Majorization Minimization Methods for Distributed Pose Graph Optimization with Convergence Guarantees

In this paper, we consider the problem of distributed pose graph optimization (PGO) that has extensive applications in multi-robot simultaneous localization and mapping (SLAM). We propose majorization minimization methods for distributed PGO and show that our methods are guaranteed to converge to first-order critical points under mild conditions. Furthermore, since our methods rely a proximal operator of distributed PGO, the convergence rate can be significantly accelerated with Nesterov's method, and more importantly, the acceleration induces no compromise of convergence guarantees. In addition, we also present accelerated majorization minimization methods for the distributed chordal initialization that have a quadratic convergence, which can be used to compute an initial guess for distributed PGO. The efficacy of this work is validated through applications on a number of 2D and 3D SLAM datasets and comparisons with existing state-of-the- art methods, which indicates that our methods have faster convergence and result in better solutions to distributed PGO.

Authors

• Taosha Fan
• Todd D. Murphey

Keywords

• Simultaneous localization and mapping
• Minimization methods
• Three-dimensional displays
• Optimization
• Convergence
• Accelerometers
• Two-dimensional displays
• Convergence Guarantees
• Majorization
• Pose Graph Optimization
• Mild Conditions
• Convergence Rate
• Art Methods
• Proximal Operator
• Chordal
• 2D Datasets
• Matter Of Fact
• Convex Optimization
• Neighboring Nodes
• Single Node
• Convex Optimization Problem
• Positive Semidefinite Matrix
• Block Diagonal Matrix
• Noisy Measurements
• Gauss-Newton Method