Precise Calibration Of Stewart Platform Based On Improved Cuckoo Search Algorithm

Relative position between the primary and secondary mirrors of a space camera Seriously affects image quality.The Stewart platform is often chosen as the adjustment mechanism for the secondary mirror,and its calibration is the primary means of improving the accuracy of the mirror.In this paper,the mathematical modeling,error analysis,calibration algorithm and other aspects involved in the calibration of Stewart platform are elaborated,and the calibration experiment and precision test are carried out.First,the space vector method is used to establish the inverse kinematics model.The iterative optimization method is applied to establish the forward kinematics model,and the simulation results of Matlab prove that the model is correct.The residual function is deduced,so that the calibration is converted into Parameter optimization with boundaries.And build a model based on this optimization problem.Second,an analysis is assigned to the parameter coupling,and accordingly,the positioning accuracy after the selected calibration is selected as the evaluation index of the calibration.Based on the laser tracker design pose measurement scheme,the measurement error of the measurement scheme is analyzed,and the relationship between the measurement error and the coordinate system deviation is explained based on the analysis.The independence of the calibration parameters was analyzed,and the dimension of the parameter to be calibrated was reduced from 42 to 36,and the simulation proved that the parameter correction was reasonable.In order to improve the accuracy of the calibration optimization problem,the cuckoo algorithm has been improved by the simplex method,adaptive step size and limit processing.And the effectiveness of the algorithm improvement is proved by the simulation results.The SMCS algorithm and the VSA-SMCS-TH algorithm were used to calibrate the simulation.The results of the two algorithms were: the positioning error was reduced by 143.8 times and 1368.9 times,when the initial maximum error is 532.07?m and 374.02".The VSA-SMCS-TH algorithm is suitable for high precision calibration.Finally,we designed the calibration experiment and the accuracy test experiment with the second-mirror Stewart platform prototype.In the calibration experiment,the conditions for ensuring that the calibration result is valid in the full stroke region are summarized,that is,the pose sampling point must include all positive and negative combinations of the six-degree-freedom generalized displacement.After calibration,the maximum displacement error at the sampling point is reduced from 16.94?m to 7.62?m,where the accuracy is increased by 1.22 times,and the maximum corner error is reduced from 123.84" to a maximum of 8.83",which is about 15 times higher.Even the error of non-sampling point and sampling point is the same order of magnitude.This result tells us that the calibration method in this paper effectively improves the positioning accuracy of the platform,and the calibration effect is spread throughout the entire workspace.The accuracy test results show that the positioning accuracy of the platform in single degree of freedom is 9.8/1.59/3.41?m,0.8/1.2/2.1" in the range of 1mm,0.2°,which indirectly indicates that the calibration is accurate in the entire workspace.