The back-end module of Distributed Collaborative Simultaneous Localization and Mapping (DCSLAM) requires solving a nonlinear Pose Graph Optimization (PGO) under a distributed setting, also known as SE(d)-synchronization. Most existing distributed graph optimization algorithms employ a simple sequential partitioning scheme, which may result in unbalanced subgraph dimensions due to the different geographic locations of each robot, and hence imposes extra communication load. Moreover, the performance of current Riemannian optimization algorithms can be further accelerated. In this letter, we propose a novel distributed pose graph optimization algorithm combining multi-level partitioning with an accelerated Riemannian optimization method. Firstly, we employ the multi-level graph partitioning algorithm to preprocess the naive pose graph to formulate a balanced optimization problem. In addition, inspired by the accelerated coordinate descent method, we devise an Improved Riemannian Block Coordinate Descent (IRBCD) algorithm and the critical point obtained is globally optimal. Finally, we evaluate the effects of four common graph partitioning approaches on the correlation of the inter-subgraphs, and discover that the Highest scheme has the best partitioning performance. Also, we implement simulations to quantitatively demonstrate that our proposed algorithm outperforms the state-of-the-art distributed pose graph optimization protocols.

翻译：分布式协同同时定位与建图（DCSLAM）的后端模块需要在分布式设置下求解非线性位姿图优化问题，即SE(d)-同步。现有的大多数分布式图优化算法采用简单的顺序划分方案，由于各机器人所处地理位置不同，可能导致子图维度不平衡，从而增加额外的通信负载。此外，当前黎曼优化算法的性能仍有进一步加速的空间。本文提出一种结合多级划分与加速黎曼优化方法的新型分布式位姿图优化算法。首先，采用多级图划分算法对原始位姿图进行预处理，以构建平衡优化问题。其次，受加速坐标下降法启发，设计了一种改进黎曼块坐标下降（IRBCD）算法，且所获得的临界点具有全局最优性。最后，评估了四种常见图划分方法对子图间相关性的影响，发现Highest方案具有最佳划分性能。同时，通过仿真实验定量表明，本文所提算法优于现有最先进的分布式位姿图优化协议。