A branch-and-prune algorithm for solving systems of distance constraints

Given a set of affine varieties in R/sup 3/, i.e. planes, lines, and points, the problem tackled in this paper is that of finding all possible configurations for these varieties that satisfy a set of pairwise euclidean distances between them. Many problems in robotics - such as the forward kinematic...

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Vydáno v:2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422) Ročník 1; s. 342 - 348 vol.1
Hlavní autoři: Porta, J.M., Thomas, F., Ros, L., Torras, C.
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 2003
Témata:
Assembly systems
Computer aided manufacturing
Equations
Informatics
Intelligent systems
Kinematics
Manipulators
Parallel robots
Path planning
Robotic assembly
ISBN:0780377362, 9780780377363
ISSN:1050-4729
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Shrnutí:Given a set of affine varieties in R/sup 3/, i.e. planes, lines, and points, the problem tackled in this paper is that of finding all possible configurations for these varieties that satisfy a set of pairwise euclidean distances between them. Many problems in robotics - such as the forward kinematics of patroller manipulators or the contact formation problem between polyhedral models - can be formulated in this way. We propose herein a strategy that consists in finding some distances, that are unknown a priori, and whose derivation permits solving the problem rather trivially. Finding these distances relies on a branch-and-prune technique that iteratively eliminates from the space of distances entire regions which cannot contain any solution. The elimination is accomplished by applying redundant necessary conditions derived from the theory of Cayley-Menger determinants. The experimental results obtained qualify this approach as a promising one.
ISBN:0780377362
9780780377363
ISSN:1050-4729
DOI:10.1109/ROBOT.2003.1241619