M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sMAE 512: Robotics and Mechatronics Lecture 1 Introduction, Homogeneous Transformations, and Coordinate framesM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sClass Information Lecture: TT 5-6:20pm in SEC217 Instructor: Jingang Yi, Associate Professor Office: Engineering Building D-157 Email: jgyi@rutgers.edu, Tel: 848-445-3282 Grader: To Be Announced Office hours: TT 3:30-5pm in D-157, or by appointment Exams: One midterm exam and one final exam Project: One final project M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sClass Information (contd) Textbooks: Introduction to Robotics by Craig, 3rd edition, Prentice Hall, 2005 Robot Modeling and Control by Spong et al., John Wiley & Sons, 2006 References: Robotics: Modeling, Planning and Control by Siciliano et al., Springer, 2009 A Mathematical Introduction to Robotic Manipulation by Murray et al., CRC Press, 1994 M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sClass Information (contd) Grading Policy: Homework: 20% in total Class attendance: 5% Midterm exam: 25% Final exam: 25% Final project: 25% Class website: http://sakai.rutgers.edu Other class policies: see syllabus for details M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sCourse Schedule Introduction to robotics, rigid motions and homogeneous transformation Forward and inverse kinematics Jacobians: Velocity kinematics and static forces Manipulator dynamics and path generation Linear and nonlinear control of manipulators Actuators and sensors for manipulators Force control of manipulators Geometric nonlinear control Mobile robots and motion planning M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sIntroduction Robots in movie 6M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sModern Robots Robot in life Industry Medical 7M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sModern Robots Robot in life Home/Entertainment 8M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sModern Robots Robots in life Military/Unmanned Vehicle 9M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sMore Modern Robots Mobile robots (wheeled, legged, tracked, etc.) 10Aerial robots (fixed-wing, helicopter, quadrotors, etc.) Bio-inspired robots Micro/nano robots Medical robots Modular robots Service robots M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sWhat is a Robot? A robot is a reprogrammable multifunctional manipulator designed to move material, parts, tools, or specialized devices through variable programmed motions for the performance of a variety of tasks by Robot Institute of America 11M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sScope of MAE 512 12PlanningSensingControlDynamicsKinematicsRigid body mechanicsM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sScope of MAE 512 Mechanical design of robots is not covered Advanced topics, such as computer vision and visual servoing, probabilistic motion planning, etc. not covered 13PlanningSensingControlDynamicsKinematicsRigid body mechanics M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sSpatial Descriptions and Transformations Space Type Physical, Geometry, Functional Dimension & Direction Basis vectors Distance Norm Description Coordinate System Matrix Robots live in 3D Euclidean space 14M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sGeneralized Coordinates M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sEnd-Effector Configuration Parameters M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sA review of vectors and matrix Vectors Column vector and row vector

Norm of a vector 19( ( ( ( ( =nv v vv

2 1||nvvvv

21=22221...||nvvvv+++=M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sDot product of two vectors Vector v and w If |v|=|w|=1, 20ucos||||wvwv=-ucos=-wvuvwM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sPosition Description Coordinate System A PA21AXAYAZ( ( ( ( =z y xPAM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sOrientation Description Coordinate System A ( ( ( ( =z y xPAPA22AXAYAZM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sOrientation Description Coordinate System A Attach Frame B (Coordinate System B) PA23AXAYAZABZBYBX( ( ( ( =z y xPAM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sOrientation Description Coordinate System A Attach Frame Coordinate System B Rotation matrix ||( ( ( ( ==333231232221131211rrrrrrrrrZYXRBABABAABPA24AXAYAZBZBYBXABXXr11-=ABYXr21-=ABZXr31-=M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sRotation matrix ||( ( ( ( ---------==ABABABABABABABABABBABABAABZZZYZXYZYYYXXZXYXXZYXR25BAXTABX||TBATABABABTABTABTABRZYXZ Y X==( ( ( ( = Directional CosinesDirectional CosinesM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sRotation matrix For matrix M, If M-1 = MT , M is orthogonal matrix is orthogonal!! 261==RRIRRBAABBAABTBAABRR=1=RRBATBARABM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sOrthogonal Matrix ||( ( ( ( ---------==ABABABABABABABABABBABABAABZZZYZXYZYYYXXZXYXXZYXR279 Parameters to describe orientation! M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sDescription of a frame Position + orientation 28BORGAPAXAZBZBYBX},{}{BORGAABPRB=AYM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sGraphical representation 29BORGAPAXAZBZBYBXAY{A}{B}{U}uZuXuY},{}{AORGuuAPRA=},{},{}{BORGAABBORGuuBPRPRB==BORGuPM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sMapping: Change Coordinates Translation Difference 30BORGAPAXAZBZBYBXAYPBPPPBBORGAA+=PA( ( =( ( 11PTPBABA( ( ( ( ( =1000BORGAABPITM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sMapping rotation difference 31AXAZAYBZBYBXPBPRP P PZYXZPYPXPPZPYPXPP P PPBABz y xBBABABABAzBAyBAxABzByBxz y xBB=( ( ( ( =++=++=( ( ( ( =][PRPBABA=( ( =( ( 11PTPBABA( ( ( ( ( =10000RTABABM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sExample ||( ( ( ( =( ( ( ( ---------==$$$$$$$$$0cos90cos90cos90cos30cos120cos90cos60cos30cosABABABABABABABABABBABABAABZZZYZXYZYYYXXZXYXXZYXR32BYBXAXAYPB3030ABZZ=?12 1PPAB( ( ( ( =M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sMapping: Rotation + Translation Difference 33PBPRBABBORGAPAZBZBYBXAYPAAX=PA+M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sHomogeneous Transformation for Mapping 34PRPPBABBORGAA+=( ( ( ( ( ( ( ( ( ( =( ( ( ( ( 110001_ _ _zByBxBzBORGAyBORGAABxBORGAzAyAxAP P PP PRPP P PTABM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sOperators M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sRotational Operators M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sTranslation Operator Translation operator 381PAAXAZAYQPPAAA+=12QA2PA12)(PqDPAQA=( ( ( ( ( =1000100010001)(z y xQq q qqD222zyxqqqq++=M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sRecall: Mapping rotation difference 39AXAZAYBZBYBXPBPRPAABA=( ( =( ( 11PTPBABA( ( ( ( ( =10000RTABABM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sRelationship between Mapping with only Rotational Difference and Rotation Operator ||( ( ( ( =( ( ( ( +=( ( ( ( ---------==1000cossin0sincos0cos90cos90cos90coscos)90cos(90cos)90cos(cosuuuuuuuu$$$$$$$ABABABABABABABABABBABABAABZZZYZXYZYYYXXZXYXXZYXR40AXAZAYu1PA2PABXuBYu21PPAB=M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sRelationship between Mapping with only Rotational Difference and Rotation Operator 41The rotation matrix that rotates vectors through some rotation, R, is the same as the rotation matrix that describes a frame rotated by R relative to the reference frame. M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sGeneral Operators M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sInverse Transform M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sHomogeneous Transform Interpretations M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sTransform Equation M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sCompound Transformations TTTBCABAC=M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sM A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c sTransform Equation M A E 5 1 2 R o b o t i c s a n d M e c h a t r o n i c s