Affine-SLAM: A closed-form solution to the landmark-SLAM via affine relaxation

Abstract

We propose a closed-form solution to the landmark simultaneous localization and mapping (landmarkSLAM) problem. The core idea is to extend the recent advancement in the generalized Procrustes analysis (GPA) research by incorporating an affine-relaxed odometry term. We show that the resulting affine relaxed landmark-SLAM formulation, termed affine-SLAM, can be solved globally in closed-form. Through numerical experiments, we demonstrate that the affine-SLAM solution is rather close to the optimal solution of the standard nonlinear least squares (NLS) optimization, and thus can be used either as a stand-alone approximate solution or as a high-quality initialization for NLS solvers.