Solving geometric constraints by iterative projections and backprojections

Most geometric constraint problems can be reduced to give coordinates to a set of points from a subset of their pairwise distances. By exploiting this fact, this paper presents an algorithm that solves geometric constraint systems by iteratively reducing and expanding the dimension of the problem. I...

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Bibliographic Details
Published in:2004 IEEE International Conference on Robotics and Automation Vol. 2; pp. 1789 - 1794 Vol.2
Main Author: Thomas, F.
Format: Conference Proceeding
Language:English
Published: Piscataway NJ IEEE 2004
Subjects:
Applied sciences
Assembly systems
Computer science; control theory; systems
Control theory. Systems
Couplings
Equations
Exact sciences and technology
Iterative algorithms
Joining processes
Parallel robots
Path planning
Robot kinematics
Robotic assembly
Symmetric matrices
Branching
Set point
Constraint satisfaction
Iterative method
Search algorithm
ISBN:9780780382329, 0780382323
ISSN:1050-4729
Online Access:Get full text
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Summary:Most geometric constraint problems can be reduced to give coordinates to a set of points from a subset of their pairwise distances. By exploiting this fact, this paper presents an algorithm that solves geometric constraint systems by iteratively reducing and expanding the dimension of the problem. In general, these projection/backprojection iterations permit tightening the ranges for the possible solutions but, if at a given point no progress is made, the algorithm bisects the search space and proceeds recursively for both subproblems. This branch-and-prune strategy is shown to converge to all solutions.
ISBN:9780780382329
0780382323
ISSN:1050-4729
DOI:10.1109/ROBOT.2004.1308083