Unified Representation of Geometric Primitives for Graph-SLAM Optimization Using Decomposed Quadrics

Weikun Zhen, Huai Yu, Yaoyu Hu, Sebastian A. Scherer

Abstract: In Simultaneous Localization And Mapping (SLAM) problems, high-level landmarks have the potential to build compact and informative maps compared to traditional point-based landmarks. In this work, we focus on the param-eterization of frequently used geometric primitives including points, lines, planes, ellipsoids, cylinders, and cones. We first present a unified representation based on quadrics, an algebraic representation of quadratic surfaces in 3D. Then we propose a decomposed model of quadrics that discloses the symmetry and degeneration properties of a primitive. Based on the decomposition, we develop geometrically meaningful quadrics factors for the graph-SLAM problem. Then in simulation, it is shown that the decomposed formulation has better efficiency and robustness to observation noises than baseline parame-terizations. Finally, in real-world experiments, the proposed back-end framework is demonstrated to be capable of building compact and regularized maps.