Reference: Bhansali, S. & Kramer, G. A. Planning from First Principles for Geometric Constraint Satisfaction. Seattle, WA, 1994.
Abstract: An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by symbolically reasoning about geometry using a degrees of freedom analysis. The approach employs a set of specialized routines called plan fragments that specify how to change the configuration of a set of bodies to satisfy a new constraint while preserving existing constraints. In this paper we show how these plan fragments can be automatically synthesized using first principles about geometric bodies, actions, and topology.
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