Distributed Certifiably Correct Pose-Graph Optimization.

Area of Science:

• Robotics
• Computer Vision
• Optimization

Background:

• Pose-graph optimization (PGO) is fundamental for collaborative simultaneous localization and mapping (CSLAM) and camera network localization (CNL).
• Existing methods often rely on centralized approaches, limiting scalability and robustness in distributed systems.
• There is a need for certifiably correct distributed algorithms for PGO.

Purpose of the Study:

• To develop the first certifiably correct algorithm for distributed pose-graph optimization (PGO).
• To enable distributed systems to achieve globally optimal PGO solutions.
• To provide decentralized methods for solution verification and saddle point escape.

Main Methods:

• A sparse semidefinite relaxation is employed to ensure globally optimal PGO solutions under moderate noise.
• The low-rank Riemannian Staircase framework is adapted for distributed optimization.
• Riemannian block coordinate descent (RBCD) is introduced for minimizing functions over product Riemannian manifolds.
• Distributed solution verification and saddle escape methods are proposed for global optimality certification.

Main Results:

• The proposed algorithm achieves certifiably correct, globally optimal PGO solutions in a distributed manner.
• The method matches the guarantees of state-of-the-art centralized approaches.
• Evaluations show superior solution precision and convergence speed compared to alternative distributed techniques.
• The approach is inherently decentralized, supporting local communication, privacy, and parallelization.

Conclusions:

• This work presents a significant advancement in distributed PGO, enabling robust and scalable CSLAM and CNL.
• The developed RBCD and verification methods offer a reliable framework for decentralized optimization problems.
• The algorithm's ability to certify global optimality in a distributed setting opens new avenues for real-world applications.