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Reduction of placement problems using Minkowski decomposition

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2 Author(s)
Dorst, L. ; Informatics Inst., Univ. of Amsterdam, Netherlands ; Ahmed, N.

The problem of finding collision-free placements for an object amid obstacles has two well-known solutions: the task space approach and the configuration space approach. In this correspondence, we study the mathematical structure of the placement problem, and show that Minkowski decomposition of the object produces a hierarchy of intermediate reformulations. This provides the mathematical foundation for common approximate solution methods already used in applications. In particular, it provides a recipe for discretizing rotations consistently. The methods discussed are particularly effective for simple shapes.

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Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on  (Volume:33 ,  Issue: 1 )