2. Some parts of this question refer to the attached research paper: Mili Shah (2013), Solving the Robot-World/Hand-Eye

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2 Some Parts Of This Question Refer To The Attached Research Paper Mili Shah 2013 Solving The Robot World Hand Eye 1 (118.14 KiB) Viewed 25 times

2. Some parts of this question refer to the attached research paper: Mili Shah (2013), Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product, Journal of Mechanisms and Robotics, Volume 5, Issue 3 (2013). You do not need to add a bibliography to reference this paper, and you may refer to it in your answer as: Shah (2013). (a) A rotation matrix is a 3 x 3 matrix R such that det(R) = 1 and R-1 = RT. Let R and S be rotation matrices, and let t, u E R3. (i) Prove that RS is a rotation matrix. and t = y r11 r12 r13 (ii) Given R = r21 1 22 23 [131 132 133 4 x 4 matrix E R3, we write R 0 for the 2 ru r12 r13 7 21 122 123 Y Т31 32 T33 2 0 0 0 1 From page 1 of the attached paper, the product Rt [ ]] [81] 1 R v is a matrix of the form where R' is a rotation matrix and v E R3. 0 1 Write down expressions for R' and v in terms of R, S, t and u. For this question only, you do not need to give any reasons for your answer.