论文标题
光谱稀疏，用于沟通效率的协作旋转和翻译估计
Spectral Sparsification for Communication-Efficient Collaborative Rotation and Translation Estimation
论文作者
论文摘要
我们提出了用于多机器人旋转平均和翻译估计问题的快速和沟通优化算法，这些算法是由协作同时定位和映射（SLAM），结构 - 触发器（SFM）和相机网络本地化应用产生的。我们的方法基于基本的里曼优化问题的黑森人与适当加权图的拉普拉斯人之间的理论关系。我们利用这些结果来设计一个协作求解器，在该求解器中，机器人与中央服务器协调，以在每次迭代中求解laplacian系统进行近似二阶优化。至关重要的是，我们的算法允许机器人在通信之前使用光谱稀疏来稀疏中间密集的矩阵，从而提供了一种机制，可以通过可证明的保证和可证明的沟通效率进行准确的贸易准确性。我们对我们的方法进行严格的理论分析，并证明他们享受（局部）线性收敛速率。此外，我们表明我们的方法可以与渐变的非凸度结合在一起，以实现异常表现估计。对现实世界大满贯和SFM方案的广泛实验证明了我们方法的较高收敛率和沟通效率。
We propose fast and communication-efficient optimization algorithms for multi-robot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and camera network localization applications. Our methods are based on theoretical relations between the Hessians of the underlying Riemannian optimization problems and the Laplacians of suitably weighted graphs. We leverage these results to design a collaborative solver in which robots coordinate with a central server to perform approximate second-order optimization, by solving a Laplacian system at each iteration. Crucially, our algorithms permit robots to employ spectral sparsification to sparsify intermediate dense matrices before communication, and hence provide a mechanism to trade off accuracy with communication efficiency with provable guarantees. We perform rigorous theoretical analysis of our methods and prove that they enjoy (local) linear rate of convergence. Furthermore, we show that our methods can be combined with graduated non-convexity to achieve outlier-robust estimation. Extensive experiments on real-world SLAM and SfM scenarios demonstrate the superior convergence rate and communication efficiency of our methods.
