Probabilistic Multi-Robot Gas Source Localization with Uncalibrated Sensors: A Distributed Estimation Approach

Estimating environmental states with multi-robot systems becomes particularly challenging when robots are equipped with uncalibrated and therefore heterogeneous sensors, whose nonlinear and inconsistent responses prevent reliable information fusion. In this paper, we propose a distributed probabilistic framework for source localization tasks that enables calibration-free estimation in the presence of sensor heterogeneity. The key idea is that each robot independently estimates a local belief using a rank-based feature that captures the relative evolution of observations and is invariant to sensor scaling and nonlinearities. These local beliefs are then fused through a product of experts formulation to obtain a consistent global estimate across the team. To further improve the efficiency of team coordination, we introduce an informative region allocation and path planning strategy that reduces redundant exploration while balancing exploration and exploitation. We validate the proposed framework using high-fidelity simulations with realistic gas sensor models. Results demonstrate that our method significantly outperforms a benchmark method based on standard measurement aggregation, achieving reliable source localization accuracy despite strong sensor heterogeneity. More broadly, this work demonstrates how calibration-free sensing representations can be effectively extended to distributed robotic systems, paving the way for their application to other estimation tasks involving heterogeneous sensors.