On the Angular Control of Rotating Lasers by Means of Line Calculus on Hyperboloids

Area of Science:

• Robotics and Automation
• Computer Vision
• Optical Engineering

Background:

• Laser scanners with rotational symmetry, such as lidars and galvanometric systems, require precise calibration for accurate data acquisition.
• Traditional calibration methods often rely on complex physical models and numerous measurements, which can be time-consuming and data-intensive.

Purpose of the Study:

• To propose a new paradigm for modeling and calibrating laser scanners with rotational symmetry using geometric properties.
• To develop a line-data-driven procedure that simplifies the calibration process and reduces measurement requirements.

Main Methods:

• Modeling the laser scanner as a specific configuration of lines based on its geometric properties, rather than relying on intrinsic physical parameters.
• Utilizing an algebraic-geometric approach that requires only a few measurements for calibration.
• Representing a two-mirror galvanometric laser scanner as a grid of hyperboloids, approximated by a 3x3 grid of lines, forming a novel line-based lookup table.

Main Results:

• The proposed method successfully models and calibrates laser scanners with rotational symmetry using a reduced number of measurements.
• A new type of lookup table, comprising nine lines instead of points, enables exact affine combinations, replacing traditional interpolation.
• Validation in a realistic virtual setting confirmed the method's efficacy, with a collateral contribution of a robust algorithm for fitting ruled surfaces of revolution to noisy line data.

Conclusions:

• The developed algebraic-geometric approach offers a more efficient and data-light alternative for calibrating rotational symmetric laser scanners.
• The line-based modeling paradigm provides a simplified yet accurate representation, enhancing the practical application of laser scanning technologies.
• The method's robustness and reduced measurement needs pave the way for broader adoption in various fields utilizing laser scanning.