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Modern Robotics: Understanding Homogeneous Transformations and Coordinate Frames

Learn about robots in movies, daily life, industry, Medicare, home entertainment, and military applications. Understand the scope of CPSC 452 covering planning, sensing, control, dynamics, kinematics, and rigid body mechanics. Explore vectors, matrices, orientation descriptions, and transformation mapping in robotics.

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Modern Robotics: Understanding Homogeneous Transformations and Coordinate Frames

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  1. CPSC 452: Lecture 1 Introduction, Homogeneous transformations and Coordinate frames

  2. Introduction • Robots in movie

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

  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. Intro • Space • Type – Physical, Geometry, Functional • Dimension • Direction • Basis vectors • Distance • Norm • Description – Coordinate System • Matrix

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

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

  12. Position Description • Coordinate System A

  13. Orientation Description • Coordinate System A

  14. Orientation Description • Coordinate System A • Attach Frame Coordinate System B

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

  16. Rotation matrix Directional Cosines Directional Cosines

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

  18. Orthogonal Matrix 9 Parameters to describe orientation!

  19. Description of a frame • Position + orientation

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

  21. Mapping – Translation Difference

  22. Mapping – rotation difference

  23. Example 30 30

  24. Rotation + Translation Difference

  25. Homogeneous Transformation

  26. Mapping – Translation Difference

  27. Translation Operator • Translation operator

  28. Mapping – rotation difference

  29. Rotation Operator   

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