Question 3 (10 marks)

A coordinate frame {B} is located at the base of a robot manipulator. Frame {C} describes the

position and orientation of a depth camera that was originally coincident with {B} then

translated - 1 unit in g, translated 2 units in Pg, translated 3 units in 2g; the resulting frame

is denoted by {C'}. The frame is then rotated about & by 45° into a new frame {C"}. The

final transform is rotated about fe by -45° into the frame {C}. The camera detects an object

having coordinates P = [1.0 1.0 1.01.

(a) Determine PCORG

(b) Formulate the homogeneous transformation T.

(c) Calculate the object coordinates in frame (B), i.e., BP. You can use hand calculation or

computer calculation (by PYTHON or MATLAB). Please provide your source code if you

use computer calculation.