机械臂运动的轨迹规划

摘 要

空间机械臂是一个机、电、热、控一体化的高集成的空间机械系统。随着科技的发展，特别是航空飞机、机器人等的诞生得到了广泛的应用，空间机械臂作为在轨迹的支持、服务等以备受人们的关注。本文将以空间机械臂为研究对象，针对空间机械臂的直线运动、关节的规划、空间直线以及弧线的轨迹规划几个面进行研究，对机械臂运动和工作空间进行了分析，同时对机械臂的轨迹规划进行了验证，利用MATLAB软件对机械臂的轨迹进行仿真，验证算法的正确性和可行性，同时此路径规划法可以提高机械臂的作业效率，为机械臂操作提高理论指导，为机器人更复杂的运动仿真与路径规划打下基础。

本文一共分为四章：

第一章，首先总结了机械臂运动控制与轨迹规划问题的研究现状及研究法，归纳了各种轨迹规划的算法及其优化法，阐述了机械臂的研究背景和主要容。

第二章，对机械臂的空间运动进行分析研究，采用抽样求解数值法—蒙特卡洛法，进行机械臂工作空间求解，同时在MATLAB中进行仿真，直观展示机械臂工作围，为下一章的轨迹规划提供理论基础；同时通过D-H参数法对机械臂的正、逆运动分析求解，分析两者的区别和联系。

第三章，主要针对轨迹规划的一般性问题进行分析，利用笛卡尔空间的轨迹

规划法对机械臂进行轨迹规划，同时利用MATLAB对空间直线和空间圆弧进行轨迹规划，通过仿真验证算法的正确性和可行性。

第四章，总结全文，分析本文应用到机械臂中的控制算法，通过MATLAB结果可以得出本文所建立的算确性，能够对机械臂运动提供有效的路径，而且改进了其他应用于空间机械臂的路径规划问题。

【关键词】 运动分析 工作空间 算法研究 轨迹规划

ABSTRACT

Space manipulator is a machine, electricity, heat, charged with high

integration of space mechanical system integration. With the

development of science and technology, especially the birth of aviation

aircraft, a robot has been widely used, the trajectory of space

manipulator as the support ands to people's attention. This article will

space manipulator as the research object, according to the linear motion

of the space manipulator, joint planning, space of the straight line and

curve, the trajectory planning of several aspects of mechanical arm

movement and working space are analyzed, and the trajectory planning

of manipulator is verified, the trajectory of manipulator is to make use of

MATLAB software simulation, verify the correctness and feasibility of the

algorithm, at the same time this path planning method can improve the

efficiency of mechanical arm, improve the theoretical guidance for

mechanical arm operation, simulation and path planning for robot more

complicated movement.

This article is divided into four chapters altogether:

The first chapter, first summarizes the mechanical arm motion control

and path planning problem research status and research methods,

summarizes the variety of trajectory planning algorithm and the method

of optimization, and expounds the research background and main

content of mechanical arm.

The second chapter, the paper studied the space motion of mechanical

arm, the numerical method, monte carlo method are deduced with the

method of sampling, the workspace for mechanical arm is, at the same

time the simulation in MATLAB, intuitive display mechanical arm work

scope, providing theoretical basis for the next chapter of trajectory

planning. At the same time through d-h method of positive and inverse

kinematic analysis of the mechanical arm, analyze the difference and

contact.

The third chapter, mainly aims at the general problem of trajectory

planning is analyzed, using cartesian space trajectory planning method

for trajectory planning, mechanical arm at the same time, MATLAB is

used to analyse the spatial straight line and arc trajectory planning,

through the simulation verify the correctness and feasibility of the

algorithm.

The fourth chapter, summarizes the full text, analysis of the control

algorithm is applied to the mechanical arm in this paper, through the

MATLAB results can be concluded that the correctness of algorithm, can

provide effective path of mechanical arm movement, and improved the

other used in space manipulator path planning problem.

[key words] motion analysis,work space,trajectory planning,algorithm

research

目录

摘 要 ............................................................................................................................ - 1 -

ABSTRACT ................................................................................................................. - 2 -

第一章 绪论 ............................................................................................................... - 5 -

第一节 研究背景及意义 ................................................................................... - 5 -

第二节 国外发展现状 ....................................................................................... - 6 -

一、国现状 ................................................................................................... - 6 -

二、国外现状 ............................................................................................... - 6 -

第二章 机械臂的运动分析 ...................................................................................... - 8 -

第一节 机械臂的正运动学分析 ....................................................................... - 8 -

第二节 机械臂的逆运动学求解 ..................................................................... - 10 -

第三章 五轴机械臂轨迹规划与仿真 .................................................................... - 11 -

第一节 轨迹规划一般问题 ............................................................................. - 11 -

第二节 关节空间的轨迹规划 ......................................................................... - 12 -

一、三次多项式插值法 ............................................................................ - 12 -

二、五次多项式插值 ................................................................................ - 15 -

第三节 笛卡尔空间的轨迹规划 ..................................................................... - 17 -

一、空间直线轨迹规划 ............................................................................ - 18 -

二、空间圆弧的轨迹规划 ........................................................................ - 21 -