大射电望远镜精调平台运动学分析及铰链误差研究
发布时间：2018-11-16 17:40
【摘要】：作为大射电望远镜的精调平台,Stewart平台决定了整个系统的指向精度,而指向精度直接影响的是大射电望远镜的灵敏度,故Stewart平台的运动精度在整个系统中所起的作用是举足轻重的。由于铰链制造误差会直接影响到Stewart平台末端的定位精度,而且这些误差在加工制造过程中又是不可避免的,所以对这些误差进行分析及补偿就显得尤为重要。由于在误差分析之前要先明确各铰链的运动情况,故需先对Stewart平台进行运动学分析。以Stewart平台其中一条支链为例,将虎克铰看作两个转动副、驱动杆看成一移动副、球铰看作三个转动副,依次在虎克铰、驱动杆以及球铰上建立D-H坐标系,求出相邻D-H坐标系间的D-H参数和位姿变换矩阵,从而得出各条支链的运动学方程,完成运动学模型的建立。确定Stewart平台位置正逆解算法,使下平台沿指定的轨迹运动并将轨迹离散成若干个位姿点,利用MATLAB进行逆解仿真分析,得出驱动杆杆长以及各关节运动变量的变化情况,仿真结果均符合实际情况,从而验证了逆解算法的正确性。再进行位置正解仿真分析,将利用Newton-Raphson法计算得到的位姿参数与理论位姿参数做对比,分析得到了两者之间的误差分布情况,结果显示正解的精度很高,而且迭代初值对正解的精度影响很小,由此验证了正解算法的可行性。考虑铰链的偏移误差和角度误差,利用理想情况下的位姿变换矩阵得到实际的变换矩阵,完成误差建模,确定误差分析算法;给定偏移误差和角度误差以及下平台理论位姿,即可求出下平台的实际位姿。分别在不同的情况下对下平台进行位姿误差分析,得出结论:角度误差对下平台的位姿误差影响很小,偏移误差对下平台位置误差影响较大,而对下平台姿态误差影响较小。基于精调Stewart平台的机械结构,提出一种误差识别算法。误差补偿前,利用API T3激光跟踪仪测量Stewart平台工作空间内典型位姿点的位置和姿态,分析测量的实际位姿与理论位姿之间误差的分布情况,利用最小二乘法计算出各条支链上的偏移误差。偏移误差无法直接进行补偿,故将偏移误差往驱动轴方向上投影,转化为驱动轴的控制误差,据此确定了一种误差补偿算法。利用MATLAB编写程序,进行误差补偿仿真分析,比较补偿前后的位姿误差,得出结论:误差补偿后,下平台位置精度得到大大改善,姿态精度也得到明显的提高。由此可以验证误差识别算法、误差补偿算法的正确性。
[Abstract]:As a fine-tuning platform for large radio telescopes, the Stewart platform determines the pointing accuracy of the whole system, and the pointing accuracy directly affects the sensitivity of the large radio telescope. Therefore, the motion accuracy of Stewart platform plays an important role in the whole system. Because the hinge manufacturing error will directly affect the positioning accuracy of the Stewart platform, and these errors are inevitable in the process of manufacturing, it is particularly important to analyze and compensate these errors. The kinematics analysis of Stewart platform is necessary because the motion of each hinge should be determined before error analysis. Taking one of the branches of Stewart platform as an example, the hook hinge is regarded as two rotating pairs, the driving rod as a moving pair, the ball hinge as three rotating pairs, and the D-H coordinate system is established on the hook hinge, the drive rod and the ball hinge in turn. The D-H parameter and pose transformation matrix between adjacent D-H coordinate systems are obtained, and the kinematics equations of each branch chain are obtained, and the kinematics model is established. The forward and inverse solution algorithm of the position of Stewart platform is determined to make the lower platform move along the specified trajectory and discretize the trajectory into several pose points. The inverse solution simulation analysis is carried out by using MATLAB, and the change of the length of the driving rod and the motion variables of each joint is obtained. The simulation results are in line with the actual situation, which verifies the correctness of the inverse solution algorithm. Then the position forward solution is simulated and the position and pose parameters calculated by Newton-Raphson method are compared with the theoretical pose parameters. The error distribution between them is obtained. The results show that the accuracy of the positive solution is very high. Moreover, the initial value of iteration has little effect on the accuracy of the positive solution, which verifies the feasibility of the positive solution algorithm. Considering the offset error and angle error of the hinge, the actual transformation matrix is obtained by using the position and pose transformation matrix under ideal conditions. The error modeling is completed and the error analysis algorithm is determined. Given the offset error, the angle error and the theoretical pose of the lower platform, the actual pose of the lower platform can be obtained. It is concluded that the angle error has little effect on the pose error of the lower platform, the offset error has a great influence on the position error of the lower platform, and the influence on the attitude error of the lower platform is small. Based on the mechanical structure of fine-tuned Stewart platform, an error recognition algorithm is proposed. Before error compensation, API T3 laser tracker is used to measure the position and attitude of typical position and attitude in the workspace of Stewart platform, and the error distribution between the actual position and the theoretical position is analyzed. The deviation error on each branch chain is calculated by least square method. The offset error can not be compensated directly, so the offset error is projected on the drive axis and transformed into the control error of the drive axis. Based on this, an error compensation algorithm is determined. By using MATLAB program, the error compensation simulation analysis is carried out, and the position and pose errors before and after compensation are compared. It is concluded that after the error compensation, the position accuracy of the lower platform is greatly improved, and the attitude accuracy is obviously improved. Therefore, the correctness of the error identification algorithm and the error compensation algorithm can be verified.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TH751
本文编号：2336181
[Abstract]:As a fine-tuning platform for large radio telescopes, the Stewart platform determines the pointing accuracy of the whole system, and the pointing accuracy directly affects the sensitivity of the large radio telescope. Therefore, the motion accuracy of Stewart platform plays an important role in the whole system. Because the hinge manufacturing error will directly affect the positioning accuracy of the Stewart platform, and these errors are inevitable in the process of manufacturing, it is particularly important to analyze and compensate these errors. The kinematics analysis of Stewart platform is necessary because the motion of each hinge should be determined before error analysis. Taking one of the branches of Stewart platform as an example, the hook hinge is regarded as two rotating pairs, the driving rod as a moving pair, the ball hinge as three rotating pairs, and the D-H coordinate system is established on the hook hinge, the drive rod and the ball hinge in turn. The D-H parameter and pose transformation matrix between adjacent D-H coordinate systems are obtained, and the kinematics equations of each branch chain are obtained, and the kinematics model is established. The forward and inverse solution algorithm of the position of Stewart platform is determined to make the lower platform move along the specified trajectory and discretize the trajectory into several pose points. The inverse solution simulation analysis is carried out by using MATLAB, and the change of the length of the driving rod and the motion variables of each joint is obtained. The simulation results are in line with the actual situation, which verifies the correctness of the inverse solution algorithm. Then the position forward solution is simulated and the position and pose parameters calculated by Newton-Raphson method are compared with the theoretical pose parameters. The error distribution between them is obtained. The results show that the accuracy of the positive solution is very high. Moreover, the initial value of iteration has little effect on the accuracy of the positive solution, which verifies the feasibility of the positive solution algorithm. Considering the offset error and angle error of the hinge, the actual transformation matrix is obtained by using the position and pose transformation matrix under ideal conditions. The error modeling is completed and the error analysis algorithm is determined. Given the offset error, the angle error and the theoretical pose of the lower platform, the actual pose of the lower platform can be obtained. It is concluded that the angle error has little effect on the pose error of the lower platform, the offset error has a great influence on the position error of the lower platform, and the influence on the attitude error of the lower platform is small. Based on the mechanical structure of fine-tuned Stewart platform, an error recognition algorithm is proposed. Before error compensation, API T3 laser tracker is used to measure the position and attitude of typical position and attitude in the workspace of Stewart platform, and the error distribution between the actual position and the theoretical position is analyzed. The deviation error on each branch chain is calculated by least square method. The offset error can not be compensated directly, so the offset error is projected on the drive axis and transformed into the control error of the drive axis. Based on this, an error compensation algorithm is determined. By using MATLAB program, the error compensation simulation analysis is carried out, and the position and pose errors before and after compensation are compared. It is concluded that after the error compensation, the position accuracy of the lower platform is greatly improved, and the attitude accuracy is obviously improved. Therefore, the correctness of the error identification algorithm and the error compensation algorithm can be verified.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TH751
【参考文献】
相关期刊论文 前1条
1 李永泉;张立杰;郭志民;郭菲;;基于D-H矩阵的球面5R并联机构误差建模及灵敏度分析[J];中国机械工程;2012年12期
，本文编号：2336181
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