摘 要

如今，机器人手臂作为先进科技发展的趋势，受到国内外高度关注；而乒乓球机器人手臂是其中的一种，是指专门设计来与人打乒乓球的机器人手臂。

本课题重点针对乒乓球机器人手臂运动轨迹进行设计，并采用两种控制系统算法方案进行仿真。方案一为细分法，让手臂前端进行着直线和圆弧运动，在相应轨迹上取若干个点，让末端分别到达所选位置，以让末端的运动轨迹趋近于指定的轨迹；方案二为插值算法，在直线或圆轨迹上取若干个点并让末端依次到达，采用多项式插值的方法，假设插值过后共有n个点，对每一点进行多项式带入，计算已知条件；在目标点处，根据已知条件算出相应角度，并且已知整个轨迹规划所用时间。本设计考虑了目标点与起始点的角加速度分析，用四次多项式方程来表示第一段轨迹和最后一段轨迹，以提高其性能。

本课题运用ADAMS软件对设计的机器人手臂进行仿真，通过对自由度与制定轨迹运动的仿真对比，选择了适用于机器人手臂方案；同时，对于系统的准确度也进行一定的修正，使用MATLAB 软件，对于系统的各个关节进行系统的响应速度与轨迹跟踪精度追踪，分析系统的实际运行性能。实验结果表明，采用细分法和插值法皆可满足轨迹规划的要求，而经过数据的对比，采用插值算法可以更简易的完成规划轨迹，更能满足沿指定轨迹运动的要求。

关键词：乒乓球机器人手臂；轨迹规划；多项式插值算法；D-H参数法；MATLAB仿真

Abstract

Nowadays, robots have become the trend of the development of advanced science and technology, and have attracted great attention from scientists at home and abroad. The arm of table tennis robot is one of them, which refers to the robot specially designed to play table tennis with people.

This topic focuses on the design of the arm trajectory of table tennis robot, and uses two control system algorithms to simulate. The first scheme is subdivision method, which makes the front end of the arm move in straight line and circular arc, and takes several points on the corresponding trajectory, so that the end reaches the selected position separately, so that the trajectory of the end can approach the specified trajectory; the second scheme is interpolation algorithm, which takes several points on the straight or circular trajectory and makes the end arrive in turn, using polynomial interpolation method, assuming that there are n points after interpolation. Each point is polynomially introduced to calculate the known conditions; at the target point, the corresponding angles are calculated according to the known conditions, and the whole trajectory planning time is known. In this design, the angular acceleration analysis between the target point and the starting point is considered, and the first and last trajectories are expressed by Quaternary polynomial equation to improve its performance.

In this paper, ADAMS software is used to simulate the designed robot arm. By comparing the degree of freedom with the trajectory-setting motion simulation, the scheme suitable for the robot arm is selected. At the same time, the accuracy of the system is modified to some extent. Using MATLAB software, the response speed and trajectory tracking accuracy of each joint of the system are tracked, and the system is analyzed. Actual operation performance. The experimental results show that the subdivision method and interpolation method can meet the requirements of trajectory planning. By comparing the data, the interpolation algorithm can complete the trajectory planning more easily and meet the requirements of moving along the specified trajectory better.

Key Words：Table tennis mechanical arm; Trajectory planning; Polynomial interpolation algorithm; D-H parameter method; MATLAB simulation

目 录

第一章 绪论

1.1 课题研究背景和意义

1.2 国内研究现状

1.3 国外研究现状

1.4 论文结构安排

第二章 机械手臂运动学方程

2.1 Adams机械手臂设计示意图

2.2 空间向量矩阵

2.3 相对坐标系矩阵

2.3.1 关节坐标系的矩阵

2.3.2 变换坐标系的矩阵表示

2.3.3 变换后关节的矩阵表示

2.4 D-H表示法

2.4.1 指定坐标系

2.4.2 坐标系之间的变换

2.4.3 求取变换矩阵

2.5 本章小结

第三章 乒乓球机器人手臂建立模型

3.1 乒乓球机器人手臂建模步骤

3.2建立机器人手臂坐标系

3.3正运动方程求解

3.4乒乓球机器人手臂的逆运动学方程

3.5本章小结

第四章 乒乓球机器人手臂的轨迹规划

4.1 乒乓球机器人手臂自主规划轨迹

4.1.1 一次多项式轨迹规划

4.1.2 三次多项式轨迹规划

4.1.3 五次多项式轨迹规划

4.2 指定中间点的轨迹规划

4.3 沿指定轨迹运动

4.3.1 细分法

4.3.2 插值法

4.4 本章小节

第四章 乒乓球机器人手臂的仿真研究

4.1 SimMechanics工具箱简介

4.2 运用SimMechanics工具箱搭建虚拟的乒乓球机器人手臂

4.3 对自主规划轨迹算法进行仿真验证

4.4 对指定中间点的轨迹规划算法进行仿真验证

4.5 对沿指定轨迹运动的轨迹规划算法进行仿真验证

第五章 总结与展望

5.1 总结

5.2 展望

参考文献

致谢

1. 绪论

本章将对乒乓球机械手臂的研究背景、意义以及国内外研究现状进行介绍，同时简介论文结构。

1.1 课题研究背景和意义