GenDepth: Generalizing Monocular Depth Estimation for Arbitrary Camera Parameters via Ground Plane Embedding

Learning-based monocular depth estimation leverages geometric priors present in the training data to enable metric depth perception from a single image, a traditionally ill-posed problem. However, these priors are often specific to a particular domain, leading to limited generalization performance on unseen data. Apart from the well studied environmental domain gap, monocular depth estimation is also sensitive to the domain gap induced by varying camera parameters, an aspect that is often overlooked in current state-of-the-art approaches. This issue is particularly evident in autonomous driving scenarios, where datasets are typically collected with a single vehicle-camera setup, leading to a bias in the training data due to a fixed perspective geometry. In this paper, we challenge this trend and introduce GenDepth, a novel model capable of performing metric depth estimation for arbitrary vehicle-camera setups. To address the lack of data with sufficiently diverse camera parameters, we first create a bespoke synthetic dataset collected with different vehicle-camera systems. Then, we design GenDepth to simultaneously optimize two objectives: (i) equivariance to the camera parameter variations on synthetic data, (ii) transferring the learned equivariance to real-world environmental features using a single real-world dataset with a fixed vehicle-camera system. To achieve this, we propose a novel embedding of camera parameters as the ground plane depth and present a novel architecture that integrates these embeddings with adversarial domain alignment. We validate GenDepth on several autonomous driving datasets, demonstrating its state-of-the-art generalization capability for different vehicle-camera systems.

Euclidean Equivariant Models for Generative Graphical Inverse Kinematics

Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers typically produce a single solution only and rely on local search techniques to minimize a highly nonconvex objective function. Recently, learning-based approaches that approximate the entire feasible set of solutions have shown promise as a means to generate multiple fast and accurate IK results in parallel. However, existing learning-based techniques have a significant drawback: each robot of interest requires a specialized model that must be trained from scratch. To address this shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train a generative graphical inverse kinematics solver (GGIK) that is able to produce a large number of diverse solutions in parallel while also generalizing well -- a single learned model can be used to produce IK solutions for a variety of different robots. The graphical formulation elegantly exposes the symmetry and Euclidean equivariance of the IK problem that stems from the spatial nature of robot manipulators. We exploit this symmetry by encoding it into the architecture of our learned model, yielding a flexible solver that is able to produce sets of IK solutions for multiple robots.

A Distance-Geometric Method for Recovering Robot Joint Angles From an RGB Image

Autonomous manipulation systems operating in domains where human intervention is difficult or impossible (e.g., underwater, extraterrestrial or hazardous environments) require a high degree of robustness to sensing and communication failures. Crucially, motion planning and control algorithms require a stream of accurate joint angle data provided by joint encoders, the failure of which may result in an unrecoverable loss of functionality. In this paper, we present a novel method for retrieving the joint angles of a robot manipulator using only a single RGB image of its current configuration, opening up an avenue for recovering system functionality when conventional proprioceptive sensing is unavailable. Our approach, based on a distance-geometric representation of the configuration space, exploits the knowledge of a robot's kinematic model with the goal of training a shallow neural network that performs a 2D-to-3D regression of distances associated with detected structural keypoints. It is shown that the resulting Euclidean distance matrix uniquely corresponds to the observed configuration, where joint angles can be recovered via multidimensional scaling and a simple inverse kinematics procedure. We evaluate the performance of our approach on real RGB images of a Franka Emika Panda manipulator, showing that the proposed method is efficient and exhibits solid generalization ability. Furthermore, we show that our method can be easily combined with a dense refinement technique to obtain superior results.

One Network, Many Robots: Generative Graphical Inverse Kinematics

Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers are broadly applicable, but rely on local search techniques to manage highly nonconvex objective functions. Recently, learning-based approaches have shown promise as a means to generate fast and accurate IK results; learned solvers can easily be integrated with other learning algorithms in end-to-end systems. However, learning-based methods have an Achilles' heel: each robot of interest requires a specialized model which must be trained from scratch. To address this key shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train the first learned generative graphical inverse kinematics (GGIK) solver that is, crucially, "robot-agnostic"-a single model is able to provide IK solutions for a variety of different robots. Additionally, the generative nature of GGIK allows the solver to produce a large number of diverse solutions in parallel with minimal additional computation time, making it appropriate for applications such as sampling-based motion planning. Finally, GGIK can complement local IK solvers by providing reliable initializations. These advantages, as well as the ability to use task-relevant priors and to continuously improve with new data, suggest that GGIK has the potential to be a key component of flexible, learning-based robotic manipulation systems.

Recalibrating the KITTI Dataset Camera Setup for Improved Odometry Accuracy

Over the last decade, one of the most relevant public datasets for evaluating odometry accuracy is the KITTI dataset. Beside the quality and rich sensor setup, its success is also due to the online evaluation tool, which enables researchers to benchmark and compare algorithms. The results are evaluated on the test subset solely, without any knowledge about the ground truth, yielding unbiased, overfit free and therefore relevant validation for robot localization based on cameras, 3D laser or combination of both. However, as any sensor setup, it requires prior calibration and rectified stereo images are provided, introducing dependence on the default calibration parameters. Given that, a natural question arises if a better set of calibration parameters can be found that would yield higher odometry accuracy. In this paper, we propose a new approach for one shot calibration of the KITTI dataset multiple camera setup. The approach yields better calibration parameters, both in the sense of lower calibration reprojection errors and lower visual odometry error. We conducted experiments where we show for three different odometry algorithms, namely SOFT2, ORB-SLAM2 and VISO2, that odometry accuracy is significantly improved with the proposed calibration parameters. Moreover, our odometry, SOFT2, in conjunction with the proposed calibration method achieved the highest accuracy on the official KITTI scoreboard with 0.53% translational and 0.0009 deg/m rotational error, outperforming even 3D laser-based methods.

Convex Iteration for Distance-Geometric Inverse Kinematics

Inverse kinematics (IK) is the problem of finding robot joint configurations that satisfy constraints on the position or pose of one or more end-effectors. For robots with redundant degrees of freedom, there is often an infinite, nonconvex set of solutions. The IK problem is further complicated when collision avoidance constraints are imposed by obstacles in the workspace. In general, closed-form expressions yielding feasible configurations do not exist, motivating the use of numerical solution methods. However, these approaches rely on local optimization of nonconvex problems, often requiring an accurate initialization or numerous re-initializations to converge to a valid solution. In this work, we first formulate complicated inverse kinematics problems as convex feasibility problems whose low-rank feasible points provide exact IK solutions. We then present CIDGIK (Convex Iteration for Distance-Geometric Inverse Kinematics), an algorithm that solves these feasibility problems with a sequence of semidefinite programs whose objectives are designed to encourage low-rank minimizers. Our problem formulation elegantly unifies the configuration space and workspace constraints of a robot: intrinsic robot geometry and obstacle avoidance are both expressed as simple linear matrix equations and inequalities. Our experimental results for a variety of popular manipulator models demonstrate faster and more accurate convergence than a conventional nonlinear optimization-based approach, especially in environments with many obstacles.

Riemannian Optimization for Distance Geometric Inverse Kinematics

Solving the inverse kinematics problem is a fundamental challenge in motion planning, control, and calibration for articulated robots. Kinematic models for these robots are typically parameterized by joint angles, generating a complicated mapping between a robot's configuration and end-effector pose. Alternatively, the kinematic model and task constraints can be represented using invariant distances between points attached to the robot. In this paper, we formalize the equivalence of distance-based inverse kinematics and the distance geometry problem for a large class of articulated robots and task constraints. Unlike previous approaches, we use the connection between distance geometry and low-rank matrix completion to find inverse kinematics solutions by completing a partial Euclidean distance matrix through local optimization. Furthermore, we parameterize the space of Euclidean distance matrices with the Riemannian manifold of fixed-rank Gram matrices, allowing us to leverage a variety of mature Riemannian optimization methods. Finally, we show that bound smoothing can be used to generate informed initializations without significant computational overhead, improving convergence. We demonstrate that our novel inverse kinematics solver achieves higher success rates than traditional techniques, and significantly outperforms them on problems that involve many workspace constraints.

Feature-based Event Stereo Visual Odometry

Event-based cameras are biologically inspired sensors that output events, i.e., asynchronous pixel-wise brightness changes in the scene. Their high dynamic range and temporal resolution of a microsecond makes them more reliable than standard cameras in environments of challenging illumination and in high-speed scenarios, thus developing odometry algorithms based solely on event cameras offers exciting new possibilities for autonomous systems and robots. In this paper, we propose a novel stereo visual odometry method for event cameras based on feature detection and matching with careful feature management, while pose estimation is done by reprojection error minimization. We evaluate the performance of the proposed method on two publicly available datasets: MVSEC sequences captured by an indoor flying drone and DSEC outdoor driving sequences. MVSEC offers accurate ground truth from motion capture, while for DSEC, which does not offer ground truth, in order to obtain a reference trajectory on the standard camera frames we used our SOFT visual odometry, one of the highest ranking algorithms on the KITTI scoreboards. We compared our method to the ESVO method, which is the first and still the only stereo event odometry method, showing on par performance on the MVSEC sequences, while on the DSEC dataset ESVO, unlike our method, was unable to handle outdoor driving scenario with default parameters. Furthermore, two important advantages of our method over ESVO are that it adapts tracking frequency to the asynchronous event rate and does not require initialization.

A Continuous-Time Approach for 3D Radar-to-Camera Extrinsic Calibration

Reliable operation in inclement weather is essential to the deployment of safe autonomous vehicles (AVs). Robustness and reliability can be achieved by fusing data from the standard AV sensor suite (i.e., lidars, cameras) with weather robust sensors, such as millimetre-wavelength radar. Critically, accurate sensor data fusion requires knowledge of the rigid-body transform between sensor pairs, which can be determined through the process of extrinsic calibration. A number of extrinsic calibration algorithms have been designed for 2D (planar) radar sensors - however, recently-developed, low-cost 3D millimetre-wavelength radars are set to displace their 2D counterparts in many applications. In this paper, we present a continuous-time 3D radar-to-camera extrinsic calibration algorithm that utilizes radar velocity measurements and, unlike the majority of existing techniques, does not require specialized radar retroreflectors to be present in the environment. We derive the observability properties of our formulation and demonstrate the efficacy of our algorithm through synthetic and real-world experiments.

A Riemannian Metric for Geometry-Aware Singularity Avoidance by Articulated Robots

Articulated robots such as manipulators increasingly must operate in uncertain and dynamic environments where interaction (with human coworkers, for example) is necessary. In these situations, the capacity to quickly adapt to unexpected changes in operational space constraints is essential. At certain points in a manipulator's configuration space, termed singularities, the robot loses one or more degrees of freedom (DoF) and is unable to move in specific operational space directions. The inability to move in arbitrary directions in operational space compromises adaptivity and, potentially, safety. We introduce a geometry-aware singularity index,defined using a Riemannian metric on the manifold of symmetric positive definite matrices, to provide a measure of proximity to singular configurations. We demonstrate that our index avoids some of the failure modes and difficulties inherent to other common indices. Further, we show that this index can be differentiated easily, making it compatible with local optimization approaches used for operational space control. Our experimental results establish that, for reaching and path following tasks, optimization based on our index outperforms a common manipulability maximization technique, ensuring singularity-robust motions.