论文总字数：22887字

摘 要

机械臂在现代人们的生活中有着广泛的应用，和人们的工作、出行、医疗、居住甚至是饮食都有着不可分割的关联。随着人们对生活水平和生活质量要求的不断提高，和人们生活息息相关的机械臂的工作性能的要求也在不断地提高。而机械臂中的控制算法和控制所能达到的精度则是影响机械臂性能的主要因素之一。

随着产业结构的发展和升级，传统的PID式控制方法已经不能满足当代对于机械臂性能的要求了。机械臂的运动学逆解则是机械臂的运动轨迹规划和控制的基础，机械臂运动学逆解的速度和精度会直接影响到机械臂运动控制的速度和精度，所以，在机械臂的使用中选择适用的机械臂控制方法也就显得尤为重要了。本文主要通过对平面机械臂运动学逆解方法的研究来提高平面机械臂的控制速度和控制精度。

平面机械臂的位置逆解算法问题的研究一直是机械臂的研究领域中的难点和热点之一,从逆解算法的研究中得到的逆解算法方程具有很大的理论研究价值，可以在此基础上进行很多机械控制学问题的研究;另外,运动学逆解也是平面机械臂中运动控制和轨迹规划的关键因素之一。

本文以四自由度平面机械臂作为研究对象，基于标准D-H建模法建立平面机械臂的连杆坐标系和数学模型。基于建立的平面机械臂D-H法数学模型，进行对于给定终值的平面机械臂的位姿逆解的研究，本文采用的运动学逆解的方法是数值迭代法和几何逆解法进行逆解，通过对两种方法建立数学模型，研究数值迭代法和几何逆解法的逆解原理以及逆解效果。

最后，使用Matlab中的Robotics Toolbox机器人工具箱对数值迭代法逆解和几何法逆解进行仿真和验证，对本文研究的算法的可行性进行仿真验证，通过仿真结果对两种逆解方法的精确性、有效性和实用性进行比较，为平面机械臂的运动学算法研究提供有效的理论依据。

关键词：机械臂 逆解 数值迭代法 几何法 Matlab仿真

Planar manipulator inverse kinematics problem solving algorithm research

Abstract

Mechanical arm has been widely used in modern people's life, and people's work, travel, health, living, and even diet has inseparable relation. As people's life standard and the requirement of quality of life is increasing, and people's life is closely linked performance requirements of mechanical arm is in constant increase.

While the control methods and control precision of mechanical arm is one of the main factors influencing the performance of mechanical arm.

Along with the development of the industrial structure and upgrading, the traditional PID control method can't meet the requirements of modern mechanical arm for performance. The kinematics inverse solution of mechanical arm is the basis of the mechanical arm motion trajectory planning and control, mechanical arm speed and precision of the inverse kinematic solution will directly affect the mechanical arm motion control of speed and accuracy, so, in the course of the mechanical arm use choose suitable control method of mechanical arm also is particularly important. This article mainly through to the plane of mechanical arm kinematics reverse solution method of the research to improve the control of planar mechanical arm speed and control precision.

The location of the planar manipulator inverse kinematics problem has been one of the difficult and hot spot in the research field of the mechanical arm, from inverse solution algorithm of input and output equation has great theoretical research value, can be based on the research of many mechanisms; In addition, the kinematics inverse solution is planar manipulator for motion planning and trajectory control of one of the key.

In this paper, four degrees of freedom planar manipulator as the research object, the planar mechanical arm was established based on d-h method is standard of connecting rod coordinate system, then based on d-h standard modeling method to establish the mathematical model of planar manipulator. Based on establishing the mathematical model of planar manipulator d-h method for a given final value of planar manipulator position inverse solution of the research, this article adopts the method of inverse kinematics solution is the numerical iteration method and the geometrical inverse method for inverse solution, based on the two kinds of method to establish mathematical model, the numerical iteration method and the geometrical principle of inverse solution and inverse solution of inverse method.

Finally, the use of Matlab in Robotics, Toolbox robot kit for numerical inverse iteration method and geometric method, inverse kinematics simulation and verification, this paper studies the feasibility of the algorithm for simulation, the simulation results of two kinds of inverse solution method compares the accuracy, validity and practicability of, provides the theory basis for the study of mechanical arm kinematics.

Key Words: Mechanical arm; kinematics Inverse solution ; Geometric method;The Matlab simulation

目录

摘要……………………………………………………………………Ⅰ

Abstract………………………………………………………………Ⅱ

第一章 绪论……………………………………………………………1

1.1平面机械臂的概述……………………………………………………1

1.2研究背景和意义………………………………………………………2

1.3平面机械臂研究现状…………………………………………………2

1.3.1国内机械臂研究现状………………………………………………2

1.3.2国外机械臂研究现状………………………………………………3

第二章 平面机械臂运动学算法概述…………………………………6

2.1正逆运动学算法概述…………………………………………………6

2.2逆运动学算法概述……………………………………………………7

2.2.1数值迭代算法概述…………………………………………………7

2.2.2几何法逆解概述……………………………………………………8

第三章 四自由度机械臂建模…………………………………………11

3.1概述…………………………………………………………………11

3.2四自由度机械臂模型建立……………………………………………11

3.2.1 物理模型建立……………………………………………………11

3.2.2 D-H法数学模型建立………………………………………………11

第四章 机械臂的逆运动学算法模型建立及仿真……………………15

4.1数值迭代算法模型建立………………………………………………15

4.2数值迭代算法仿真……………………………………………………17

4.3几何逆解算法模型建立………………………………………………23

4.4几何逆解算法仿真…………………………………………………26

4.5实验数据和小结……………………………………………………28

第五章 结论……………………………………………………………30

参考文献………………………………………………………………32

致谢……………………………………………………………………34

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