Multi-robot patrolling requires a team to visit all areas of an environment at regular intervals, typically minimising idleness. A practical extension, motivated by security and environmental monitoring, is to additionally form a collective ranking of all patrol locations by some measured signal, a generalisation of the best-of-n problem to the many-option, continuous-valued regime. We observe that the patrol graph admits a natural dual interpretation: it is simultaneously the topology that dictates agent movement and a factor graph over which spatial beliefs can be propagated. Exploiting this equivalence, we apply Gaussian Belief Propagation (GBP), a graph-based algorithm, to collective ranking using unary measurement factors at visited nodes and pairwise smoothness factors along patrol edges. We compare GBP against simple and visit-count-weighted averaging across a range of sensor-noise conditions in simulation, and validate the approach on four Leo Rovers tracking a propagating radio signal in an office lobby. GBP outperforms both baselines on ranking accuracy, mean squared error, and time to consensus. We find that as noise increases and the task becomes harder, GBP degrades gracefully in simulation while both averaging methods degrade substantially. Hardware trials reproduce the same performance ordering on a real propagating radio signal, supporting the practical relevance of the simulated results.
Gaussian Belief Propagation (GBP) is a distributed inference algorithm that passes messages in graphical models, making it attractive for scalable spatial intelligence. However, we find GBP most effective locally: it rapidly smooths message errors that vary sharply between neighbor variables, but corrects global errors across distant graph regions incrementally through long-range message propagations. We propose Hierarchy-GBP (H-GBP), an iterative, two-stage framework that accelerates GBP by first solving these global errors with a coarse graph approximation (abstraction) and projecting the results back to the original graph (recovery), then refining the remaining local errors with GBP. We prove H-GBP convergence to the optimum by deriving the combined matrix operator of our abstraction and recovery steps and analyzing its spectral radius. Experiments on linear sparse graphs show that H-GBP converges fundamentally faster than standard GBP. Moreover, we validate H-GBP on two important spatial problems: Pose Graph Optimization (PGO) and Bundle Adjustment (BA). H-GBP markedly accelerates large-scale PGO and achieves state-of-the-art runtime across all tested BA scales.
Robot swarms, by virtue of their decentralised architecture, are a natural tool for scalable, robust modelling of spatial fields, such as water temperature, wind velocity, or terrain elevation. However, existing methods rely on external positioning systems that allow each robot to determine its own position in space. Here, we introduce location-unaware Gaussian process regression (LU-GPR) as a solution to the modelling of spatial fields in the absence of such positioning systems. LU-GPR allows each robot to infer the posterior mean and variance of the field in space, while simultaneously agreeing on a common frame of reference with its peers, using only local sensing and communication. We propose an online algorithm that allows each robot to consistently infer local estimates as its local frame of reference converges to the common one. By means of a product of experts model, each robot also combines the estimates of its peers with its own to obtain a global model. Our results show that LU-GPR scales well with the number of robots and is robust to limited communication ranges. We also demonstrate how it can be used in real-world monitoring scenarios to estimate the flow of an evacuating crowd.
Multi-robot informative path planning (IPP) for persistent target monitoring requires robots to reason about spatial uncertainty, temporal evolution, and practical sensing and communication constraints. Recent learning-based multi-robot IPP methods use Gaussian Processes (GPs) for target uncertainty, but often rely on simplified sensing models and centralized belief updates. We propose a grid-based spatio-temporal GP-Kalman filtering framework for learning-based multi-robot IPP. Instead of maintaining one GP per target, we represent anonymous target presence as a single latent field over a discrete workspace grid. The proposed recursive update considers all visible cells inside a camera footprint and supports arbitrary fields of view and range-dependent noise. A GP-consistent temporal process update accounts for moving targets and stale information by inflating uncertainty over time. For decentralized deployment, each robot maintains its own mapper and exchanges compact belief summaries rather than raw measurements. Received beliefs are fused using diagonal covariance intersection to remain conservative under unknown inter-robot correlations. We integrate the mapper with a reinforcement-learning policy for graph-based neighbor selection. Simulation benchmarks show about 20% lower average target uncertainty and improved target visitation compared with learning-based and classical auction/coverage baselines. Real-world two-UAV experiments demonstrate transfer to outdoor multi-robot search over a large field of more than 7000 square meters.