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：分布式协作同时定位与地图构建（DCSLAM）的后端模块需要在分布式环境下求解非线性位姿图优化（PGO）问题，即SE(d)-同步问题。现有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，该方案可能导致子图维度不均衡，从而增加额外通信负担。此外，当前黎曼优化算法的性能仍有进一步提升空间。本文提出一种融合多层划分与加速黎曼优化的新型分布式位姿图优化算法。首先，采用多层图划分算法对原始位姿图进行预处理，构建平衡优化问题；其次，受加速坐标下降法启发，设计改进黎曼块坐标下降（IRBCD）算法，所得临界点具有全局最优性；最后，评估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。通过仿真实验定量验证，本文算法优于现有最先进的分布式位姿图优化协议。