There is a basic dilemma in conducting interface comparisons. On the one hand, it is impractical to do an absolutely fair comparison across different input interfaces. One common pitfall is "comparing apples with orangesTM, due to the multi-dimensional properties of interfaces. That is, one interface might be good with respect to one aspect of performance, such as speed, while another interface could be more suitable with regard to another aspect, such as control precision. On the other hand, comparison is often fundamental to our understanding of the operation and performance of various interfaces in relation to each other. It is also a practical concern to have quantitative data about how interfaces differ from each other so that designers can decide what device to use for specific applications.
Facing this dilemma, one should keep two things in mind when conducting comparative research. First, the goal of the research should not be limited to a narrow minded comparison across interfaces, but rather should be geared towards gaining a deeper and better understanding of the behaviour and performance of the human machine system, by comparatively evaluating different input control schemes. Second, a great deal of attention should be paid to ensuring that all of the interfaces in the experiment operate under similar conditions*. Optimising the control gain of each control technique is one such aspect.
The effect of control sensitivity (or gain) has attracted the attention of many researchers (e.g. Arnaut and Greenstein, 1990; Buck, 1980; Jellinek and Card, 1990) but is still not completely understood. The most common view is that performance is best at moderate gain levels. Very high gains give poor results because of the difficulty in making precise movement, even though initial gross positioning is more rapid. Very low gains allow precise movement and therefore more rapid fine positioning, but require a longer initial gross positioning time. The trade-off between initial gross positioning versus final fine adjustment typically results in a U shape gain-performance (completion time/error) curve with best performance at a moderate gain level. This view has been supported both by performance measurements from experiments, such as (Gibbs, 1962), and by subjective ratings, such as Hess (1973).
This view has been challenged by many other researchers, however. Hammerton (1981) argued that because a joystick can have only limited travel, there is a downward limit to control gain. He asserted that for all controls of joystick type, the lowest possible gain is the best. In an effort to test if power mice - i.e., computer mice that have variable control gain - improve user performance, Jellinek and Card (1990) concluded that user performance should be independent of mouse gain. In one of their experiments, Jellinek and Card (1990) did find that performance declined as the mouse gain increased from the standard value (1:2), but they argued that this was an artifact of mouse resolution limitation, rather than a result of human characteristics. For the gain value that was smaller than the standard, performance also declined but this was because subjects had to lift and reposition the mouse more frequently, as Jellinek and Card suggested. Jellinek and Card further argued that gain should not affect user's performance, because that would violate Fitts' law. This argument is difficult to accept, however, because Fitts' law was not meant to address variables other than movement amplitude and precision. Finally, in a recent study, MacKenzie and Riddersma (1994) found that although subjects had the shortest mean movement times with a medium mouse gain (approximately 1:5, in comparisons with a low gain of 1:2 and a high gain of 1:7), they also had the highest mean error rates in a Fitts' law task. MacKenzie (1995) concluded that the claim that an optimal control gain exists is weak at the best.
In the present experiment, it was found that performance with
each input control technique was indeed a function of control
gain or sensitivity. The relationship between task completion
time and sensitivity appeared as a U-shaped function with sensitivity
plotted on a logarithmic scale. Taking isometric rate control
as an example, Figure 2.7 shows the experimenter's mean task completion
times (over 15 trials) for different sensitivity settings. The
horizontal axis was normalised by the lowest control gain tested.
Note that there was a wide range of settings at the bottom of
the U shape, for which performance differences were relatively
small. The control gain eventually used in the experiment for
the isometric rate condition was set at the value corresponding
to the bottom of the U shape. The gains for the other three experimental
conditions were optimised through similar systematic parameter
searching. In the case of the isotonic position mode, the optimal
control gain was 1. At this value, the hand motions and object
motions had a one to one correspondence, thus taking the maximal
advantage of the directness of isotonic position control. This
is particularly important for rotation control.
Judging from above pilot data and the literature, a tentative conclusion about control gain is as follows. Performance is indeed a function of control gain and in general follows a U shape curve when the gain is plotted on a logarithmic scale. This is obviously true for the extreme cases. For a very low gain, such as 1: 0.01 for a position control system, the user needs a longer time to reach the target. For a very high gain, such as 1:100, precise positioning will be difficult. Performance improves as the gain shifts to more moderate values. However, for a large range (many folds) of moderate gain values, including those used by MacKenzie and Riddersma (1994) , user's performance change is relatively small.
Another important dimension of optimisation is to create appropriate non-linearities in the input devices to accommodate the human sensorimotor system. Orlansky (1949) speculated various non-linearities suitable for controls in aircraft. Rutledge and Selker (1990) reported a study of non-linear transfer functions for a miniature isometric joystick mounted between the G and H keys of a keyboard for portable computers. They found that a "two-plateau" non-linear transfer function to be their "current favourite". Similar effort was also spent in optimising the Spaceball (personal communication with Spaceball Technologies Inc.) and the chosen non-linear mappings of the Spaceball were:
for translation outputs:
, 
is the force applied
to the Spaceball;
for rotation outputs:
, 
is the torque applied
to the Spaceball.
The author also experimented with various non-linear mapping functions
for the 6 DOF isotonic device (the bird), including a "power-bird"
mode (making the gain of the bird proportional to the speed, as
in a "power mouse"). None of these non-linear mappings,
however, appeared to be advantageous. Linear mappings were therefore
kept for the isotonic conditions.