Multi-Robot Allocation for Information Gathering in Non-Uniform Spatiotemporal Environments

2025-09-26

AI Summary

For multi-robot collaborative sensing of non-stationary spatiotemporal fields (e.g., wind, temperature, gas concentration), existing Gaussian process (GP) methods fail to jointly capture local heterogeneity across both spatial and temporal scales, leading to biased uncertainty estimates. This paper proposes a two-stage cooperative sampling framework: first, a variogram-driven online learning method jointly models region-adaptive spatial and temporal length scales; second, a clarity-weighted information entropy metric enables dynamic task allocation. Theoretical contributions include a proof of spatial-scale convergence and an analysis of dynamic regret bounds. Experiments across diverse time-varying environments demonstrate significant improvements in field estimation accuracy and uncertainty calibration compared to state-of-the-art GP-based approaches.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Autonomous robots are increasingly deployed to estimate spatiotemporal fields (e.g., wind, temperature, gas concentration) that vary across space and time. We consider environments divided into non-overlapping regions with distinct spatial and temporal dynamics, termed non-uniform spatiotemporal environments. Gaussian Processes (GPs) can be used to estimate these fields. The GP model depends on a kernel that encodes how the field co-varies in space and time, with its spatial and temporal lengthscales defining the correlation. Hence, when these lengthscales are incorrect or do not correspond to the actual field, the estimates of uncertainty can be highly inaccurate. Existing GP methods often assume one global lengthscale or update only periodically; some allow spatial variation but ignore temporal changes. To address these limitations, we propose a two-phase framework for multi-robot field estimation. Phase 1 uses a variogram-driven planner to learn region-specific spatial lengthscales. Phase 2 employs an allocation strategy that reassigns robots based on the current uncertainty, and updates sampling as temporal lengthscales are refined. For encoding uncertainty, we utilize clarity, an information metric from our earlier work. We evaluate the proposed method across diverse environments and provide convergence analysis for spatial lengthscale estimation, along with dynamic regret bounds quantifying the gap to the oracle's allocation sequence.

Problem

• Estimating spatiotemporal fields with inaccurate Gaussian Process lengthscales
• Allocating multi-robot teams in non-uniform spatiotemporal environments
• Improving uncertainty quantification through region-specific lengthscale learning

Innovation

• Two-phase framework for multi-robot field estimation
• Variogram-driven planner learns region-specific spatial lengthscales
• Allocation strategy reassigns robots based on current uncertainty