Studies in human factors research often have limitations in their generalisability. This thesis is no exception in this respect. Caution has to be exercised in considering the strength of the findings in the experiments for a number of reasons. First, the experimental conditions were implemented using available technologies. None of the technical products used in the experiment were ideal. For instance, the 6 DOF position sensor used is known to have a significant amount (about 60 msec) of time delay (Adelstein, Johnston, and Ellis, 1992a 1992b). A tracker with much less delay may have improved the conditions implemented with the tracker (the Glove, EGG, and Fball); however, changes in the relative performance scores between the conditions is not expected. Second, these experiments were conducted with elemental tasks that do not cover the entire rich task space for practical 6 DOF interaction tasks. Third, the analyses of the experimental results were limited to integrated performance scores, even though Appendix 2 provides a dimensional decomposition analysis. It is believed that more insights into the nature of 6 DOF control with each device could have been gained through more trajectory based analysis, as discussed in the following section.
The work reported in this thesis is thus merely one earnest endeavour
towards understanding human performance issues in input control.
Many research questions that have been identified during this
work are to be addressed in the future. The following are a few
viable future research topics.
6.3.1. The interaction between device resistance and transfer function in low DOF input control
A very important finding of Experiment 1 is the interaction pattern
between isometric versus isotonic resistance and position versus
rate control transfer functions. The isotonic device worked better
with position control than with rate control, whereas the isometric
device worked better with rate control than with position control.
The reason behind this interaction pattern appears to be rather
straightforward: the self-centring effect in the isometric device
helps the reversal actions required for rate control. Without
the self-centring force (in the case of isotonic devices), a reversal
action has to be made more expressly and effortfully, either by
returning the manipulandum back to a null position or by releasing
a clutch. Conversely, however, this self-centring force makes
it more unstable and fatiguing to maintain a cursor location in
position control mode, unless an explicit clutch is used to disengage
the device frequently, which makes the control process less "seamless".
Surprisingly, this seemingly rather obvious interaction pattern
between resistance mode and transfer function had not been formally
reported in the literature prior to Experiment 1 in this thesis.
Instead, the literature extensively deals with the relative superiority
of isometric versus isotonic devices without much attention paid
to the effect of transfer function (see Chapter 2 for a review).
In light of the interaction pattern found in Experiment 1, much
of the controversy in the literature with respect to the relative
performance between isometric and isotonic devices can be reduced
to a simple explanation in these terms. However, Experiment 1
was conducted with a 6 DOF docking task while the classical studies
were all done with lower DOF tasks. An experimental study with
two modes of control resistance (isometric and isotonic) and two
modes of transfer function (position control and rate control)
with 1 or 2 DOF devices would therefore be a valuable contribution
to the literature, even though the same interaction pattern found
in Experiment 1 is expected to be found in low 2 DOF devices but
perhaps to a less extent. In practice, isotonic devices, such
as the computer mouse, are usually used in position control mode
but some applications, such as some driving simulation games and
some 3D graphics packages, do use the mouse in rate control mode.
A user would probably find such a combination difficult to master.
One the other hand, this might be ameliorated somewhat for cases
such as an isotonic 2 DOF joystick, where even though the self-centring
force that facilitates rate control is absent, the pivot of the
joystick may still provide an anchor to the user for forming the
reversal actions required in rate control.
6.3.2. Systematic examination of the effect of elastic resistance in rate control
In chapter 3, it was proposed that two factors, compatibility and proprioception, impose conflicting requirements for the setting of the level of elasticity in rate control. For the sake of compatibility with rate control, a stiff (therefore strongly self-centred) elasticity is desirable. However, a stiff (near isometric) elastic device provides less rich proprioception than a loose one that allows more movement within a range of non-fatiguing forces. How exactly input control behaviour and performance change as a function of elasticity levels ranging from isotonic to isometric is a question which deserves a more detailed examination. Such a study should be done, at least initially, with a 1 DOF positioning (step tracking) task for simplicity of experimental data analysis. Five levels of elasticity should be tested, including isotonic, weak elastic, medium elastic, strong elastic, and isometric. Both dynamic measures (overshoot, number of cursor movement reversals over the target, settling time, pure time delay etc.) and steady state performance (e.g. static accuracy) should be recorded. It is hypothesised that when the elasticity is on the weak side (isotonic or weakly elastic), poor compatibility with rate control will be manifested by large overshoots (due to less timely returning to the null position) or by a large number of reversals. On the strong elasticity side (isometric or strongly elastic), insufficient proprioception will be manifested by larger steady state errors.
One difficulty in conducting this experiment will be with the setting of control gains. One possible arrangement is to optimise control gain for every level of elasticity. A more rigorous arrangement, perhaps, would be to set the gain constant across all conditions. However, for a (finite) elastic controller, the overall control gain is actually a product of two gains, i.e., K = K1 K2 where K1 is the gain between the force applied to the control handle and the displacement of the control handle (i.e., K1 is the inverse of elastic stiffness) and K2 is the gain between the control handle position and the cursor speed for rate control. In the pure isotonic condition, K1 does not exist and K = K2. In the pure isometric condition, K2 does not exist and K = K1 (from the force to the cursor speed). A reasonable arrangement would therefore be to test all levels of elasticity under two modes of gain arrangement. In Mode 1, a constant position-to-display gain is held for all levels of elasticity (i.e., keep K2 constant and let K1 float with different elasticity settings). In Mode 2, a constant force-to-display gain is held for all levels of elasticity (i.e., keeping K = K1 K2 constant and as K1 increases with the level of elasticity, while decreasing K2 accordingly). This two mode design may provide some insights into the role of force, position and elasticity in input control. If subjects' performance were invariant in Mode 1, force and the level of elasticity would be proved to be ineffective factors in input control. If subjects' performance were invariant in Mode 2, position and the level of elasticity would be proved to be ineffective. Both of these two cases are expected to be false.
There is a problem in the extreme cases (isotonic and isometric) for the two mode gain arrangement. For Mode 1 (position-to-display constant), the isometric condition has undefined gain. One solution to this might be to assign the same value of force gain (K = K1 K2) for the next-to-isometric condition (i.e. strong elastic) to the isometric condition. Similarly, for Mode 2 (force-to-display constant ), the isotonic condition has undefined gain. The position to display gain (K2) value in the next-to-isotonic condition (i.e. loose elastic) could then be taken for the gain of the isotonic condition.
Such an experiment requires frequent adjustments to the level
of elasticity and the level of control gain, making the experiment
very difficult to conduct. One candidate apparatus for this experiment
is the pantograph, described by Ramstein and Hayward (1994),
which is a 2 DOF computer-controlled force reflecting device.
Such a device can produce various levels of elasticity by programming
the motor control algorithm. For the isometric condition, however,
an alternative device has to be used.
6.3.3. Psychophysical study of motor accuracy with both force and displacement
Research on input control requires a deep level of understanding of human motor behaviour. As indicated in the motor control literature, it is still unclear what muscle variable(s) the nervous system actually controls in limb movements: force, length, velocity, stiffness, viscosity, more than one of the above, or none of the above (Stein, 1982). Some psychophysical experiments have investigated the just-noticeable difference (JND) for perceiving increments in force and for extent of movement (see 3.1.4 in Chapter 3 for a review) but JND for length combined with force is unknown. It is both theoretically and practically valuable to know the human motor accuracy when force and length are linearly linked, i.e., the human's ability to discriminate different kinaesthetic states when the hand is coupled to various spring loadings. Would the redundancy between force and length augmented each other or disturb each other? Is motor accuracy better with one of the variables alone or better when both are present? Such questions are obviously important for understanding the design of controller resistance.
The proposed experimental paradigm for addressing these issues is manual recall without visual feedback. The procedure would be approximately as follows. (a) S is presented with a fixed target (vertical bar) at the middle of a computer screen and a cursor (a cross hair) at one end of the screen. (b) S is asked to generate just amount of input (move/pull the controller) for the cursor to reach the target. (c) S is asked to remember the hand/arm state (a combination of force and displacement) corresponding to this input and then return to the rest position. (d) Without cursor display, S tries to move the controller to the same state as the trial in step (b). S pushes a key (to mark the end of the trial) when she feels that invisible cursor has reached the correct position. (e) Error is displayed. ( f) Go back to (a), repeat for a few trials.
Five experimental conditions would be tested. All can be considered as a spring-loaded manipulandum with certain spring constant, that is:
D = K F
where D is displacement, K is the spring constant and F is the force applied to the spring. The five conditions would be:
K1 = 0 (isometric)
K2 = 2 cm/N (Stiff Spring)
K3 = 4 cm/N (Medium Spring)
K4 = 8 cm/N (Loose Spring)
K5 = infinity (Free)
Each of these 5 levels of spring loading can be represented as
a thick line segment shown in Figure 6.3. Under each spring loading,
two points would be tested. These testing points are labelled
with X signs in Figure 6.3.
The arrangement in Figure 6.3 is designed to examine the interactive patterns of the two channels of cues contributing to motor performance. Testing points (X's) on each horizontal line in Figure 6.3 share the same displacement but differ in the level of force stimulation. If displacement is the dominant cue and force does not serve as an augmentation, testing points (X's) on the right side would not generate better performance than points on the left. If force serves as perturbation instead of augmentation to displacement perception, testing points (X's) on the right side would generate worse performance than points on the left. Similarly, testing points (X's) on each vertical line in Figure 6.3 share the same force stimulation but differ in displacement magnitude. Testing points (X's) on each of the thick lines would have the same elasticity but differ in amount of stimulation magnitude (both force and displacement). How subjects' accuracy changes as a function of force and movement cues and how these two variables interact would be clearly revealed in this experiment.
Note that the target is always located at the middle of the screen
in this experiment. For different operating points, the control
gain would be calibrated so that the cursor reaches the target
with the designated amount of force/displacement input. This arrangement
would eliminate the possible bias introduced by different display
scales for each condition.
6.3.4. Investigating the quality and coordination in multiple DOF input control
Input control has been traditionally evaluated using 'performance' or product oriented measures. These measures include speed (e.g., task completion time), accuracy (e.g., RMS error, error rate) or information processing rate (e.g., bandwidth in FittsÌ law). As far as multiple degrees of freedom are concerned, however, these measures do not capture completely the quality of manipulation trials. Other than how quickly a trial is accomplished or how accurate the cursor position overlaps with the target position, it can also be useful to know what trajectory the control object moves through. In other words, we need to have "process" or trajectory based measures.
One important process oriented concern is how co-ordinated a controlled trajectory is. Can users control 6 degrees of freedom at the same time? Or do users actually control fewer degrees of freedom at a time? When an operator wants to move an object in translation only, can she do it without rotating it? When she needs to rotate an object, can she do it without introducing translational cross talk? In order words, can the user integrate and separate the 6 degrees of freedom at will? All of these questions are related to the coordination of multiple degrees of freedom.
The first problem in studying the coordination of multiple DOF input is to define and quantify the concept of coordination. For simplicity, let us examine trajectories on a 2D space, as illustrated in Figure 6.4. As we can see, in order to move from Point A to B in this space, two variables x and y have to be changed from xA to xB and yA to yB respectively. Supposing we had only a 1 DOF input device that time-multiplexed between the x and y axis, one possible trajectory would be AC-CB, as a result of moving in the x dimension first and in the y dimension later. In such a case, the two degrees of freedom are completely un-co-ordinated, because x and y are not moved at the same time, resulting in a longer trajectory than necessary and possibly a longer movement time. If we had a 2 DOF device such as a mouse that allows movement in the x and y directions simultaneously, we may produce a trajectory that is close to the straight line AB, which is optimal because it is shortest and is also most co-ordinated in the sense that x and y move simultaneously at the same relative pace . Any deviation from the path AB can be considered as a result of lack of coordination, which will result in a longer trajectory. In light of this analysis, we define the translation coordination coefficient as:
Translation Coordination Coefficient = Length of shortest path / Length of actual path
By this definition, trajectory 
in Figure
6.4 is better co-ordinated than trajectory 
.
Figure 6.4 Measuring coordination:
on a 2D plane, the shortest, most co-ordinated trajectory from
A to B is the straight line AB, Trajectory AC-CB is completely
uncoordinated (see text)
The same definition of coordination coefficient can be easily generalised to translations in 3D space simply by measuring 3D instead of 2D Euclidean distances. To generalise this concept to rotation in 3D space is less straightforward, however. Parameterisation of rotations is more complicated than it appears (Hughes, 1986, p.15) . The parameters commonly used in engineering, pitch, yaw, roll (Euler angles) are often misleading. A more valid metric is the rotation vector discussed in Appendix 2. Define the initial mismatch between a cursor and a target (both are 3D objects in 3D space) to be
A
,
where A is the rotation vector
signifying an angle 
of rotation about 
,
where 
is a unit vector defining the axis
of the rotation in x, y, z frame of reference, then the minimum amount of rotation that the cursor has to go through to reach
the target is . The ratio between
and the actual amount of rotation of the cursor upon reaching
the target is defined as the rotation coordination coefficient:
Rotation Coordination Coefficient = Initial rotation mismatch/Amount of actual rotation
When one can control all 3 rotation degrees of freedom with perfect
coordination, the rotation mismatch between the cursor and the
target will be reduced from 
to 
,
without changing the direction of the mismatching rotation
vector . Otherwise, if the 3 rotational degrees of freedom
cannot be controlled simultaneously at the same relative
pace, at an instant of time 
the mismatch
will be 
( 
), causing
a larger amount of actual cursor rotation.
The two coordination coefficients defined above deal with translation and rotation separately but do not reveal the coordination aspect between translation and rotation taken together. In other words, a trial can be perfectly co-ordinated with respect to both its translation trajectory and rotation trajectory, but the rotation and the translation may not necessarily be performed at the same time. Hence, a third coordination factor is defined as:
Translation/Rotation Coefficient
= Ideal path in translation-rotation space / Actual path in translation-rotation space
This new translation-rotation space has two dimensions. One is
the translation distance, 
, between the
cursor and the target centres of mass, and the other is the rotation
mismatch 
(the magnitude of rotation vector)
between the cursor and the target. Note that both
and are function of time, which define
a 2D trajectory over the course of an experiment trial.
With the measurements of coordination thus formulated, we can now start to study the quality and coordination of 6 DOF manipulation as a function of different control input interfaces. Following the discussion of direct manipulation versus tool operation in the previous section, the EGG and the Fball are proposed here as two experimental input interfaces. The Fball (using position control), which is on the isomorphic side, is expected to outperform the EGG (using rate control), which is more tool-like as measured by task completion times. However, the EGG may produce better co-ordinated control trajectories, since it is not constrained by anatomical hand/arm limitations.
The proposed experimental task can be 6 DOF docking, similar to Experiment 4. Other than input interfaces, experimental phase should also be included as an independent variable, since subjects' ability to co-ordinate 6 degrees of freedom is expected to be strongly influenced by their experience.
This experiment should be conducted with a between subjects design so that follow-up experimental conditions can be added later. One follow-up condition, for example, could be an isometric rate controller. Both the EGG and the Spaceball are tools, but they offer different proprioceptive feedback to the user. One of the current theories in motor control is that proprioception plays an important role in organising human motor control movement (Hasan, 1992; Ghez, Gordon, Ghilardi, Christakos, and Cooper, 1990; Ghez and Sainburg, in press; Sainburg, Poizner, and Ghez 1993). If so, the elastic device should produce more co-ordinated manipulation trials than the isometric device.
Many more interesting future studies could be proposed within
the framework that this thesis has laid out. Some of these future
studies will undoubtedly further generalise concepts, ideas, hypotheses
and findings in this thesis and uncover new ones. Others may modify,
correct or reject some of the conclusions in this thesis. What
is certain is that the literature, which already has a long history,
will continue to develop with this process and our understanding
of human manipulation performance will continue to improve, thereby
allowing us to design input control interfaces on a continuously
more scientific basis.