Novel Parameterization for Gauss–Newton Methods in 3-D Pose Graph Optimization

Pose graph optimization (PGO), or equivalently pose synchronization, that is synchronizing rotations and positions, is the state-of-the-art formulation for simultaneous localization and mapping in robotics. In this article, we first present a new manifold Gauss-Newton method for solving the rotation synchronization problem. In this article, we derive an efficient implementation of the method and develop a convergence theory thereof. A structural parameter appears in the proof, which has a significant influence on the convergence basin. In this article, we show that this structural parameter is the norm of the inverse of the reduced graph Laplacian and obtains the explicit relation of this parameter for special graph structures. We also present another method that directly solves the pose synchronization using both relative rotation and translation observations. Experimental results show that our rotation synchronization method can be successfully used to initialize iterative PGO solvers. Furthermore, we show that our pose synchronization algorithm outperforms state-of-the-art solvers in high-noise cases.