Distributed Pose Graph Optimization using the Splitting Method based on the Alternating Direction Method of Multipliers

TL;DR

This paper tackles distributed pose graph optimization under non-convex rotation constraints by introducing a Splitting Orthogonality Constraints (SOC) approach that couples ADMM with Split Bregman iterations to solve rotation subproblems without relaxing the non-convex constraints. The rotation updates are complemented by translations, enabling full pose recovery on $SE(n)$ with $R_i\in SO(n)$ and $t_i\in\mathbb{R}^n$. Compared to centralized SE-Sync and distributed Gauss-Seidel (DGS), the SOC method achieves near-global minima with competitive run times and robust performance on large-scale pose graphs, demonstrating a scalable distributed non-convex optimization framework for SLAM-like settings. The approach offers practical advantages for multi-robot systems, preserving non-convex constraints while delivering accuracy and efficiency improvements over state-of-the-art baselines.

Abstract

Distributed optimization aims to leverage the local computation and communication capabilities of each agent to achieve a desired global objective. This paper addresses the distributed pose graph optimization (PGO) problem under non-convex constraints, with the goal of approximating the rotation and translation of each pose given relevant noisy measurements. To achieve this goal, the splitting method based on the concepts of the alternating direction method of multipliers (ADMM) and Bregman iteration are applied to solve the rotation subproblems. The proposed approach enables the iterative resolution of constrained problems, achieved through solving unconstrained problems and orthogonality-constrained quadratic problems that have analytical solutions. The performance of the proposed algorithm is compared against two practical methods in pose graph optimization: the Distributed Gauss-Seidel (DGS) algorithm and the centralized pose graph optimizer with an optimality certificate (SE-Sync). The efficiency of the proposed method is verified through its application to several simulated and real-world pose graph datasets. Unlike the DGS method, our approach attempts to solve distributed PGO problems without relaxing the non-convex constraints.

Figures (4)

• Figure 1: Pose graph structure instance with 4 robots, each with 4 poses. Each edge represents a relative pose measurement. The inter-robot measurements are illustrated with the dotted line between two connected robots. The solid line denotes the intra-robot measurements of each robot.
• Figure 2: The flow chart of the proposed algorithm.
• Figure 3: Circular, sphere, and grid pose graphs from left to right. The first row demonstrates the ground truth of network topologies. The second row illustrates the obtained solution by applying the SOC algorithm.
• Figure 4: The outcomes regarding the SOC algorithm for the parking garage, cubicle, and torus pose graphs are depicted from left to right.

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3