Page 40 - Introduction to AI Robotics

1.4 A Brief History of Robotics
FEEDBACK
a. b. 23
Figure 1.4 A MOVEMASTER robot: a.) the robot arm and b.) the associated joints.
and a new trajectory and profile is computed and executed, then modified on
the next update, and so on. Closed-loop control requires external sensors to
provide the error signal, or feedback.
In general, if the structural properties of the robot and its cargo are known,
these questions can be answered and a program can be developed. In prac-
tice, the control theory is complex. The dynamics (how the mechanism moves
and deforms) and kinematics (how the components of the mechanism are
connected) of the system have to be computed for each joint of the robot, then
those motions can be propagated to the next joint iteratively. This requires a
computationally consuming change of coordinate systems from one joint to
the next. To move the gripper in Fig 1.4 requires four changes of coordinates
to go from the base of the arm to the gripper. The coordinate transformations
often have singularities, causing the equations to perform divide by zeros. It
can take a programmer weeks to reprogram a manipulator.
One simplifying solution is to make the robot rigid at the desired velocities,
reducing the dynamics. This eliminates having to compute the terms for
overshooting and oscillating. However, a robot is made rigid by making it