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

François Guay 1 Jean-François Collard 2 Marc Gouttefarde 2, * Philippe Cardou 1
* Corresponding author
2 DEXTER - Conception et commande de robots pour la manipulation
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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 conformbetter 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.
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Contributor : Marc Gouttefarde-Tanich <>
Submitted on : Monday, October 1, 2012 - 2:18:46 PM
Last modification on : Monday, July 20, 2020 - 1:06:04 PM


  • HAL Id : lirmm-00737245, version 1



François Guay, Jean-François Collard, Marc Gouttefarde, Philippe Cardou. An Improved Branch-and-Bound Algorithm for Minimizing the Potential Energy of a Cable-Suspended Rigid Body. ASME'2011: International Design Engineering Technical Conferences & Annual Mechanisms and Robotics Conference, United States. pp.01-10. ⟨lirmm-00737245⟩



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