This paper presents Neural Visibility Field (NVF), a novel uncertainty quantification method for Neural Radiance Fields (NeRF) applied to active mapping. Our key insight is that regions not visible in the training views lead to inherently unreliable color predictions by NeRF at this region, resulting in increased uncertainty in the synthesized views. To address this, we propose to use Bayesian Networks to composite position-based field uncertainty into ray-based uncertainty in camera observations. Consequently, NVF naturally assigns higher uncertainty to unobserved regions, aiding robots to select the most informative next viewpoints. Extensive evaluations show that NVF excels not only in uncertainty quantification but also in scene reconstruction for active mapping, outperforming existing methods.

Abstract-- Robot art presents an opportunity to both showcase and advance state-of-the-art robotics through the challenging task of creating art. Creating large-scale artworks in particular engages the public in a way that small-scale works cannot, and the distinct qualities of brush strokes contribute to an organic and human-like quality. Combining the large scale of murals with the strokes of the brush medium presents an especially impactful result, but also introduces unique challenges in maintaining precise, dextrous motion control of the brush across such a large workspace. In this work, we present the first robot to our knowledge that can paint architectural-scale murals with a brush. We create a hybrid robot consisting of a cable-driven parallel robot and 4 degree of freedom (DoF) serial manipulator to paint a 27m by 3.7m mural on windows spanning 2-stories of a building. We discuss our approach to achieving both the scale and accuracy required for brush-painting a mural through a combination of novel mechanical design elements, coordinated planning and control, and on-site calibration algorithms with experimental validations.

We propose a new metric for robot state estimation based on the recently introduced $\text{SE}_2(3)$ Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state estimate, improving over current pose-based trajectory analysis. This has the benefit of providing a single, quantitative metric to evaluate state estimation algorithms against, while being compatible with existing tools and libraries. Since ground truth data generally consists of pose data from motion capture systems, we also propose an approach to compute the ground truth linear velocity based on polynomial interpolation. Using Chebyshev interpolation and a pseudospectral parameterization, we can accurately estimate the ground truth linear velocity of the trajectory in an optimal fashion with best approximation error. We demonstrate how this approach performs on multiple robotic platforms where accurate state estimation is vital, and compare it to alternative approaches such as finite differences. The pseudospectral parameterization also provides a means of trajectory data compression as an additional benefit. Experimental results show our method provides a valid and accurate means of comparing state estimation systems, which is also easy to interpret and report.

While initial approaches to Structure-from-Motion (SfM) revolved around both global and incremental methods, most recent applications rely on incremental systems to estimate camera poses due to their superior robustness. Though there has been tremendous progress in SfM `front-ends' powered by deep models learned from data, the state-of-the-art (incremental) SfM pipelines still rely on classical SIFT features, developed in 2004. In this work, we investigate whether leveraging the developments in feature extraction and matching helps global SfM perform on par with the SOTA incremental SfM approach (COLMAP). To do so, we design a modular SfM framework that allows us to easily combine developments in different stages of the SfM pipeline. Our experiments show that while developments in deep-learning based two-view correspondence estimation do translate to improvements in point density for scenes reconstructed with global SfM, none of them outperform SIFT when comparing with incremental SfM results on a range of datasets. Our SfM system is designed from the ground up to leverage distributed computation, enabling us to parallelize computation on multiple machines and scale to large scenes.

Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a speed profile that satisfies kino-dynamic and other constraints. While trajectory retiming is most often formulated with the minimum-time objective (i.e. traverse the path as fast as possible), it is not always the most desirable objective, particularly when we seek to balance multiple objectives or when bang-bang control is unsuitable. In this paper, we present a novel algorithm based on factor graph variable elimination that can solve for the global optimum of the retiming problem with quadratic objectives as well (e.g. minimize control effort or match a nominal speed by minimizing squared error), which may extend to arbitrary objectives with iteration. Our work extends prior works, which find only solutions on the boundary of the feasible region, while maintaining the same linear time complexity from a single forward-backward pass. We experimentally demonstrate that (1) we achieve better real-world robot performance by using quadratic objectives in place of the minimum-time objective, and (2) our implementation is comparable or faster than state-of-the-art retiming algorithms.

Legged robot locomotion is a challenging task due to a myriad of sub-problems, such as the hybrid dynamics of foot contact and the effects of the desired gait on the terrain. Accurate and efficient state estimation of the floating base and the feet joints can help alleviate much of these issues by providing feedback information to robot controllers. Current state estimation methods are highly reliant on a conjunction of visual and inertial measurements to provide real-time estimates, thus being handicapped in perceptually poor environments. In this work, we show that by leveraging the kinematic chain model of the robot via a factor graph formulation, we can perform state estimation of the base and the leg joints using primarily proprioceptive inertial data. We perform state estimation using a combination of preintegrated IMU measurements, forward kinematic computations, and contact detections in a factor-graph based framework, allowing our state estimate to be constrained by the robot model. Experimental results in simulation and on hardware show that our approach out-performs current proprioceptive state estimation methods by 27% on average, while being generalizable to a variety of legged robot platforms. We demonstrate our results both quantitatively and qualitatively on a wide variety of trajectories.

Quadrupeds are highly versatile robots that can traverse over difficult terrain that wheeled mobile robots are unable to. This flexibility makes quadrupeds appealing for various applications, such as inspection, surveying construction sites, and search-and-rescue. However, to effectively perform these tasks autonomously, quadrupeds, as with other mobile robots, require a form of perception that will enable them to localize when placed in an environment without a priori knowledge. For robots to know its location in the environment, it must localize against a predefined map, but a robot can only create a map based on its known location. To solve this chicken-and-egg problem, simultaneous localization and mapping, or SLAM, is the standard approach used for mobile robots by optimizing for the robot's location and map simultaneously. The estimated poses and map from SLAM algorithms can then be used for downstream tasks such as facilitating controllers depending on the terrain or planning in navigation. Despite the recent developments in both quadruped robotics and in SLAM research, there has yet to be an open-source package that is specifically designed for high performing SLAM on quadrupeds.

Visual Inertial Odometry (VIO) is one of the most established state estimation methods for mobile platforms. However, when visual tracking fails, VIO algorithms quickly diverge due to rapid error accumulation during inertial data integration. This error is typically modeled as a combination of additive Gaussian noise and a slowly changing bias which evolves as a random walk. In this work, we propose to train a neural network to learn the true bias evolution. We implement and compare two common sequential deep learning architectures: LSTMs and Transformers. Our approach follows from recent learning-based inertial estimators, but, instead of learning a motion model, we target IMU bias explicitly, which allows us to generalize to locomotion patterns unseen in training. We show that our proposed method improves state estimation in visually challenging situations across a wide range of motions by quadrupedal robots, walking humans, and drones. Our experiments show an average 15% reduction in drift rate, with much larger reductions when there is total vision failure. Importantly, we also demonstrate that models trained with one locomotion pattern (human walking) can be applied to another (quadruped robot trotting) without retraining.

We present a novel continuous time trajectory representation based on a Chebyshev polynomial basis, which when governed by known dynamics models, allows for full trajectory and robot dynamics estimation, particularly useful for high-performance robotics applications such as unmanned aerial vehicles. We show that we can gracefully incorporate model dynamics to our trajectory representation, within a factor-graph based framework, and leverage ideas from pseudo-spectral optimal control to parameterize the state and the control trajectories as interpolating polynomials. This allows us to perform efficient optimization at specifically chosen points derived from the theory, while recovering full trajectory estimates. Through simulated experiments we demonstrate the applicability of our representation for accurate flight dynamics estimation for multirotor aerial vehicles. The representation framework is general and can thus be applied to a multitude of high-performance applications beyond multirotor platforms.

In this paper, we provide a modern synthesis of the classic inverse compositional algorithm for dense image alignment. We first discuss the assumptions made by this well-established technique, and subsequently propose to relax these assumptions by incorporating data-driven priors into this model. More specifically, we unroll a robust version of the inverse compositional algorithm and replace multiple components of this algorithm using more expressive models whose parameters we train in an end-to-end fashion from data. Our experiments on several challenging 3D rigid motion estimation tasks demonstrate the advantages of combining optimization with learning-based techniques, outperforming the classic inverse compositional algorithm as well as data-driven image-to-pose regression approaches.