Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated least squares (TLS), maximum consensus, Geman-McClure, Tukey's biweight, among others, can be reformulated as polynomial optimization problems (POPs). By focusing on the TLS cost, our second contribution is to exploit sparsity in the POP and propose a sparse semidefinite programming (SDP) relaxation that is much smaller than the standard Lasserre's hierarchy while preserving empirical exactness, i.e., the SDP recovers the optimizer of the nonconvex POP with an optimality certificate. Our third contribution is to solve the SDP relaxations at an unprecedented scale and accuracy by presenting [Formula: see text], a solver that blends global descent on the convex SDP with fast local search on the nonconvex POP. Our fourth contribution is an evaluation of the proposed framework on six geometric perception problems including single and multiple rotation averaging, point cloud and mesh registration, absolute pose estimation, and category-level object pose and shape estimation. Our experiments demonstrate that (i) our sparse SDP relaxation is empirically exact with up to 60%- 90% outliers across applications; (ii) while still being far from real-time, [Formula: see text] is up to 100 times faster than existing SDP solvers on medium-scale problems, and is the only solver that can solve large-scale SDPs with hundreds of thousands of constraints to high accuracy; (iii) [Formula: see text] safeguards existing fast heuristics for robust estimation (e.g., [Formula: see text] or Graduated Non-Convexity), i.e., it certifies global optimality if the heuristic estimates are optimal, or detects and allows escaping local optima when the heuristic estimates are suboptimal.

Using a Two-Stage Method to Reject False Loop Closures and Improve the Accuracy of Collaborative SLAM Systems

Loop-closure detection is an essential means to reduce accumulated errors of simultaneous localization and mapping (SLAM) systems. However, even false positive loop closures could seriously interfere and even corrupt the back-end optimization process. For a collaborative SLAM system that generally uses both intra-robot and inter-robot loop closures to optimize the pose graph, it is a tough job to reject those false positive loop closures without a reliable a priori knowledge of the relative pose transformation between robots. Aiming at this solving problem, this paper proposes a two-stage false positive loop-closure rejection method based on three types of consistency checks. Firstly, a multi-robot pose-graph optimization model is given which transforms the multi-robot pose optimization problem into a maximum likelihood estimation model. Then, the principle of the false positive loop-closure rejection method based on χ2 test is proposed, in which clustering is used to reject those intra-robot false loop-closures in the first step, and a largest mutually consistent loop-based χ2 test is constructed to reject inter-robot false loop closures in the second step. Finally, an open dataset and synthetic data are used to evaluate the performance of the algorithms. The experimental results demonstrate that our method improves the accuracy and robustness of the back-end pose-graph optimization with a strong ability to reject false positive loop closures, and it is not sensitive to the initial pose at the same time. In the Computer Science and Artificial Intelligence Lab (CSAIL) dataset, the absolute position error is reduced by 55.37% compared to the dynamic scaling covariance method, and the absolute rotation error is reduced by 77.27%; in the city10,000 synthetic dataset, the absolute position error is reduced by 89.37% compared to the pairwise consistency maximization (PCM) and the absolute rotation error is reduced by 97.9%.

Assistive Navigation Using Deep Reinforcement Learning Guiding Robot With UWB/Voice Beacons and Semantic Feedbacks for Blind and Visually Impaired People

Facilitating navigation in pedestrian environments is critical for enabling people who are blind and visually impaired (BVI) to achieve independent mobility. A deep reinforcement learning (DRL)-based assistive guiding robot with ultrawide-bandwidth (UWB) beacons that can navigate through routes with designated waypoints was designed in this study. Typically, a simultaneous localization and mapping (SLAM) framework is used to estimate the robot pose and navigational goal; however, SLAM frameworks are vulnerable in certain dynamic environments. The proposed navigation method is a learning approach based on state-of-the-art DRL and can effectively avoid obstacles. When used with UWB beacons, the proposed strategy is suitable for environments with dynamic pedestrians. We also designed a handle device with an audio interface that enables BVI users to interact with the guiding robot through intuitive feedback. The UWB beacons were installed with an audio interface to obtain environmental information. The on-handle and on-beacon verbal feedback provides points of interests and turn-by-turn information to BVI users. BVI users were recruited in this study to conduct navigation tasks in different scenarios. A route was designed in a simulated ward to represent daily activities. In real-world situations, SLAM-based state estimation might be affected by dynamic obstacles, and the visual-based trail may suffer from occlusions from pedestrians or other obstacles. The proposed system successfully navigated through environments with dynamic pedestrians, in which systems based on existing SLAM algorithms have failed.

Robust Extrinsic Calibration of Multiple RGB-D Cameras with Body Tracking and Feature Matching

RGB-D cameras have been commercialized, and many applications using them have been proposed. In this paper, we propose a robust registration method of multiple RGB-D cameras. We use a human body tracking system provided by Azure Kinect SDK to estimate a coarse global registration between cameras. As this coarse global registration has some error, we refine it using feature matching. However, the matched feature pairs include mismatches, hindering good performance. Therefore, we propose a registration refinement procedure that removes these mismatches and uses the global registration. In an experiment, the ratio of inliers among the matched features is greater than 95% for all tested feature matchers. Thus, we experimentally confirm that mismatches can be eliminated via the proposed method even in difficult situations and that a more precise global registration of RGB-D cameras can be obtained.

Reliable and Fast Localization in Ambiguous Environments Using Ambiguity Grid Map

In real-world robotic navigation, some ambiguous environments contain symmetrical or featureless areas that may cause the perceptual aliasing of external sensors. As a result of that, the uncorrected localization errors will accumulate during the localization process, which imposes difficulties to locate a robot in such a situation. Using the ambiguity grid map (AGM), we address this problem by proposing a novel probabilistic localization method, referred to as AGM-based adaptive Monte Carlo localization. AGM has the capacity of evaluating the environmental ambiguity with average ambiguity error and estimating the possible localization error at a given pose. Benefiting from the constructed AGM, our localization method is derived from an improved Dynamic Bayes network to reason about the robot's pose as well as the accumulated localization error. Moreover, a portal motion model is presented to achieve more reliable pose prediction without time-consuming implementation, and thus the accumulated localization error can be corrected immediately when the robot moving through an ambiguous area. Simulation and real-world experiments demonstrate that the proposed method improves localization reliability while maintains efficiency in ambiguous environments.