ECE555 HW 3 solution

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Given a robot end-effector aligned to coordinate system, orientation q = 1<0,0,0>, located at 7i + 3j +2k.
The end-effector is rotated about the two successive axes then linearly translated, use homogeneous
transformations to determine the final pose of the end-effector. The end-effector is rotated 90 degrees
anti-clockwise about the Z-axis to the via v; after that, the end-effector is further rotated 90 degrees
clockwise about the object X-axis, from the v to w. The goal pose, x, is reached in 5 seconds after w is
translated by the object 4i -3j + 7k.
What is the final pose of the end-effector? [15 pts]
Determine the cubic trajectory coefficients (ao, a1, a2, a3) of the s function [15 pts]
Plot the position and trajectory profile of the transformation [30 pts]
What is the position and orientation of the system at its maximum velocity [40pts]