Fast error calibration of Flexible Measuring Arm based on an adaptive Genetic Algorithm

Abstract

With the development of measurement technology, the Flexible Measuring Arm (FMA) is widely used in quality test of automobile processing and industrial production. FMA is a kind of nonlinear system with many parameters. Low cost and efficient calibration method have become the focuses of attention. This article presents a fast calibration method for FMA based on an adaptive Genetic Algorithm (GA) just with several standard balls and a ball plate. It can greatly reduce the calibration cost than common external calibration method which needs high precision instruments and sensors. Firstly, the kinematic model of FMA is established by RPY theory. Secondly, the common GA is optimized and improved, and an adaptive mechanism is added to the algorithms which can realize the automatic adjustment of crossover and mutation operators. A Normalized Genetic Algorithm (NGA) with adaptive mechanism is proposed to complete the optimization calculation. It can improve the numbers of optimal individuals and the convergence speed. So, the search efficiency will be enhanced greatly. Finally, the Least square method (LSM), the General Genetic Algorithm (GGA), and the proposed NGA are respectively used to finish the calibration work. The compensation accuracy and the search efficiency with the above three different algorithms have been systematically analyzed. Experiment indicates that the performance of NGA is much better than LSM and GGA. The data also has proved that the LSM is suitable to complete optimization calculation for linear system. Its convergence stability is much poorer than NGA and GGA because of the ill-condition Jacobin matrix. GGA is easy to fall into local optimization because of the fixed operators. The proposed NGA obviously owns fast convergence speed, high accuracy and better stability than GGA. The position error is reduced from 3.17 to 0.5 mm after compensation with the proposed NGA. Its convergence rate is almost two time of GGA which applies constant genetic factors. The effectiveness and feasibility of proposed method are verified by experiment.