Coordination: In Time and Space
Simultaneity and Efficiency
Maurice R. Masliah
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 *
Recent work presented at CHI í98 (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.ís 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 RockiníMouse (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)?
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 userís actual trajectory can be compared to the optimal. The ratio of the userís 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 userís 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.
A Definition of Coordination
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.
Coordination vs. Control
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.
Coordination vs. Performance
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 userís 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:
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