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

TL;DR

This paper introduces CT-RIO, a novel continuous-time relative localization framework for multi-robot systems that employs clamped non-uniform B-splines to achieve high accuracy, low latency, and computational efficiency in asynchronous, high-frequency scenarios.

Contribution

It pioneers the use of Clamped Non-Uniform B-splines in continuous-time multi-robot localization, enabling real-time, high-accuracy relative localization with scalable parallel computation.

Findings

Converges from 263 ms time-offsets to sub-millisecond within 3 seconds

Achieves RMSE of 0.046 m and 1.8° in localization accuracy

Outperforms state-of-the-art methods by up to 60% in high-speed motion

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 {\deg}. It consistently outperforms state-of-the-art methods, with improvements of up to 60% under high-speed motion.