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

2. CSCE 452 Intro to Robotics Introduction Robots in movie 2

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

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

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

6. 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

7. CSCE 452 Intro to Robotics Scope of CPSC 452 7 PlanningSensing Control Dynamics Kinematics Rigid body mechanics

8. CSCE 452 Intro to Robotics Scope of CPSC 452 8 PlanningSensing Control Dynamics Kinematics Rigid body mechanics

9. 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

10. CSCE 452 Intro to Robotics

11. Generalized Coordinates

12. CSCE 452 Intro to Robotics End-Effector Configuration Parameters

13. CSCE 452 Intro to Robotics

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

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

16. CSCE 452 Intro to Robotics Position Description Coordinate System A 16

17. CSCE 452 Intro to Robotics Orientation Description Coordinate System A 17

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

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

20. CSCE 452 Intro to Robotics Rotation matrix 20 Directional Cosines

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

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

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

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

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

26. CSCE 452 Intro to Robotics Mapping – rotation difference 26

27. CSCE 452 Intro to Robotics Example 27 30 

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

29. CSCE 452 Intro to Robotics Homogeneous Transformation for Mapping 29

30. CSCE 452 Intro to Robotics

31. Operators

32. CSCE 452 Intro to Robotics Rotational Operators

33. CSCE 452 Intro to Robotics Translation Operator Translation operator 33

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

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

36. 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.

37. CSCE 452 Intro to Robotics General Operators

38. CSCE 452 Intro to Robotics Inverse Transform

39. CSCE 452 Intro to Robotics Homogeneous Transform Interpretations

40. CSCE 452 Intro to Robotics Transform Equation

41. CSCE 452 Intro to Robotics Compound Transformations

42. CSCE 452 Intro to Robotics

43. Transform Equation

44. CSCE 452 Intro to Robotics