October. 12, 2017 Name PROBLEM 1: (20%) A camera is used to visually aid the rob

Question

October. 12, 2017 Name PROBLEM 1: (20%) A camera is used to visually aid the robot end-effector to catch a flying ball. There are three coordinate frames in the system as shown in the figure below: the inertia frame (0), the camera frame {e), and the end-effector frame {e). The vectors poc = [ 10, 2, 1 ]T, poe-[5, 3, 2)" . The 1 0 -1 1/2 -1/2 V2/4 rotation matrices Re =100 01.R2=11/2 1/2V2/41 The coordinate vector 0 -1 0 of the ball in the camera frame is pib [0,-3,3]. The velocity vector of the ball in the camera frame is v:-[0-3, 3)" 0 Vb Pcb ye Xe Zo oc yo Poc RO (896) (a) Calculate the velocity of the ball represented in the end-effector frame

Explanation / Answer

given

Rotation matric to move from camera to origin frame ,

ORc = [1 0 -1]

[0 0 0]

[0 -1 0]

Rotation matric to move from effectro frame to origin frame

ORe = [1/2 -1/2 1/sqrt(2)]

[1/2 1/2 sqroot(2)/4]

[-sqroot(2)/2 0 1/2]

velocity in camera frame Vc = [0, -3, 3]T

then velocity in origin frame = Vo = Orc*Vc

Vo = [1 0 -1] [0]

[0 0 0] * [-3]

[0 -1 0] [3]

Vo = [-3,0,3]T

velocity in end effector frame = Ve

Ve = [ORe]-1*Vo

[ORe]-1 = [0.4 0.4 -0.84853]

[-0.799 1.2 0.28284]

[0.56568 0.56568 0.8 ]

Ve = [0.4 0.4 -0.84853] [-3]

[-0.799 1.2 0.28284]* [0]

[0.56568 0.56568 0.8 ] [3]

Ve = [-3.74559, 3.24552, 0.70296 ] T

hence velcoty of ball in end effector fram eis

Ve = [-3.74559, 3.24552, 0.70296 ] T

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