The Optimal Next Exploration: Uncertainty Minimization in Mobile Robot Self-Location

Abstract

The accurate self-location of a mobile robot is often required, when moving from a navigation phase to a manipulation phase. In many cases, the self-location can take advantage from the knowledge of the geometric models of some of the objects present in the environment of the mobile robot (e.g. architectonic elements). The sensor detections aimed at locating the robot with respect to the environment are noise sensitive, and hence yield an uncertain position. Therefore, in order to reduce the position uncertainty, redundant sensor detections must be utilized [1]. In this paper the use of range measurements is considered. In order to expedite the robot location, the number of the required sensor detections must be restricted: therefore detections must be selected, that maximally reduce the residual positional uncertainty. An intuitive approach to the selection of a detection, that minimizes the a posteriori variance of the robot position estimate, would involve the examination of the whole set of the possible exploration directions. In this paper a criterion is adopted, based on the variance of the translational parameters of the position. In the case the uncertainty affecting the single range measurements is supposed to be constant (as assumed in [2]), some useful geometric properties can be shown that allow, once an arbitrary exploration direction has been chosen, to i) evaluate its distance from the optimum; and ii) remove from further consideration all the exploration directions, having criterion not better than that of the chosen exploration direction.

Work partially supported with grants of CNR, PFR 3.2 “TISANA”