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.

翻译：精确的相对定位对多机器人协同至关重要。在机器人集群中，来自不同机器人的测量数据以异步方式到达且存在时钟偏移。尽管连续时间（CT）方法已被证明在单机器人SLAM与标定中处理异步测量具有效性，但将CT方法扩展至多机器人场景时，要实现高精度、低延迟与高频性能仍面临巨大挑战。尤其现有CT方法存在非夹持B样条的固有查询延迟问题及高昂计算成本。本文提出CT-RIO——一种新型连续时间相对惯性里程计框架。我们首次采用夹持非均匀B样条（C-NUBS）表征机器人状态，彻底消除了查询延迟。进一步通过闭式扩展与收缩操作对C-NUBS进行增强，该操作在保持样条形状的同时，使其适用于在线估计并实现灵活的节点管理。这种灵活性催生了节点-关键节点策略，支持高频样条扩展的同时保留稀疏关键节点以进行自适应相对运动建模。随后构建了纯基于相对运动学与机器人间约束的滑动窗口相对定位问题。为满足集群规模所需的严苛计算需求，我们将紧耦合优化分解为按机器人划分的子问题，并采用增量异步块坐标下降法进行并行求解。大量实验表明：CT-RIO能在3秒内将高达263毫秒的时间偏移收敛至亚毫秒级，并实现0.046米与1.8°的均方根误差。其性能持续超越现有先进方法，在高速运动场景下最高可提升60%。