Recent work by members of the DCIST alliance 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. The proposed method is based upon a sparse semidefinite relaxation that provably 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, the paper develops Riemannian block coordinate descent (RBCD), a novel method for (locally) minimizing a function over a product of Riemannian manifolds. The paper also proposes 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). All components of the proposed approach are inherently decentralized: they require only local communication, provide privacy protection, and are easily parallelizable. Extensive evaluations on synthetic and real-world datasets demonstrate that the proposed method correctly recovers globally optimal solutions under moderate noise, and outperforms alternative distributed techniques in terms of solution precision and convergence speed.
Points of Contact: Jonathan How (PI), Yulun Tian
Citation: Y. Tian, K. Khosoussi, D. M. Rosen and J. P. How, “Distributed Certifiably Correct Pose-Graph Optimization,” in IEEE Transactions on Robotics, Dec. 2021, https://arxiv.org/pdf/1911.03721.pdf