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Computing the lowest equilibrium pose of a cable-suspended rigid body

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Collard, Jean-François [UCL] Cardou, Philippe [Université Laval]

We solve the problem of finding the lowest stable-equilibrium pose of a rigid body subjected to gravity and suspended in space by an arbitrary number of cables. Besides representing a contribution to fundamental rigid-body mechanics, this solution finds application in two areas of robotics research: underconstrained cable-driven parallel robots and cooperative towing. The proposed approach consists in globally minimizing the rigid-body potential energy. This is done by applying a branch-and-bound algorithm over the group of rotations, which is partitioned into boxes in the space of Euler-Rodrigues parameters. The lower bound on the objective is obtained through a semidefinite relaxation of the optimization problem, whereas the upper bound is obtained by solving the same problem for a fixed orientation. The resulting algorithm is applied to several examples drawn from the literature. The reported Matlab implementation converges to the lowest stable equilibrium pose generally in a few seconds for cable-robot applications. Interestingly, the proposed method is only mildly sensitive to the number of suspending cables, which is shown by solving an example with 1000 cables in two hours.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2013
Language Anglais
Journal information "Optimization and Engineering : international multidisciplinary journal to promote optimization theory and applications in engineering sciences" - Vol. 14, no. 3, p. 457-476 (Sept. 2013)
Peer reviewed yes
Publisher Springer New York LLC ((United States) New York)
issn 1389-4420
e-issn 1573-2924
Publication status Publié
Affiliations Université Laval - Laboratoire de Robotique
UCL - SST/IMMC/MEED - Mechatronic, Electrical Energy, and Dynamics Systems
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Bibliographic reference Collard, Jean-François ; Cardou, Philippe. Computing the lowest equilibrium pose of a cable-suspended rigid body. In: Optimization and Engineering : international multidisciplinary journal to promote optimization theory and applications in engineering sciences, Vol. 14, no. 3, p. 457-476 (Sept. 2013)
Permanent URL http://hdl.handle.net/2078.1/108311