RoboticsRobotics

R b tiR b ti

Syllabus

Robotics Robotics

전공 선택, 인증 선택

담당교수곽관웅kwgwak@sejong.ac.krT l 02 3408 3785Tel. 02-3408-3785Lecture : Mon/Wed 12:00 -13:30, 광개토관 106호Office hour : Tue/Thr 09:00 – 10:30, 충무관 1114호

Main text: 문승빈, 고경철, 곽관웅 외, 지능형 로봇공학 , 사이텍 미디어, 2009

공지사항, Lecture notes, 교재 정오표: http://www.dasan.sejong.ac.kr/~kwgwak

참고도서:John J. Craig, Introduction to Robotics, Mechanics and Control (3rd edition), Wiley.Mark W. Spong, Seth Hutchinson, M. Vidyasagar, Robot Modeling and Control , John p g, , y g , g ,Wiley & Sons, 2006.Saeed B. Niku, Introduction to Robotics: Analysis, Systems, Applications (2판), Prentice Hall.정슬 로봇공학:Matlab 및 Simulink 응용 충남대학교 출판부ll정슬, 로봇공학:Matlab 및 Simulink 응용, 충남대학교 출판부ll.Matlab/Simulink manualhttp://www.engin.umich.edu/class/ctms/ (Control tutorials for MATLAB and Simulink)

Grade (성적 평가)

A d (10 %) 8회 이상 결석 F 지각 2회 결석 1회 결석 1회당 1점 감점• Attendance (10 %): 8회 이상 결석 F, 지각 2회=결석 1회, 결석 1회당 1점 감점

• H/W (10 %): 각 문제당 1점

• 실습 (5 %): 6자유도 ABB로봇 및 gripper를 이용한 이적재 작업

• Midterm (30 %)

• Final (30 %)

• Term Project (20 %)Term Project (20 %)

Homework

L h k ill b d• Late homework will not be accepted.• For full credit, work must be done in a neat and professional manner; all relevant sketches and intermediate results must be shown; and numerical answers must include relevant magnitudes, directions, and units.answers must include relevant magnitudes, directions, and units.

Exam

• Midterm covers material up to and through the prior week. • The final exam is comprehensive. • Missed exams (without an official excuse) will receive a zero grade

Term project

• Robot motion control & visualization simulation (Matlab proficiency will be required)

• Team project but report should be submitted individually

Study tips!

• spend three times of the lecture hours every week ( 3hr lecture = 9 hours of study per week)• Homework is the best material preparing for the examp p g

공학인증 설문 조사http://abeek.sejong.ac.kr/index.aspx

반대표 선출

Concerned about English lecture?- Don’t worry. Both Korean & English will be used y g- English usage will be gradually increased as class progresses- important concepts will be elaborated in Korean

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What is robot?

Seeing is believing!

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Let’s taste some…

6 DOF Industrial Robot most popular, symbol of robot

M j f t ABB FANUC KUKA Y k 현대중공업 Ad t8

Major manufactures: ABB, FANUC, KUKA, Yaskawa, 현대중공업, Adept

Whil t hi ti i tWhile watching motion pictures,please be advised to characterizethe joint, link & end-effectors

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Automotive line spot welding robot

http://wwwyoutube com/watch?v=362vMN7Ra4whttp://www.youtube.com/watch?v=362vMN7Ra4wWelding robot in Honda Automotive

http://www.youtube.com/watch?v=LEgGqSybLTohttp://www.youtube.com/watch?v LEgGqSybLToMercedes-Benz E-Class Production (first part & @2:25)

LCD glass handling robot

http://www.youtube.com/watch?v=4SBr4tClbf4ttp // youtube co / atc S tC bLCD panel handling robot in clean room

Electronics & semiconductor manufacturing robots

Wafer handling robot in clean room

SCARA Robot pick & placeSCARA Robot pick & placehttp://www.youtube.com/watch?v=BLCsCzq9NoI

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Injection molding applications with a KUKA robothttp://www.youtube.com/watch?v=uTI4oKj4lmE

deburring robothttp://www.youtube.com/watch?v=K8yqeENphfg

KUKA Robotics: Robocoaster(Harry porter in Orlando Universal Studio)http://www.youtube.com/watch?v=ruc1YB9fQCg

F1 Ferrari Driving Simulator from Max Planck Institutehttp://www youtube com/watch?v=shdS-hynLHghttp://www.youtube.com/watch?v=shdS-hynLHg

Medical robot

Robot arm toolRobot arm tool

Davinci Surgery robot(Intuitive Surgical)

14Control console

Knee/hip replacement surgery robotKnee/hip replacement surgery robot

ROBODOC (Curexo)

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Boston Dynamics Big Dog (Military)http://www.youtube.com/watch?v=W1czBcnX1Ww

BigDog – The most advanced rough-terrain robot on earth by Boston Dynamicswalks, runs, climbs and carries heavy loads, , ypowered by an engine that drives a hydraulic actuation systemBigDog has four legs that are articulated like an animal’s, with compliant elements to absorb shock and recycle energy from one step to the nextsize of a large dog or small mule; about 3 feet long, 2.5 feet tall and weighs 240 lbs.

Big Dog parody! Fun! http://www.youtube.com/watch?v=VXJZVZFRFJc

Wearable Robot (exoskeleton)

Raytheon XOS Exoskeleton (military, industry, rehabilitation applications)Raytheon XOS Exoskeleton (military, industry, rehabilitation applications)http://www.youtube.com/watch?v=V87lSB5XWVs

Rehabilitation robot WalkbotRehabilitation robot Walkbothttp://www.youtube.com/watch?v=RZppbdbtLS0

surveillance robot SuperDroid HD2 SWAT / EOD Tactical Treaded Robot w / 5DOF Arm Price : USD $33599.99

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Entertainment robot

SONY AIBOSONY AIBO

Education robot

유진로봇 아이로비

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Personal care robotPersonal care robot

안내로봇 http://www.youtube.com/watch?v=tOx4RRlsMzQ

원격진료로봇

mobile servant robothttp://www.youtube.com/watch?v=0q7Uh1SleWQ

Construction robot

Concrete spraying robot at tunnel construction site, Switzerland

고층 건설 현장용 Bolting robot (KIST)http://www tagstory com/video/video post aspx?media id=V000146592http://www.tagstory.com/video/video_post.aspx?media_id=V000146592

경사 구간 낙석 방지 작업용 4족 보행 로봇(JAPAN)경사 구간 낙석 방지 작업용 4족 보행 로봇(JAPAN)

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Shipbuilding robots

Mostly welding robotsMostly welding robots

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Space robot

NASA Mars Rover

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Humanoid

Hubo (KAIST) at 김장훈 concertHonda Asimohttp://www.youtube.com/watch?v=eU93VmFyZbg

Hubo (KAIST) at 김장훈 concert

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Carnegie Mellon university SARCOShttp://www.youtube.com/watch?v=2WKt_TMeAyg

• Many different robots

Real world robots

Many different robots– Welding / Palletizing / Deburring / Material handling / Painting– Surgery / Diagnostic / Rehabilitation (neuromuscular patient / amputee aid) / Nursery

Exoskeleton (wearable robot Iron men)– Exoskeleton (wearable robot, Iron men)– Construction – Guide / Maid / helper / Study helper /Entertainment (sony AIBO)

Militar / S r eillance / sec rit– Military / Surveillance / security– Space robot– AGV(UGV) / AAV(UAV) / AUV(UUV)

M bil b t– Mobile robot– Humanoid (cognition, AI) / Terminator– etc

• Types of robots– Industrial– ServiceService– Personal care / professional care– Medical– EntertainmentEntertainment– Military– etc

Basic structure of the robots

Robot = mechanism (기구부) + Controller (제어기)

Typically,

mechanism ManipulatorMobile robot without manipulatorp

with manipulator

Manipulator Mobile robot Mobile robot with manipulator

manipulator = link + joint (mechanical connection between links)

Without manipulator with manipulator

serialmanipulator serialparallel

Serial manipulatorParallel manipulator(Stewart platform)

http://www.youtube.com/watch?v= 7vKVYqu5Zwp y _ q

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prismatic (or sliding ,직동 관절) represented by P

revolute (or rotational , 회전관절) represented by R

cylindrical

joint

Actually, combination of two or more joints yspherical difficult to control precisely not often used

- adjacent links rotate withadjacent links translate adjacent links rotate with respect to each other about the joint axis- represented by joint angle

- adjacent links translate linearly to each other along the joint axis- joint variable dj

일종의 ball & socketmechanism

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actuator

- power mechanism used to effect motion of the robot- Attached at each joints

actuator

j- Drives each links- Types

A Electrical actuatorA. Electrical actuator- Rotary / linear motor- High precision, easy maintenance, and less expensive- Used for most robots- AC servo motor / DC motor / step motor

B. Hydraulic actuatorU d f th l t t- Used for the large output

C. Pneumatic - used for simple operation (on/off, robot gripper)

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Reducer (감속기)

• Connects actuator and link• For robotic motion low speed and high torque is required while motor speed• For robotic motion, low speed and high torque is required while motor speed

is high need to use reduction mechanism Typical reduction ration: tens ~ hundreds : 1

• ReducersReducers– Harmonic Drive (하모닉드라이브)

- Large reduction ratio- Could support large torque- compact structure- large payload and high precision position control

– RV reducer( planetary gear, cycloid reducer)– Ball Screw (볼스크류)( )

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Definition of robots

A programmable multi-functional manipulator designed to move parts, materials, tools or specialized devices through which variable programmed motions for the performance of a variety of tasks

- By RIA (Robotics Institute of America)-Industrial robot centered definition

actuated mechanism programmable in two or more axes with a degree of autonomy, moving within its environment, to perform intended tasks (원하는 작업을 수행하기 위하여 주변 환경 내에서 움직이며, 어느 정도의 자율성을 가진, 2축 이상 프로그램이 가능한 구동기구)2축 이상 프로그램이 가능한 구동기구)- definition by ISO 8373- consider service robot as well

Autonomy: ability to control movement and communication to perform intended tasks without outside control

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Vocabulary

Link

ISO 8373 Robots and robotic devices—Vocabulary

rigid (flexible) bodies connecting neighboring joints

JointAssembly between two links enable one to have a motion relative to the other

Degree of Freedom (D.O.F.)h i i b f i d d i bl hi h h d ib h ithe minimum number of independent variables which are enough to describe the motion

of all the system parts

Working space (volume)Working space (volume)operational range (reachable) of the manipulator(손목 원점이 도달 가능한 영역에 손목 각 조인트의 가동 범위를 합한 영역)

Manipulatormachine in which the mechanism usually consists of a series of segments, jointed or sliding relative to one another for the purpose of grasping and/or moving objects (piecessliding relative to one another, for the purpose of grasping and/or moving objects (pieces or tools) usually in several degrees of freedom

End-effector

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d e ectodevice specifically designed for attachment to the mechanical interface to enable the robot to perform its task ex) Gripper, nut runner, welding gun, spray gun, sealing gun, robot hand, other tools

mechanical interface wristarm

- mounting surface at the end of the manipulator to which the end effector is attached

arm(팔)arm(팔)– interconnected set of links and powered joints of the manipulator, comprising links of longitudinal shape, which positions the wrist

Mechanical interface

– 머니퓰레이터의 길이방향으로 형상을 구성하는 연결된 링크 및 관절 구조, 손목의 위치 결정

Wrist(손목)Wrist(손목)– interconnected set of links and powered joints of the manipulator between the arm and end effector which supports, positions and orients the end effectorpp p

Wrist Origin (손목 원점) or Wrist Reference Point(손목 기준점)Wrist Origin (손목 원점) or Wrist Reference Point(손목 기준점)-intersection point of the two innermost wrist axes or, if this does not exist, a specified point on the innermost wrist axes (손목을 구성하는 관절 중에서 가장 베이스 쪽에 있는 2축의 교점교점이 없는 경우에는 가장 베이스 쪽 축 상에 지정한 점

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교점이 없는 경우에는 가장 베이스 쪽 축 상에 지정한 점)

Pose Combination of position and orientation in space = position + orientation

Dexterityend-effector reaches any points with any arbitrary orientation

Redundant Robot (여유자유도 로봇)Robot that has more independently controllable degrees of freedom than the DOFsRobot that has more independently controllable degrees of freedom than the DOFs required to implement the position and the orientation completely(독립적으로 제어 가능한 자유도의 개수가 물체의 위치와 방위를 완전하게 나타내기 위해 최소한으로 필요한 자유도보다 많은 로봇))

Compliance (순응성)flexible behaviour of a robot or any associated tool in response to external forces

t d itexerted on it 로봇에 작용한 외력에 대한 로봇이나 공구의 유연한 거동을 의미강직도(stiffness)의 반대 개념

Teleoperation (원격조작)real-time control of motion of robot or robotic device from a remote site by a human

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C di t t

Coordinates

Coordinate system- required to represent the position and orientation- right hand rule rectangular coordinate system

World Coordinate System (월드 좌표계)– stationary coordinate system referenced to earth,which is

independent of the robot motionindependent of the robot motion

Base Coordinate System (기저 좌표계)di t t f d t th b ti f– coordinate system referenced to the base mounting surface

– 로봇 베이스 설치 표면을 기준으로 하는 좌표계

기계접속 좌표계

Mech. Interface coord. sys

Mechanical Interface Co. System (기계접속 좌표계) – coordinate system referenced to the mechanical interface– 로봇의 선단에 위치한 기계 접속면에 기준한 좌표계

y

World Base d

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cord. Sys.

cord sys.

Joint Coordinate System (관절 좌표계)– coordinate system referenced to the joint axes, the joint coordinates of which

are defined relative to the preceding joint coordinates or to some other coordinate system (more details in Ch.3)

Tool Coordinate System (TCS, 공구 좌표계)– coordinate system referenced to the tool or to the end effector attached to the

mechanical interface

Mobile Platform Coordinate System (이동플랫폼 좌표)– coordinate system referenced to one of the

components of a mobile platform

T l C t P i t (TCP 공구 중심점)이동 플랫폼의진행방향

Tool Center Point (TCP, 공구 중심점)– A representative point of the end-effector referenced to

the mechanical interface coordinate system기계접속 좌표계에 기준하여 정한 말단장치( d– 기계접속 좌표계에 기준하여 정한 말단장치(end-effector)의 대표점

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Classification of the robots (로봇의 분류)

1 General classification

industrial robot(산업용 로봇)

1. General classification

service robot (서비스 로봇) Personal service robot (개인서비스 로봇)

Professional service robot (전문서비스 로봇)

Robot

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Industrial Robot (산업용 로봇)automatically controlled, reprogrammable, multipurpose manipulator,programmable in three or more axes, which can be either fixed in place or mobilefor use in industrial automation applications

Service Robot (서비스 로봇)robot that is useful for human, society and devices excluding industrial automation application

Personal Service Robot (개인 서비스 로봇)service robot that non-trained person uses for non-commercial purposes ex) home cleaning robot, entertainment robot, teacher robot

Professional Service Robot (전문 서비스 로봇 )service robots that adequately trained operator use for commercial purposesex) building cleaning robot medical robot demining robot fire fighter robotex) building cleaning robot, medical robot, demining robot, fire fighter robot, rehabilitation robot

Intelligent Robot (지능형 로봇)Intelligent Robot (지능형 로봇)all the robots that have intelligence including industrial robot and service robot

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2. Classification by mechanism

M i lManipulatorMobile robot without manipulator

with manipulator

robot

A. Manipulator (머니퓰레이터)- controller and mechanism are typically separated and connected bycablecable

B. Mobile Robot (이동 로봇)- has ability to change its locationhas ability to change its location - mobile platform only or mobile platform with manipulator- controller and mechanism in one unit

43mobile platform with manipulatormobile platform only

A. manipulator type by geometry or kinematic arrangement- Cartesian robot (직교로봇)- Cylindrical robot (원통형 로봇)- polar robot (구형 로봇)

카라 봇- SCARA robot(Selective Compliance Assembly Robot Arm, 스카라 로봇)- ariticulated robot (다관절 로봇)- parallel robot (병렬형 로봇)

B mobile robot (이동로봇)B. mobile robot (이동로봇)- Wheeled robot (바퀴형)- biped robot (이족 로봇)- legged robot (다족 로봇)legged robot (다족 로봇)- tracked robot (궤도형 로봇)- snake robot (뱀형 로봇)- unmanned ground vehicle (UGV, 무인자동차)g ( , )- unmanned aerial vehicle (UAV, 무인비행 로봇)- unmanned underwater vehicle (UUV, 수중 무인로봇)

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Cartesian Robot (직교 로봇)Good for ‘pick and place’ in a planeNot good to use for the workspacewith obstacles (use SCARA)with obstacles (use SCARA)Typically 4 axis(PPPR)Mainly used for electronics part assembly

http://www.youtube.com/watch?v=xwnU1OjoI5A

Cylindrical Robot (원통형 로봇)Adequate for operations where payload(가반중

zr −−θz q p p y (

량) is large and wide working space is requiredRPP typeMainly used forθ

rMainly used for Palletizing Robot (이적재 로봇)Wafer Handing Robot (웨이퍼 처리 로봇)

θ

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http://www.youtube.com/watch?v=N2cVwlLU1Jw

SCARA RobotSelective Compliant Assembly Robot ArmSelective Compliant Assembly Robot Arm Useful for planar operationSimilar to cylindrical type, but only the last axis moves up and down fitted for light-duty payloadRRPR typeMain use: electronics assemblyMain use: electronics assembly

Polar Robot (구형 로봇)

http://www.youtube.com/watch?v=v5eR0eHknZk

Polar Robot (구형 로봇)Not popular any moreSpecial operations where arm needs p pto be stretched longRRP type

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Articulated Robot (다관절 로봇)Various end effector pose possible in a small spaceVarious end-effector pose possible in a small space- Expensive due to multi DOFsFirst three axis (Arm, RRR) : controls the wrist position last three axes (Wrist, RRR) : determines the orientationMain use: operations where various posture is required

W ldi b t i ti b teg. Welding robot, painting robot

Parallel Robot (병렬형 로봇)Motion of upper/lower plate is controlled by several parallel prismatic jointsAppropriate for operations where workspace isAppropriate for operations where workspace is small but precision and rigidity is requiredStewart Platform

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http://www.youtube.com/watch?v=wwKucXHto0w

Wheeled RobotWheeled RobotEasy to designgood mobilityMain use: cleaning robot, guide robot, industrial AGV used in factory to parts move

Biped RobotBiped RobotGetting more attention after 2000Mainly used for the research and promotionMay develop into riding robot

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Multi-Legged RobotDeveloping from biomimeticsDeveloping from biomimetics(생체(곤충)모방 연구)Suited for rough-terrain mobility

T k C l R b (궤도형 로봇)Track or Crawler Robo (궤도형 로봇)Equipped with continuous tracksGood mobility on stairs and slopesy p감시 경계용, 위험물 처리용 등

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3. Classification by application

industrial robot(산업용 로봇)industrial robot(산업용 로봇)

service robot (서비스 로봇) Personal service robot (개인서비스 로봇)

Professional service robot (전문서비스 로봇)

Robot

• Electronic Parts AssemblyS l t bl ld

A. Industrial robot

( )

– Supply parts, assemble, solder– usually under 4DOF robots, such as Cartesian robot or SCARA type are

used

• Material Handling (부품 처리) robt– Move the payload 중량물 이동을 위한 로봇Move the payload 중량물 이동을 위한 로봇

– 6축 다관절 로봇이 일반적

• Arc Welding robot– Due to fume, sparks, ultraviolet ray of arc welding,in most welding operation, 6-axis articulated robot withg ppayload 5~10kg is used

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Spot Welding (스폿 용접) robotDue to heavy high voltage welding gun end effectory6 axis articulated robot with payload 100 kg is used(recently heavy duty robot with 1000 Kg payload is developed)Oft d f hi l h i blOften used for vehicle chassis assembly process

Palletizing (이적재) 로봇

중량물을 컨베이어에 공급 / 완성품 이동 적재

C /Cylindrical 4-axis / 6-axis articulated 10’s~100’s Kg payload

Painting (도장) robotPainting (도장) robotVehicle/ship painting Long arm with flame proof(방폭) and waterproof (방수) feature6-axis articulated 52

Wafer Handling (웨이퍼처리) 로봇

Wafer supply and move in semiconductor factoryCylindrical robot

Flat Panel Display Handling (FPD처리) robotMove glass panel (LCD, TFD)As glass size increases, so does the end-effector

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B. Service robot personal service robotprofessional service robot

House cleaning(가정 청소) robotVacuum cleaning by autonomous navigationOptimal trajectory can be calculated by p j y ylocalization(위치 인식)Highest growth rate in service robot market

Education (교육) robotEducational tool robot : used as study material for robotic technology예) small scale humanoid, line tracerTeaching assist robot (교사보조로봇) : teaches educational contentsex) English teacher robot

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ex) English teacher robot

Entertainment (오락)로봇

C ith hCommune with humanSONY AIBO, 다사로봇의 제니보

People Carrier (탑승) 로봇

사람을 태우고 자율적으로 또는 조작에 의해 이동 가능한 로봇

예) 지능형 휠체어(Wheel Chair) 로봇

무인자동차(UGV, Unmanned Ground Vehicle) 기립탑승형(Segway)

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수술(Surgery) 로봇

최소 침습 수술최소 침습 수술

(MIS, Minimally Invasive Surgery)수술절개부위를 최소화 시킴

원격 작동 형태 : 센서를 이용해 의사에게 감각 전달(3D Vision, Force Feedback)

Military (군사) 로봇Military (군사) 로봇

경계감시 / 정보탐지 / 전투 / 보급품 수송 등

미래 전투 체계(Future Combat System) 에 무인로봇이 중요한 역할인로봇이 중요한 역할

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Guide/Surveillance (안내/경비) robotGuide/surveillance in offices school publicGuide/surveillance in offices, school, public office, hospitals, airport, exhibition, library, etc.

Space Exploration (우주탐사) 로봇

Investigate unknown environment and collect materialcollect materialAble to run on rough-terrain

재난Rescue (재난구조) robotTrack/crawler typeUsing sensors, transmits information of the

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gdisaster site

Space Exploration (우주탐사) 로봇

I ti t k i t dInvestigate unknown environment and collect materialAble to run on rough-terrain

Rescue (재난구조) robotTrack/crawler typeypUsing sensors, transmits information of the disaster site

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Homework #1Homework #1

1. Draw the kinematic arrangement of the human arm and determine DOF. Also mark the each joint with R or P

2. For six different geometric arrangement of manipulatorsD th i lifi d ki ti dia. Draw the simplified kinematic diagram

b. Mark each joint with R or P

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Chapter 0-2

O tli f th COutline of the Course

Robotics

Kinematics ForwardI

Position (위치)e at cs

Jacobian

Inverse

ForwardI

( )

Velocity (속도)

Dynamics ForwardI

Inverse Velocity (속도)

Acceleration (가속도)

Control (Position, Force)

Inverse

Robotics?

로봇을 직접 구동/제어할 수 있는 구동모터 변수인 Joint variable 와인간이 작업을 쉽게 구상/설계할 수 있는 직교좌표인 x사이의 관계

θ

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C id t li k i l tConsider a two link manipulator

2θ2l

),( yx

1θ1l

(a) Forward Kinematics ( ): The problem of determining the position and orientation of the end-effector in termsof the joint variables

Given: l1 & l2 (link length), & (joint angles) to find (x,y)

Ex) for RR type manipulator

1θ 2θ

)sin(sin)cos(cos

21211

21211

θθθθθθ

++=++=

llyllx ---

---

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(b) Inverse Kinematics : The problem of determining the joint variables for a given end-effector location

Given: end effector position (x, y) and l1 & l2 To find & 1θ 2θ

)(for a given configuration, if we apply Law of CosinesEx)

2θ

l

2l

),( yxg g , pp y

Dllyx

llllyx

−≡+++−

=−⇒

−−+=+22

21

22

2

22122

21

22

)()180cos(

)180cos(2)(

θ

θ

1θ1l

D

Dll

−=−⇒

≡⇒

2

212

cos2

)180cos(

θ

θ

22

2

22

2

22

22

cos1sin

1cossin

−±=⇒

=+

θθ

θθusing

DD

D2

12

22

22

1tancossintan

1sin

−±=⇒=∴

−±=⇒

−θθθθ

θ+: elbow up- : elbow downD2cosθ

By doing same manipulation2211 sinθθ ly

221

22111 cos

sintantanθ

θθll

lxy

+−=∴ −−

Found & joint angles!1θ 2θ63

Note

Solution to Forward kinematics: unique

Inverse kinematics:noneuniquemany

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(c) Jacobian: relationship between the velocity of the joint and end-effector velocities

Differentiate & )sin(sin)cos(cos

21211

21211

θθθθθθ

++=++=

llyllx

++−−= 21212111 ))(sin(sin θθθθθθ&&&

&&&& llx

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡++++−+−−

=⎥⎦

⎤⎢⎣

⎡⇒

+++=

1

21221211

21221211

21212111

)cos()cos(cos)sin()sin(sin

))(cos(cos

θθ

θθθθθθθθθθ

θθθθθθ

&

&

&

&

&

llllll

yx

lly

⎦⎣⎦⎣ +++⎦⎣ 221221211 )cos()cos(cos θθθθθθ llly

θJx && )(θ=⇒

Jacobian : Joint velocity와 end-effector velocity의 관계를 정의

Th j i t l iti f d i d d ff t l it ( ) b bt i dx&The joint velocities for a desired end-effector velocity( ) can be obtained as

dxJθ && )(1 θ−=

dx

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Singular point

21221211 )sin()sin(sin θθθθθ lll +−+−−

21212221121

21221211

21221211

)cos()sin()cos(sin

)cos()cos(cos)sin()sin(sin

det

θθθθθθθ

θθθθθθθθθθ

lll

llllll

J

++−+−=

+++++

=

221

21212221121

sin)cos()sin()sin(cos

θθθθθθθθ

lllll

=+++++

πθ ,00det 2 == atJ

- does not exist!1−J

Singular points

- solution to does not exist- No joint velocity that could realize desired end-effector velocity exists.- cannot be realized at the singular configurations (some motions are not achievable!)

dxJθ && )(1 θ−=

dx& g g ( )

achievableNOT achievable direction (lost D.O.F. in this direction)

1l2l

- Cannot move in the direction parallel to l1

O c ev b e d ec o ( os .O. . s d ec o )

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(d) Dynamicst d f f i d t ti ∑= ταI: study of force required to cause motion

Forward dynamics: for a given joint torques compute joint acceleration and then integrate to find

∑= ταI

: for a given joint torques, compute joint acceleration and then integrate to find velocities and positions

Inverse Dynamics: for a given desired positions(trajectories) find the joint torques to achieve it: for a given desired positions(trajectories), find the joint torques to achieve it

(e) Control- Position control

: design the control input to follow a desired trajectory: design the control input to follow a desired trajectory- Force control

: complementary to position control when a robot is in contact with any objects

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Areas of Robotics

A l i (Ki ti / St ti / D i )Analysis (Kinematics / Statics / Dynamics )Control (position / velocity /force / toque)Trajectory planningDesign (Act ator / po er transmission / sensing)

this course will coverDesign (Actuator / power transmission / sensing) Metrology (position / velocity / force / torque )Machine visionLocomotion(주행 / 보행)Locomotion(주행 / 보행)LocalizationArtificial intelligence TeleoperationTeleoperationGraspingEtc.

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