光电望远镜次镜精调Stewart机构优化标定方法

Optimization of Calibration Method for the Secondary Mirror Fine Tuning Stewart Mechanism of Optoelectronic Telescope

摘要:

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0.1 μm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。

Abstract:

Aiming at the parameters calibration of the fine tuning Stewart mechanism for the secondary mirror of the optoelectronic telescope, based on the previous calibration method, first of all, a method for calibrating model of Stewart mechanism is proposed based on the inverse kinematics model, which avoids the problem of the difficulty of solving the forward kinematics, the low efficiency of numerical solution and the error of the numerical solution. Secondly, the problem of solving the calibration model is analyzed, and the Jacobian matrix is solved and an improved Gauss-Newton iteration method and a specific experimental procedure are presented for the case that the model coefficient matrix is not reversible. Finally, the effect of measurement error caused by the least square principle is analyzed, the calibration simulation experiment on the designed Stewart mechanism is carried out by using the Matlab. The results show that the calibration accuracy is increased by 56 times when the measurement error is less than 0.1 μm, the average precision is only increase by 7.8 times when the measurement error is less than 1 μm. After the calibration of the prototype, the average position precision is increased by 30.77 times, and the attitude accuracy is increased by 20.73 times. The more accurate structure parameters of Stewart mechanism can be obtained by using the optimization proposed calibration method, which can effectively improve the accuracy of position and attitude.