机器人学基础(全套ppt课件470P)

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,单击此处编辑母版文本样式,第二级,单击此处编辑母版标题样式,机器人学基础,Fundamentals of Robotics,智能科学基础系列课程国家级教学团队,“机器人学” 课程,Fundamentals of Robotics,1,2024/11/25,2,Ch. 1 Introduction,第,1,章 绪 论,Ch. 1 Introduction,Contents,Course Schedule,Top 10 Robotics News of 2008,Development of Robotics,Structure, Feature, and Classification of Robots,Robotics and AI,3,Ch. 1 Introduction,The Textbooks,教材,Cai Zixing. Fundamentals of Robotics,机器人学基础,.,机械工业出版社，,2009,John J Craig. Introduction to Robotics, Mechanics and Control. Pearson Education, Inc. , Publishing, 2005,机器人学导论,.,机械工业出版社，,2005,4,Ch. 1 Introduction,机器人学基础,国家级,“智能科学基础,系列课程,教学团队”,机器人学课程,配套教材,机械工业出版社,2009,5,Ch. 1 Introduction,机器人学（,2000,）,获全国高校优秀教材一等奖（,2002,）,6,Ch. 1 Introduction,机器人学,二零零九,7,Ch. 1 Introduction,教学进度安排（,1,）,月,日,周次,教学内容,教学时数,教学方式,课外时数,备注,3,2,1,绪论,2,讲授,3,5,1,机器人学的数学基础,2,讲授,3,9,2,数学基础,/,机器人运动学,2,讲授,3,12,2,机器人运动学,2,讲授,3,16,3,机器人动力学,2,讲授,3,19,3,机器人控制（,1,）,2,讲授,3,23,4,机器人控制（,2,）,2,讲授,8,教学进度安排（,2,）,月,日,周次,教学内容,教学时数,教学方式,课外时数,备注,3,26,4,机器人控制（,3,）,2,讲授,3,30,5,实验一,2,实验,4,2,5,机器人传感器,2,讲授,4,6,6,机器人传感器,/,机器人轨迹规划,2,讲授,4,9,6,机器人轨迹规划,2,讲授,4,13,7,主题讨论,2,课堂报告,4,16,7,实验二,2,实验,9,教学进度安排（,3,）,月,日,周次,教学内容,教学时数,教学方式,课外时数,备注,4,20,8,机器人编程,2,讲授,2,4,23,8,机器人编程,训练,2,训练,4,27,9,综合实验,:,智能机器人的路径规划与行为决策实验,2,综合实验,4,30,9,机器人应用,2,讲授,5,4,10,机器人与展望,2,讲授,2,5,7,10,考试,2,讲授,10,Question,What is Robot looks like in your mind,？,11,Ch. 1 Introduction,Robots in Movies,12,Ch. 1 Introduction,Robots in Movies,13,Ch. 1 Introduction,14,Robots in Movies,Ch. 1 Introduction,Contents,Course Schedule,Top 10 Robotics News of 2008,Development of Robotics,Structure, Feature, and Classification of Robots,Robotics and AI,15,Ch. 1 Introduction,16,Ch. 1 Introduction,1 The U.S. Big Dog,In March 2008, the U.S. government released a video of the military robots called Big Dog, which has amazing,mobility,and,adaptability,.,Latest Big Dog can climb up 35 slopes, carry more than 40 kg equipment, representing about 30% of its weight,It can move along a simple route, or by remote control.,17,Ch. 1 Introduction,2 Robot ride on a wheelbarrow,In September 2008 Japanese Murata Manufacturing Institute launched a new type of robot riding on a wheelbarrow, named seiko. This new type of robot can maintain its balance through a series of sensors and gyroscopes, and easy to complete riding of a wheelbarrow.,This new robot seiko is 50cm high, 5kg weight, designed to look like a little girl.,18,Ch. 1 Introduction,3 Washing robot launched in Japan,This robot can help people washing dishes, especially useful for the families with elders and patients.,Washing robot confirms the shape and location of the tableware through a,camera,installed in the,ceiling roof, and sorts out all tableware with the help of,sensors equipped in the palm,.,19,Ch. 1 Introduction,4 Olympic robot Fuwa debut at Beijing,The Olympic robot Fuwa perform dancing at the Beijing Capital International Airport July 15, 2008. Five robot Fuwa debut on Tuesday inside the newly-built Terminal 3 of the airport. The robots can provide guiding services for passengers with language contact.,20,Ch. 1 Introduction,5 Domestic underwater robots in expedition of the North Pole,In July 2008, the North Pole ARV underwater robot starting from Shenyang, participated in Chinas third Arctic scientific expedition.,This is the first time for Chinas underwater robots to carry out experiment at high latitudes. It will provide a larger content of continuous, real-time ice observation techniques.,21,Ch. 1 Introduction,6 The first robot that can kill cancer cells,Scientists at the University of California have invented a new form of robot with a strong ability to kill cancer cells.,The birth of cancer killer nano thrusters is not only a success of nanotechnology, but also a new platform for the development of next-generation medical nano-robots.,22,Ch. 1 Introduction,7 Robot World Cup held in China for the first time,China successfully held the Robot World Cup through July 14-20, 2008 for the first time.,23,Ch. 1 Introduction,8 Phoenix probe landing on Mars,After more than nine months of space travel, the U.S. Mars probe Phoenix successful land on Mars near the North Pole region on May 25, 2008.,This is the first time for a human detector to land near the north pole of Mars.,24,Ch. 1 Introduction,9 Robot Controlled By Rat Brain Cells,Some idiotic scientists at Reading University have developed a robot that is controlled by rat brain cells.,The neurons are now being taught to steer the robot around obstacles and avoid the walls of the small pen in which it is kept. By studying what happens to the neurons as they learn its creators hope to reveal how memories are laid down.,25,Ch. 1 Introduction,10 Chinas first family service intelligent Robot,26,Tami has a relatively high intelligence, who can speak freely like human beings, it understands more than 200 English sentences, could identify the owner and objects through eyes, and to give their names.,Tami is mainly used for family services, to take care of the elders, and to accompany with children.,Ch. 1 Introduction,27,1.1Development of Robotics,机器人学的发展,1.1.1 Origin of Robotics,机器人的由来,人类长期以来的愿望：创造出一种像人一样的机器来代替人类进行各种工作；,木牛流马？,记里鼓车,写字机器人,1.1 Development of Robotics,Contents,Course Schedule,Top 10 Robotics News of 2008,Development of Robotics,Structure, Feature, and Classification of Robots,Robotics and AI,28,Ch. 1 Introduction,29,1.1.1 History of Robotics,1950,年，美国科学幻想小说巨匠阿西摩夫在小说,我是机器人,中，提出了著名的 “,机器人三定律,(Three Laws of Robotics),” ：,First Law,: A robot may not injure a human being, or, through inaction, allow a human being to come to harm.,Second Law,: A robot must obey orders given it by human beings, except where such orders would conflict with the First Law.,Third Law,: A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.,Isaac Asimov,1.1 Development of Robotics,30,1.1.1 History of Robotics,1962,年，美国万能自动化公司（,Unimation,）的第一台机器人,Unimate,在美国通用汽车公司投入使用，标志着第一代机器人的诞生。,1.1 Development of Robotics,31,1.1.1 History of Robotics,1969,年 日本早稻田大学加藤一郎实验室研发出第一台以双脚走路的机器人。加藤一郎长期致力于研究仿人机器人,(Humanoid Robot),，被誉为“仿人机器人之父”。,日本专家一向以研发仿人机器人和娱乐机器人的技术见长，后来更进一步，催生出本田公司的,ASIMO,和索尼公司的,QRIO,。,1.1 Development of Robotics,32,1.1.1 History of Robotics,1978,年，美国,Unimation,公司推出通用工业机器人,PUMA,，这标志着工业机器人技术已经完全成熟。,PUMA,至今仍然工作在工厂第一线。,1.1 Development of Robotics,33,1.1.1 History of Robotics,2002,年 丹麦,iRobot,公司推出了吸尘器机器人,Roomba,，它能避开障碍，自动设计行进路线，还能在电量不足时，自动驶向充电座。,Roomba,是目前世界上销量最大、最商业化的家用机器人。,1.1 Development of Robotics,34,1.1.1 History of Robotics,2006,年,6,月，微软公司推出,Microsoft Robotics Studio,，机器人模块化、平台统一化的趋势越来越明显，比尔,盖茨预言，家用机器人很快将席卷全球。,1.1 Development of Robotics,35,1.1.2 Definition of Robotics,机器人的定义,Definition 1,机器人是“貌似人的自动机，具有智力的和顺从于人的但不具人格的机器” 。,(The Concise Oxford Dictionary, COD),Definition 2,“A reprogrammable, multifunctional manipulator designed to move material, parts, tools, or specialized devices through various programmed motions for the performance of a variety of tasks”,（,Robotic Industries Association, RIA,）,1.1 Development of Robotics,36,1.1.2 Definition of Robotics,Definition 3,工业机器人是“一种装备有记忆装置和末端执行器,(end effector),的，能够转动并通过自动完成各种移动来代替人类劳动的通用机器”。,（,Japan Industrial Robot Association, JIRA,）,Definition 4,机器人是“一种能够进行编程并在自动控制下执行某些操作和移动作业任务的机械装置”。,(National Bureau of Standards, NBS),1.1 Development of Robotics,37,1.1.2 Definition of Robotics,Definition 5,“机器人是一种自动的、位置可控的、具有编程能力的多功能机械手，这种机械手具有几个轴，能够借助于可编程序操作来处理各种材料、零件、工具和专用装置，以执行种种任务”。,国际标准组织（,ISO,）,Definition 6,机器人（,1,）像人或人的上肢，并能模仿人的动作；（,2,）具有智力或感觉与识别能力；（,3,）是人造的机器或机械电子装置。,中国,1.1 Development of Robotics,38,1.1.3 Advances in Robotics,机器人学的进展,20,世纪,70,年代以来，机器人学的发展特点,机器人偿还期,(Payback period),理论促进对机器人产业的投资；,日本后来居上，成为“机器人王国”；,机器人产业在全世界迅速发展；,应用范围遍及工业、科技和国防的各个领域 ；,形成了新学科,机器人学,(Robotics),；,机器人向智能化,(Intellectual),方向发展 。,1.1 Development of Robotics,Estimated yearly shipments of industrial robots,39,1.1 Development of Robotics,Estimated yearly supply of industrial robots at year-endin Total World by main Industries 2006-2007,40,1.1 Development of Robotics,Contents,Course Schedule,Top 10 Robotics News of 2008,Development of Robotics,Structure, Feature, and Classification of Robots,Robotics and AI,41,Ch. 1 Introduction,42,1.2 Features, Structure and Classification of Robots,机器人特点、结构与分类,1.2.1 Main Features of Robots,通用性（,Versatility,）,通用性指的是某种执行不同的功能和完成多样的简单任务的实际能力，它取决于其几何特性和机械能力 。,适应性（,Adaptability,）,适应性是指其对环境的自适应能力，即所设计的机器,人能够自我执行未经完全指定的任务，而不管任务执,行过程中所发生的没有预计到的环境变化。,1.2 Features, Structure and Classification of Robots,43,1.2.2 Structure of A Robot System,一个机器人系统，一般由机械手、环境、任务和控制器四个互相作用的部分组成,图,1.1,机器人系统的基本结构,机械手,(Manipulator),具有,传动执行装置,的机械，由,臂,、,关节,和,末端执行装置,（工具等）构成。,1.2 Features, Structure and Classification of Robots,44,一个机器人系统，一般由机械手、环境、任务和控制器四个互相作用的部分组成,图,1.1,机器人系统的基本结构,环境,(Environment),环境即指导机器人所处的周围环境。环境不仅由几何条件（可达空间）所决定，而且由环境和它所包含的每个事物的全部自然特性所决定的。,1.2.2 Structure of A Robot System,1.2 Features, Structure and Classification of Robots,45,一个机器人系统，一般由机械手、环境、任务和控制器四个互相作用的部分组成,图,1.1,机器人系统的基本结构,任务,(Task),任务定义为环境的两种状态（初始状态和目标状态）之间的差别。必须用适当的程序设计语言来描述这些任务。,1.2.2 Structure of A Robot System,1.2 Features, Structure and Classification of Robots,46,一个机器人系统，一般由机械手、环境、任务和控制器四个互相作用的部分组成,图,1.1,机器人系统的基本结构,控制器,(Controller),机器人接收来自传感器的信号，对之进行数据处理，并按照预存信息、机器人的状态及其环境情况等，产生出控制信号去驱动机器人的各个关节。,控制器内存主要存有：,（,1,）机器人动作模型,（,2,）环境模型,（,3,）任务程序,（,4,）控制算法,1.2.2 Structure of A Robot System,1.2 Features, Structure and Classification of Robots,47,1.2.3 Degree of Freedom,（,DOF,）,of Robots,机器人的自由度,DOF of a Rigid Body,刚体的自由度,图,1.3,刚体的六个自由度,1.2 Features, Structure and Classification of Robots,48,1.2.3 DOF of Robots,DOF of Robots,机器人的自由度,图,1.4,机器人自由度举例,1.2 Features, Structure and Classification of Robots,49,1.2.4 Classification of Robots,1. Classified by Geometry Structure,柱面坐标机器人,(Cylindrical),图,1.6,柱面坐标机器人,1.2 Features, Structure and Classification of Robots,50,1. Classified by Geometry Structure,球面坐标机器人,(Spherical),图,1.7,球面坐标机器人,1.2.4 Classification of Robots,1.2 Features, Structure and Classification of Robots,51,关节式球面坐标机器人,(Articulated),图,1.8,关节式球面机器人,1.2.4 Classification of Robots,1. Classified by Geometry Structure,1.2 Features, Structure and Classification of Robots,52,非伺服机器人（,Non-servo robots,）,按照预先编好的程序,顺序,进行工作,图,1.9,有限顺序机器人方块图,1.2.4 Classification of Robots,2. Classified by Control Mode,1.2 Features, Structure and Classification of Robots,53,伺服控制机器人（,Servo-controlled robots,）,是一个,反馈控制系统,(Feedback control system),图,1.10,伺服控制机器人方块图,1.2.4 Classification of Robots,2. Classified by Control Mode,1.2 Features, Structure and Classification of Robots,54,3. Classified by Input Message of Controller,日本工业机器人协会（,JIRA,） 分类法,手动操作手,定序机器人,变序机器人,复演式机器人,程控机器人,智能机器人,美国机器人协会（,RIA,） 分类法,把,JIRA,分类法中的后四种当作机器人 。,1.2.4 Classification of Robots,1.2 Features, Structure and Classification of Robots,55,法国工业机器人协会（,French Association of Industrial Robotics, AFRI,） 分类法,A,型：手控或遥控加工设备。,B,型：具有预编工作周期的自动加工设备。,C,型：程序可编和伺服机器人，具有点位或连续路径轨迹，称为第一代机器人。,D,型：能获取一定的环境数据，称为第二代机器人。,3. Classified by Input Message of Controller,1.2.4 Classification of Robots,1.2 Features, Structure and Classification of Robots,56,1.2.4 Classification of Robots,4. Classified by Intellectual Level,一般机器人，不具有智能，只具有一般编程能力和操作功能。,智能机器人,(Intellectual Robot),，具有不同程度的智能,传感型机器人,(Sensory Robot),交互型机器人,(Interactive Robot),自立型机器人,(Autonomous Robot),1.2 Features, Structure and Classification of Robots,57,1.2.4 Classification of Robots,5. Classified by Application,工业机器人或产业机器人,(Industry Robot),1.2 Features, Structure and Classification of Robots,58,1.2.4 Classification of Robots,5. Classified by Application,工业机器人或产业机器人,(Industry Robot),探索机器人,(Exploration Robot),1.2 Features, Structure and Classification of Robots,59,1.2.4 Classification of Robots,5. Classified by Application,工业机器人或产业机器人,(Industry Robot),探索机器人,(Exploration Robot),服务机器人,(Service Robot),1.2 Features, Structure and Classification of Robots,60,1.2.4 Classification of Robots,5. Classified by Application,工业机器人或产业机器人,(Industry Robot),探索机器人,(Exploration Robot),服务机器人,(Service Robot),军事机器人,(Military Robot),1.2 Features, Structure and Classification of Robots,1.2 Features, Structure and Classification of Robots,5. Classified by Application,工业机器人或产业机器人,(Industry Robot),探索机器人,(Exploration Robot),服务机器人,(Service Robot),军事机器人,(Military Robot),61,1.2.4 Classification of Robots,1.2,机器人特点、结构与分类,62,1.2.4 Classification of Robots,6. Classified by Mobility,固定式机器人,(Fixed Robot),移动机器人,(Mobile Robot),轮式,Wheeled robot,履带式,Pedrail robot,足式,Foot robot,1.2 Features, Structure and Classification of Robots,Contents,Course Schedule,Top 10 Robotics News of 2008,Development of Robotics,Structure, Feature, and Classification of Robots,Robotics and AI,63,Ch. 1 Introduction,64,1.3 Robotics and AI,机器人学与人工智能,Relationship Between Robotics and AI,机器人学的进一步发展需要人工智能基本原理的指导，并采用各种人工智能技术；,机器人学的出现与发展为人工智能的发展产生了新的推动力，并提供一个很好的试验与应用场所。,AI Research Topics in Robotics,Sensor Information Processing,Robot Planning,Expert System,Natural Language Understanding,1.3 Robotics and AI,65,1.3.2 Research Fields of Robotics,Sensor and Sensory System,Drive, Modeling, and Control,Automatic Planning,Robot-used Computer System,Application Research,1.3 Robotics and AI,66,1.3.3 Intelligent Robots,智能机器人,智能机器人的控制系统主要组成,:,以知识为基础的知识决策系统和信号识别与处理系统。,图,1.11,一种智能机器人系统典型方框图,1.3 Robotics and AI,67,1. Main Academic Circles in AI,符号主义（,Symbolicism,）,认为人工智能源于数理逻辑,(Symbolic logic),；,其原理主要为物理符号系统（即符号操作系统）假设和有限合理性原理；,代表人物有纽厄尔（,Newell,）、肖,(Shaw),、西蒙,(Simon),和尼尔逊（,Nilsson,）等 ；,代表成果为,专家系统,(Expert System),。,1.3.4 Debate of AI and Its Influence to Robotics,1.3 Robotics and AI,68,1. Main Academic Circles in AI,连接主义（,Connectionism,）,认为人工智能源于仿生学,(Bionics),，特别是人脑模型的研究；,其原理主要为,神经网络,(Neural Network),及神经网络间的连接机制与学习算法；,代表人物有,Hopfield,、鲁梅尔哈特（,Rumelhart,）等 。,行为主义（,Actionism,）,认为人工智能源于控制论,(Cybernetics),；,其原理为,控制理论,(Control Theory),及感知,动作型控制系统；,代表人物有布鲁克斯（,Brooks,）。,1.3 Robotics and AI,69,1.3.4 Debate of AI and Its Influence to Robotics,2. Debate on AI Theory,符号主义（,Symbolicism,）,人的认知基元是符号，而且认知过程即符号操作过程,人是一个物理符号系统，计算机也是一个物理符号系统，因此，我们就能够用计算机来模拟人的智能行为，即用计算机的符号操作来模拟人的认知过程。,人工智能的核心问题是知识表示、知识推理和知识运用。,1.3 Robotics and AI,70,2. Debate on AI Theory,连接主义（,Connectionism,）,人的思维基元是神经元；,它对物理符号系统假设持反对意见，认为人脑不同于电脑，并提出连接主义的大脑工作模式。,行为主义（,Actionism,）,智能取决于感知和行动，提出智能行为的“感知,动作”模式；,智能不需要知识、不需要表示、不需要推理；人工智能可以象人类智能一样逐步进化,智能行为只能在现实世界中与周围环境交互作用而表现出来。,1.3 Robotics and AI,71,3. Debate of AI and Its Influence to Robotics,这些争论在机器人学上有所反映；在机器人学上，人工智能各派思想能够“和睦共处”，不存在排他性，甚至可在一个机器人系统上同时共存几个学派的思想。,1.3.4 Debate of AI and Its Influence to Robotics,1.3 Robotics and AI,72,1.,Introduction to Robotics,:,the origin and development of Robotics; definition of a robot; feature, structure, and classification of robots; relationship between Robotics and AI.,2.,Mathematical Foundations,:,Representation of position and attitude;,coordinate transformation; homogeneous transformation; general rotation transformation.,3.,Kinematics of Manipulator,:,Representation of Kinetic Equation; Solving method of Kinetic Equation; Motion Analysis of PUMA 560.,1.4 Main Contents of the Course,1.4 Main Contents of the Course,73,1.4 Main Contents of the Course,4.,Manipulator Dynamics,:,Dynamics of a Rigid Body; Dynamic Equation of a Manipulator.,5.,Robot Control,:,Basic Principles of Robot Control;,Position Control;,Hybrid Position/Force Control ;,Intelligent Control,.,6.,Robot Sensors,:,Internal Sensors; External Sensors; Considerations in Robot Sensor Application .,7.,Trajectory Planning,:,General Considerations on Trajectory Planning; Interpolated Calculation of Joint Trajectory; Planning of Cartesian Path Trajectories; Real-Time Generation of Trajectory.,1.4 Main Contents of the Course,74,1.4 Main Contents of the Course,8.,Robot Programming,:,Requirements and Language Types to Robot Programming; Structure and Basic Functions of Robot Language; Commonly-Used Language for Robot Programming; Off-Line Programming of Robots.,9.,Robot Applications,:,Factors Considered in Applying Industrial Robots; Application Areas of Robots; Application Examples of Industrial Robots.,10.,Prospect to Robotics:,Robot Technology and its Market; Developing Trends of Robot Technology in the 21st Century; Social Problems Caused by Applying Robots.,1.4 Main Contents of the Course,75,1.5,Summary,Origin, Definition and Development of robot;,Feature, Structure, and Classification of robot;.,Feature: Versatility,and Adaptivity.,Structure: End effector, Environment, Task, and Controller.,Classified by Geometry Structure, Control Mode, Input Information, Intellectual Level, Application, and Mobility,Relationship between Robotics and AI, debate on AI and its influence to Robotics.,Ch. 1 Introduction,结束语,“,机器人学,的进步和应用是,20,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,”。,中国工程院原院长宋健,机器人技术综合了多学科的发展成果，代表了高技术的发展前沿，它在人类生活应用领域的不断扩大，正引起国际上重新认识机器人技术的作用和影响。,76,Ch. 1 Introduction,第二章 数学基础,Review,78,Course Schedule,Top 10 Robotics News of 2008,Development of Robotics,Structure, Feature, and Classification of Robots,Robotics and AI,Fundamentals of Robotics,Contents,Representation of Position and Attitude,Coordinate Transformation,Homogeneous Transformation,Transformation of Object,General Rotation Transformation,79,Ch.2 Mathematical Foundations,80,Ch.2 Mathematic Basis,2.1 Representation of Position and Attitude,位置和姿态的表示,Description,of Position,2.1 Representation of Position and Attitude,81,2.1 Representation of Position and Attitude,Description,of,Orientation,2.1 Representation of Position and Attitude,82,Description,of,Frames,相对参考系,A,，坐标系,B,的原点位置和坐标轴的方位，分别由,位置矢量,(Position Vector),和,旋转矩阵,(Rotation Matrix),描述。这样，刚体的位姿（位置和姿态）可由坐标系,B,来描述，即,2.1 Representation of Position and Attitude,2.1 Representation of Position and Attitude,Contents,Representation of Position and Attitude,Coordinate Transformation,Homogeneous Transformation,Transformation of Object,General Rotation Transformation,83,Ch.2 Mathematical Foundations,84,2.2 Coordinate Transformation,坐标变换,平移坐标变换,(Translation Transform),2.2 Coordinate Transformation,85,旋转坐标变换,(Rotation Transform),2.2 Coordinate Transformation,2.2 Coordinate Transformation,86,Rotation about an axis,2.2 Coordinate Transformation,2.2 Coordinate Transformation,87,2.2 Coordinate Transformation,Rotation about an axis,2.2 Coordinate Transformation,88,复合变换,(Composite Transform),2.2 Coordinate Transformation,2.2 Coordinate Transformation,例,2.1,已知坐标系,B,的初始位姿与,A,重合，首先,B,相对于坐标系,A,的,z,A,轴转,30,，再沿,A,的,x,A,轴移动,12,单位，并沿,A,的,y,A,轴移动,6,单位。求位置矢量,A,p,B0,和旋转矩阵 。假设点,p,在坐标系,B,的描述为,B,p,=3,7,0,T,，求它在坐标系,A,中的描述,A,p,。,89,2.2 Coordinate Transformation,解：,2.2 Coordinate Transformation,例,2.1,已知坐标系,B,的初始位姿与,A,重合，首先,B,相对于坐标系,A,的,z,A,轴转,30,，再沿,A,的,x,A,轴移动,12,单位，并沿,A,的,y,A,轴移动,6,单位。求位置矢量,A,p,B0,和旋转矩阵 。假设点,p,在坐标系,B,的描述为,B,p,=3,7,0,T,，求它在坐标系,A,中的描述,A,p,。,90,2.2 Coordinate Transformation,解：,2.2 Coordinate Transformation,例,2.1,已知坐标系,B,的初始位姿与,A,重合，首先,B,相对于坐标系,A,的,z,A,轴转,30,，再沿,A,的,x,A,轴移动,12,单位，并沿,A,的,y,A,轴移动,6,单位。求位置矢量,A,p,B0,和旋转矩阵 。假设点,p,在坐标系,B,的描述为,B,p,=3,7,0,T,，求它在坐标系,A,中的描述,A,p,。,91,2.2 Coordinate Transformation,解：,2.2 Coordinate Transformation,Contents,Representation of Position and Attitude,Coordinate Transformation,Homogeneous Transformation,Transformation of Object,General Rotation Transformation,92,Ch.2 Mathematical Foundations,已知一直角坐标系中的某点坐标，则该点在另一直角坐标系中的坐标可通过,齐次坐标变换