DeepAI AI Chat
Log In Sign Up

Sparse Pose Graph Optimization in Cycle Space

by   Fang Bai, et al.
University of Technology Sydney
Sapienza University of Rome

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: < of our approach.>


page 1

page 15

page 20


Incremental cycle bases for cycle-based pose graph optimization

Pose graph optimization is a special case of the simultaneous localizati...

Cycle Intersection Graphs and Minimum Decycling Sets of Even Graphs

We introduce the cycle intersection graph of a graph, an adaptation of t...

On the Price of Independence for Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal

Let vc(G), fvs(G) and oct(G), respectively, denote the size of a minimum...

Erdős-Pósa property of chordless cycles and its applications

A chordless cycle in a graph G is an induced subgraph of G which is a cy...

A Dynamic MaxSAT-based Approach to Directed Feedback Vertex Sets

We propose a new approach to the Directed Feedback Vertex Set Problem (D...

Matrix Difference in Pose-Graph Optimization

Pose-Graph optimization is a crucial component of many modern SLAM syste...

RMB-DPOP: Refining MB-DPOP by Reducing Redundant Inferences

MB-DPOP is an important complete algorithm for solving Distributed Const...