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Robotic Information Gathering (RIG) is a foundational research topic that answers how a robot (team) collects informative data to efficiently build an accurate model of an unknown target function under robot embodiment constraints. RIG has many applications, including but not limited to autonomous exploration and mapping, 3D reconstruction or inspection, search and rescue, and environmental monitoring. A RIG system relies on a probabilistic model’s prediction uncertainty to identify critical areas for informative data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling. However, real-world spatial data is typically non-stationary—different locations do not have the same degree of variability. As a result, the prediction uncertainty does not accurately reveal prediction error, limiting the success of RIG algorithms. We propose a family of non-stationary kernels named Attentive Kernel (AK), which is simple and robust and can extend any existing kernel to a non-stationary one. We evaluate the new kernel in elevation mapping tasks, where AK provides better accuracy and uncertainty quantification over the commonly used stationary kernels and the leading non-stationary kernels. The improved uncertainty quantification guides the downstream informative planner to collect more valuable data around the high-error area, further increasing prediction accuracy. A field experiment demonstrates that the proposed method can guide an Autonomous Surface Vehicle (ASV) to prioritize data collection in locations with significant spatial variations, enabling the model to characterize salient environmental features. 

The paper introduces DiSProD, an online planner developed forenvironments with probabilistic transitions in continuous state andaction spaces. DiSProD builds a symbolic graph that captures thedistribution of future trajectories, conditioned on a given policy,using independence assumptions and approximate propagation ofdistributions. The symbolic graph provides a differentiablerepresentation of the policy's value, enabling efficient gradient-basedoptimization for long-horizon search. The propagation of approximatedistributions can be seen as an aggregation of many trajectories, makingit well-suited for dealing with sparse rewards and stochasticenvironments. An extensive experimental evaluation compares DiSProD tostate-of-the-art planners in discrete-time planning and real-timecontrol of robotic systems. The proposed method improves over existingplanners in handling stochastic environments, sensitivity to searchdepth, sparsity of rewards, and large action spaces. Additionalreal-world experiments demonstrate that DiSProD can control groundvehicles and surface vessels to successfully navigate around obstacles.