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

TL;DR

This work tackles GPS-denied relative localization in multi-robot systems by introducing HGP-RL, a distributed RSSI-based framework that maps Wi-Fi RSSI to the AP position using a three-level hierarchical Gaussian Process. Each robot runs local GP regression, performs hierarchical AP-position inference, and then applies AP-oriented algebra to compute relative positions of neighbors, enabling scalable, communication-efficient localization on resource-constrained platforms. The approach outperforms state-of-the-art GPR-based sources and relative localization methods in accuracy, computation, and bandwidth, demonstrated in Robotarium simulations and real ROS-based rendezvous experiments. The combination of hierarchical, sparse GP inference and AP-centric transformations offers a practical, scalable solution for cooperative tasks like rendezvous and formation control in cluttered or LOS-limited environments, with publicly released code for replication and extension.

Abstract

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. 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 HGR-PL in Robotarium simulations against several state-of-the-art methods. The results indicate superior performance of HGP-RL regarding localization accuracy, computation, and communication overheads. 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.

Figures (7)

• Figure 1: An overview of HGP-RL with three levels of Gaussian Processes and relative localization using Access Point position. $\alpha,\beta$ and $\gamma$ are resolution parameters for $N\times N$ grid space, $_i\mathbf{p}^{AP}$ and $_j\mathbf{p}^{AP}$ are the position vectors from the robot's position to the predicted AP position, and $_i\mathbf{p}^j$ is the relative position vector from robot $i$ to $j$.
• Figure 2: A distributed system architecture of HGP-RL for robot $i$ to relatively localize other robots $j$ using hierarchical GP inferencing of the AP location.
• Figure 3: AP predictions for gradient search and hierarchical inferencing.
• Figure 4: Gaussian processes inferencing for global and local frames along with the ground truth and predicted robot trajectories of HGP-RL.
• Figure 5: AP prediction performance plots (Absolute Localization Error and GPR Training and Inferences Times) of HGP-RL (ours) compared with GPR quattrini2020multi and xue2019locate (with Sparse and Dense resolutions). The effect of the number of hierarchy levels in HGP-RL is also shown in the right-most plots.

Theorems & Definitions (2)

• Lemma 1
• proof