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An Improved Branch-and-Bound Algorithm for Minimizing the Potential Energy of a Cable-Suspended Rigid Body

[+] Author Affiliations
François Guay, Philippe Cardou

Université Laval, Québec, QC, Canada

Jean-François Collard, Marc Gouttefarde

Université Montpellier, Montpellier, France

Paper No. DETC2011-48169, pp. 1291-1300; 10 pages
doi:10.1115/DETC2011-48169
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME

abstract

We compute the lowest stable-equilibrium pose of a rigid body suspended in space by an arbitrary number of cables, being given the cable lengths and the attachment-point positions on the fixed frame and on the rigid body. This fundamental problem of mechanics if of interest in the fields of underconstrained cable-driven parallel robots and cooperative towing. The approach of the present work is very similar to one that is reported in a previous paper by the authors. Indeed, the problem is formulated as a potential energy minimization, and is solved using a branch-and-bound algorithm. Hence, we report mainly on improvements in the branching and bounding parts of the algorithm. In short, the idea is to search for the optimum rigid-body pose by partitioning only the rotation subgroup of rigid-body displacements. This is done here by dividing the four-dimensional space of Euler-Rodrigues parameters with polyhedral cones instead of boxes, the latter being normally used for this type of problem. The advantage is that cones conform better to the four-dimensional unit-sphere of Euler-Rodrigues parameters. The convex relaxations of the original optimization problem are then adapted to the newly defined conical subsets. Besides resulting in a more elegant algorithm, this new conical branch-and-bound method leads to a higher efficiency in the case of reported examples.

Copyright © 2011 by ASME

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