机器人学导论(英) 第二讲
机器人学导论-JohnJCraig - v1
第2章 空间描述和变换
• 2.1 概述 • 2.2 描述：位置、姿态与坐标系 • 2.3 映射：从坐标系到坐标系的变换
• 2.4 算子：平移、旋转和变换
• 2.5 总结和说明 • 2.6 变换算法
• 2.7 变换方程
• 2.8 姿态的其他描述方法 • 2.9 自由矢量的变换
机器人学导论 （美）John.J.Craig
2.2 描述：位置、姿态与坐标系 相关知识：点积
机器人学导论 （美）John.J.Craig
2.2 描述：位置、姿态与坐标系 相关知识：点积
机器人学导论 （美）John.J.Craig
2.2 描述：位置、姿态与坐标系 相关知识：点积
机器人学导论 （美）John.J.Craig
2.2 描述：位置、姿态与坐标系 相关知识：点积
机器人学导论 （美）John.J.Craig 2.1 和姿态两个特性，在数学上就需要定
义坐标系来表达相关参数。
我们定义一个世界坐标系，任何问题都能够参照这个坐标系。位置和姿态都是参照这个世界坐标系或者由世界坐 标系定义的笛卡尔坐标系。
机器人学导论 （美）John.J.Craig
机器人学导论 （美）John.J.Craig
机器人学导论 （美）John.J.Craig
机器人学导论 （美）John.J.Craig
机器人学导论 （美）John.J.Craig
机器人学导论 （美）John.J.Craig
2.2 描述：位置、姿态与坐标系 相关知识：点积
《机器人学导论》课程教学大纲
《机器人学导论》课程教学大纲课程名称：机器人学导论课程编号：BF（英文）：Introduction to Robotics先修课程：线性代数、机构学、自动控制适用专业：机械电子、机械工程及自动化开课系（所）：机械与动力工程学院机器人研究所教材和教学参考书：1．1．教材：机器人学、蔡自兴、清华大学出版社、20002．教学参考书: 机器人学导论，约翰J.克雷格、西北工业大学出版社、1987 注：上述教材和参考书将根据教材课购买情况可互换一、一、本课程的性质、地位、作用和任务面对21世纪知识经济时代的机遇与挑战，人类（地球人）正在以非凡的智慧构思新世纪的蓝图。
世界的明天将更加美好。
但是，地球人在发展中也面临着环境、人口、资源、战争和贫困等普遍问题，同时还要学会与机器人共处,这是21世纪地球人必须正视和处理的紧要问题，是影响地球人生存和发展的休戚与共的重大事件。
机器人学是一门高度交叉的前沿学科，机器人技术是集力学、机械学、生物学、人类学、计算机科学与工程、控制论与控制工程学、电子工程学、人工智能、社会学等多学科知识之大成，是一项综合性很强的新技术。
自第一台电子编程工业机器人问世以来，机器人学已取得令人瞩目的成就。
正如宋健教授1999年7月5日在国际自动控制联合会第14届大会报告中所指出的：“机器人学的进步和应用是本世纪自动控制最有说服力的成就，是当代最高意义上的自动化。
”机器人技术的出现与发展，不但使传统的工业生产面貌发生根本性的变化，而且将对人类的社会生活产生深远的影响。
二、二、本课程的教学内容和基本要求1．1．绪言简述机器人学的起源与发展，讨论机器人学的定义，分析机器人的特点、结构与分类。
2．2．机器人学的数学基础空间任意点的位置和姿态变换、坐标变换、齐次坐标变换、物体的变换和逆变换，以及通用旋转变换等。
3．3．机器人运动方程的表示与求解机械手运动姿态、方向角、运动位置和坐标的运动方程以及连杆变换矩阵的表示，欧拉变换、滚-仰-偏变换和球面变换等求解方法，机器人微分运动及其雅可比矩阵等4．4．机器人动力学机器人动力学方程、动态特性和静态特性；着重分析机械手动力学方程的两种求法，即拉格朗日功能平衡法和牛顿-欧拉动态平衡法；然后总结出建立拉格朗日方程的步骤5．5．机器人的控制机器人控制与规划6．6．机器人学的现状、未来包括国内外机器人技术和市场的发展现状和预测、21世纪机器人技术的发展趋势、我国新世纪机器人学的发展战略等。
智能机器人技术导论 课件 第二章：机器人系统基础
1.直角坐标系
空间直角坐标系下一点P坐标表示
直角坐标系
空间直角坐标系也称笛卡尔坐标系，
直角坐标系任意一点P的坐标（x,y,z） 进行表示。
空间任意位置可以沿着X,Y,Z轴来获 得。
直角坐标系型机械臂（PPP ）
直角坐标系型机械臂运动是X,Y,Z三 轴平动。
PPP的作业空间是一个长方体
直角坐标系机械臂模型
3.三自由度手腕同样是俯仰型和回转型的组 合。常用的结构PPR,RRR,PRR,RPR。三自由度 手腕的运动空间是一个立体空间。
3.机械臂组成——臂部
● 臂部可由大臂、小臂或多臂所组成，其作用是支 撑手部和腕部，并且可以通过伸缩、回转、俯仰 和升降等运动改变手部的空间位置。
机械臂简图
臂部设计的基本要求
手爪
操作工具——喷枪
手部——按加持原理分类
手部——按夹持方式——机械钳爪式
手部又可分为机械钳爪式和吸附式两大类
内撑式钳爪
外夹式钳爪
手部——按夹持方式——吸附式
吸附式手部可分为磁力吸附式和真空吸附式两种
磁力吸附式
真空吸附式
2.机械臂组成——腕部
● 腕部是连接手部和手臂的部件，并可用来调整被 抓取物件的方姿势。
● 腕部的设计一般依据作业任务的运动空间和轨迹 来选取不同的类型结构。
机械臂简图
腕部设计分类
● 自由度是指机械手各运动部件在三维空间坐标轴上所具有的独立运动数。
腕部设计
腕部
1.一般单自由度手腕的运动形式为俯仰型（ 用字母P表示）或回转型（我们用字母R表示 ）。单自由度手腕的运动轨迹是一条线。
2.二自由度手腕则是俯仰型和回转型的组合 。可以组合成双俯仰型和俯仰回转型，但是 不能构成双回转型。二自由度手腕的运动空 间是一个面。
机器人学导论
机器人的动力学模型
牛顿-欧拉方程
拉格朗日方程
凯恩方法
雅可比矩阵
机器人的运动规划与控制
运动学：研究机器人末端执行器的位置和姿态信息 动力学：研究机器人末端执行器的力和力矩信息 运动规划：根据任务要求，规划机器人的运动轨迹 控制：通过控制器对机器人进行实时控制，实现运动规划
机器人的感知与感
05
知融合
01
添加章节标题
02
机器人学概述
机器人的定义与分类
机器人的定义： 机器人是一种能 够自动执行任务 的机器系统，具 有感知、决策、
执行等能力
机器人的分类： 根据应用领域、 结构形式、智能 化程度等不同， 机器人可分为多 种类型，如工业 机器人、服务机 器人、特种机器
人等
机器人学的研究领域
机器人设计：研究机器人的结构、 运动学和动力学
机器人的感知技术
添加项标题
视觉感知技术：通 过摄像头获取环境 信息，识别物体、 场景等，实现机器 人视觉导航、物体 识别等功能。
添加项标题
听觉感知技术：通 过麦克风获取声音 信息，识别语音、 音乐等，实现机器 人语音交互、音乐 识别等功能。
添加项标题
触觉感知技术：通过 触觉传感器获取接触 信息，识别物体的形 状、大小、硬度等， 实现机器人触觉导航、 物体抓取等功能。
执行器作用：根据控制信号执行相应的动作，如移动、转动等
机器人的感知系统
传感器类型：视觉、听觉、触觉等 传感器工作原理：图像处理、语音识别、触觉反馈等 传感器在机器人中的应用：导航、目标识别、物体抓取等 感知系统对机器人性能的影响：精度、稳定性、安全性等
机器人的运动学与
04
动力学
机器人的运动学方程
机器学习导论第2章
偏倚与方差
方差
偏倚
2.10 回归
• 数值输出写成输入的函数。假定数值输出 是输入的确定性函数与随机噪音的和：
• 其中 是未知函数，我们用定义在参数 上的估计 来近似它。如果
与估计无关， 可省略
等价于最小化
线性回归
关于w0求导 关于w1求导
可以解得
偏倚/方差 trade-off
• 由某个带噪声的 产生一组数据集 • 根据每个数据集形成一个估计 • 现实中 的估计为
2.7 模型的选择与泛化
• 实例学习布尔函数中，输入输出均为2元的。 • d个2元值有2d个写法，因此对于d个输入有 2d个样本实例，将有22d个可能的布尔函数。
2.7 模型的选择与泛化
• 学习一个样本的过程是去掉猜测出错的假 设。
– X1=0, x2=1 输出为0。 去掉了假设h5 h6 h7 h8 h 13 h14 h15. – 随着更多的实验样本，逐步去掉与训练数据不 一致的假设。
• 噪声来源？
– 记录输入属性可能不准确。 – 标记点可能有错。（指导噪声） – 可能存在我们没有考虑到的附加属性。这些属性可能 是隐藏的或潜在的，是不可以预测的。是一种随机成 分
• 当有噪声时，正负实例之间没有简单的边界。
– 利用复杂模型，更好地拟合数据，得到零误差。 – 保持模型的简单性并允许一定误差的存在。
– 现有一组汽车实例和一组被测人，展示汽车， 被测人对汽车标记：
• 正例：标记为家用汽车 • 负例：其他类型汽车
– 机器学习后预测未见过的汽车是否为家用 – 汽车特征包括 价格、发动机功率、座位数量、 车身颜色等。
2.1 由实例学习类
• 仅考虑价格（x1）和发动机功率（x2）
机器人学导论(英) 第三讲
•Point•Vector•Matrix•Calculus•Linear algebra •Dot product •Cross product •Position/Orientation •Rotation matrix •Direction cosine•Coordinate system •Frame•Mapping •Translation •Rotation •Homogeneous transorm •Cross product •Operator •Translational operator •Rotational operator•Transformation operator •Compound transformation •Inverting a transformChapter3 Manipulator Kinematics•What is kinematics ?Kinematics is the sciences of motion that treats the subject without regard to the forces that cause it.•Example:With the knowledge of manipulator’s link length and joint angles, how to compute the position and orientation of the manipulatorsIn kinematics, we consider about the position, the velocity,the acceleration, and the higher derivatives of the position.The study of kinematics refers to all the geometrical and time-based properties of the motion.•Forward kinematicsGiven the joint variables of the robot, determine the position and orientation of the end-effector.[]12...T n θθθΘ=),,,,,(αβγz y x Y =•Kinematic ChainA robot can be treated as a set of right bodies (rigid links) connected together at various joints.•Lower pair:describe the connection between a pair of bodies when relative motion is characterized by two surface sliding over on another.•Joint type (lower pair):1. Revolute2. Prismatic3. Cylindrical4. Planar5. Screw6. Spherical•We consider the joint with 1degree-of-freedom (DOF). A joint with m DOF can be modeled as m joints of 1DOF connected by m-1links of zero length.•The action of joint can be described by a single real number: the angle of rotation in the case of a revolute joint, or the displacement in the case of a prismatic joint.•Number of the links starts from the immobile base (link 0), the first moving body is link 1and so on, out to the freed end of the arm, which is link n .…link1link2link0link6•In kinematics, a link is considered as a rigid body that define the relationship between two neighboring joint axes.1−i a axis i-1axis ilink i-11−i α1−i α:twist angle•Two parameters: link length and link twist angle are used to define the relative location of the two axes.•L ink length: the distance between two axes is measured along a line that is mutually perpendicular to both axes. This line is unique except in the case that two axes are parallel.axis i-1axis ilink i-1a1−ia:link length1−i•Imagine that a plane, whose normal is the mutuallyperpendicular line just constructed, we can project the axis i-1and axis i onto that plane and measure the angle from axis i-1to axis i by the right-hand rule .axis i-1axis ilink n-11−i α:twist angle1−i a•Intermediate links in the chain:Neighboring links has a common joint axis between them. The distance along this common axis from one link to another is defined as “link offset”. It will be variable for prismatic joint.axis i-1axis ilink i-11−iαid1−iaiθiaid:link offset•The angle that rotates about this common axis between one link and its neighboring link is defined as “joint angle ”. It will be variable for revolute joint.axis i-1axis ilink i-11−i αid 1−i a iθia i θ:joint angle•Link length and link twist angle depend on joint axes i and i+1.•For first link in the chain, we set and .00=a 00=α•For last link in the chain, we set and .0=n a 0=n α•If joint 1 is revolute, is set to be 0, zero position ofwill be chosen arbitrarily.1d 1θ•If joint 1 is prismatic, is set to be 0; zero position ofwill be chosen arbitrarily.1θ1d•Link parameters¾For revolute joint, the joint angle is called “joint variable”, and the other three quantities are fixed link parameters.¾For prismatic joint, the link offset is called “jointvariable”, and the other three link quantities are fixed link parameters.θd •Any robot can be described kinematically by giving the values of four quantities for each link, i.e., Denavit-Hartenberg notation[]i i iid a θαvariableconstant• A frame is attached to each link to describe the location of a link relative to its neighbors.•The link frame are named by number according to the link to which they are attached. Step1: frame {i}link {i}link1link2link0link6{0}{1}{2}{6}•Step2: intermediate link in the chain:iZ ˆjoint axis i frame {i}axis i-1axis ilink i-11−i αid 1−i a iθia 1ˆ−i Z 1ˆ−i X 1ˆ−i Y iZ ˆiX ˆiY ˆlink i•Step 3: direction of -along , from joint i to joint i+1iX ˆi a axis i-1axis ilink i-11−i αid 1−i a iθia 1ˆ−i Z 1ˆ−i X 1ˆ−i Y iZ ˆiX ˆiY ˆlink i•Step 4: direction of can be determined by right-hand rule ˆiY•How about if intersect ?is normal to the plane of and .i Z ˆ1ˆ+i Z iX ˆi Z ˆ1ˆ+i Z •First link in the chainsSelection of frame {0} is arbitrarily, will be selected along .0ˆZ 1ˆZ •Last link in the chainsFor revolute joint is chosen along when , the origin of frame {n} is chosen to set . n X ˆ0=n d 1ˆ−n X 0=n θFor prismatic joint, the direction of is chose to make and the origin of {n} is chosen at the intersection of and joint axis n when .0=n θnX ˆ1ˆ−n X 0=n daxis i-1axis ilink i-11−i αid 1−i a iθia 1ˆ−i Z 1ˆ−i X 1ˆ−i Y iZ ˆiX ˆiY ˆlink i•Summary of link parameters: the distance from to measured along : the angle from to measured about : the distance from to measured along : the angle from to measured about iX ˆi a i αi Z ˆ1ˆ+i Z i Z ˆ1ˆ+i Z iX ˆi d i θ1ˆ−i X i X ˆi Z ˆ1ˆ−i X iX ˆi Z ˆ•Summary of link-frame attachment procedure:Step1: identify the join axis (revolute joint/prismatic joint)Step2: identify the common perpendicular between two neighbouring joint axes, at the point of where the common perpendicular meets the i-th axis, assign the link-frame origin. (special case: the two axes intersect)Step3: assign the axis pointing along the i-th joint axis Step4: assign the axis pointing along the common perpendicular (special case: the two axes intersect)iX ˆi Z ˆStep5: assign the axis to complete a right-hand coordinate system.iY ˆStep6: assign the {0} to match {1} when first joint variable is 0.For {n}, chosen origin and directly of freely, but so as to cause as many link parameters as possible to be zero.nX ˆExample 3.3 in the text book(a)(b)Example 3.4 in the text bookwhere two adjacentaxes intersect(a)(b)D-H Tablei1−i a 1−i αid i θ11ˆZ 1ˆX 2ˆZ 2ˆX 3ˆZ 3ˆX 2L Link1Link2Link323D 90000)(2t d 2L )(1t θ)(3t θFrame {0} is coincident with frame {1}.Example 3.5 in the text bookwhere two adjacentaxes intersect•It is possible that there is no unique attachment of frames to link and result in several possible D-H representation.¾There are two choice of direction in which to point .¾In the case of intersecting axes, there are two choices fordirection of . 2ˆZ iX ˆ01=a 901−=α01=d 22L a =02=α12L d =1ˆZ 1ˆX 2ˆZ 2ˆX 3ˆZ 1L 2L case 111()t θθ=22()t θθ=−1=a 901=α01=d 22L a =02=α12L d −=1ˆZ 1ˆX 2ˆZ 2ˆX 3ˆZ 1L 2L case 2•When the direction of is changed, some link parameters willalso be changed. There are four more possible assignments offrames with pointing down.1X 11()t θθ=22()t θθ=1ˆZ•The above problem will be broken into four sub-sub-problems.Each sub-sub problem will be a function of only one link parameter.[]i i i i d a θα11−−Ti i1−•Sub-problem: construct the transform that define frame {i} to frame {i-1}•Problem statement: solve for the position and orientation of link n relative to link 0.•The problem can be broken into n sub-problem. Each sub-problem will involve transformation from one link to its neighboring link.•Introduce three intermediate frames: {P}, {Q}, and {R} for each link for transformationaxis i-1axis ilink n-11−iαid1−iaiθia 1ˆ−iZ1ˆ−iXiZˆiXˆRZˆRXˆQXˆQZˆPZˆPXˆ•Step1: {i}--->{P}, translation transform•Step2: {P}--->{Q}, rotation transform•Step3: {Q}--->{R}, translation transform•Step4: {R}--->{i-1}, rotation transform)(ˆi z P id D T i =)(ˆi z Q Pi R T θ=)(1ˆ1−−=i X R Qa D T i )(1ˆ11−−−=i X i Ri R T α)()()()(ˆˆ1ˆ1ˆ111i Z i Z i X i X i id D R a D R T iii i θα−−−−−=We can write))()()((11T T T T T P iQ P R Q i R i i−−=⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡−−−=−−−−−−−−−−10001111111111i i i i i i i i i i i i i i i i i i i d c c s c s s d s s c c c s a s c T αααθαθαααθαθθθBy substituting the link parameters into above equation, we have•The Unimation Puma 560 is a robot with 6 degree of freedom, and all rotational joints (6R).•The link frames are assigned in the position corresponding to all joint angles equal to 0.forearm•Join axes of joint 4,5,6 intersect at a common point, and the joint axes 4,5,6 are mutually orthogonal. This design is used in many industrial robot.Schematic of the 3R wrist of PUMA 560•Link parameters of the PUMA 560 is listed in the following D-H table.•Transformation of each link can be computed as follows:•The transformation of all six link:•For a manipulator with n DOF, the position of all the links can be specified with a set of n joint variable. This set is often called as joint vector.•The space of joint vectors is referred as joint space.•Cartensian space: position is measured along orthogonal axes, and orientation is described by the rotation matrix wespecified before.•Cartensian space is often called as task-oriented space or operational space.•In the case that joint is not actuated directly by actuator, and the position sensors are often located at the actuators, actuator position should be considered.•Actuator vector: a set of actuator position•Actuator space: the space of actuator vectorsActuator SpaceJoint Space Cartesian Space•Base frame {B}, or frame {0}. It is attached to a non-moving part of the robot, i.e., the base, sometimes called link 0link1link2link0link6{B}{W}{T}{S}{G}link1link2link0link6{B}{W }{T }{S}{G}•The station frame {S}, located in a task-relevant location. Sometimes is called universe frame , task frame or world frame . It is often specified with respect to frame {B} as:TS B S =}{link1link2link0link6{B}{W }{T }{S}{G}•The wrist frame {W}, attached to the last link of themanipulator (frame {N}). It is defined relative to the base frame {B} asTT W N B W 0}{==link1link2link0link6{B}{W }{T }{S}{G}•The tool frame {T}, attached to the end of tool that the robot isholding. It can be defined according to wrist frame {W}.TT W T=}{link1link2link0link6{B}{W}{T }{S}{G}•The goal frame is utilized to describe the location to which therobot is to move the tool. It is specified relative to the station frame {S}.TG S G=}{•Where is the tool?The problem is to locate the position and the orientation of the tool that the robot is holding.))(()(1T T T T W TB W BS ST −=}{}{S T →•Example of the assignment of standard frames:Thank You!。
机器人学导论英文版课后习题答案-(美)John-J.-Craig
S OLUTIONS M ANUALI NTRODUCTION TOR OBOTICSM ECHANICS AND C ONTROLT HIRD E DITIONJ OHN J.C RAIGUpper Saddle River, New Jersey 07458Associate Editor: Alice DworkinExecutive Managing Editor: Vince O'BrienManaging Editor: David A. GeorgeProduction Editor: Craig LittleSupplement Cover Manager: Daniel SandinManufacturing Buyer: Ilene Kahn©2005 by Pearson Education, Inc.Pearson Prentice HallPearson Education, Inc.Upper Saddle River, NJ 07458All rights reserved. No part of this book may be reproduced in any form or by any means, without permission in writing from the publisher.The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and pub-lisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs.Pearson Prentice Hall®is a trademark of Pearson Education, Inc.This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.Printed in the United States of America10 9 8 7 6 5 4 3 2 1ISBN 0201-54362-1Pearson Education Ltd., LondonPearson Education Australia Pty. Ltd., SydneyPearson Education Singapore, Pte. Ltd.Pearson Education North Asia Ltd., Hong KongPearson Education Canada, Inc., TorontoPearson Educación de Mexico, S.A. de C.V.Pearson Education—Japan,TokyoPearson Education Malaysia, Pte. Ltd.Pearson Education, Inc., Upper Saddle River, New Jersey。
机器人导论01绪论PPT课件
1927年，美国西屋公司工程师温兹利制造了第一个机器人“电报 箱”，并在纽约举行的世界博览会上展出，它是一个电动机器人， 装有无线电发报机，可以回答一些问题，但该机器人不能走动。
春秋后期，据《墨经》记载，鲁班曾制造过一只木鸟，能在空中飞行 “三日不下” 。
公元前2世纪，古希腊人发明了最原始的机器人──太罗斯，它是以水、 空气和蒸汽压力为动力的会动的青铜雕像，它可以自己开门，还可以 借助蒸汽唱歌。
1800年前的汉代，大科学家张衡不仅发明了地动仪，而且发明了计 里鼓车，计里鼓车每行一里，车上木人击鼓一下，每行十里击钟一下。
(6) 机器人语言；
(7) 装置与系统结构；
(8) 机器人智能等。
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1.3 机器人的定义和分类
（Definition and Classifying for Robots）
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1.2 机器人的发展历史
( The Developing History of Robots )
古代“机器人”——现代机器人的雏形
人类对机器人的幻想与追求已有3000多年的历史
西周时期，我国的能工巧匠偃师研制出的歌舞艺人，是我国最早记载 的机器人。
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