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.
Highlights
In recent years, industrial Flexible Measuring Arm (FMA) have been widely used in manufacturing industries
Its low accuracy restricts that this kind of measuring equipment is difficult to be used in the high precision field.[1,2,3,4,5]
A fast calibration method is proposed for FMA which is widely used in industry
Summary
Industrial Flexible Measuring Arm (FMA) have been widely used in manufacturing industries. External calibration owns high compensation accuracy with high precision instruments and sensors This calibration method owns high cost, complex operation, and low efficiency.[6,7,8,9] Self-calibration method applies optimization algorithm to finish the calibration work based on measuring data. The proposed method in this paper just applies one ball plate and several standard balls to realize the error calibration of FMA, which has obvious advantages of fast, high efficiency, and low cost, and experiments has proved the effectiveness and feasibility of the proposed numerical method. If the iterative initial value has much difference with the actual value for LSM, its accuracy is much lower because the initial values make a great influence on the accuracy This kind of methods own poor stability.[10] The paper proposes a Normalized Genetic Algorithm with adaptive operators to finish data calibration work. Once the error is less than 0.5 mm after compensation, the algorithm will stop calculating
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