Geodesic
Quaternion model of programmed control over motion of a Chaplygin ball
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 3, pp. 408-421
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This paper deals with the problem of program control of the motion of a dynamically asymmetric balanced ball on the plane using three flywheel motors, provided that the ball rolls without slipping. The center of mass of the mechanical system coincides with the geometric center of the ball. Control laws are found to ensure the motion of the ball along the basic trajectories (line and circle), as well as along an arbitrarily given piecewise smooth trajectory on the plane. In this paper, we propose a quaternion model of ball motion. The model does not require using the traditional trigonometric functions. Kinematic equations are written in the form of linear differential equations eliminating the disadvantages associated with the use of Euler angles. The solution of the problem is carried out using the quaternion function of time, which is determined by the type of trajectory and the law of motion of the point of contact of the ball with the plane. An example of ball motion control is given and a visualization of the ball–flywheel system motion in a computer algebra package is presented.
Mots-clés : quaternions
Keywords: control, nonholonomic connection, geometric dynamics, smooth movement, spherical robot. 
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     title = {Quaternion model of programmed control over motion of a {Chaplygin} ball},
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E. A. Mityushov; N. E. Misyura; S. A. Berestova. Quaternion model of programmed control over motion of a Chaplygin ball. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 29 (2019) no. 3, pp. 408-421. http://geodesic.mathdoc.fr/item/VUU_2019_29_3_a9/

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