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Lecture 1

Lecture 1. Introduction, Homogeneous Transformations, and Coordinate frames. Introduction. Robots in movie. Modern Robots. Robot in life Industry Medical. Modern Robots. Robot in life Home/Entertainment. Modern Robots. Robots in life Military/Unmanned Vehicle. What is a robot.

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Lecture 1

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  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

  10. Generalized Coordinates

  11. End-Effector Configuration Parameters

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

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

  14. Position Description • Coordinate System A

  15. Orientation Description • Coordinate System A

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

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

  18. Rotation matrix Directional Cosines Directional Cosines

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

  20. Orthogonal Matrix 9 Parameters to describe orientation!

  21. Description of a frame • Position + orientation

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

  23. Mapping: Change Coordinates – Translation Difference

  24. Mapping – rotation difference

  25. Example 30 30

  26. Mapping: Rotation + Translation Difference

  27. Homogeneous Transformation for Mapping

  28. Operators

  29. Rotational Operators

  30. Translation Operator • Translation operator

  31. Recall: Mapping – rotation difference

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

  33. 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.

  34. General Operators

  35. Inverse Transform

  36. Homogeneous Transform Interpretations

  37. Transform Equation

  38. Compound Transformations

  39. Transform Equation

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