CSCE 452 Intro to Robotics CSCE 452: Lecture 1 Introduction, Homogeneous Transformations, and Coordinate frames

CSCE 452 Intro to Robotics Introduction Robots in movie 2

CSCE 452 Intro to Robotics Modern Robots Robot in life –Industry –Medical 3

CSCE 452 Intro to Robotics Modern Robots Robot in life –Home/Entertainment 4

CSCE 452 Intro to Robotics Modern Robots Robots in life –Military/Unmanned Vehicle 5

CSCE 452 Intro to Robotics What 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 6

CSCE 452 Intro to Robotics Scope of CPSC PlanningSensing Control Dynamics Kinematics Rigid body mechanics

CSCE 452 Intro to Robotics Scope of CPSC PlanningSensing Control Dynamics Kinematics Rigid body mechanics

CSCE 452 Intro to Robotics Spatial Descriptions and Transformations Space –Type – Physical, Geometry, Functional –Dimension & Direction Basis vectors –Distance Norm –Description – Coordinate System Matrix –Robots live in 3D Euclidean space 9

CSCE 452 Intro to Robotics

Generalized Coordinates

CSCE 452 Intro to Robotics End-Effector Configuration Parameters

CSCE 452 Intro to Robotics

A review of vectors and matrix Vectors –Column vector and row vector –Norm of a vector 14

CSCE 452 Intro to Robotics Dot product of two vectors Vector v and w If |v|=|w|=1, 15  v w

CSCE 452 Intro to Robotics Position Description Coordinate System A 16

CSCE 452 Intro to Robotics Orientation Description Coordinate System A 17

CSCE 452 Intro to Robotics Orientation Description Coordinate System A Attach Frame B (Coordinate System B) 18

CSCE 452 Intro to Robotics Orientation Description Coordinate System A Attach Frame Coordinate System B Rotation matrix 19

CSCE 452 Intro to Robotics Rotation matrix 20 Directional Cosines

CSCE 452 Intro to Robotics Rotation matrix For matrix M, –If M -1 = M T, M is orthogonal matrix – is orthogonal!! 21

CSCE 452 Intro to Robotics Orthogonal Matrix 22 9 Parameters to describe orientation!

CSCE 452 Intro to Robotics Description of a frame Position + orientation 23

CSCE 452 Intro to Robotics Graphical representation 24 {A} {B} {U}

CSCE 452 Intro to Robotics Mapping: Change Coordinates – Translation Difference 25

CSCE 452 Intro to Robotics Mapping – rotation difference 26

CSCE 452 Intro to Robotics Example 

CSCE 452 Intro to Robotics Mapping: Rotation + Translation Difference 28

CSCE 452 Intro to Robotics Homogeneous Transformation for Mapping 29

CSCE 452 Intro to Robotics

Operators

CSCE 452 Intro to Robotics Rotational Operators

CSCE 452 Intro to Robotics Translation Operator Translation operator 33

CSCE 452 Intro to Robotics Recall: Mapping – rotation difference 34

CSCE 452 Intro to Robotics Relationship between Mapping with only Rotational Difference and Rotation Operator 35   

CSCE 452 Intro to Robotics Relationship between Mapping with only Rotational Difference and Rotation Operator 36 The 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.

CSCE 452 Intro to Robotics General Operators

CSCE 452 Intro to Robotics Inverse Transform

CSCE 452 Intro to Robotics Homogeneous Transform Interpretations

CSCE 452 Intro to Robotics Transform Equation

CSCE 452 Intro to Robotics Compound Transformations

CSCE 452 Intro to Robotics

Transform Equation

CSCE 452 Intro to Robotics