Block-Coordinate Descent on the Riemannian Staircase for Certifiably Correct Distributed Rotation and Pose Synchronization
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This paper presents the first certifiably correct solver for distributed pose-graph optimization (PGO), the backbone of modern collaborative simultaneous localization and mapping (CSLAM) and camera network localization (CNL) systems. By pursuing a sparse semidefinite relaxation, our approach provides formal performance guarantees that match state-of-the-art centralized techniques. In particular, under low noise, the proposed distributed solver is guaranteed to find globally optimal solutions despite the non-convexity of PGO. To solve the resulting large-scale semidefinite programs, we adopt the state-of-the-art Riemannian Staircase framework and develop Riemannian block-coordinate descent (RBCD) as the core distributed local search algorithm. RBCD is well-suited to distributed synchronization problems (such as rotation and pose synchronization) as it only requires local communication, provides privacy protection, and is easily parallelizable. Furthermore, we prove that RBCD converges to first-order critical points for general Riemannian optimization problems over product manifolds, and establish a global sublinear convergence rate. Extensive evaluations on real and synthetic PGO datasets demonstrate state-of-the-art performance of the proposed distributed solver.
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