Distributed Pose-graph Optimization with Multi-level Partitioning for Collaborative SLAM

TL;DR

This work targets the distributed backend of collaborative SLAM by addressing SE(d)-synchronization in pose-graph optimization. It combines multi-level graph partitioning to produce balanced subproblems with an Improved Riemannian Block Coordinate Descent (IRBCD) algorithm applied to a Low-Rank Convex Relaxation (LRCR) of the SDP-formulated PGO, ensuring convergence to a first-order stationary point. The Highest KaHIP partitioning scheme yields the best balance and the IRBCD solver accelerates convergence compared to prior RBCD-based methods. Empirical results show reduced inter-subgraph communication, faster convergence, and improved objective values over state-of-the-art distributed PGO methods across multiple datasets and robot counts, highlighting practical benefits for scalable CSLAM back-ends.

Abstract

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.

Figures (6)

• Figure 1: Representation of (a) sequential partitioning and (b) graph partitioning. We denote the pose variable blocks by $T_1, \cdots,T_8$, use solid black lines to represent the loop closure within the robot, and use dashed red lines to represent the relative pose relationship between the robots. (a) and (b) exhibit the subgraphs obtained by each robot after sequential partitioning and graph partitioning, respectively.
• Figure 2: The relationship among the “Centralized PGO”, “DPGO (Problem 1-3)”, “IRBCD Algorithm”, and “Theorem 1” that are discussed in this work.
• Figure 3: The procedure of the multi-level graph partitioning. The whole process is divided into three stages: 1) nodes with high coupling degree are matched according to the evaluation function; 2) methods such as edge-cut partitioning or vertex-cut partitioning are used to split the original graph into balanced subgraphs equal to the number of robots; 3) the subgraphs are fine-tuned to generate the agent-level pose graphs.
• Figure 4: The impact of different graph partitioning methods on the performance of optimization algorithm. We integrate each of the four multi-level graph partitioning methods with the RBCD algorithm and conduct experiments on the Garage and Grid datasets. Meanwhile, we take the RBCD algorithm based on sequential graph partitioning as the baseline.
• Figure 5: The performance comparison of IRBCD algorithm (ours) and RBCD, RBCD++ optimization algorithms. The Torus and Grid datasets are used to test the performance of three distributed optimization algorithms, and their convergence results are obtained.

Theorems & Definitions (1)

• Theorem 1