Parallel Continuous-Time Relative Localization with Augmented Clamped Non-Uniform B-Splines

Accurate relative localization is critical for multi-robot cooperation. In robot swarms, measurements from different robots arrive asynchronously and with clock time-offsets. Although Continuous-Time (CT) formulations have proved effective for handling asynchronous measurements in single-robot SLAM and calibration, extending CT methods to multi-robot settings faces great challenges to achieve high-accuracy, low-latency, and high-frequency performance. Especially, existing CT methods suffer from the inherent query-time delay of unclamped B-splines and high computational cost. This paper proposes CT-RIO, a novel Continuous-Time Relative-Inertial Odometry framework. We employ Clamped Non-Uniform B-splines (C-NUBS) to represent robot states for the first time, eliminating the query-time delay. We further augment C-NUBS with closed-form extension and shrinkage operations that preserve the spline shape, making it suitable for online estimation and enabling flexible knot management. This flexibility leads to the concept of knot-keyknot strategy, which supports spline extension at high-frequency while retaining sparse keyknots for adaptive relative-motion modeling. We then formulate a sliding-window relative localization problem that operates purely on relative kinematics and inter-robot constraints. To meet the demanding computation required at swarm scale, we decompose the tightly-coupled optimization into robot-wise sub-problems and solve them in parallel using incremental asynchronous block coordinate descent. Extensive experiments show that CT-RIO converges from time-offsets as large as 263 ms to sub-millisecond within 3 s, and achieves RMSEs of 0.046 m and 1.8 °. It consistently outperforms state-of-the-art methods, with improvements of up to 60% under high-speed motion.

CREPES-X: Hierarchical Bearing-Distance-Inertial Direct Cooperative Relative Pose Estimation System

Relative localization is critical for cooperation in autonomous multi-robot systems. Existing approaches either rely on shared environmental features or inertial assumptions or suffer from non-line-of-sight degradation and outliers in complex environments. Robust and efficient fusion of inter-robot measurements such as bearings, distances, and inertials for tens of robots remains challenging. We present CREPES-X (Cooperative RElative Pose Estimation System with multiple eXtended features), a hierarchical relative localization framework that enhances speed, accuracy, and robustness under challenging conditions, without requiring any global information. CREPES-X starts with a compact hardware design: InfraRed (IR) LEDs, an IR camera, an ultra-wideband module, and an IMU housed in a cube no larger than 6cm on each side. Then CREPES-X implements a two-stage hierarchical estimator to meet different requirements, considering speed, accuracy, and robustness. First, we propose a single-frame relative estimator that provides instant relative poses for multi-robot setups through a closed-form solution and robust bearing outlier rejection. Then a multi-frame relative estimator is designed to offer accurate and robust relative states by exploring IMU pre-integration via robocentric relative kinematics with loosely- and tightly-coupled optimization. Extensive simulations and real-world experiments validate the effectiveness of CREPES-X, showing robustness to up to 90% bearing outliers, proving resilience in challenging conditions, and achieving RMSE of 0.073m and 1.817° in real-world datasets.

Mr. Virgil: Learning Multi-robot Visual-range Relative Localization

Ultra-wideband (UWB)-vision fusion localization has achieved extensive applications in the domain of multi-agent relative localization. The challenging matching problem between robots and visual detection renders existing methods highly dependent on identity-encoded hardware or delicate tuning algorithms. Overconfident yet erroneous matches may bring about irreversible damage to the localization system. To address this issue, we introduce Mr. Virgil, an end-to-end learning multi-robot visual-range relative localization framework, consisting of a graph neural network for data association between UWB rangings and visual detections, and a differentiable pose graph optimization (PGO) back-end. The graph-based front-end supplies robust matching results, accurate initial position predictions, and credible uncertainty estimates, which are subsequently integrated into the PGO back-end to elevate the accuracy of the final pose estimation. Additionally, a decentralized system is implemented for real-world applications. Experiments spanning varying robot numbers, simulation and real-world, occlusion and non-occlusion conditions showcase the stability and exactitude under various scenes compared to conventional methods. Our code is available at: https://github.com/HiOnes/Mr-Virgil.