A branch and prune algorithm for the computation of generalized aspects of parallel robots

Parallel robots enjoy enhanced mechanical characteristics that have to be contrasted with a more complicated design. In particular, they often have parallel singularities at some poses, and the robots may become uncontrollable, and could even be damaged, in such configurations. The computation of th...

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Published in:	Artificial intelligence Vol. 211; pp. 34 - 50
Main Authors:	Caro, S., Chablat, D., Goldsztejn, A., Ishii, D., Jermann, C.
Format:	Journal Article
Language:	English
Published:	Oxford Elsevier B.V 01.06.2014 Elsevier
Subjects:	Applied sciences Computer science; control theory; systems Control theory. Systems Electronics Engineering Sciences Exact sciences and technology Generalized aspects Modelling and identification Numerical constraints Parallel robots Robotics Singularities Numerical constraints Parallel robots Singularities Generalized aspects Branching Lower bound Singularity Parallel mechanism Reachability analysis Computational complexity Robotics Reachability Mechanical characteristic Linkage mechanism Collision avoidance Counting Workspace
ISSN:	0004-3702, 1872-7921
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Abstract	Parallel robots enjoy enhanced mechanical characteristics that have to be contrasted with a more complicated design. In particular, they often have parallel singularities at some poses, and the robots may become uncontrollable, and could even be damaged, in such configurations. The computation of the connected components in the set of nonsingular reachable configurations, called generalized aspects, is therefore a key issue in their design. This paper introduces a new method, based on numerical constraint programming, to compute a certified enclosure of the generalized aspects. Though this method does not allow counting their number rigorously, it constructs inner approximations of the nonsingular workspace that allow commanding parallel robots safely. It also provides a lower-bound on the exact number of generalized aspects. It is moreover the first general method able to handle any parallel robot in theory, though its computational complexity currently restricts its usage to robots with three degrees of freedom. Finally, the constraint programming paradigm it relies on makes it possible to consider various additional constraints (e.g., collision avoidance), making it suitable for practical considerations.
AbstractList	Parallel robots enjoy enhanced mechanical characteristics that have to be contrasted with a more complicated design. In particular, they often have parallel singularities at some poses, and the robots may become uncontrollable, and could even be damaged, in such configurations. The computation of the connected components in the set of nonsingular reachable configurations, called generalized aspects, is therefore a key issue in their design. This paper introduces a new method, based on numerical constraint programming, to compute a certified enclosure of the generalized aspects. Though this method does not allow counting their number rigorously, it constructs inner approximations of the nonsingular workspace that allow commanding parallel robots safely. It also provides a lower-bound on the exact number of generalized aspects. It is moreover the first general method able to handle any parallel robot in theory, though its computational complexity currently restricts its usage to robots with three degrees of freedom. Finally, the contraint programming paradigm it relies on makes it possible to consider various additional constraints (e.g., collision avoidance), making it suitable for practical considerations. Parallel robots enjoy enhanced mechanical characteristics that have to be contrasted with a more complicated design. In particular, they often have parallel singularities at some poses, and the robots may become uncontrollable, and could even be damaged, in such configurations. The computation of the connected components in the set of nonsingular reachable configurations, called generalized aspects, is therefore a key issue in their design. This paper introduces a new method, based on numerical constraint programming, to compute a certified enclosure of the generalized aspects. Though this method does not allow counting their number rigorously, it constructs inner approximations of the nonsingular workspace that allow commanding parallel robots safely. It also provides a lower-bound on the exact number of generalized aspects. It is moreover the first general method able to handle any parallel robot in theory, though its computational complexity currently restricts its usage to robots with three degrees of freedom. Finally, the constraint programming paradigm it relies on makes it possible to consider various additional constraints (e.g., collision avoidance), making it suitable for practical considerations.
Author	Jermann, C. Goldsztejn, A. Caro, S. Chablat, D. Ishii, D.
Author_xml	– sequence: 1 givenname: S. surname: Caro fullname: Caro, S. organization: CNRS, IRCCyN, Nantes, France – sequence: 2 givenname: D. surname: Chablat fullname: Chablat, D. organization: CNRS, IRCCyN, Nantes, France – sequence: 3 givenname: A. surname: Goldsztejn fullname: Goldsztejn, A. organization: CNRS, LINA (UMR-6241), Nantes, France – sequence: 4 givenname: D. surname: Ishii fullname: Ishii, D. organization: Tokyo Institute of Technology, Tokyo, Japan – sequence: 5 givenname: C. orcidid: 0000-0002-1383-3103 surname: Jermann fullname: Jermann, C. organization: Université de Nantes, LINA (UMR-6241), Nantes, France
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Keywords	Numerical constraints Parallel robots Singularities Generalized aspects Branching Lower bound Singularity Parallel mechanism Reachability analysis Computational complexity Robotics Reachability Mechanical characteristic Linkage mechanism Collision avoidance Counting Workspace
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Mech. Robot. doi: 10.1115/1.4007487
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Snippet	Parallel robots enjoy enhanced mechanical characteristics that have to be contrasted with a more complicated design. In particular, they often have parallel...
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SubjectTerms	Applied sciences Computer science; control theory; systems Control theory. Systems Electronics Engineering Sciences Exact sciences and technology Generalized aspects Modelling and identification Numerical constraints Parallel robots Robotics Singularities
Title	A branch and prune algorithm for the computation of generalized aspects of parallel robots
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