Global Unifying Intrinsic Calibration for Spinning and Solid-State LiDARs

Abstract

Sensor calibration, which can be intrinsic or extrinsic, is an essential step to achieve the measurement accuracy required for modern perception and navigation systems deployed on autonomous robots. To date, intrinsic calibration models for spinning LiDARs have been based on hypothesized based on their physical mechanisms, resulting in anywhere from three to ten parameters to be estimated from data, while no phenomenological models have yet been proposed for solid-state LiDARs. Instead of going down that road, we propose to abstract away from the physics of a LiDAR type (spinning vs solid-state, for example), and focus on the spatial geometry of the point cloud generated by the sensor. By modeling the calibration parameters as an element of a special matrix Lie Group, we achieve a unifying view of calibration for different types of LiDARs. We further prove mathematically that the proposed model is well-constrained (has a unique answer) given four appropriately orientated targets. The proof provides a guideline for target positioning in the form of a tetrahedron. Moreover, an existing Semidefinite programming global solver for SE(3) can be modified to compute efficiently the optimal calibration parameters. For solid state LiDARs, we illustrate how the method works in simulation. For spinning LiDARs, we show with experimental data that the proposed matrix Lie Group model performs equally well as physics-based models in terms of reducing the P2P distance, while being more robust to noise.

Optimal Target Shape for LiDAR Pose Estimation

“…Before carrying out experiments with the new target shape, we used a MATLAB-based LiDAR simulator introduced in [10] to extensively evaluate the pose and vertex estimation of the optimal shape. Both quantitative and qualitative results are provided.…”

“…Target-based LiDAR-camera calibration utilizes targets to identify and estimate the corresponding features, such as vertices, 2D/3D edge lines, normal vectors, or the plane equations of the targets. References [10]- [13] have noted that placing the targets so that the rings of the LiDAR ran parallel to its edges led to ambiguity in the vertical position due to the spacing of the rings and thus was detrimental to vertex or feature estimation. References [16], [20] utilize RANSAC [26] and plane fitting to remove the outliers of the LiDAR returns, while [13] proposes a "denoising process" for LiDAR returns around the target boundaries before applying RANSAC to extract features.…”

“…(12) From ( 8), (10), (11), and (12), the gradient of the edge point with respect to the LiDAR ring is…”

“…Targets have been widely employed as fiducial markers [1]- [9] and for target-based sensor calibration [10]- [21]. Fiducial markers (artificial landmarks or targets) help robots estimate their pose by estimating the target pose and are applied to simultaneous localization and mapping (SLAM) systems for robot state estimation and loop closures.…”

Informable Multi-Objective and Multi-Directional RRT* System for Robot Path Planning

“…In the future, we shall use the developed system within autonomy systems [30,[51][52][53][54][55][56][57][58][59][60][61][62] on a robot to perform point-to-point tomometric navigation in graph-based maps while locally avoiding obstacles and uneven terrain. It would also be interesting to deploy the system with multi-layered graphs and maps [63][64][65] to incorporate different types of information.…”