A MATHEMATICAL SENSOR MODEL FOR INDOOR USE OF A MULTI-BEAM ROTATING 3D LIDAR

Abstract

Our contribution presents a new perspective in the mathematical description of a rotating multi-beam LiDAR sensor, in a sense that we make use of projective geometry along with the “homogeneous general equation of the second degree” to parametrize scan lines. We describe the scan geometry of a typical multi-beam rotating 3D LiDAR by representing scan lines as pojective conics that represent a projective figure (a cone) in an embedding plane. This approach enables the parameterization of each scan line using a generic conic section equation. Most modeling approachs model spinning LiDAR sensors in terms of individual points sampled by a laser beam. On the contrary, we propose a model that provides a high-level geometric interpretation both for the environment and the laser scans. Possible application scenarios include exterior and interior calibration of multiple rotating multi-beam sensors, scan distortion correction and localization in planar maps.