An important problem in geometric reasoning is to find the configuration of acollection of geometric bodies so as to satisfy a set of given constraints.Recently, it has been suggested that this problem can be solved efficiently bysymbolically reasoning about geometry. This approach, called degrees of freedomanalysis, employs a set of specialized routines called plan fragments thatspecify how to change the configuration of a set of bodies to satisfy a newconstraint while preserving existing constraints. A potential drawback, whichlimits the scalability of this approach, is concerned with the difficulty ofwriting plan fragments. In this paper we address this limitation by showing howthese plan fragments can be automatically synthesized using first principlesabout geometric bodies, actions, and topology.
展开▼
