A Thermodynamic Approach to the Analysis of Multi-robot Cooperative Localization under Independent Errors

We propose a new approach to the simultaneous cooperative localization of a group of robots capable of sensing their own motion and the relative position of nearby robots. In the last decade, the use of distributed optimal Kalman filters (KF) to solve this problem have been studied extensively. In this paper, we propose to use a sub-optimal Kalman filter (denoted by EA). EA requires significantly less computation and communication resources then KF. Furthermore, in some cases, EA provides better localization. In this paper EA is analyzed in a soft “thermodynamic” fashion i.e. relaxing assumptions are used during the analysis. The goal is not to derive hard lower or upper bounds but rather to characterize the robots expected behavior. In particular, to predict the expected localization error. The predictions were validated using simulations. We believe that this kind of analysis can be beneficial in many other cases.