HGP-RL: Distributed Hierarchical Gaussian Processes for Wi-Fi-based Relative Localization in Multi-Robot Systems

Relative localization is crucial for multi-robot systems to perform cooperative tasks, especially in GPS-denied environments. Current techniques for multi-robot relative localization rely on expensive or short-range sensors such as cameras and LIDARs. As a result, these algorithms face challenges such as high computational complexity (e.g., map merging), dependencies on well-structured environments, etc. To remedy this gap, we propose a new distributed approach to perform relative localization (RL) using a common Access Point (AP). To achieve this efficiently, we propose a novel Hierarchical Gaussian Processes (HGP) mapping of the Radio Signal Strength Indicator (RSSI) values from a Wi-Fi AP to which the robots are connected. We termed this approach as HGP-RL (Hierarchical Gaussian Process for Relative Localization). Each robot performs hierarchical inference using the HGP map to locate the AP in its reference frame, and the robots obtain relative locations of the neighboring robots leveraging AP-oriented algebraic transformations. The approach readily applies to resource-constrained devices and relies only on the ubiquitously-available WiFi RSSI measurement. We extensively validate the performance of the proposed HGP-RL in Robotarium simulations against several state-of-the-art methods. The results indicate superior performance of HGP-RL regarding localization accuracy, computation, and communication over-heads. Finally, we showcase the utility of HGP-RL through a multi-robot cooperative experiment to achieve a rendezvous task in a team of three mobile robots.