Optimal Localizability Criterion for Positioning with Distance-Deteriorated Relative Measurements

Abstract

Position estimation in Multi-Robot Systems (MRS) relies on relative angle or distance measurements between the robots, which generally deteriorate as distances increase. Moreover, the localization accuracy is strongly influenced both by the quality of the raw measurements but also by the overall geometry of the network. In this paper, we design a cost function that accounts for these two issues and can be used to develop motion planning algorithms that optimize the localizability in MRS, i.e., the ability of individual robots to localize themselves accurately. This cost function is based on computing new Cramér Rao Lower Bounds characterizing the achievable positioning performance with range and angle measurements that deteriorate with increasing distances. We describe a gradient-based motion-planning algorithm for MRS deployment that can be implemented in a distributed manner, as well as a non-myopic strategy to escape local minima. Finally, we test the proposed methodology experimentally for range measurements obtained using ultra-wide band transceivers and illustrate the improvements resulting from leveraging the more accurate measurement model in the robot placement algorithms.