Spatial reasoning about robot compliant movements and optimal paths in qualitatively modeled environments

This article describes a framework for qualitatively representing and reasoning about spatial configurations. The framework contains interval/region-based formalisms for describing distances, angles, and locations. These representations lead to the formulation of inference rules, as well as search-heuristics that enable the derivation of spatial relationships and paths among objects. The qualitative framework can be used in two principal ways: to formulate solutions to spatial configuration problems where exact geometric knowledge is not available, and to provide guidance for the application of quantitative configuration analysis and planning methods. The applications of the proposed framework are demonstrated through simulation examples that involve inferring constrained instantaneous configurations as well as coupler curves for compliant motion planning and deriving collision-free paths for open-chain mechanisms moving among static obstacles.