Question

3. A robot workstation that includes a robotic arm and a camera has been setup, see figure below. The camera can see both the origin of the base coordinate system of a 6-link robot arm and the centre of the object to be manipulated by the robot. If a coordinate system has been established at the centre of the object, then the object as seen by the camera can be expressed by the homogenous transformation matrix T 0 1 0 1 1 0 0 10 0 0 1 9 0 0 0 1 Similarly, the origin of the robot base coordinate system as seen by the camera can be represented by the homogenous transformation matrix T 10 0-10 0 0 20 20 01 10 0 00 1 a). After the equipment has been setup and these coordinate systems have been established, someone rated the camera 90 about the z axis of the camera. What is the position/orientation of the camera with respect to the robot's base coordinate system? b). After this rotation happened in a), the object is also rotated by 90 about the x axis of the object and translated by 4 units along the rotated y axis. What is the postion/orientation of the object with respect to the robot's base coordinate system? What is the postion/orientation of the object with respect to the rotated camera coordinate system?

Answer 1

(a)So given the homogenous transformation matrix T₁ since the camera is rotated by 90 about the z axis -

Hence rotatioan matrix is given as -

Hence the new position can be given as -

given is the new position of the camera ..

(b)

Since object is rotatated by 90^o about x-axis Hence-

Since given robot is translated 4 units by rotated system -

Hence the object is -

Robot new position -

Distance between roatated cordinate -