CHAPTER 5
ROBOT KINEMATIC MODEL
The kinematic relationships between the joints and links of the robot are presented in
this section. In the field of robotics, homogeneous transformations are used to describe the
position and orientation of one link coordinate system with respect to another one. By
describing the position and orientation of a coordinate frame which is assigned to a link of the
manipulator, the homogeneous transformation describes the position and orientation of the link
itself. According to Paul's method (1981), the product of these homogeneous transformations
(called a T matrix) will be used to calculate the position values of each joint necessary to place
the final coordinate frame (corresponding to the robot camera) at a given position and
orientation in the robot's workspace. The inverse of this T matrix will be useful in calculating
the position and orientation of the camera coordinate frame when given the joint variable
positions. A vector will be defined to relate the position of the centroid of a fruit in the camera
coordinate frame. The T matrix will then be used to relate the position of the fruit to the origin
of the base frame of the manipulator. A similar kinematic relationship will be used to relate
the position of a fruit in the robot's workspace to the position of the fruit's image in the
imaging array of the CCD camera. After establishing this relationship, the information will
be used to present the change in position of the fruit in the imaging array for small changes in
the joint angles of the robot. The vision-servoing gains will be established for adjusting the
gains of the vision control system based on the position of the fruit and position of the robot joint
angles.
Manipulator Kinematics
The citrus-picking robot consisted of three joints which were numbered 0, 1, and 2. Joints
0 and 1 were revolute with intersecting and perpendicular axes of rotation (Zo and Z1,
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