- Please Answer All Questions 2 1 (118.36 KiB) Viewed 31 times
Please answer all questions 2
-
answerhappygod
- Site Admin
- Posts: 899604
- Joined: Mon Aug 02, 2021 8:13 am
Please answer all questions 2
Please answer all questions 2
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 € R³. (i) Prove that RS is a rotation matrix. X (ii) Given R = T11 T12 T13 721 T22 723 [T31 732 733, and t = E R³, we write R 0 for the Z 4 x 4 matrix T11 12 13 X T21 22 23 Y T31 32 33 2 0 0 0 From page 1 of the attached paper, the product Rt S 0 R' is a matrix of the form where R' is a rotation matrix and v € R³. 0 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 R₁,Rx = Ry RB₁ 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.
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 € R³. (i) Prove that RS is a rotation matrix. X (ii) Given R = T11 T12 T13 721 T22 723 [T31 732 733, and t = E R³, we write R 0 for the Z 4 x 4 matrix T11 12 13 X T21 22 23 Y T31 32 33 2 0 0 0 From page 1 of the attached paper, the product Rt S 0 R' is a matrix of the form where R' is a rotation matrix and v € R³. 0 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 R₁,Rx = Ry RB₁ 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.
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!