Optimizing Scan Homogeneity for Building Full-3D Lidars Based on Rotating a Multi-Beam Velodyne Range-Finder

Multi-beam lidar (MBL) scanners are compact, light, and accessible 3D sensors with high data rates, but they offer limited vertical resolution and field of view (FOV). Some recent robotics research has profited from the addition of a degree-of-freedom (DOF) to an MBL to build rotating multibeam lidars (RMBL) that can achieve high-resolution scans with full spherical FOV. In a previous work, we offered a methodology to analyze the complex 3D scan measurement distributions produced by RMBLs with a rolling DOF and no pitching. In this paper, we investigate the effect of introducing constant pitch angles in the construction of the RMBLs with the purpose of finding a kinematic configuration that optimizes scan homogeneity with a spherical FOV. To this end, we propose a scalar index of 3D sensor homogeneity that is based on the spherical formulation of Ripley's K function. The optimization is performed for the widely used Puck (VLP-16) and HDL-32 sensors by Velodyne.