HW 03: 3D open-chain robot representation
Answer the questions below with text, mathematical statements, and supporting sketches where appropriate. You should use Matlab to perform intermediate symbolic computations. Include a commented copy of your Matlab code.
1. Make a function in Matlab to convert ZYX Euler angle to an orientation matrix, and nd the orintation matrices coincide to:
ZYX
Matrices:
Code:
2. Make a function in Matlab to construct SE(3) from rotation matrix and translation vector, and make a function to multiply two SE(3)s and make a function to invert SE(3), then nd the transformation matrix of frame{3} to frame{0} T03 from the following Euler angles and translation vectors: frame{0}: Euler angle ZYX = (0, 0, 0), position: (0, 0, 0). frame{1}: Euler angle ZYX = (0.3, 0.2, 0.5), position: (0.4, 0.8, 1.2). frame{2}: Euler angle ZYX = (0.7, π, π/2), position: (-0.4, 0.5, 1.0). frame{3}: Euler angle ZYX = (π/3, 0, 0), position: (0.5, -0.8, 1.2).
Matrix:
Code:
3. Plot above frame{1}, frame{2}, frame{3} in global coordinate frame{0}. You can use the given "drawCoordinat3D.m" funtion to plot and refer to "matlab_test3D.m" for instruction.
Figure:
Code:
4. Show the animation of frame EE at frame 3. Let frame EE has the same rotation matrix as frame 3 and the translation vector is [x, y, z] where x=0.1sin(ωt)+0.05, y=0.3cos(ωt)+0.08, z=sin(ωt)+0.5. t lasts a few seconds. Refer to "animation2D.m" for instruction. Please provide several screen shots to represent the animation.
Snapshots of motion:
Code:
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