为了提高1P3R型柔性测量臂的检测精度, 提出了一种自适应误差标定方法来完成它的参数标定和误差补偿。首先, 基于RPY理论建立柔性测量臂的运动学模型并应用微分法推导了误差模型。然后, 基于马尔柯夫链收敛性理论进行实数编码; 在遗传算法(GA)中引入自适应控制算子, 提高了父代种群的多样性和最优个体变异数量; 最后, 对比分析了归一化GA、一般GA和最小二乘法等3种算法的误差标定精度及其收敛性, 验证了所提出方法的有效性和可行性。结果显示: 归一化GA仅用328代寻优计算, 其精度达到5.2 μm, 收敛速度是一般GA的2.3倍且精度提高了3.1 μm; 最小二乘法经20次迭代计算后停止收敛, 精度仅为18.4 μm。实验结果表明: 归一化GA具有收敛速度快、标定精度高和收敛稳定性好等明显优势, 更易于实现该类测量机的高精度检测。

An adaptive error calibration method was proposed to complete parameter calibration and error compensation to realize the high accuracy test for a 1P3R flexible measuring arm. Firstly, a kinematic model of 1P3R flexible measuring arm was built based on RPY theory and a differential method was used to deduce the error model of system. Then, the real number encoding was performed based on the theory of Markova chain convergence. Adaptive control factors were added to Genetic Algorithm(GA) to improve population diversity and the quantity of the best individual. Finally,the calibration accuracy and convergence performance of a normalized GA, a general GA and least square method were compared and analyzed and the results were used to verify the feasibility and effectiveness of the proposed method. It shows that the accuracy of the normalized GA has been enhanced from 3.1 μm to 5.2 μm just after 328 generation searching, and its convergence velocity is 2.3 times that of the general GA. Moreover, the convergence of least square method is stopped after 20 generations and its calibration accuracy is only 18.4 μm. Experiments indicate that normalized GA is characterized by some advantages of fast convergence speed, high calibration accuracy and better stability. It is suitable for measuring these kinds of flexible measuring arms in high accuracy.