并行连续时间相对定位与增强钳制非均匀B样条
Parallel Reference-Centric Continuous-Time Relative Localization with Augmented Clamped Non-Uniform B-Splines
AI总结：
本文提出CT-RIO框架，利用钳制非均匀B样条实现高精度、低延迟的多机器人相对定位，通过灵活的节点管理提升计算效率。
摘要：
准确的相对定位对于多机器人协作至关重要。在机器人群体中，不同机器人的测量数据到达时间不同且存在时钟偏移。尽管连续时间（CT）方法在单机器人SLAM和校准中已被证明能有效处理异步测量，但将其扩展到多机器人环境面临巨大挑战，以实现高精度、低延迟和高频率性能。特别是，现有CT方法存在未钳制B样条的固有查询时间延迟和高计算成本。本文提出CT-RIO，一种新的连续时间相对惯性里程计框架。我们首次使用钳制非均匀B样条（C-NUBS）表示机器人状态，从而消除查询时间延迟。我们进一步通过闭式扩展和收缩操作增强C-NUBS，保持样条形状，使其适合在线估计，并实现灵活的节点管理。这种灵活性导致了节点-键节点策略的概念，该策略支持高频样条扩展，同时保留稀疏键节点以适应相对运动建模。然后，我们提出一个滑动窗口相对定位问题，该问题仅基于相对运动学和机器人间约束。为满足群体规模的计算需求，我们将紧密耦合的优化分解为机器人级别的子问题，并使用增量异步块坐标下降法并行求解。广泛的实验表明，CT-RIO在3秒内将时间偏移从263毫秒收敛到亚毫秒级别，并达到RMSE为0.046米和1.8度。它在高速运动下比最先进的方法改进达60%。
英文摘要：
Accurate relative localization is critical for multi-robot cooperation. In robot groups, 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 in achieving high-accuracy, low-latency, and high-frequency performance. In particular, existing CT methods suffer from the inherent query-time delay of unclamped B-splines and high optimization latency. This paper proposes CT-RIO, a novel Continuous-Time Relative-Inertial Odometry framework. We adopt Clamped Non-Uniform B-splines (C-NUBS) to represent states, 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 a knot-keyknot strategy, which supports spline extension at high frequency while retaining sparse keyknots for adaptive relative motion modeling. We then formulate a reference-centric sliding-window relative localization problem that operates purely on relative kinematics and inter-robot constraints. To enable low-latency and high-frequency estimation, we decompose the tightly coupled optimization into robot-wise subproblems and solve them in parallel using asynchronous block coordinate descent. Extensive experiments show that CT-RIO converges from time-offsets as large as 264 ms to sub-millisecond within 3 s, and achieves RMSEs of 0.046 m and 1.8 degree. It consistently outperforms evaluated published methods, with improvements of up to 60% under high-speed motion.
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