These Magic Moments: Differentiable Uncertainty Quantification of Radiance Field Models

This paper introduces a novel approach to uncertainty quantification for radiance fields by leveraging higher-order moments of the rendering equation. Uncertainty quantification is crucial for downstream tasks including view planning and scene understanding, where safety and robustness are paramount. However, the high dimensionality and complexity of radiance fields pose significant challenges for uncertainty quantification, limiting the use of these uncertainty quantification methods in high-speed decision-making. We demonstrate that the probabilistic nature of the rendering process enables efficient and differentiable computation of higher-order moments for radiance field outputs, including color, depth, and semantic predictions. Our method outperforms existing radiance field uncertainty estimation techniques while offering a more direct, computationally efficient, and differentiable formulation without the need for post-processing. Beyond uncertainty quantification, we also illustrate the utility of our approach in downstream applications such as next-best-view (NBV) selection and active ray sampling for neural radiance field training. Extensive experiments on synthetic and real-world scenes confirm the efficacy of our approach, which achieves state-of-the-art performance while maintaining simplicity.

Modeling Uncertainty in 3D Gaussian Splatting through Continuous Semantic Splatting

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.

Latent BKI: Open-Dictionary Continuous Mapping in Visual-Language Latent Spaces with Quantifiable Uncertainty

This paper introduces a novel probabilistic mapping algorithm, Latent BKI, which enables open-vocabulary mapping with quantifiable uncertainty. Traditionally, semantic mapping algorithms focus on a fixed set of semantic categories which limits their applicability for complex robotic tasks. Vision-Language (VL) models have recently emerged as a technique to jointly model language and visual features in a latent space, enabling semantic recognition beyond a predefined, fixed set of semantic classes. Latent BKI recurrently incorporates neural embeddings from VL models into a voxel map with quantifiable uncertainty, leveraging the spatial correlations of nearby observations through Bayesian Kernel Inference (BKI). Latent BKI is evaluated against similar explicit semantic mapping and VL mapping frameworks on the popular MatterPort-3D and Semantic KITTI data sets, demonstrating that Latent BKI maintains the probabilistic benefits of continuous mapping with the additional benefit of open-dictionary queries. Real-world experiments demonstrate applicability to challenging indoor environments.

Let's Make a Splan: Risk-Aware Trajectory Optimization in a Normalized Gaussian Splat

Neural Radiance Fields and Gaussian Splatting have transformed the field of computer vision by enabling photo-realistic representation of complex scenes. Despite this success, they have seen only limited use in real-world robotics tasks such as trajectory optimization. Two key factors have contributed to this limited success. First, it is challenging to reason about collisions in radiance models. Second, it is difficult to perform inference of radiance models fast enough for real-time trajectory synthesis. This paper addresses these challenges by proposing SPLANNING, a risk-aware trajectory optimizer that operates in a Gaussian Splatting model. This paper first derives a method for rigorously upper-bounding the probability of collision between a robot and a radiance field. Second, this paper introduces a normalized reformulation of Gaussian Splatting that enables the efficient computation of the collision bound in a Gaussian Splat. Third, a method is presented to optimize trajectories while avoiding collisions with a scene represented by a Gaussian Splat. Experiments demonstrate that SPLANNING outperforms state-of-the-art methods in generating collision-free trajectories in highly cluttered environments. The proposed system is also tested on a real-world robot manipulator. A project page is available at https://roahmlab.github.io/splanning.

You've Got to Feel It To Believe It: Multi-Modal Bayesian Inference for Semantic and Property Prediction

Robots must be able to understand their surroundings to perform complex tasks in challenging environments and many of these complex tasks require estimates of physical properties such as friction or weight. Estimating such properties using learning is challenging due to the large amounts of labelled data required for training and the difficulty of updating these learned models online at run time. To overcome these challenges, this paper introduces a novel, multi-modal approach for representing semantic predictions and physical property estimates jointly in a probabilistic manner. By using conjugate pairs, the proposed method enables closed-form Bayesian updates given visual and tactile measurements without requiring additional training data. The efficacy of the proposed algorithm is demonstrated through several hardware experiments. In particular, this paper illustrates that by conditioning semantic classifications on physical properties, the proposed method quantitatively outperforms state-of-the-art semantic classification methods that rely on vision alone. To further illustrate its utility, the proposed method is used in several applications including to represent affordance-based properties probabilistically and a challenging terrain traversal task using a legged robot. In the latter task, the proposed method represents the coefficient of friction of the terrain probabilistically, which enables the use of an on-line risk-aware planner that switches the legged robot from a dynamic gait to a static, stable gait when the expected value of the coefficient of friction falls below a given threshold. Videos of these case studies as well as the open-source C++ and ROS interface can be found at https://roahmlab.github.io/multimodal_mapping/.

ConvBKI: Real-Time Probabilistic Semantic Mapping Network with Quantifiable Uncertainty

In this paper, we develop a modular neural network for real-time semantic mapping in uncertain environments, which explicitly updates per-voxel probabilistic distributions within a neural network layer. Our approach combines the reliability of classical probabilistic algorithms with the performance and efficiency of modern neural networks. Although robotic perception is often divided between modern differentiable methods and classical explicit methods, a union of both is necessary for real-time and trustworthy performance. We introduce a novel Convolutional Bayesian Kernel Inference (ConvBKI) layer which incorporates semantic segmentation predictions online into a 3D map through a depthwise convolution layer by leveraging conjugate priors. We compare ConvBKI against state-of-the-art deep learning approaches and probabilistic algorithms for mapping to evaluate reliability and performance. We also create a Robot Operating System (ROS) package of ConvBKI and test it on real-world perceptually challenging off-road driving data.

Not All Actions Are Created Equal: Bayesian Optimal Experimental Design for Safe and Optimal Nonlinear System Identification

Uncertainty in state or model parameters is common in robotics and typically handled by acquiring system measurements that yield information about the uncertain quantities of interest. Inputs to a nonlinear dynamical system yield outcomes that produce varying amounts of information about the underlying uncertain parameters of the system. To maximize information gained with respect to these uncertain parameters we present a Bayesian approach to data collection for system identification called Bayesian Optimal Experimental Design (BOED). The formulation uses parameterized trajectories and cubature to compute maximally informative system trajectories which obtain as much information as possible about unknown system parameters while also ensuring safety under mild assumptions. The proposed method is applicable to non-linear and non-Gaussian systems and is applied to a high-fidelity vehicle model from the literature. It is shown the proposed approach requires orders of magnitude fewer samples compared to state-of-the-art BOED algorithms from the literature while simultaneously providing safety guarantees.

These Maps Are Made For Walking: Real-Time Terrain Property Estimation for Mobile Robots

The equations of motion governing mobile robots are dependent on terrain properties such as the coefficient of friction, and contact model parameters. Estimating these properties is thus essential for robotic navigation. Ideally any map estimating terrain properties should run in real time, mitigate sensor noise, and provide probability distributions of the aforementioned properties, thus enabling risk-mitigating navigation and planning. This paper addresses these needs and proposes a Bayesian inference framework for semantic mapping which recursively estimates both the terrain surface profile and a probability distribution for terrain properties using data from a single RGB-D camera. The proposed framework is evaluated in simulation against other semantic mapping methods and is shown to outperform these state-of-the-art methods in terms of correctly estimating simulated ground-truth terrain properties when evaluated using a precision-recall curve and the Kullback-Leibler divergence test. Additionally, the proposed method is deployed on a physical legged robotic platform in both indoor and outdoor environments, and we show our method correctly predicts terrain properties in both cases. The proposed framework runs in real-time and includes a ROS interface for easy integration.

Generating Continuous Motion and Force Plans in Real-Time for Legged Mobile Manipulation

Manipulators can be added to legged robots, allowing them to interact with and change their environment. Legged mobile manipulation planners must consider how contact forces generated by these manipulators affect the system. Current planning strategies either treat these forces as immutable during planning or are unable to optimize over these contact forces while operating in real-time. This paper presents the Stability and Task Oriented Receding-Horizon Motion and Manipulation Autonomous Planner (STORMMAP) that is able to generate continuous plans for the robot's motion and manipulation force trajectories that ensure dynamic feasibility and stability of the platform, and incentivizes accomplishing manipulation and motion tasks specified by a user. STORMMAP uses a nonlinear optimization problem to compute these plans and is able to run in real-time by assuming contact locations are given a-priori, either by a user or an external algorithm. A variety of simulated experiments on a quadruped with a manipulator mounted to its torso demonstrate the versatility of STORMMAP. In contrast to existing state of the art methods, the approach described in this paper generates continuous plans in under ten milliseconds, an order of magnitude faster than previous strategies.