Closed-Loop Control of the Motion of a Sphere Rolling on a Moving Horizontal Plane

Y. Yavin, G. W. Ehlers and C. Frangos
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Y. Yavin: University of Pretoria
G. W. Ehlers: University of Pretoria
C. Frangos: University of Pretoria

Journal of Optimization Theory and Applications, 1997, vol. 92, issue 2, No 9, 377-391

Abstract: Abstract A uniform sphere is rolling without slipping on a horizontal plane. The motion of the sphere is controlled via the control of the acceleration of the plane. At the time t=0, the sphere and the plane are stationary and the center of the sphere is located at a point A in the plane. Given a time interval [0, t f], the problem dealt with here is: Find a closed-loop strategy for the acceleration of the moving plane such that, at the time t=t f, the plane and the sphere will be nearly at rest and the center of the sphere will be in a given neighborhood of the origin. By introducing the concept of path controllability, a closed-loop strategy for the solution of the above-mentioned problem is proposed and its efficiency is demonstrated by solving numerically some examples.

Keywords: Rolling sphere; nonholonomic constraints; path controllability; closed-loop control (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022663331512

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