Non-convex Pose Graph Optimization in SLAM via Proximal Linearized Riemannian ADMM

TL;DR

This paper introduces a novel non-convex pose graph optimization method for SLAM using a Riemannian ADMM approach, leveraging quaternion representations and the von Mises-Fisher distribution for improved efficiency and parallel pose updates.

Contribution

It proposes a new PGO model based on the von Mises-Fisher distribution and develops a proximal linearized Riemannian ADMM algorithm with proven iteration complexity for SLAM.

Findings

Efficient algorithm demonstrated on synthetic and real datasets.

Parallel pose updates reduce computation time.

The method achieves accurate pose estimations in benchmark tests.

Abstract

Pose graph optimization (PGO) is a well-known technique for solving the pose-based simultaneous localization and mapping (SLAM) problem. In this paper, we represent the rotation and translation by a unit quaternion and a three-dimensional vector, and propose a new PGO model based on the von Mises-Fisher distribution. The constraints derived from the unit quaternions are spherical manifolds, and the projection onto the constraints can be calculated by normalization. Then a proximal linearized Riemannian alternating direction method of multipliers (PieADMM) is developed to solve the proposed model, which not only has low memory requirements, but also can update the poses in parallel. Furthermore, we establish the iteration complexity of $O(1/\epsilon^{2})$ of PieADMM for finding an $\epsilon$-stationary solution of our model. The efficiency of our proposed algorithm is demonstrated by numerical experiments on two synthetic and four 3D SLAM benchmark datasets.