Sparse Pose Graph Optimization in Cycle Space

TL;DR

This paper introduces a cycle space-based approach to pose graph optimization that leverages the graph's cycle structure for improved convergence and efficiency, especially in sparse graphs, validated through experiments and open-source code.

Contribution

It proposes a novel cycle space-based pose graph optimization method, including an algorithm for minimum cycle basis computation, with demonstrated superior convergence and efficiency.

Findings

Cycle space approach converges faster than vertex-based methods.

Cycle space method is more time-efficient for sparse graphs.

Validated on benchmarks and simulated datasets.

Abstract

The state-of-the-art modern pose-graph optimization (PGO) systems are vertex based. In this context the number of variables might be high, albeit the number of cycles in the graph (loop closures) is relatively low. For sparse problems particularly, the cycle space has a significantly smaller dimension than the number of vertices. By exploiting this observation, in this paper we propose an alternative solution to PGO, that directly exploits the cycle space. We characterize the topology of the graph as a cycle matrix, and re-parameterize the problem using relative poses, which are further constrained by a cycle basis of the graph. We show that by using a minimum cycle basis, the cycle-based approach has superior convergence properties against its vertex-based counterpart, in terms of convergence speed and convergence to the global minimum. For sparse graphs, our cycle-based approach is also more time efficient than the vertex-based. As an additional contribution of this work we present an effective algorithm to compute the minimum cycle basis. Albeit known in computer science, we believe that this algorithm is not familiar to the robotics community. All the claims are validated by experiments on both standard benchmarks and simulated datasets. To foster the reproduction of the results, we provide a complete open-source C++ implementation (Code: \url{https://bitbucket.org/FangBai/cycleBasedPGO) of our approach.