Relative Localizability and Localization for Multirobot Systems

Inter-robot relative positions are crucial for executing various multirobot missions, such as formation maneuvering and collaborative inspection. However, the current sensing technology usually provides part of relative position information, such as inter-robot distances, bearings and angles. This prompts the study of determining inter-robot relative positions, i.e., relative localization, from these partial measurements. Based on the existing results of static networks' localizability and mobile robots' relative localization, we propose a novel concept, relative localizability to describe whether a multirobot system is relatively localizable. Given each robot's self-displacement measurements and inter-robot partial measurements in $d$ ($d\leq 4$) sampling instants, we show that a multirobot system's relative localization can be achieved in a purely algebraic and distributed manner, in which the multirobot system is said to be $d$-step relatively localizable. To make the results more general, we consider that the multirobot system consists of landmarks, leaders, and followers, and that the inter-robot measurements can be distances, bearings or angles. When robots' coordinate frames have different orientations, we show that the given local measurements can be used to determine robots' relative positions and their coordinate frames' relative orientations simultaneously. Simulations and experiments of relative localization for ground robots are conducted to validate the obtained results.