Motion Planning for a Spherical Mobile Robot: Revisiting the Classical Ball-Plate Problem

[+] Author and Article Information
Ranjan Mukherjee

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226e-mail: mukherji@egr.msu.edu

Mark A. Minor

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84112

Jay T. Pukrushpan

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109

J. Dyn. Sys., Meas., Control 124(4), 502-511 (Dec 16, 2002) (10 pages) doi:10.1115/1.1513177 History: Received July 01, 2000; Revised March 01, 2002; Online December 16, 2002
Copyright © 2002 by ASME
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Initial and final configurations of sphere
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Motion of the sphere under control actions (A) and (B)
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Motion of the sphere under (A)-(B)-(A) sequence of control actions
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Plot of Δβ versus Δα for different values of r, shown for both counter-clockwise and clockwise paths
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Basis for complete reconfiguration of the sphere
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(a) A spherical triangle, (b) Image of the spherical triangle on the x-y plane
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Open loop reconfiguration using spherical triangles
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Reconfiguration of the sphere using the geometric motion planner
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A spherical triangle maneuver for reconfiguration



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