Robustness Study of Optimal Geometries for Cooperative Multi-Robot Localization

This work focuses on localizing a single target robot with multi-robot formations in 2D space. The cooperative robots employ inter-robot range measurements to assess the target position. In the presence of noisy measurements, the choice of formation geometries significantly impacts the accuracy of the target robot’s pose estimation. While an infinite number of geometries exists to optimize localization accuracy, the current practice is to choose the final formation geometry based on convenience criteria such as simplicity or proximity to the initial position of the robots. The former leads to the selection of regular polygon-shaped formations, while the latter results in behaviour-based formations. Different from existing works, we conduct a complete robustness study of formation geometries in the presence of deviations from the desired formation and range measurement errors. In 2D scenarios, we establish necessary and sufficient conditions for formation geometries to be robust against robot positioning errors. This result substantiates the extensive use of regular polygon formations. However, our analysis reveals the lack of robustness of the commonly used square formation geometry, which stands as an exception. Simulation results illustrate the advantages of these robust geometries in enhancing target localization accuracy.