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

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Some Parts Of This Question Refer To The Attached Research Paper Mili Shah 2013 Solving The Robot World Hand Eye Cal 1 (323.82 KiB) Viewed 30 times

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 = R. Let R and S be rotation matrices, and let t, u € R3. (i) Prove that RS is a rotation matrix. r11 r12 r13 R (ii) Given R= 721 122 23 and t = E R3, we write for the 131 T32 133 4 x 4 matrix rui r12 r13 r21 122 T23 9 731 732 133 0 0 0 1 From page 1 of the attached paper, the product 間 C 2 (1181 Rt 0 1 0 R v is a matrix of the form where R' is a rotation matrix and v ER3. 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. (b) Suppose a robot is posed n times, leading to the equations RA, Rx = - Ry RB; where RA;, Ry, Ry and RB; are rotation matrices, for j = 1,2, ..., n. Write a few sentences to summarise the results of the attached paper by Shah on: (i) the number of poses needed to obtain unique matrices Rx and Ry which satisfy these equations; and (ii) how the position errors for the method presented in the attached paper compare to the position errors for the method of Li et al, on simulated data and real-world data.