The University of Missouri - Columbia Electrical & Computer Engineering Department EE4330 Robotic Control and Intelligence
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1 The University of Missouri - Columbia Final Exam 1) Clear your desk top of all handwritten papers and personal notes. You may keep only your textbook, a cheat sheet, the test paper, a calculator and a pencil. 2) Read through the test completely and work the problems you can, leave the difficult ones till last. 3) Keep your eyes on your own paper. Cheating will not be tolerated 4) Work problems on the back of the previous page if necessary. 5) Show your work! NAME: Final Exam /18
2 The University of Missouri - Columbia Question 1 In class (and in the textbook), we derived the dynamic equations for two degree of freedom and six degree of freedom robots. In the 2-DOF case, we obtained the following equation in matrix form: where i = 1 and j = 2. Similarly, for the 6-DOF case, we obtained in non-matrix form: for i = {1,2,...6 }. For the questions below, assume a robot with seven (7) degrees of freedom. Final Exam /18
3 The University of Missouri - Columbia a) Extend either one of the notations above (i.e. in matrix or non-matrix form) to represent the dynamic equations of a 7-DOF robot. Final Exam /18
4 The University of Missouri - Columbia b) Expand the term D 654 as a function of the A i and J p matrices (i.e. the A i matrices from the D-H representation, and the pseudo inertia matrices J p. Final Exam /18
5 The University of Missouri - Columbia c) Expand the term D 76 as a function of the A i and J p matrices (i.e. the A i matrices from the D-H representation, and the pseudo inertia matrices J p. Final Exam /18
6 The University of Missouri - Columbia Question 2 Consider the following RPP robot manipulator. Using the D-H method, assign frames to this robot; construct the D-H parameter table; find the A matrices; and derive the inverse kinematics equations for this robot. Final Exam /18
7 Final Exam /18 The University of Missouri - Columbia
8 Final Exam /18 The University of Missouri - Columbia
9 Final Exam /18 The University of Missouri - Columbia
10 The University of Missouri - Columbia Question 3 Describe the algorithm used by your team in the robot competition i.e. flowchart, block diagram, etc. Make sure you give details on both the image processing part and the game strategy part. Final Exam /18
11 Final Exam /18 The University of Missouri - Columbia
12 Final Exam /18 The University of Missouri - Columbia
13 Final Exam /18 The University of Missouri - Columbia
14 The University of Missouri - Columbia Question 4 A stereo rig with left camera (L) and right camera (R) have been calibrated and the calibration parameters are given below Left Camera (c=l) Right Camera (c=r) u v α u α v k 1, g 1, g 2, g 3, and g , 0, 0, 0, and , 0, 0, 0, and c H w a) Find the Fundamental matrix F, such that: m L T.F.m R = 0, where m L is the coordinate of a pixel in the left image and m R is the coordinate of the corresponding pixel in the right image. (If you don t have a calculator, show your work ALL the way so all that s left is the multiplication of numbers only) Final Exam /18
15 Final Exam /18 The University of Missouri - Columbia
16 The University of Missouri - Columbia b) The following table gives the D-H parameters for a 3-link robot manipulator. Joint Θ d a α 1 Θ π/2 2 Θ π/2 3 0 d Draw the configuration of the robot when joint 1 has an angle of 0, joint 2 has an angle of π/2, and joint 3 has an offset of 1. For full credit you must draw the coordinate frames at each joint and at the end-effector. Final Exam /18
17 Final Exam /18 The University of Missouri - Columbia
18 Final Exam /18 The University of Missouri - Columbia
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