonstration is based on the program published in [4]. The numerical parameters of the program's example correspond to a one-wheeled robot [1, 2] developed at the Institute of Mechanics of the Lomonosov Moscow State University. The animation of the robot in the form of a disk without a flywheel can be obtained as a particular case from the program [4].

Snapshot 1: an arbitrary motion of the disk with flywheel

Snapshot 2: the steady motion in which the disk spins about a vertical diameter and the flywheel does not rotate relative to the disk

Snapshot 3: the steady motion in which the contact point of the disk with the plane moves in a circle

Snapshot 4: the steady motion in which the contact point of the disk with the plane moves in a straight line.

Snapshot 5: the steady motion in which the nutation angle is constant; the disk rotates around the fixed vertical axis at a permanent velocity

Snapshot 6: the physically nonrealizable motion of a disk with flywheel

[1] Y. G. Martynenko, A. V. Lenskii, A. I. Kobrin, "Decomposition of the Problem of Controlling a Mobile One-Wheel Robot with an Unperturbed Gyrostabilized Platform," Doklady Physics, 47(10), 2002 pp. 772–774.

[2] Y. G. Martynenko, "Motion Control of Mobile Wheeled Robots," Journal of Mathematical Science, 147(2), 2007 pp. 6569–6606.

[3] Y. G. Martynenko, "Stability of Uncontrolled Motions of the One-Wheeled Mobile Robot with Flywheel Stabilization System," in Proceedings of the International Conference on Problems of Mechanics of Modern Machines, Vol. 1, Ulan-Ude, Russia, 2000 pp. 96–101 (in Russian).

[4] O. M. Kapustina and Y. G. Martynenko, "Using Animation TechnologyMathematica6 in the Theoretical Mechanics Tasks," in Proceedings of the 3rd International Scientific-Practical Conference on Modern Information Technology and IT Education, Moscow, 2008 pp. 429–436 (in Russian).