Distributed Certifiably Correct Pose-Graph Optimization

Understand

This paper presents the first certifiably correct algorithm for distributed pose-graph optimization (PGO), the backbone of modern collaborative simultaneous localization and mapping (CSLAM) and camera network localization (CNL) systems.

• Our method is based upon a sparse semidefinite relaxation that we prove provides globally-optimal PGO solutions under moderate measurement noise (matching the guarantees enjoyed by state-of-the-art centralized methods), but is amenable to distributed optimization using the low-rank Riemannian Staircase framework.
• To implement the Riemannian Staircase in the distributed setting, we develop Riemannian block coordinate descent (RBCD), a novel method for (locally) minimizing a function over a product of Riemannian manifolds.
• We also propose the first distributed solution verification and saddle escape methods to certify the global optimality of critical points recovered via RBCD, and to descend from suboptimal critical points (if necessary).