Research on the base station calibration of multi-station and time-sharing measurement based on hybrid genetic algorithm

•The hybrid genetic algorithm constituted is used to determine the base station position and measuring point coordinates.•The method of determining the initial ranges of base station is provided.•Simulations and experiments verify the effectiveness of this measurement algorithm.

In order to detect the motion error of machine tool quickly and accurately, the multi-station and time-sharing measurement by laser tracker is introduced in the paper. Merely distance is involved in the measurement, thus the influence of angle measurement on the whole measuring accuracy of laser tracker can be effectively avoided. With this method, the measurement algorithm mainly relates to base station calibration and measuring point determination. Moreover, how to quickly and accurately calibrate the position of base station is a critical issue, which directly influences measuring accuracy. To solve the problem, the redundant measurement method is adopted. By establishing the mathematical model of detecting the motion error of machine tool with multi-station and time-sharing measurement, the nonlinear redundant equations concerning base station calibration and measuring point determination can be obtained by large amount of measured data based on the GPS principle. To overcome the deficiencies of prematurity and poor local searching ability of standard genetic algorithm in solving nonlinear problem, the simplex method is integrated into the genetic algorithm to constitute a hybrid genetic algorithm, then the deficiencies can be effectively overcome for further improvement of the solving accuracy. The hybrid genetic algorithm derived is used to determine the position of base station and the coordinates of measuring point, and the simulations and experiments are conducted to verify the effectiveness of multi-station and time-sharing measurement algorithm deduced on the basis of hybrid genetic algorithm.