Multi-robot Learning-based Informative Path Planning Using Spatio-Temporal Gaussian Process Kalman Filter

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.