In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it does not natively quantify uncertainty or information, posing a challenge for real-world applications such as 3D-GS SLAM. We propose to quantify information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution widely used in literature. By restructuring information quantification of 3D-GS through optimal experimental design, we arrive at multiple solutions, of which T-Optimality and D-Optimality perform the best quantitatively and qualitatively as measured on two popular datasets. Additionally, we propose a block diagonal covariance approximation which provides a measure of correlation at the expense of a greater computation cost.

When a mobile robot autonomously explores an indoor space to produce a localization and navigation map, it is important to create both a stable pose graph and a high-quality occupancy map that covers all the navigable areas. In this work, we propose a novel probabilistic active loop closure framework which attempts to maximally reduce pose graph uncertainty during exploration and improves occupancy map quality. We calculate a probabilistic reward of getting a loop closure at any pose on a pose graph, which considers both how much pose graph uncertainty would be reduced by getting a loop closure there, and the robot’s travel cost to navigate to that pose. By choosing poses that provide the largest rewards, we can maximally reduce pose graph uncertainty while avoiding long travel times. The effectiveness of the method is illustrated through on-device testing in various floor plans.