Adaptive exploration under localization uncertainty using multi-fidelity Gaussian processes

Abstract This paper considers a robot moving in a 3D environment that is tasked with estimating a quasi-stationary environmental field (e.g., temperature, concentration of a chemical pollutant, or distribution of light radiation density) in the presence of localization uncertainties, as is typical in underwater or other GPS-denied environments. Gaussian process regression has been widely adopted to model environmental fields. However, a drawback of Gaussian process regression is its difficulty in accounting for data with uncertain input. This work proposes a novel multi-fidelity Gaussian process-based regression approach to address the challenge by splitting the data collected by the robot into different datasets corresponding to the amount of input (localization) uncertainty. Furthermore, a sampling-based trajectory planning algorithm is proposed for adaptive robot exploration that optimizes a field-reconstruction objective function while accommodating resource constraints. The proposed approach is experimentally evaluated using a miniature gliding robotic fish that measures light intensity in a large indoor tank. The adaptive exploration algorithm is tested using both a multi-fidelity Gaussian process model and a baseline single-fidelity model. Two objective functions, based on the information gain and an ergodic metric, respectively, are adopted in the evaluation. The experiments show that, for both objective functions, using multi-fidelity Gaussian process reduces the weighted mean squared error between the model prediction and the ground-truth field compared to using the baseline single-fidelity model that ignores localization uncertainty. Accompanying code available at Coleman (Adaptive exploration under localization uncertainty using multi-fidelity Gaussian processes, 2025, https://github.com/colem404/Adaptive-Exploration-Under-Localization-Uncertainty-Using-Multi-fidelity-Gaussian-Processes/tree/main ).