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Robotic Arms and Matrices

Learn about the Canadarm, its operation in the International Space Station, translation, rotation, homogeneous coordinates, and matrix multiplication. Explore how multiple arms work together through coordinate systems and movements in space.

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Robotic Arms and Matrices

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  1. Robotic Arms and Matrices By Chris Wong and Chris Marino

  2. The Canadarm First operation 1998 Used for assembly of the International Space Station Composed of a series of arms of fixed length connected by rotating joints

  3. Key Concepts • Translation • Rotation • Homogeneous Coordinates • Matrix Multiplication

  4. Translation • Not a linear transformation • Translation along vector V = [a,b] in R2 • Transformation represented by T(x) = x + V in R2 • Translation is caused by the position of the previous arm

  5. Rotation • Rotation is a Linear Transformation • Rotates any Vector about the origin

  6. Homogeneous Coordinates • Represents vector in R2 as a vector in R3 • x = [x,y] in R2 • X = [x,y,1] in R3 • Rotation and Translation operations can thus be represented using homogeneous coordinates

  7. Translation and Rotation in one • Represented through Matrix Multiplication • T  R represents Translation by Rotation • R  T does not equal T  R

  8. Second Arm • To represent second arm’s movement • Same as representing the first • Give each arm its own coordinate system • a and b are the x and y coordinates of the origin of the second arm with respect to the origin of the first arm • This new origin is obtained when by taking the components of the first arm when it is rotated about an angle theta • Now combining movements of the first and second arm • T2 * T1

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