Parallel Continuous-Time Relative Localization with Augmented Clamped Non-Uniform B-Splines 基于增广钳制非均匀 B 样条的并行连续时间相对定位
Overview 项目概述
Bearing, range and inertial measurements arrive at different rates and often on unsynchronized robot clocks. CT-RIO represents relative motion with augmented clamped non-uniform B-splines, allowing each observation to constrain the trajectory at its native timestamp rather than being interpolated or discarded at discrete keyframes. Knot density adapts to the motion, and inter-robot clock offsets are estimated jointly with the trajectory; an initial offset of 263 ms converges to sub-millisecond accuracy within 3 s. Closed-form spline extension and shrinkage preserve the existing curve while supporting online updates. To keep the tightly coupled problem tractable as the team grows, CT-RIO decomposes it into robot-wise subproblems and solves them with incremental asynchronous block coordinate descent, for which convergence is established. Real-world experiments report 0.046 m / 1.8° RMSE and up to 60% lower error than discrete-time optimization under high-speed motion.
方位、测距与惯性观测具有不同频率，而且不同机器人的系统时钟往往并不同步。CT-RIO 使用增广钳制非均匀 B 样条表示相对运动，使每条观测都能在原始时间戳处约束轨迹，无需将其插值到离散关键帧或直接丢弃。样条节点密度随运动状态自适应变化，机间时钟偏移则与轨迹联合估计；263 ms 的初始时偏可在 3 s 内收敛至亚毫秒级。闭式样条扩展与收缩在在线更新控制点时保持已有曲线形状不变。为控制多机器人紧耦合优化的计算开销，CT-RIO 将问题拆分为逐机器人子问题，并采用具有收敛性保证的增量异步块坐标下降并行求解。真机实验报告 0.046 m / 1.8° RMSE，高速运动下的误差较离散时间优化最高降低 60%。
Key Contributions 主要贡献
- Native-timestamp fusion. A continuous-time spline lets asynchronous, multi-rate measurements constrain the trajectory where they occur, without keyframe interpolation or sample dropping.
- Adaptive trajectory and clock modeling. Non-uniform knots follow motion complexity, while inter-robot time offsets are estimated directly from the same factor graph.
- Shape-preserving online updates. Closed-form extension and shrinkage add or remove spline support without deforming the represented trajectory.
- Parallel optimization with convergence guarantees. Robot-wise decomposition and incremental asynchronous block coordinate descent provide scalable online inference.
- High-speed accuracy. Real-world experiments report 0.046 m / 1.8° RMSE and improvements of up to 60% over discrete-time optimization.
- 原始时间戳融合。连续时间样条使异步、异频观测在真实发生时刻约束轨迹，无需关键帧插值或丢弃数据。
- 自适应轨迹与时钟建模。非均匀节点随运动复杂度调整，同时在同一因子图中直接估计机间时偏。
- 保形在线更新。闭式扩展与收缩能够增删样条支撑，同时保持所表示的已有轨迹不变。
- 具有收敛保证的并行优化。逐机器人分解与增量异步块坐标下降支持可扩展的在线求解。
- 高速运动精度。真机实验报告 0.046 m / 1.8° RMSE，较离散时间优化最多降低 60% 误差。
BibTeX
@article{lu2026parallel,
title = {Parallel Continuous-Time Relative Localization with Augmented Clamped Non-Uniform B-Splines},
author = {Lu, Jiadong and Li, Zhehan and Han, Tao and Xu, Miao and Xu, Chao and Cao, Yanjun},
journal = {arXiv preprint arXiv:2602.22006},
year = {2026}
}