Planning from First Princi les for Cm etric Constraint Satisfae

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. Operators are actions, e.g.rotate, that change the configuration of geoms, thereby violating or achieving some constraint. An initial state is specified by the set of existing invariants on a geom and a final state by the additional constraints to be satisfied. A plan is a sequence of actions that when applied to the initial state achieves the final state.