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 (67.31 KiB) Viewed 207 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). (a) A rotation matriz 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. T11 T12 T13 (ii) Given R=121 722 723 and t = A y ER³, we write [81] for the 731 132 133 4 x 4 matrix T11 712 713 121 122 123 Y 731 732 733 0 0 01 From page 1 of the attached paper, the product [61] [69] R is a matrix of the form [51] Y]. where R' is a rotation matrix and v R³. 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,, Rx, 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.