Practice Final Exam - Robotics Design Lab

PRACTICE EXAMMETR4202 Advanced Control & Robotics1. Rotation Matrices ........................................................................................... [10 marks]In order to demonstrate your understanding of general rotations in 3D Cartesian space,please provide short answers to the following questions.(a) Given unit frames {A} (a x , a y , a z ) and {B} (b x , b y , b z ).What are three ways of describing the orientationbetween them?{B}b Z{A}a Zb Ya Ya Xb X(b) What is the transformation matrix for the case described in (a)?AB T (c) In the following expressions, what is “ρ”?pˆ px py pzT(d) Very briefly, how is SE(n) related to SO(n)?Page 3 of 7