POAM: Probabilistic Online Attentive Mapping for Efficient Robotic Information Gathering

Gaussian Process (GP) models are widely used for Robotic Information Gathering (RIG) in exploring unknown environments due to their ability to model complex phenomena with non-parametric flexibility and accurately quantify prediction uncertainty. Previous work has developed informative planners and adaptive GP models to enhance the data efficiency of RIG by improving the robot's sampling strategy to focus on informative regions in non-stationary environments. However, computational efficiency becomes a bottleneck when using GP models in large-scale environments with limited computational resources. We propose a framework -- Probabilistic Online Attentive Mapping (POAM) -- that leverages the modeling strengths of the non-stationary Attentive Kernel while achieving constant-time computational complexity for online decision-making. POAM guides the optimization process via variational Expectation Maximization, providing constant-time update rules for inducing inputs, variational parameters, and hyperparameters. Extensive experiments in active bathymetric mapping tasks demonstrate that POAM significantly improves computational efficiency, model accuracy, and uncertainty quantification capability compared to existing online sparse GP models.