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**Abstract ***

**Introduction: Previous Work on Human Coordination ***

Simultaneity (Wang et al. 1998) *

Efficiency (Zhai and Milgram 1998) *

**Incompleteness of Previous Work ***

A Definition of Coordination *

Coordination vs. Control *

Coordination vs. Performance *

**Future Work ***

**References ***

Recent work presented at CHI ’98 (Computer Human Interaction)
included two papers (Wang et al. 1998; Zhai and Milgram 1998) on the topic
of measuring human coordination between translational and rotational degrees
of freedom. While both papers are attempts at measuring human coordination,
the two methods, simultaneity and efficiency are quite different. Both
methods are reviewed and it is argued that neither of these two metrics
alone entirely captures the concept of coordination. Rather, a true measure
of coordination must take into account performance in both the time domain
*and* the space domain. Simultaneity and efficiency each alone only
captures one of the two dimensions which encompasses human coordination.
A qualitative definition of coordination is proposed and is compared to
the related concepts of simultaneity, efficiency, performance, and control.

**Introduction:
Previous Work on Human Coordination**

This paper is hardly a complete review of all previous
work on the topic of coordination; rather it is a review of recent papers
from the human computer interaction literature. The emphasis is upon the
methods used in each paper to quantify coordination. First, two papers,
one measuring simultaneity and one measuring the efficiency of users ability
to coordinate movement between translational and rotational degrees of
freedom, will be reviewed and contrasted. Rather than arguing that simultaneity
or inefficiency are *incorrect* measures of coordination, it is argued
that each alone is an *incomplete* measure.

*Simultaneity
(Wang et al. 1998)*

Wang et al.’s work is an extension of (Jacob et al. 1994) work on the integrality and separability of input devices. Integrality refers to the ability to move diagonally across a multi-dimensional space, while separability describes movement along one degree of freedom at a time. In other words, shortest distance straight-line Euclidean trajectories are evidence of integral movements while "city-block" trajectories are evidence of separable movements, see Figure 1.

*Figure 1. Depiction of integral and separable movements.
The degrees of freedom "X" and "Y" may represent any
two degrees of freedom that are being manipulated.*

For a given timeline, it is possible to compute the ratio of Euclidean to city-block movements for a given task. This ratio is a measure of the integrality of a given input device (Jacob et al. 1994), which can then be compared to the integrality ratio of other input devices for the same task. The higher the ratio, the greater the integrality of the device. One example of the use of this measurement has been to demonstrate that users can control three degrees of freedom simultaneously in a two translational and one rotational degree of freedom device, the Rockin’Mouse (Balakrishman et al. 1997).

Essentially, integrality is a measure of the simultaneity
of motion among multiple degrees of freedom. The Jacob et al. method of
measuring integration looks at movement that is greater than a fixed threshold
in order to filter out very small movements. Other than the fixed threshold,
**integration/ simultaneity is measurement in the time domain only**,
and says nothing about magnitude or the direction of the movement. Neither
Jacob et al. nor Wang et al. has made the claim that integrality is a measure
of coordination. However, they are clearly related concepts. Exactly how
does integrality differ from an "ideal" measure of coordination
(which has yet to be defined)?

- Selecting different constants for the different threshold parameters in the integration measure can lead to different results. Ideally, a measure of coordination should not be a function of constants chosen by the experimenter.
- Just because there is motion in all degrees of freedom does not necessarily mean that the motion is contributing towards reaching the goal. For example, randomly generated movements above the threshold would qualify as integrated motion but should not be consider as coordinated motion.
- Sometimes not moving in one degree of freedom is just as important as movement in another degree of freedom. It is possible to imagine a task where city-block motion is required for all or part of the task. The measure of integration is independent of the task, it only checks whether there is motion in more one dimension regardless of whether that motion is required or not. A measure of coordination should be a function of the task. (Consider, for example, motion in a circle within an environment which has two degrees of freedom. The amount of movement on each degree of freedom will range from zero to maximum, and only a task dependent measure of coordination can possibly track these changes in magnitude.)

*Efficiency
(Zhai and Milgram 1998)*

A coordinated movement is generally recognized as being
an *efficient* movement. One possible measure of efficiency is to
examine the length of a trajectory or the amount of rotation performed
by a user. The assumption is that the shortest possible trajectory is also
the most efficient. Equating coordination to efficiency has been proposed
by Zhai (Zhai 1995; Zhai and Milgram 1998). If there exists an ideal or
an optimal trajectory, the user’s actual trajectory can be compared to
the optimal. The ratio of the user’s trajectory to the optimal trajectory
is a sort of inverse measure of coordination, such that

equals the inefficiency of the performance. A zero value
equals perfect coordination, while all other values represent the amount
of wasted motion performed by the user. Notice that, complementary to the
Jacob et al. integrality metric, that **efficiency is measurement in the
space domain only**, and says nothing about the timing of *when*
the movements were made.

**Incompleteness
of Previous Work**

Either metric, simultaneity or efficiency, will give a
very high coordination measure when the user is performing near or at optimal.
The ability to recognize optimality is not a true test of any measure of
coordination, in that all performance measures converge upon the ideal.
What is more interesting is the answers different metrics give for deviations
from optimality. Coordination, as a measure of the *quality* of a
user’s performance should be useful for distinguishing between different
types of non-optimality.

Figure 4 shows four different user performances for a two degree of freedom positioning task (moving from one position to another). Figure 4a shows an optimal trajectory, while 4b, c, & d are non-optimal. For simplicity, assume that the rate of motion is constant across trials 4b-d. Both simultaneity and efficiency are ability to distinguish between trials 4a and the other three trials 4b-d, which is a case of distinguishing between optimal and non-optimal. The trajectories in trials 4b-d are visually very different from each other, and the goal of a definition of coordination should be to distinguish and quantify those differences. However, simultaneity can not distinguish between 4c and 4d, because there is activity in both degrees of freedom for the entire length of the trial. Efficiency, on the other hand, can not distinguish between 4b and 4c, because the length of the trajectories are identical.

*Figure 2. Four different trajectory examples. a) high
coordination and high control trajectory, b) low coordiation and high control
trajectory, c) high coordination and low control trajectory, d) low coordination
and low control trajectory.*

The following qualitative definition of coordination is
proposed. *Coordinated movement is the simultaneous control along multiple
degrees of freedom, which results in an efficient trajectory.* This
definition recognizes the spatio-temporal characteristics of coordination.

Traditionally, in the field of human factors, no distinction
has been drawn between the definition of coordination and that of control.
One domain that has studied the differences intensely is that of motor
control, the study of human movement. As defined by Kugler, Kelso, &
Turvey (Kugler et al. 1980), coordination is the imposing, or *constraining*,
of a relationship among multiple variables. Control, on the other hand,
is described in terms of the absolute magnitude of that relationship (i.e.,
the magnitude or level of force, position, velocity, or displacement affected).
In other words, requiring that when x increases y should also increase
is a type of constraint, while the exact values of x and y is determined
by the control. Coordination is tied with the concept of constraint, while
control is the parameterization of the constrained variables. Identifying
the constraints in an interaction is one of the cornerstones of ecological
psychology theory, but for this paper, the discussion of constraints has
been restricted to those found only in the task.

While the terms coordination and control have often been used interchangeably, a high level of coordination or performance is also usually taken to mean the same thing. Traditional measures of performance include task completion times, constant position error (average error) root-mean-squared (RMS) error, the standard deviation of the error, modulus mean error (absolute error), and time on target (for a review, see (Poulton 1974)). While it is true that maximum performance implies maximum coordination, the converse is not. In typical user interactions, performance is less than optimum, and none of the traditional measures captures the degree of coordination of the user’s input. Figure 3 is an example of the difference between coordination and performance, taken from a two degree of freedom curve tracing task.

*Figure 3. Coordinated vs.
uncoordinated user inputs in a curve-tracing task. A) Input device A: Large
bias error and small random error. B) Input device B: Small bias error
and large random error.*

Regardless of which performance measure is used, the performance
with input device B will score higher than the performance of input device
A. However, clearly the *quality* of the performances are different.
This quality of the performance is precisely what any definition of coordination
should try to capture. Figure 4 shows the results from a single user shooting
two different guns at targets. Coordination is to precision as performance
is to accuracy.

*Figure 4. Precision vs.
accuracy in gun shoots at a target. A) Gun A: Large bias error and small
random error. B) Gun B: Small bias error and large random error. Adapted
from Bendat and Piersol (Bendat and Piersol 1986). The difference between
coordinated and uncoordinated motion is analogous to the better known difference
between precision and accuracy.*

What is needed now is a quantitative definition of coordination. While, like for performance, there may exist multiple definitions of coordination, an ideal definition should include the following:

- a task dependent measure
- a measure of the simultaneity of motion in the time domain
- a measure of the efficiency of motion in the space domain

Balakrishman, R., Baudel, T., Kurtenbach, G., and Fitzmaurice,
G. "The Rockin'Mouse: Integral 3D Manipulation on a Plane." *CHI
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Bendat, J. S., and Piersol, A. G. (1986). *Random Data:
Analysis and Measurement Procedures*, John Wiley & Sons, Inc.

Jacob, R. J. K., Sibert, L. E., McFarlane, D. C., and
M. Preston Mullen, J. (1994). "Integrality and Separability of Input
Devices." *ACM Transactions on Computer-Human Interaction*, 1(1),
3-26.

Kugler, N. P., Kelso, J. A. S., and Turvey, M. T. (1980). "On the concept of coordinative structures as dissipative structures: I. Theoretical lines of convergence." Tutorials in Motor Behavior, G. E. Stelmach and J. Requin, eds., North-Holland Publishing Company.

Poulton, E. C. (1974). *Tracking Skill and Manual Control*,
Academic Press, Inc.

Wang, Y., MacKenzie, C. L., Summers, V. A., and Booth,
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Interaction." *Proceedings of the Conference on Human Factors in
Computing Systems CHI '98*, Los Angeles, 312-319.

Zhai, S. (1995). "Human Performance in Six Degree of Freedom Input Control," Ph.D., University of Toronto, Toronto.

Zhai, S., and Milgram, P. "Quantifying Coordination
in Multiple DOF Movement and Its Application to Evaluating 6 DOF Input
Devices." *Proceedings of the Conference on Human Factors in Computing
Systems CHI '98*, Los Angeles, 320-327.