Figure 2.2 Idealised control inputs (left column) for obtaining step changes in output level (right column) for position, rate and acceleration control
2.3.1 Theoretical Analysis of Position versus Rate Control
Position control refers to the control mechanisms by which the human operator controls object positions directly. More precisely, the transfer function from human operator to object movement in position control is a constant (i.e., a zero order transfer function). In contrast, Rate control maps human input to the velocity of the object movement. In other words the transfer function from human input to object movement is an integral (i.e., first order transfer function).
It has been conclusively demonstrated that position control and rate control are both superior to higher order control in most tracking tasks (Wickens, 1992; Poulton, 1974). Acceleration control, for example, is usually more difficult and unstable than position and rate control. This has also been verified in 6 DOF placement tasks (Massimino, Sheridan, and Roseborough, 1989) .
The performance difference between position control and rate control is less obvious. Much work has been done in comparing position control with rate control, again mostly in 1 or 2 DOF tasks. The majority of these studies concluded that rate control is inferior to position control. From an isomorphism point of view, position control can be considered more direct (more isomorphic) than rate control. It has 1-to-1 (or 1-to-K) correspondence between input and output, requiring little mental transformation in generating control actions (Figure 2.2). It therefore provides a more intuitive control mode to the human operator. Note that the directness of position control is still subject to other design considerations, including stimulus-response compatibility (Fitts and Seeger, 1953) .
Rate control, on the other hand, controls movement through velocity. As illustrated in Figure 2.2, input control patterns for rate control are more complex than for position control. In order to cause a change of state from one level to another, a pair of reversal control actions has to be given. Figure 2.2 shows only idealised control patterns. In reality, control motions will not be instantaneous but the basic feature of paired reversal inputs for rate control (speed-up, maintain a level of control and then slow down) remains.
Position control also has its conceivable disadvantages relative
to rate control. First, it transfers all human limb movements,
whether voluntary or involuntary, to the manipulation task. In
contrast, the low pass filtering effect introduced by the integral
function in a rate control scheme will suppress many high frequency
involuntary noises. Second, by definition, rate control lets the
user control the velocity of the controlled object, resulting
in smoother movement. With position control, on the other hand,
it is more difficult to maintain control of the velocity of the
movement, increasing the likelihood of jerky motions. Third, with
position control, the maximum operating range is limited unless
clutching or indexing (Johnsen and Corliss, 1971) is adopted,
whilst rate control has an effectively unlimited operational range
(auto-indexed).
2.3.2 The Literature on Position versus Rate Control
The literature on position and rate control is more consistent than that of isometric versus isotonic devices. It is generally found that position control is superior to that of rate control. Lincoln (1953) , in one of the early studies, showed that subjects' tracking performance (time on target) with position control was substantially better than with rate control. The experiment was done with a mechanical manual tracking system described in (Lincoln and Smith, 1950) . Subjects tracked an irregularly moving target mounted on the circumference of a rotating wheel with a cursor mounted on a smaller concentric wheel driven by a hand crank.
Jagacinski, Hartzell, Ward, and Bishop (1978) studied position control versus rate control in a FittsÌ law task, both with an elastic joystick. They found that, in Fitts' law modelling, the linear regression line of rate control mode had a steeper slope than that of position control mode and the two linear regression lines intersected at 4.7 bits of index of difficulty. When the index of difficulty was below 4.7 bits, position control was slower. Above 4.7 bits, rate control was slower. In other words, position control was better for higher index of difficulty (precise) tasks while rate control was good for lower index of difficulty (coarse) tasks. However, two years later in a very similar study, Jagacinski and colleagues (Jagacinski, Repperger, Moran, Ward, and Class, 1980) found that rate control consistently gave lower performance than position control at all levels of difficulty.
Driven by teleoperation applications, Kim, Tendick, Ellis, and Stark (1987) did a comprehensive comparison study of rate control versus position control with two types of tasks. One was a 2 DOF pick and place task. The second was tracking a one dimensional sinusoidal movement. They ran only two subjects in their experiments, much less than the minimum number of subjects (six) recommended for this type of research by Poulton (1974). Some of the primary researchers seemed also to have served as their own experimental subjects. Nevertheless, this was still a very comprehensive (in terms of factors investigated) and valuable comparison of rate versus position control. In their first task, position control yielded better performance than rate control, with completion time about 1.5 times faster for the position control. This was true with both an isometric joystick and an isotonic joystick, even though the magnitude of the difference varied with the joystick type, with the difference between position and rate control being larger when the joystick was isotonic. Kim et al concluded that rate control generated longer mean completion times because rate control required a pair of opposite movements to reposition the manipulator while position control required only one movement. In their second task (sinusoidal tracking), position control had consistently smaller RMS error than rate control.
In summary, the literature generally supports the conclusion that
position control is superior to rate control.