Figure 3.7 6 DOF tracking task subjects were asked to track the randomly moving target with the cursor
3.3 Experiment 3 - Isometric and Elastic Rate Control in 6 DOF Tracking
3.3.1.1 Platform
The same experimental platform as in Experiments 1 and 2 was used in this experiment.
3.3.1.2 Experimental Task
Figure 3.7 6 DOF tracking task subjects were asked to track the randomly moving target with the cursor
A 6 DOF pursuit tracking task was designed for this experiment. Subjects were asked to continuously control a cursor and track (capture) a target which moved unpredictably (in both translation and rotation) within a 3D virtual environment (Figure 3.7). The tracking target was a wireframe tetrahedron. In order to overcome any orientation ambiguities due to the symmetry of the tetrahedron shape, two connected edges of the tetrahedron were coloured blue and the remaining edges were coloured red.
The tracking cursor was of the same shape as the target tetrahedron
but differed from it in three ways. First, the radius (from the
centre to each vertex) of the target tetrahedron was 3.55 graphic
units (1 graphic unit = 1.4 cm, all lengths in this experiment
are measured in the same scale) while the cursor was 1.3 times
as large as the target. Second, the cursor had semi-transparent
surfaces (indicated by dots in Figure 3.7), while the target was
drawn in wireframe. Third, the cursor edges were slightly brighter
than the target, although they were of identical hue (i.e. two
blue and four red edges).
Each degree of freedom of the target was driven by an independent forcing function. In order to make the target path sufficiently unpredictable to the experimental subjects, each forcing function was derived from a weighted summation of 20 sine functions, i.e.,
(3.1)
Here t is the time duration from the beginning of each experimental
phase (measured in seconds); constants A = 3.5, p = 1.25, f0 =
0.01; 
is a pseudo-random number, ranging
uniformly between 0 and 2
.
Similarly, y and z dimension translations were driven by:
(3.2)
(3.3)
Rotations about x, y, z axes (i.e. pitch 
(t),
yaw 
(t), roll 
(t))
were driven by similar forcing functions:
(3.4)
(3.5)
(3.6)
where B = /R, and R is the radius of the
target tetrahedron.
These forcing functions are similar to those used by Tachi and Yasuda (1993), but more complex than the once conventional sum-of-sines method (e.g. Poulton, 1974).
3.3.1.3 Task Performance Measure
In traditional 1 or 2 DOF tracking experiments, the tracking error at any moment is defined simply as the distance between the target centre point and the cursor centre point. However, defining the tracking error between two 3D objects, both of which have 6 DOF, is much more complicated and needs to be elaborated further. One way of analysing the tracking performance in such a task is by studying each degree of freedom separately. This approach will be presented in Appendix 2. However, an overall single measure of the tracking quality is necessary both for feedback to the subject (at the end of each trial) and for general data analysis. In the experiment, subjects were instructed to track the target as "closely" as possible, which therefore requires both a translational and a rotational match.
We have therefore adopted an integrated measure for evaluating the tracking quality. At any tracking instant k (t = kT, where T is the sampling period), the tracking error e(k) is defined as:
(3.7)
where dist(X1, X2) is defined as the Euclidean distance between
two points X1 and X2 in 3D space. 
are
the four vertices of the target tetrahedron and 
are the four vertices of an equivalent imaginary tetrahedron with
the same size as the target but coinciding with the centre and
orientation of the cursor (Figure 3.8). This integrated error
measure is based on both psychological and mathematical considerations.
Psychologically, this measure is meant to correspond with the
subjects' perception of the "distance" between two 3D
objects; that is, when subjects perceive the two objects to move
closer, this measure indeed decreases monotonically. Mathematically,
this measure converts rotation to an equivalent translational
distance. For each trial (40 seconds, 800 tracking steps) overall
tracking performance was calculated by root mean square (RMS)
error, as conventionally accepted in the literature (e.g. Poulton,
1974):
RMS error = 
(3.8)
3.3.1.4 Display
The graphical display used in this experiment was very similar to that of Experiments 1 and 2. For two reasons, semi-transparency was used in addition to all the other depth cues that were implemented in Experiments 1 and 2. First, as shown in Figure 3.9, the partial occlusion effect introduced by semi-transparency may help the subjects in perceiving the relative displacement (location and orientation) between the cursor and the target. It is well known that the occlusion cue is among the strongest depth cues in human perception. If object A is being obscured by object B, object B will appear closer to the viewer. However, complete occlusion may not be very useful for graphical computer displays since the occluding objects will block the userís view of the background completely. When semi-transparent surfaces are used, on the other hand, objects being blocked by a semi-transparent surface appear in lower contrast (i.e. partially occluded) but remain visible. The question of whether this partial occlusion technique will in fact serve as a useful and strong depth cue is addressed in a separate experiment (Experiment 5) presented in Chapter 5.
The second reason for using semi-transparency was to make the cursor appear very different from the target. The 6 DOF tracking task required the design of two 3D objects (cursor and target) that are sufficiently similar so that the subjects could perceive the correspondence of the two to perform the task. Conversely, the task also required the two objects to be distinctively different so the subjects could know which one was the autonomously moving target and which one was the cursor under her control. Before the semi-transparent surfaces were implemented, pilot subjects often mistakenly identified the cursor as the target and tracked their own motion. In that case, the control loop became positive feedback: the harder they pushed (twisted) their input in order to minimise the distance between the cursor and the target, the larger the distance became! An attempt was made to implement the cursor using dotted lines or blinking at certain frequencies but none of these techniques proved to be acceptable.
3.3.1.5 Controllers and Optimisation
The controllers used in this experiment were the same as in Experiment
2. The control gains (sensitivity) for each controller were optimised
again in this task through systematic parameter searching with
two pilot subjects, one experienced and one naïve. U-shaped
performance-gain curves were again found for both control modes
(Figure 3.10). The optimal gains found in this task were very
close to the optimal value previously found in the docking task.
Fortuitously, although the experienced pilot subject and the naïve
pilot subject produced different absolute error scores, the optimal
gain values were approximately the same for both of them, which
made it straightforward to select the optimal gains for the experiment.
Other parameters such as the elasticity of the elastic rate controller, were optimised in a similar fashion. Same as in Experiment 2, non-linear transformations identical to those embedded in the Spaceball were implemented in the EGG condition.
3.3.2.1 Subjects
30 paid volunteers who had not participated in Experiment 1 and 2 were recruited. All of them had experience with a computer mouse but none of them had used a 6 DOF control device before the experiment. All subjects were screened using a Bausch and Lomb Orthorater. Three subjects were rejected for having weak stereo-acuity, and one was rejected for having poor corrected near-vision acuity. The remaining 26 male and female subjects completed the experiment. As in Experiment 2, a between-subjects design was employed. The 26 accepted subjects were alternatively assigned to two experimental groups, with consideration of balanced gender composition in each group. Each group had 9 male subjects and 4 female subjects. Three subjects were left-handed and the others were right-handed. Each controller was located at the side of the subject's dominant hand.
3.3.2.2 Procedure
Each experimental session was preceded by a 15 minute vision screening
test, handedness check and signing of a consent form. A 3 minute
long questionnaire survey was also conducted at the end of each
session. The data gathering was divided into five phases, as illustrated
in Figure 3.11. Each phase consisted of practice, followed by
a test comprising 4 trials of tracking. Each trial lasted 40 seconds.
In contrast to Experiment 1 and 2, the first test, Phase 0, was
conducted before the subjects had much experience. This change
was made in light of the results from Experiment 2: the principal
difference between the isometric and elastic controllers appeared
to be affected mainly by learning, much of which could have occurred
in the first 10 minutes. Practice in Phase 0 was therefore
arranged as follows: The subject was first showed how to use the
assigned controller by the experimenter. He/she was then asked
to control each of the six degrees of freedom (x, y, z, pitch,
yaw, roll), as well as translations and rotations in/about arbitrary
axes. After that, the subject was asked to do one trial of tracking,
to learn what was required in the task. The total duration of
Phase 0 practice was about 3 minutes (Figure 3.11). Practice in
Phases 1, 2, 3 and 4 lasted 7 minutes each, and consisted of demonstrations
and coaching by the experimenter, together with actual practice
trials.
A short beep signalled the end of each trial, after which the integrated RMS error was presented. The subject was asked to press the spacebar of the workstation keyboard to start the next trial. At the end of each test, a text file containing the RMS errors for each trial, as well as the average score over the four trials, was displayed to the subject.
Each of the four trials in a test had a distinct target trajectory. Each trial began with the cursor coincident with the target (zero error). During the experiment, subjects were instructed to track the target as closely as possible in both translation and rotation.
3.3.3.1 Performance Results
Figure 3.12 displays the means and standard errors of the two techniques over the five phases of experiment. The results of a repeated measure variance analysis of the entire data set are summarised in Table A3.3.1 in Appendix 2. The differences between the controllers appeared in the same pattern as in Experiment 2. The mean difference between the two input techniques across the entire experiment was not statistically significant: F(1, 24) < 1, p = 0.52, although the elastic controller had smaller RMS error on average. The interaction Phase x Input, however, was significant: F(4, 96) = 2.52, p < 0.05. This again indicates that the relative performance differences between the elastic and the isometric controllers are related to learning. Repeated measure analysis (Table A3.3.2, Appendix 3) showed that RMS error with the elastic rate control was significantly smaller than that of the isometric rate control in Phase 0: F(1, 24) = 4.7, p < 0.05. This difference decreased as learning progressed, however.
Subjects' performance improved over the five experimental phases
significantly: F(4, 96) = 113.7, p < 0.0001, indicating significant
leaning over the course of the experiment. The different tracking
paths were also a significant factor in affecting trial completion
time: F(3, 72) = 12.7, p < 0.0001, as shown in Figure 3.13.
This was due to two reasons. First, since the four paths were
arranged in a fixed order (path1, path2, path3, path4), learning
tended to improve for the performance in paths tested later in
any particular sequence. Second, since the paths were randomly
generated, some of them were apparently more difficult than others.
3.3.3.2 Subjective Ratings
After each session of the experiment, the subjects were asked to comment on the ease of use/difficulty and the degree of fatigue caused by the controller used. As in Experiment 2, subjects were told that they were randomly assigned to a particular controller whose quality was unknown and that their honest opinion was needed for the evaluation.
The subjective ratings on ease of use and fatigue are shown in
Figure 3.14. The elastic controller received a slightly higher
average score than the isometric controller (3.23 versus 3.15).
With respect to fatigue, the results appear to be more clearly
in favour of the elastic controller (2.85 versus 2.23). However,
these differences are not strong enough to produce statistical
significance. For ease of use: F(1, 24) = 0.058, p = 0.81; for
fatigue, F(1, 24) = 2.46, p = 0.13.
3.3.3.3 Dimensional Analysis
The above RMS error analysis was conducted based on the integrated RMS error. The experimental results were also analysed by decomposing the tracking process into separate dimensions. This dimensional analysis did not provide additional information with regard to the main topic of this chapter: the differences between isometric and elastic rate control. However, it did produce some very interesting results regarding the isotropy of manipulation in 6 degrees of freedom. By decomposing the performance scores in this integrated tracking task into separate dimensions, an opportunity was created to observe the differences and similarities (or isotropies) among the 6 degrees of freedom. The degree of the difference between the Z dimension and the X, Y dimensions served as a measure for the quality of the 3 dimensional interface. As expected, subjects' performance in the Z (depth) dimension was poorer than in the X (horizontal) and Y (vertical) dimensions. The extent of performance reduction in the Z dimension was not very large, however, indicating the effectiveness of the 3D displays used in the experiment. Interestingly, the mean tracking error in the Y dimension was larger than the mean error in the X dimension and this trend was related to experimental phase, indicating a probable learning process. The complete dimensional analysis is presented in Appendix 2.
The same performance pattern in Experiment 2 reappeared in Experiment
3, although to a more obvious extent. The relative advantages
of the isometric and the elastic devices were affected by experimental
phase and thus were clearly a function of learning. That is, the
elastic device was advantageous in the early but not later learning
phases.