POAM: Probabilistic Online Attentive Mapping for Efficient Robotic Information Gathering

TL;DR

POAM addresses the challenge of efficient, uncertainty-aware robotic information gathering in non-stationary environments by marrying a probabilistic Gaussian Process (GP) with a non-stationary Attentive Kernel (AK) and designing constant-time online updates. It introduces a Probabilistic Online Attentive Mapping framework that uses Pivoted Cholesky Decomposition (PCD) for inducing-input selection, analytic updates for variational parameters, and mini-batch optimization for hyperparameters within a variational EM scheme. The method achieves online, data-efficient, and attentive mapping, demonstrated by active bathymetric mapping tasks where POAM outperforms online sparse GP baselines in accuracy, uncertainty quantification, and computation time. The work provides open-source code and highlights limitations related to online inducing-input updates in streaming settings and the need for extending the approach beyond regression tasks to broader active information gathering problems.

Abstract

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.

Figures (9)

• Figure 1: An elevation dataset sampled via lawnmower path in the environment for illustrative purposes. (a) The ground-truth elevation map of the environment. Red and blue colors represent high and low elevations, respectively. (b) A dense dataset sampled by lawnmower path in the environment, which is used to train the GP model for elevation mapping.
• Figure 2: Prediction and lengthscale maps from jointly training all parameters with an Adam optimizer. (a) The predictive mean map exhibits uniform smoothness due to the uniform scattering of inducing points (black dots) across the space and the failure to learn an input-dependent lengthscale. (b) The lengthscale map is flat, indicating that the attentive kernel has degenerated to a stationary kernel.
• Figure 3: Prediction and lengthscale maps from the proposed Probabilistic Attentive Mapping (PAM) training paradigm. (a) A higher density of inducing points is allocated to the complex region, enabling the predictive mean to capture finer elevation details. (b) The learned lengthscale map delineates the relatively smooth area on the left (large lengthscale) from the highly varying region near the right boundary (small lengthscale).
• Figure 4: Illustration of the initial waypoints generated by a Bézier curve.
• Figure 5: Benchmarking results of the evaluated methods across four environments and three metrics. The proposed method (POAM) is compared against an online sparse GP baseline (OVC) and two improved baselines (OVC++ and SSGP++) in terms of standardized mean squared error (SMSE), mean standardized log loss (MSLL), and training time.