SE-Sync

a certifiably correct algorithm for synchronization over the special Euclidean group

David M. Rosen, Luca Carlone, Afonso Bandeira, John J. Leonard

Research output: Contribution to journalArticle

Abstract

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown group elements (Formula presented.) given noisy measurements of a subset of their pairwise relative transforms (Formula presented.). Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a non-convex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation (MLE) whose minimizer provides an exact maximum-likelihood estimate so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so significantly faster than the Gauss–Newton-based approach that forms the basis of current state-of-the-art techniques.

Original languageEnglish (US)
JournalInternational Journal of Robotics Research
DOIs
StateAccepted/In press - Jan 1 2018

Fingerprint

Euclidean
Synchronization
Maximum likelihood estimation
Semidefinite Relaxation
Computer vision
Simultaneous Localization and Mapping
Robotics
Maximum Likelihood Estimation
Computer Vision
Graph in graph theory
Optimal Solution
Motion estimation
Distributed Sensing
Critical Threshold
Trust Region Method
Maximum likelihood
Sensor networks
Optimization
Exactness
Rounding

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Applied Mathematics

Cite this

SE-Sync : a certifiably correct algorithm for synchronization over the special Euclidean group. / Rosen, David M.; Carlone, Luca; Bandeira, Afonso; Leonard, John J.

In: International Journal of Robotics Research, 01.01.2018.

Research output: Contribution to journalArticle

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