大射電望遠鏡精調(diào)平臺運動學(xué)分析及鉸鏈誤差研究
發(fā)布時間：2018-11-16 17:40
【摘要】：作為大射電望遠鏡的精調(diào)平臺,Stewart平臺決定了整個系統(tǒng)的指向精度,而指向精度直接影響的是大射電望遠鏡的靈敏度,故Stewart平臺的運動精度在整個系統(tǒng)中所起的作用是舉足輕重的。由于鉸鏈制造誤差會直接影響到Stewart平臺末端的定位精度,而且這些誤差在加工制造過程中又是不可避免的,所以對這些誤差進行分析及補償就顯得尤為重要。由于在誤差分析之前要先明確各鉸鏈的運動情況,故需先對Stewart平臺進行運動學(xué)分析。以Stewart平臺其中一條支鏈為例,將虎克鉸看作兩個轉(zhuǎn)動副、驅(qū)動桿看成一移動副、球鉸看作三個轉(zhuǎn)動副,依次在虎克鉸、驅(qū)動桿以及球鉸上建立D-H坐標系,求出相鄰D-H坐標系間的D-H參數(shù)和位姿變換矩陣,從而得出各條支鏈的運動學(xué)方程,完成運動學(xué)模型的建立。確定Stewart平臺位置正逆解算法,使下平臺沿指定的軌跡運動并將軌跡離散成若干個位姿點,利用MATLAB進行逆解仿真分析,得出驅(qū)動桿桿長以及各關(guān)節(jié)運動變量的變化情況,仿真結(jié)果均符合實際情況,從而驗證了逆解算法的正確性。再進行位置正解仿真分析,將利用Newton-Raphson法計算得到的位姿參數(shù)與理論位姿參數(shù)做對比,分析得到了兩者之間的誤差分布情況,結(jié)果顯示正解的精度很高,而且迭代初值對正解的精度影響很小,由此驗證了正解算法的可行性�？紤]鉸鏈的偏移誤差和角度誤差,利用理想情況下的位姿變換矩陣得到實際的變換矩陣,完成誤差建模,確定誤差分析算法;給定偏移誤差和角度誤差以及下平臺理論位姿,即可求出下平臺的實際位姿。分別在不同的情況下對下平臺進行位姿誤差分析,得出結(jié)論:角度誤差對下平臺的位姿誤差影響很小,偏移誤差對下平臺位置誤差影響較大,而對下平臺姿態(tài)誤差影響較小�；诰{(diào)Stewart平臺的機械結(jié)構(gòu),提出一種誤差識別算法。誤差補償前,利用API T3激光跟蹤儀測量Stewart平臺工作空間內(nèi)典型位姿點的位置和姿態(tài),分析測量的實際位姿與理論位姿之間誤差的分布情況,利用最小二乘法計算出各條支鏈上的偏移誤差。偏移誤差無法直接進行補償,故將偏移誤差往驅(qū)動軸方向上投影,轉(zhuǎn)化為驅(qū)動軸的控制誤差,據(jù)此確定了一種誤差補償算法。利用MATLAB編寫程序,進行誤差補償仿真分析,比較補償前后的位姿誤差,得出結(jié)論:誤差補償后,下平臺位置精度得到大大改善,姿態(tài)精度也得到明顯的提高。由此可以驗證誤差識別算法、誤差補償算法的正確性。
[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.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TH751
本文編號：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.
【學(xué)位授予單位】：西安電子科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TH751
【參考文獻】
相關(guān)期刊論文 前1條
1 李永泉;張立杰;郭志民;郭菲;;基于D-H矩陣的球面5R并聯(lián)機構(gòu)誤差建模及靈敏度分析[J];中國機械工程;2012年12期
，本文編號：2336181
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