论文总字数：29142字

摘 要

在全球现代化工业自动化的前景下，工业机器人被广泛地应用于各种相关的制造业，不仅仅被应用于机车制造业，大到卫星，航天飞行器的生产，航母，军用器械，高铁的开发，小到小小的圆珠笔的滚珠的生产都有广泛的应用。并且随着其水平的不断提升和制造业中的需求日益增加。为满足机器人在不同场合下的功能的需求，诞生了搬运机器人、协作机器人、移动机器人、码垛机器人等不同机器人。所以为了普及工业机器人在各个工艺流程中的不同作用，降低自动化机器人系统的集成研发及运营成本。因此在满足不同的工业化生产之前，需要对工业机器人的机械臂的机械结构设计，以及对所设计的机械臂的正运动学和逆运动学进行分析判断其所建立的机械臂是否合理。其次对所设计的机械臂进行轨迹规划算法上的研究，使其能够更好地满足工作过程中的轨迹，并且需要了解所建立的机械臂的工作空间范围为多少，使其不会因超出工作空间而无法工作。

本课题以六自由度机械臂为基础，研究机器人运动学、三次和五次多项式插补、关节空间和笛卡尔空间的轨迹规划、蒙特卡罗空间上的应用。做出其各部分的仿真分析从而验证仿真结果的正确性。

首先根据D-H参数法建立改进型与标准型的空间坐标并得出D-H参数，在创建坐标系的过程中可以清晰得发现两种坐标系虽然建立方法不完全相同，但是其所建立的总体的坐标系相似，改进型会因为建立的第一个坐标系为基座的坐标系而比标准型少部分数据。根据所得出的机械臂参数进行运动学正逆解计算分析出改进型和标准型的末端执行器的位姿在三个轴上的旋转位姿是相同的，唯一不同的仅为两个的平移位姿，并通过MATLAB仿真验证运动学正逆解的正确性。

对机械臂进行关节和笛卡尔空间的轨迹规划。在关节空间中，根据其不同的多项式以及相对应的运动约束条件，可以发现机械臂在运动过程中不断发生变化的速度以及加速度等的特点。建立笛卡尔直线轨迹规划，并在MATLAB语言环境中编程实现不同算法的轨迹规划，以此来模拟现实生活中工业机械臂在完成工作过程中的部分路径来增加工作效率。

应用蒙特卡罗分析法在MATLAB软件中对工作空间进行仿真，可以相对更加具体地模拟出工业机械臂在工作过程中所能达到的最大的工作空间范围。只有在清楚其工作空间的情况下，才能够更好地建立机械臂的工作台，使其工作均可以在其工作空间内完成，并且不会误伤到操作的工人。

六自由度机械臂在进行运动学建模的时候需要先了解其标准型与改进型的相邻连杆之间的位置关系，建立不同的坐标系后就会发现其选取的基坐标系不同而导致各机械臂参数存在细微差距。但是其末端执行器的位姿的旋转矢量是相同的。其中关节空间的五次多项式最适合进行轨迹规划，因为其可以对机械臂的末端执行器进行速度加速度等的规划。利用蒙特卡罗分析机械臂的工作空间时对不同的机械臂关节进行分析可以发现每个机械臂的关节所到达的空间不一，但都存在着很多无法到达的空间，而机械臂的第六轴所到达的空间最大，并且可以形成一个球形。

关键词：六自由度机械臂；运动学分析；轨迹规划；蒙特卡罗分析法

Modeling and Trajectory Planning of 6-DOF Manipulator

Abstract

In the global prospect of modern industrial automation, industrial robots are widely used in various related manufacturing industries, not only in the locomotive manufacturing industry, large to the production of satellites, space vehicles, aircraft carriers, military instruments, high-speed rail development, small to small ball pen ball production has a wide range of applications. And with the continuous improvement of its level and increasing demand in the manufacturing industry. In order to meet the functional needs of robots in different occasions, different robots such as handling robot, cooperative robot, mobile robot and palletizing robot were born. Therefore, in order to popularize the different roles of industrial robots in various technological processes, reduce the integrated research and development and operating costs of automated robot systems. Therefore, before meeting different industrial production, it is necessary to design the mechanical structure of the manipulator arm of the industrial robot, and analyze the forward kinematics and inverse kinematics of the designed manipulator arm to determine whether the established manipulator arm is reasonable. Secondly, the trajectory planning algorithm of the designed manipulator is studied, so that it can better meet the trajectory in the working process. Moreover, the workspace range of the established manipulator is needed to be understood, so that it will not be unable to work due to exceeding the workspace.

This topic is based on the six degrees of freedom manipulator, the study of robot kinematics, cubic and quintic polynomial interpolation, joint space and Cartesian space trajectory planning, Monte Carlo space applications. Make the simulation analysis of each part to verify the correctness of the simulation results.

First based on d-h method to establish advanced and standard of the space coordinates and d-h parameters, in the process of creating coordinate system can be clearly found two kinds of methods to set up coordinate system while not identical, but the overall coordinate system established by similar, because modified will set up the first coordinate system as the base of a few data rather than the standard. According to the obtained parameters of the manipulator arm, the forward and inverse kinematics solutions were calculated and analyzed. It was found that the improved and standard end-effectors had the same rotational poses on the three axes, and the only difference was the two translational poses. The correctness of the forward and inverse kinematics solutions was verified by MATLAB simulation.

The joint and Cartesian space trajectories of the manipulator are planned. In joint space, according to its different polynomials and the corresponding motion constraints, we can find the characteristics of the speed and acceleration that constantly change during the motion of the manipulator. The Cartesian linear trajectory planning is established, and the trajectory planning of different algorithms is programmed in the Matlab language environment, so as to simulate part of the path of industrial manipulator in the process of completing the work in real life to increase the work efficiency.

By using Monte Carlo analysis method to simulate the workspace in MATLAB, the maximum workspace range that the industrial manipulator can achieve in the working process can be simulated more specifically. Only when its workspace is clear, can the workbench of the manipulator be better established, so that its work can be completed in its workspace without accidentally injuring the operator.

In the kinematics modeling of the 6-DOF manipulator, it is necessary to first understand the position relationship between the adjacent connecting rods of the standard type and the improved type. After the establishment of different coordinate systems, it will be found that the different base coordinate systems are selected, leading to slight differences in the parameters of each manipulator. But the rotation vector of the end-effector is the same. Among them, the quintic polynomial in joint space is the most suitable for trajectory planning, because it can plan the velocity and acceleration of the end-effector of the manipulator arm. When using Monte Carlo to analyze the working space of the manipulator arm, it can be found that the space reached by the joint of each manipulator arm is different, but there is a lot of unreachable space, and the sixth axis of the manipulator arm reaches the largest space, and can form a sphere.

Key words: 6-DOF manipulator， Kinematics analysis， Trajectory planning，Monte Carlo analysis

目录

摘要 I

Abstract II

第一章 绪论 1

1.1 课题研究背景及意义 1

1.2 国内外相关研究现状 2

1.2.1 国内的发展现状 2

1.2.2 国外的发展现状 3

1.3 本文主要研究内容及章节安排 3

第二章 方案设计 5

第三章 六自由度机械臂运动学分析 6

3.1 六自由度机械臂运动学概述 6

3.1.1 刚体的自由度 6

3.2 运动学建模基础 6

3.2.1 连杆坐标系建立 6

3.2.2 坐标变换矩阵求解 7

3.3 六自由度机械臂正运动学解 9

3.4 六自由度机械臂逆运动学解 14

3.6 机械臂运动学仿真 15

3.6.1 MATLAB构建六自由度机械臂模型 15

3.6.2 六自由度机械臂正逆运动学仿真 16

3.6.3 四元素、欧拉角、旋转矩阵转换 17

第四章 六自由度机械臂轨迹规划 20

4.1 轨迹规划的概念 20

4.2 笛卡尔空间的轨迹规划算法研究 20

4.3 关节空间下的轨迹规划算法 21

4.3.1 三次多项式下的轨迹规划 21

4.3.2 五次多项式下的轨迹规划 25

4.3.3 关节空间下的圆弧轨迹规划 26

4.4 蒙特卡罗空间分析 27

第五章 结束语 30

谢辞 31

参考文献 32

附录 33

剩余内容已隐藏，请支付后下载全文，论文总字数：29142字