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针对光电望远镜次镜精调Stewart机构的参数标定问题,在以往标定方法的基础上,首先,提出了在逆运动学模型基础上推导Stewart机构标定模型的方法,避免了正运动学求解析解困难、数值求解效率低且存在误差的问题;其次,对推导出的标定模型求解问题进行了分析,求解了其雅克比矩阵,针对模型系数矩阵不可逆的情况,提出了一种改进的高斯牛顿迭代法及具体的实验步骤;最后,分析了最小二乘原理导致的测量误差对精度影响大的现象,在Matlab中对设计的Stewart机构进行了标定仿真实验,在测量误差为0.1μm以下、标定精度平均提高56倍时,平均精度仅提高7.8倍。对样机进行标定后,位置精度平均提高了30.77倍,姿态精度平均提高了20.73倍。结果表明:该优化标定方法可以得到Stewart机构较精确的结构参数,从而有效提高其位姿调整精度。
Aiming at the parameter calibration problem of Stewart mechanism of secondary telescopic mirror, based on the previous calibration method, firstly, a method of deriving the calibration model of Stewart mechanism based on inverse kinematics model is proposed, which avoids the problem of positive kinematics , The numerical solution is inefficient and there is an error problem. Secondly, the problem of solving the calibration model is analyzed and its Jacobi ratio matrix is solved. In view of the irreversibility of the model coefficient matrix, an improved Gauss Newton method Finally, the phenomena that the measurement error caused by the least-squares principle has a great influence on the accuracy are analyzed. The calibrated simulation experiment of the designed Stewart mechanism is carried out in Matlab. Under the measurement error of 0.1μm, the calibration accuracy is average When 56 times higher, the average precision is only 7.8 times higher. After calibrating the prototype, the position accuracy increased 30.77 times on average, and the attitude accuracy increased 20.73 times on average. The results show that the optimized calibration method can obtain the precise structural parameters of the Stewart mechanism so as to effectively improve the pose adjustment accuracy.