复指数变换法在工业机器人轨迹规划中的应用研究
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摘要
针对目前在工业机器人的执行机构运动研究中，缺少高效的分析方法的现状，本文提出了一种新方法——三维矢量的复指数形式并探讨了应用该法表示三维矢量的坐标变换形式及其导数形式。实例证明它能够简化工业机器人的执行机构运动分析的坐标变换过程。对于其数值解，可以利用计算机方便求得。进而，可以利用它更方便地对工业机器人进行轨迹规划。
首先，本论文介绍了工业机器人及其发展、应用概况、分类及组成。然后，提出了三维矢量的复指数形式，并探讨了其基本的坐标变换形式，即复指数变换法及其导数形式以便于进一步的分析。其次，对于给定的工业机器人实例，建立起适当的参考、运动坐标系，对比应用了坐标矩阵变换法和复指数变换法，来分析工业机器人执行机构的运动问题。由求解过程可以看出，复指数变换法是一种解决此类问题的有效的、直观的方法。最后，对于结构给定而构件尺度未定的工业机器人执行机构，先根据机构尺度优化目标，建立数学模型、用复合形法进行构件尺度优化；再根据给定的期望轨迹和规划目标，建立数学模型，利用复指数变换法对执行机构进行运动分析的结果，采用进化算法对工业机器人进行轨迹规划。接着，用优化参数进行计算机仿真，评价仿真结果。这些优化参数可作为实际工业机器人执行机构设计和机器人控制的理论依据。
Aimed at the situation lack of efficient analysis tool in the study of the industrial robots' executor motion, a new method, the complex index form of the 3 dimensional vectors, is put forward. The way of coordinate transformation and the derivative are also explored while expressing vectors by using this method.when it being used in several examples, the motion analysis of the industrial robots' executor can be simplified. Numerical solution can also be got with computer. Consequently, trajectory planning for the industrial robots'executor can simply be implemented in this way.
Firstly, this paper introduces industrial robots, their development, their engineering application, their category and their composing in broad outline. Secondly, the basic concept of the complex index form of the 3 dimensional vectors and the way of coordinate transformation, the complex index form transformation, are discussed. In order to simplify the further analysis, the derivative of this form is also put forward. Thirdly, the coordinate matrix transformation that is popularly used and the complex index form transformation are applied to the living examples of industrial robots respectively with the proper referent and motive coordinate systems. While two solutions being contrasted, it is shown that the complex index form transformation presented by the paper is an intuition!stic and convenient tool to analyze the industrial robots' executor motion. Finally, for the definite mechanism and indefinite size of industrial robots'executor as well as the size^optimization goal, the mathematic model is set up
to optimize the executor'size with using complex optimization method. Next, for the optimized executor, the desired trajectory and planning goal, the kinematics model and proper referent and motive coordinates systems are set up. By making use of the result of the previous motion analysis, genetic algorithm is applied to the trajectory planning of executor. Next, the practical trajectory is simulated with the optimized parameters. Then the simulated result is also evaluated with the planning goal. The practical mechanism design and motion control of industrial robots can be carried out according to the optimized parameters.
首先，本论文介绍了工业机器人及其发展、应用概况、分类及组成。然后，提出了三维矢量的复指数形式，并探讨了其基本的坐标变换形式，即复指数变换法及其导数形式以便于进一步的分析。其次，对于给定的工业机器人实例，建立起适当的参考、运动坐标系，对比应用了坐标矩阵变换法和复指数变换法，来分析工业机器人执行机构的运动问题。由求解过程可以看出，复指数变换法是一种解决此类问题的有效的、直观的方法。最后，对于结构给定而构件尺度未定的工业机器人执行机构，先根据机构尺度优化目标，建立数学模型、用复合形法进行构件尺度优化；再根据给定的期望轨迹和规划目标，建立数学模型，利用复指数变换法对执行机构进行运动分析的结果，采用进化算法对工业机器人进行轨迹规划。接着，用优化参数进行计算机仿真，评价仿真结果。这些优化参数可作为实际工业机器人执行机构设计和机器人控制的理论依据。
Aimed at the situation lack of efficient analysis tool in the study of the industrial robots' executor motion, a new method, the complex index form of the 3 dimensional vectors, is put forward. The way of coordinate transformation and the derivative are also explored while expressing vectors by using this method.when it being used in several examples, the motion analysis of the industrial robots' executor can be simplified. Numerical solution can also be got with computer. Consequently, trajectory planning for the industrial robots'executor can simply be implemented in this way.
Firstly, this paper introduces industrial robots, their development, their engineering application, their category and their composing in broad outline. Secondly, the basic concept of the complex index form of the 3 dimensional vectors and the way of coordinate transformation, the complex index form transformation, are discussed. In order to simplify the further analysis, the derivative of this form is also put forward. Thirdly, the coordinate matrix transformation that is popularly used and the complex index form transformation are applied to the living examples of industrial robots respectively with the proper referent and motive coordinate systems. While two solutions being contrasted, it is shown that the complex index form transformation presented by the paper is an intuition!stic and convenient tool to analyze the industrial robots' executor motion. Finally, for the definite mechanism and indefinite size of industrial robots'executor as well as the size^optimization goal, the mathematic model is set up
to optimize the executor'size with using complex optimization method. Next, for the optimized executor, the desired trajectory and planning goal, the kinematics model and proper referent and motive coordinates systems are set up. By making use of the result of the previous motion analysis, genetic algorithm is applied to the trajectory planning of executor. Next, the practical trajectory is simulated with the optimized parameters. Then the simulated result is also evaluated with the planning goal. The practical mechanism design and motion control of industrial robots can be carried out according to the optimized parameters.
引文
[1]张启先．空间机构的分析与综合(上、下册)．北京：机械工业出版社，1984．
[2]王智圣．三维矢量的复指数形式坐标变换及应用．济南：济南新技术研究所，1996．
[3]余达太，马香峰．工业机器人应用工程．北京：冶金工业出版社，2001．
[4]金广业，陶兴旺，孙福维．工业机器人与控制．沈阳：东北工业学院出版社，1991．
[5]陆祥生，杨秀莲．机械手理论及应用．北京：中国铁道出版社，1983．
[6]马香峰．机器人机构学．北京：机械工业出版社，1991．
[7]付京逊等．机器人学．北京：中国科学技术出版社，1989．
[8] 孙迪生，王炎．机器人控制技术．北京：机械工业出版社，1997．
[9] 黄真．空间机构学．北京：机械工业出版社，1989．
[10] 曹惟庆．连杆机构的分析与综合．北京：科学出版社，2002．
[11] 白师贤．高等机构学．上海：上海科学技术出版社，1988．
[12] 潘晓辉，陈强．MATLAB 5.3全攻略宝典．武汉：水利水电大学出版社，2000．
[13] 薛定宇．控制系统计算机辅助设计—MATLAB语言及应用．北京：清华大学出版社，1999．
[14] 钱能．C++程序设计教程．北京：清华大学出版社，1999．
[15] Stephen R Davis(卢凌云 译)．C++编程指南．北京：电子工业出版社，1999．
[16] 宛延闿．C++语言和面向对象程序设计．北京：清华大学，1993．
[17] Bjarne Stroustrup. The C++ Programming Language 3rd edition. Addison Wesley Long Man, 1997.
[18] 许贤泽．空间关节机器人轨迹规划．兰州：甘肃工业大学学报，1995 21(4)。
[19] 周伯英．工业机器人设计．北京：机械工业出版社，1995．
[20] 马香峰等．工业机器人的操作机设计．北京：冶金工业出版社，1985．
[21] 华大年，华志宏，吕静平．连杆的机构设计．上海：上海科学技术出版社，1985．
[22] 梁崇高，阮平生．连杆机构的计算机辅助设计．北京：机械工业出版社，1985．
[23] 傅则绍，卢子馨．机构设计．北京：石油大学出版社，1995．
[24] 龚振邦，汪勤悫，陈振华，钱晋武．机器人机械设计．北京：电子工业出版社，1995．
[25] 刘惟信．机械最优化设计．北京：清华大学出版社，1994．
[26] 何献忠，李萍．优化技术及应用．北京：北京理工大学出版社，1995．
[27] 李炳威．结构最优化设计．北京：科学出版社，1979．
[28] 张济川．机械最优化设计及应用实例．北京：新时代出版社，1990．
[29] 高健．机械优化设计基础．广州：科学出版社，2000．
[31] (美)A.H．伯尔，汪一麟．机械分析与机械设计．北京：机械工业出版社，1988．
[31] 王正志，薄涛．进化算法．长沙：国防科技大学出版社，2000．
[32] Angeline,P.J.,et(editors)Proceedings of the 5th Annual Conference on Evolutionary Programming(EP'96),1996.
[33] Wright, A. H., Genetic Algorithms for Real Parameter Optimization, in[108],pp.205-218,1991.
[34] ChenJuhua·Application of Fuzzy Mathematic In Multi_objective Optimal Design·College of Mecb Eng Shandong University of Technology.
[35] 蔡自兴，徐光佑．人工智能及其应用．北京：清华大学出版社，1996．
[36] 潘正君，康立山，陈疏屏．演化算法．北京：清华大学出版社，1998．
[37] 陈宝林．数值优化方法的理论与应用．北京：清华大学出版社，1989
[38] Brady R M. Optimization Strategies Gleaned form Biological Evolution. Nature 317,804—806,1985.
[39][美]演化算法Z．米凯利维茨．演化程序．北京：科学出版社，2000．
[40] Davidor, Y., Genetic Algoritms and Robotics, World Scientific, 1991.
[41] 肖用元．张燕云，陈加坡．系统仿真导论·北京：清华大学出版社·2000。
[42] John Fles·Simulation for AS/RS Retrofits·January 1998·Material Handling Engineering.
[2]王智圣．三维矢量的复指数形式坐标变换及应用．济南：济南新技术研究所，1996．
[3]余达太，马香峰．工业机器人应用工程．北京：冶金工业出版社，2001．
[4]金广业，陶兴旺，孙福维．工业机器人与控制．沈阳：东北工业学院出版社，1991．
[5]陆祥生，杨秀莲．机械手理论及应用．北京：中国铁道出版社，1983．
[6]马香峰．机器人机构学．北京：机械工业出版社，1991．
[7]付京逊等．机器人学．北京：中国科学技术出版社，1989．
[8] 孙迪生，王炎．机器人控制技术．北京：机械工业出版社，1997．
[9] 黄真．空间机构学．北京：机械工业出版社，1989．
[10] 曹惟庆．连杆机构的分析与综合．北京：科学出版社，2002．
[11] 白师贤．高等机构学．上海：上海科学技术出版社，1988．
[12] 潘晓辉，陈强．MATLAB 5.3全攻略宝典．武汉：水利水电大学出版社，2000．
[13] 薛定宇．控制系统计算机辅助设计—MATLAB语言及应用．北京：清华大学出版社，1999．
[14] 钱能．C++程序设计教程．北京：清华大学出版社，1999．
[15] Stephen R Davis(卢凌云 译)．C++编程指南．北京：电子工业出版社，1999．
[16] 宛延闿．C++语言和面向对象程序设计．北京：清华大学，1993．
[17] Bjarne Stroustrup. The C++ Programming Language 3rd edition. Addison Wesley Long Man, 1997.
[18] 许贤泽．空间关节机器人轨迹规划．兰州：甘肃工业大学学报，1995 21(4)。
[19] 周伯英．工业机器人设计．北京：机械工业出版社，1995．
[20] 马香峰等．工业机器人的操作机设计．北京：冶金工业出版社，1985．
[21] 华大年，华志宏，吕静平．连杆的机构设计．上海：上海科学技术出版社，1985．
[22] 梁崇高，阮平生．连杆机构的计算机辅助设计．北京：机械工业出版社，1985．
[23] 傅则绍，卢子馨．机构设计．北京：石油大学出版社，1995．
[24] 龚振邦，汪勤悫，陈振华，钱晋武．机器人机械设计．北京：电子工业出版社，1995．
[25] 刘惟信．机械最优化设计．北京：清华大学出版社，1994．
[26] 何献忠，李萍．优化技术及应用．北京：北京理工大学出版社，1995．
[27] 李炳威．结构最优化设计．北京：科学出版社，1979．
[28] 张济川．机械最优化设计及应用实例．北京：新时代出版社，1990．
[29] 高健．机械优化设计基础．广州：科学出版社，2000．
[31] (美)A.H．伯尔，汪一麟．机械分析与机械设计．北京：机械工业出版社，1988．
[31] 王正志，薄涛．进化算法．长沙：国防科技大学出版社，2000．
[32] Angeline,P.J.,et(editors)Proceedings of the 5th Annual Conference on Evolutionary Programming(EP'96),1996.
[33] Wright, A. H., Genetic Algorithms for Real Parameter Optimization, in[108],pp.205-218,1991.
[34] ChenJuhua·Application of Fuzzy Mathematic In Multi_objective Optimal Design·College of Mecb Eng Shandong University of Technology.
[35] 蔡自兴，徐光佑．人工智能及其应用．北京：清华大学出版社，1996．
[36] 潘正君，康立山，陈疏屏．演化算法．北京：清华大学出版社，1998．
[37] 陈宝林．数值优化方法的理论与应用．北京：清华大学出版社，1989
[38] Brady R M. Optimization Strategies Gleaned form Biological Evolution. Nature 317,804—806,1985.
[39][美]演化算法Z．米凯利维茨．演化程序．北京：科学出版社，2000．
[40] Davidor, Y., Genetic Algoritms and Robotics, World Scientific, 1991.
[41] 肖用元．张燕云，陈加坡．系统仿真导论·北京：清华大学出版社·2000。
[42] John Fles·Simulation for AS/RS Retrofits·January 1998·Material Handling Engineering.