the variables could be set to 0, the robot would be configured so that the outer link would be

parallel with the supports of the base. The inner link would be positioned at a right angle to

the outer link so that the sliding tube would point through the actuated mounting shaft of the

outer link. The sliding tube would be retracted so that the axis of the inner link would pass

through the lens of the camera in the end-effector.

 However, the action of the orange-picking robot was limited by the mechanical stops

 on each of the joints. In addition, these mechanical stops restricted the boundaries of the

 individual parameters which governed the motion of the coordinate frames. The range of

 motion for each of the joint variables is shown in Table 5.2. These ranges of motion for each joint

 defined the working envelope of the orange-picking robot.


 Table 5.2. Range of motion for the joint parameters of the orange-picking robot.

 Range
 Parameter Minimum Maximum
 91 -390 +390
 92 +670 +1130
 d3 +51.0 cm +182.5 cm


 Imaging Kinematics

 Vision-servoing of the robot required that the relationship between actual position of a

fruit and the position of the fruit's image in the imaging array of the camera be established

(see Figure 5.3). For this derivation, the position of the fruit was defined by a vector, pc = [ x y

z 1 ]T, from the origin of the camera coordinate frame to the centroid of the fruit. The position

of the fruit's image was defined by another vector, pi = [ xi i zi 1 ]T, from the camera coordinate

frame to the centroid of the fruit's image in the imaging array.

 The CCD imaging array of the camera was parallel to the X-Y plane of the camera

frame and positioned in the negative Z direction from the origin of the frame the distance of

the focal length of the lens, zi = -f. The position of a fruit's projection in the image plane, pi,

was related to Pc, its actual position, by


Pi = Tp pc


(5-5)