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.

In this paper, we present a novel algorithm for probabilistically updating and rasterizing semantic maps within 3D Gaussian Splatting (3D-GS). Although previous methods have introduced algorithms which learn to rasterize features in 3D-GS for enhanced scene understanding, 3D-GS can fail without warning which presents a challenge for safety-critical robotic applications. To address this gap, we propose a method which advances the literature of continuous semantic mapping from voxels to ellipsoids, combining the precise structure of 3D-GS with the ability to quantify uncertainty of probabilistic robotic maps. Given a set of images, our algorithm performs a probabilistic semantic update directly on the 3D ellipsoids to obtain an expectation and variance through the use of conjugate priors. We also propose a probabilistic rasterization which returns per-pixel segmentation predictions with quantifiable uncertainty. We compare our method with similar probabilistic voxel-based methods to verify our extension to 3D ellipsoids, and perform ablation studies on uncertainty quantification and temporal smoothing.

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.

Autonomous and mobile cyber-physical machines are becoming an inevitable part of our future. In particular, Micro Aerial Vehicles (MAVs) have seen a resurgence in activity. With multiple use cases, such as surveillance, search and rescue, package delivery, and more, these unmanned aerial systems are on the cusp of demonstrating their full potential. Despite such promises, these systems face many challenges, one of the most prominent of which is their low endurance caused by their limited onboard energy. Since the success of a mission depends on whether the drone can finish it within such duration and before it runs out of battery, improving both the time and energy associated with the mission are of high importance. Such improvements have traditionally been arrived at through the use of better algorithms. But our premise is that more powerful and efficient onboard compute can also address the problem. In this article, we investigate how the compute subsystem, in a cyber-physical mobile machine such as a Micro Aerial Vehicle, can impact mission time (time to complete a mission) and energy. Specifically, we pose the question as what is the role of computing for cyber-physical mobile robots? We show that compute and motion are tightly intertwined, and as such a close examination of cyber and physical processes and their impact on one another is necessary. We show different “impact paths” through which compute impacts mission metrics and examine them using a combination of analytical models, simulation, and micro and end-to-end benchmarking. To enable similar studies, we open sourced MAVBench , our tool-set, which consists of (1) a closed-loop real-time feedback simulator and (2) an end-to-end benchmark suite composed of state-of-the-art kernels. By combining MAVBench, analytical modeling, and an understanding of various compute impacts, we show up to 2X and 1.8X improvements for mission time and mission energy for two optimization case studies, respectively. Our investigations, as well as our optimizations, show that cyber-physical co-design, a methodology with which both the cyber and physical processes/quantities of the robot are developed with consideration of one another, similar to hardware-software co-design, is necessary for arriving at the design of the optimal robot.

This paper addresses the problem of generating quadcopter minimum snap trajectories for real time applications. Previous efforts addressed this problem by either employing a gradient descent method, or by greatly sacrificing optimality for faster solutions that are amenable for onboard implementation. In this work, outputs of the gradient descent method are used offline to train a supervised neural network. We show that the use of neural networks results typically in two orders of magnitude reduction in computational time. Our proposed approach can be used for warm-starting onboard implementable iterative methods with an “educated ” initial guess. This work is motivated by the application for human-machine interface in which a human provides desired trajectory through a smart-tablet interface, which has to be translated into a dynamically feasible trajectory for a quadcopter. The proposed solution is tested in thousands of different examples, demonstrating its effectiveness as a booster for minimum snap trajectory generation for quadcopters.