Lecture 1

1. Lecture 1 • Introduction, • Homogeneous Transformations, • and Coordinate frames

2. Introduction • Robots in movie

3. Modern Robots • Robot in life • Industry • Medical

4. Modern Robots • Robot in life • Home/Entertainment

5. Modern Robots • Robots in life • Military/Unmanned Vehicle

6. 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

7. Scope of CPSC 452 Planning Sensing Control Dynamics Kinematics Rigid body mechanics

8. Scope of CPSC 452 Planning Sensing Control Dynamics Kinematics Rigid body mechanics

9. 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

11. Generalized Coordinates

12. End-Effector Configuration Parameters

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

15. Dot product of two vectors • Vector v and w • If |v|=|w|=1, v  w

16. Position Description • Coordinate System A

17. Orientation Description • Coordinate System A

18. Orientation Description • Coordinate System A • Attach Frame B (Coordinate System B)

19. Orientation Description • Coordinate System A • Attach Frame Coordinate System B • Rotation matrix

20. Rotation matrix Directional Cosines Directional Cosines

21. Rotation matrix • For matrix M, • If M-1 = MT , M is orthogonal matrix • is orthogonal!!

22. Orthogonal Matrix 9 Parameters to describe orientation!

23. Description of a frame • Position + orientation

24. Graphical representation {B} {U} {A}

25. Mapping: Change Coordinates – Translation Difference

26. Mapping – rotation difference

27. Example 30 30

28. Mapping: Rotation + Translation Difference

29. Homogeneous Transformation for Mapping

31. Operators

32. Rotational Operators

33. Translation Operator • Translation operator

34. Recall: Mapping – rotation difference

35. Relationship between Mapping with only Rotational Difference and Rotation Operator   

36. Relationship between Mapping with only Rotational Difference and Rotation Operator • 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. General Operators

38. Inverse Transform

39. Homogeneous Transform Interpretations

40. Transform Equation

41. Compound Transformations

43. Transform Equation