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

2026-02-25

AI Summary

This work addresses the challenge of achieving high-precision, low-latency relative localization in multi-robot systems under asynchronous measurements and significant clock offsets. To this end, the authors propose the CT-RIO framework, which introduces clamped non-uniform B-splines (C-NUBS) to represent continuous-time trajectories, thereby eliminating query latency. The framework features closed-form expansion and contraction operations for online estimation, combined with a knot-keyknot strategy to enable high-frequency updates and adaptive sparsification. Efficient optimization is achieved through a sliding-window approach coupled with parallel incremental block coordinate descent. Experiments demonstrate that the system converges to sub-millisecond clock synchronization within three seconds despite an initial 263 ms offset, achieving pose RMSE of 0.046 m and 1.8°, and outperforming state-of-the-art methods by up to 60% in high-speed scenarios.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• relative localization
• multi-robot systems
• asynchronous measurements
• time-offset
• continuous-time estimation

Innovation

• Clamped Non-Uniform B-splines
• Continuous-Time Relative Localization
• knot-keyknot strategy
• parallel asynchronous optimization
• relative-inertial odometry