A "Thermodynamic" Approach to Multi-robot Cooperative Localization with Noisy Sensors

We propose a new approach to the simultaneous cooperative localization of a very large group of simple robots capable of performing deadreckoning and sensing the relative position of nearby robots. In the last decade, the use of distributed optimal Kalman filters (KF) to address this problem has been studied extensively. In this paper, we propose to use a very simple encounter based averaging process (denoted by EA). The idea behind EA is the following: every time two robots meet, they simply average their location estimates. We assume that two robots meet whenever they are close enough to allow relative location estimation and communication. At each meeting event, the robots average their location estimations thus reducing the localization error. Naturally, the frequency of the meetings affects the localization quality. The meetings are determined by the robots’ movement pattern. In this work we consider movement patterns which are “well mixing” i.e. every robot meets other robots and eventually all of the robots frequently. For such a movement pattern, the time course of the expected localization error is derived. We prove that EA is asymptotically optimal and requires significantly less computation and communication resources than KF.