### What does a wavy line over a letter mean in a formula?

1, In mathematics, it is a mathematical symbol representing an equivalence relationship.

2. Asymptotically equivalent, as in

3. “Obeying a certain probability distribution”, as in

It means that “X obeys a normal distribution with expectation μ and variance”;

### How to learn robotics systematically

Author: Zheng Fan

Link: http://www.hu.com/question/22390802/answer/21350061

Source: Zhihu

Copyright © 2012 by the author, reproduced please contact the author for authorization.

1. Introduction to the basics

The textbooks are pretty much the same, and the two commonly used ones are recommended:

Craig: Introduction to Robotics (Douban)

Cai Zixin: Robotics (Douban)

In conjunction with the textbooks, you can look at Stanford’s Open Class: Stanford Open Class: Robotics

The above, help in create a general picture and basic concepts of robotics in your mind. Of course, you don’t have to watch all of them, but in fact a set of them is sufficient for a serious study. Usually the basic discussion of robotics are based on the robot arm, need to understand a few issues: the spatial description of the robot arm and coordinate transformation; robot arm kinematics; robot arm inverse kinematics; robot arm dynamics; trajectory planning; control of the robot arm; and others such as mechanical design, sensors, image processing etc.

Basic content, I personally believe that the most important must master a few concepts:

①Rigid body position of the coordinate description and transformation: the basis of the robot model, the importance of robotics in the English alphabet to the English language;

②D-H coordinate transformation: an important method of robotic arm modeling, a simple mathematical language to describe the robotic arm composed of a series of rigid bodies;

③Jacobi matrix: the core of the robotic arm kinematics, used for the conversion of joint speeds and terminal velocity conversion;

④ Lagrangian dynamics: a bridge for conversion between force and velocity acceleration.

Most important tool: mathematics, especially linear algebra.

2. Basic Hands-On Introduction

Engineering is not hands-on, nor is it learned. If you think the above basic content is boring (in fact, it is indeed very boring), do not put their own hands to increase the interest.

Software, you can use the almighty matlab. in fact, Clegg’s “Introduction to Robotics” has a lot of matlab exercises that you can refer to. Of course the roboticstoolboxformatlab written by PerterCorke has to be mentioned here:http://petercorke.com/Robotics_Toolbox.html.

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Hardware, personal DIY robots, then the cost is very high, positioning for the science and education function of the nao robot (this famous budding goods see the following picture, why I’m going to post this irrelevant picture because it is too cute), one on the sale of more than 100,000 it.

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BUT It’s also feasible for a student party to personally DIY a relatively rudimentary robotic arm. Buy a few tens of dollars of motors, although the precision is low, can turn up on the line. Buy a few control boards. If you circuit enough awesome, you can also design their own circuit drawing circuit diagrams sent to the processing and then welded, but always still buy ready-made boards convenient Well. For beginners, the control board can choose the student party most commonly used microcontroller, here I recommend their own messed up open source project arino: Arino-HomePage

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The good thing about arino is that the programming syntax is simple, as long as you can understand the basic C language can be, almost zero entry; editor comes with a lot of sample can be referred to; programming template versatility, a lot of times programming only need to change the template design to achieve the functionality of the statement can be; as an open source project, google to find a lot of foreign strong people to do the wildly cool DIY projects, such as: DIYRoboticHandControlledbyaGloveandArino Many DIY people are willing to make the program public, can be used for reference; there is, the price is not expensive.

Whether you buy a motor or a control board, you can turn to the almighty Taobao. A simple robotic arm to build up, a few hundred dollars enough.

Paste a I use arino board and simple motor blindly pouring mechanical arm:

<imgsrc=”https://pic3.mg.com/6ebe0575e365054c2743eadaefc9837e_b.jpg “data-rawwidth=”2000 ” data-rawheight=”3552 “class=”origin_imagezh-lightbox-thumb “width=”2000 “data-original=”https://pic3.mg.com/ 6ebe0575e365054c2743eadaefc9837e_r.jpg”> use it to draw lines on paper, because of the low precision, so the straight line shakes into that kind of frustration (shy >. <). Use it to draw lines on paper, because of the low precision, so the straight line shakes into that kind of frustration (shyness>. <).

3. Advanced

Advanced can not be told in the knowledge. First of all, there are too many directions, after learning the basics, what do you want to do (industrial robotic arms, motion humanoid robots, etc), what do you want to do (mechanical design, circuitry, image processing, control algorithms, gait planning, etc). Plus, the cost is too high, you know. Finally, advanced robotics DIY is not necessary, high financial cost is one thing, even more so is the high cost of time and effort. If you don’t take robotics as your specialty, then up to stage 1 or 2, you can just play around by yourself. If one aspires to do robotics related research or work, then participating in a related research program in college is sufficient.

### A brief description of the method for finding the inverse kinematics equations of a robot

A brief description of the method for finding the inverse kinematics equations of a robot is to determine An, which is a chi-square coordinate transformation of the joint coordinates, based on the joint coordinate settings of the manipulator, as determined by the joint variables and parameters. As follows:

Inverse kinematics content: inverse kinematics is the process of determining the parameters of the joint movable objects to be set to achieve the desired pose. For example, given a 3D model of a human body, how do you set the angles of the wrist and elbow so that the hand goes from a relaxed position to a waving position?

This question is critical in robotics because manipulating a robotic arm is controlled through joint angles. Inverse kinematics is also important in game programming and 3D modeling, although its importance is diminished by the increasing use of large databases of motion capture data.

A jointed object consists of a set of rigid segments connected by joints. Varying the angles of the joints can produce an infinite number of shapes. The solution to the forward kinematics problem is the pose of the object given these angles. A more difficult solution is to find the angles of the joints given the pose of the object, e.g., given the position of the end-effector.

In general, inverse kinematics problems do not have analytic solutions. However, inverse kinematics can be solved by nonlinear programming techniques. Specific special kinematic chains – those with spherical wrists – allow motion decoupling. This allows us to treat the orientation and position of the end effector independently and leads to an efficient closed-form solution.

Geometric Foundations of Robotics:

Most textbooks dealing with this field cover a wide variety of topics on the kinematics, dynamics, control, perception, and planning of robot manipulator arms. What sets this book apart, however, is that it introduces the mathematical tools, especially geometric tools, used to solve problems in robotics. In particular, it is geared toward readers interested in robotics and introduces Lie groups and the algebraic and geometric concepts associated with them in an accessible way.

Geometric Foundations of Robotics is a fascinating introduction to geometric concepts that have important applications in robotics. The 2nd edition provides in-depth coverage of the relevant areas and remains unique: rather than focusing on computational results in kinematics and robotics, it contains extremely important and up-to-date material that reflects important advances in the field and connects robotics to the mathematical foundations in group theory and geometry.

### What are the documents related to robot programming materials

, programming fundamentals:

1, C/C++

It is best to combine the ROS operating system, SLAM algorithm source code (such as ORB-SLAM3 downloaded from GitHub), or the Qt source code (Qt source code is very standardized), etc., and then gradually familiarize yourself with the next use, Reinforcement is much more effective than just holding onto C++Primer and chewing on it.

There are no shortcuts to improving your programming skills; reading and writing is the key. Look at the code – > write code – > look at the code – > write code – > … spiral learning up.

2, ROS operating system

In conjunction with online documentation or direct use for learning. By the way, you can master design patterns, software engineering and other ideas.

Second, the perceptual foundation:

1, image processing

Gonzalez “digital image processing”

2, computer vision

Tsinghua University Press “Computer Vision”

3, the application

GaryBradski&AdrianKaebler “LearningOpenCV. LearningOpenCV” (Tsinghua Publishing House has a Chinese version)

Other: Multivision Geometry in Computer Vision

3. Robotics:

1. Introduction to Robotics

Craig’s Introduction to Robotics

Mark Spong’s Robot Modeling and Control

Lynch, Modern Robotics (chapters from chapter 9 onwards, no need to read the previous chapters)

2. Mobile Robotics

Fourteen Lectures on Visual SLAM, be sure to figure out the ORB-SLAM algorithm in conjunction with the code. By the way can also learn ROS operating system. No electronic version.

3, PeterCorke “machine vision, robotics and control”

Two toolboxes: robotics toolbox and machine vision toolbox, both Matlab programming, to understand the concepts, algorithm validation is very helpful. Available in electronic version.

www.petercorke.com

Four, machine learning:

1, Zhou Zhihua “Machine Learning” watermelon book

2, Wu Enda “Deep Learning” video

3, NTU Hongyi Li robotics learning

Fei Feifei Li CS231n image recognition

4, 2D : YOLOv1234 code

3D: PointNet code

### Art Introduction 2023 Chapter Test Answers

Art Introduction 2023 Chapter Test Answers_Art Introduction Superstar Ergoya Answers (I) don’t know how to solve it, for this reason, I give you a collection of Art Introduction 2023 Chapter Test Answers_Art Introduction Superstar Ergoya Answers (I) solutions, interested in come and take a look at it.

Introduction to Art 2023 Chapter Test Answers_Introduction to Art Superstar Ergonomic Answers (I)

1.1 How Chinese Art Goes Global

1. [Single-choice question] Which master applied the mood in Chinese painting to oil painting? ()

A, Ding Shaoguang

B, I.M. Pei

C, Tan Dun

D, Zao Wou-ki

My Answer:D

2. [Single Choice Question] () was the architect of the Fragrant Hill Hotel in Beijing.

A. Ding Shaoguang

B. I.M. Pei

C. Tan Dun

D. Zao Wou-ki

My Answer: B

3. [Single choice question] Which painter founded the Yunnan School of Painting? ()

A, Ding Shaoguang

B, I.M. Pei

C, Tan Dun

D, Zao Wou-ki

My Answer: A

4、【Judgment Question】 It is necessary to embody China’s excellent traditional culture by using the modern art language in order to make Chinese art go global. ()

My answer: Yes

5. [Judgment question] I.M. Pei put forward the concept of organic architecture. ()

My Answer: Wrong

1.2 Cases of Chinese Art Going Global

1. [Single Choice Question] () used modern musical language to express traditional Chinese culture.

A, Ding Shaoguang

B, I.M. Pei

C, Tan Dun

D, Zao Wou-ki

My Answer:C

2. [Single-choice Question] Chinese cinema was born in ().

A, 1895

B, 1905

C, 1911

D, 1862

My Answer：B

3、【单选题】China’s highest award in TV drama awards is ().

A, Hundred Flowers Award

B, Feitian Award

C, Magnolia Award

D, Golden Eagle Award

My Answer：B

4、【Mon-choice】World Cinema was born in ().

A. 1895

B. 1905

C. 1911

D. 1862

My Answer：A/p>

My Answer：A/p>

5、【Judgment Question】A Bite of Vegetable Cake is the first TV series in China. ()

My Answer: Yes

1.3 The Three Climaxes of the Birth of Chinese Cinema

1. [Single-Choice Question] Chinese cinema has had three climaxes in its history, the first of which was in ().

A. 1950s and 1960s

B. 1970s and 1980s

C. 1980s and 1990s

D. 1930s and 1940s

My Answer: D

2. [Single-choice Question] At present, China’s movie box office is growing at the rate of () per year.

A, 0.2

B, 0.25

C, 0.3

D, 0.1

My Answer：C

3、【Mon-elective】The 17 years of Chinese cinema refers to the period of ().

A, 1949-1966

B, 1966-1983

C, 1983-2000

D, 1932-1949

My Answer：A/p>

4、【Judgment Question】The booming development of Chinese movies saw a third climax in the 1990s . ()

My Answer: Wrong

5. [Judgment Question] Tsui Hark is one of the Hong Kong New Wave directors. ()

My answer: right

1.4 Modern Expression of Traditional Chinese Culture

1. [Single Choice Question] () is the director of Red Sorghum.

A. Chen Kaige

B. Li An

C. Han Sanping

D. Zhang Yimou

My Answer：D/p>

2、【单选题】Mo Yan’s literary style was greatly influenced by which of the following? ()

A, Virgil

B, Stendhal

C, Marquez

D, Dickens

My Answer：C

3、【单选题】Director ()’s credits include Pusher, The Wedding Banquet, and Eat and Drink.

A, Chen Kaige

B, Li An

C, Han Sanping

D, Zhang Yimou

My Answer：B

4、【Judgment Question】Chen Kaige’s “The Yellow Land” expresses the tone that such a barren land has nurtured such a great nation. ()

My answer: yes

5. [Judgment question] One of the most typical ideas in traditional Chinese culture is the unity of heaven and man. ()

My answer: right