General Geometry Calibration Using Arbitrary Free-Form Surface in a Vision-Based Robot System

Geometry calibration is a critical problem in vision-based robot systems. The calibration objects of existing methods are limited to regular shapes. In this article, a general calibration method using an arbitrary free-form surface is proposed to simultaneously calibrate the geometry parameters. By incorporating a shape matching algorithm, each measured point on the surface can be regarded as a feature point to compare with the design model for a closed-form initial solution and an iterative fine solution. In the objective function of fine solution, the residual is described by the point-to-tangent distance, and the solution is proved to be Gaussian-Newton method with second-order convergence. The geometry and matching errors are iteratively compensated to improve the calibration accuracy. The characteristics of the method are large number of feature points, no need for specific features, no limitations on the size of the free-form surface and convenient robot pose control. Finally, simulations and experiments verify the availability of the proposed method in the presence of measuring noise, robot repeated positioning error, and a small number of robot poses.