Closed-loop control of the motion of a sphere rolling on a moving horizontal plane
type: Item
instance of: scholarly article
title: Closed-loop control of the motion of a sphere rolling on a moving horizontal plane
zbMATH Open document ID: 0906.70021
DOI: 10.1023/A:1022663331512
author: Bernhard Rupp
published in: Journal of Optimization Theory and Applications
publication date: 1998-04-15T00:00:00Z
review text: The motion of a sphere rolling on a plane without slipping is a typical example of a mechanical system with nonholonomic constraints. It can be modeled on the tangent bundle of the state space \(\mathbb{R}^2\times\text{SO}(3)\) corresponding to the position of the point of contact relative to some fixed origin on the plane and to the orientation of the sphere. Control problems associated to this system have been studied, for example, in a paper of \textit{V. Jurdjevic} [|Arch. Ration. Mech. Anal. 124, 305-328 (1993; Zbl 0809.70005)]. There the motion of the sphere was controlled through the motion of the plane, and the objective was to minimize a certain integral cost functional. In the paper at hand the authors study a prolongation of that control system: the motion of the sphere is controlled through the acceleration of the motion of the plane. And the objectives are different, too. The present authors consider a global tracking problem. The goal is to find a closed loop control law driving the system from an arbitrary initial configuration into a prescribed neighborhood of a particular type of equilibrium: the point of contact is the origin, the plane at rest, and the sphere is only spinning around the vertical axis. Such a control law is constructed as a full-information feedback law (all states and velocities available), and its performance is illustrated by two examples.
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 70F25
zbMATH DE Number: 1069791
zbMATH Keywords: tangent bundle of state space
zbMATH Keywords: integral cost functional
zbMATH Keywords: acceleration of plane
zbMATH Keywords: global tracking
zbMATH Keywords: full-information feedback law
reviewed by: Dirk Mittenhuber
MaRDI profile type: Publication
cites work: Q5657709
cites work: Nonlinear control systems.
cites work: Q3996565
cites work: Q3953228
cites work: Q4296187
cites work: Computation of feasible control trajectories for the navigation of a ship around an obstacle in the presence of a sea current
cites work: Feasible command strategies for the control of motion of a simple mobile robot
full work available at URL: a:1022663331512
OpenAlex ID: W88196118
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description: scientific article; zbMATH DE number 1069791