Relaxation on a mesh: a formalism for generalized localization

This paper considers two problems which at first sight appear to be quite distinct: localizing a robot in an unknown environment and calibrating an embedded sensor network. We show that both of these can be formulated as special cases of a generalized localization problem. In the standard localization problem, the aim is to determine the pose of some object (usually a mobile robot) relative to a global coordinate system. In our generalized version, the aim is to determine the pose of all elements in a network (both fixed and mobile) relative to an arbitrary global coordinate system. We have developed a physically inspired ´mesh-based´ formalism for solving such problems. This paper outlines the formalism, and describes its application to the concrete tasks of multirobot mapping and calibration of a distributed sensor network. The paper presents experimental results for both tasks obtained using a set of Pioneer mobile robots equipped with scanning laser range-finders.