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The Accuracy of Interceptive Action in Time and Space

Tresilian, James R.

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Exercise and Sport Sciences Reviews: October 2004 - Volume 32 - Issue 4 - p 167-173
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INTRODUCTION

Games such as tennis, squash, baseball, and cricket require players to strike relatively small balls with a hand-held racquet or bat. At the professional level, the ball may move extremely fast: first serves in mens tennis often exceed 60 m·s−1 and a fastball pitch in baseball may exceed 40 m·s−1. In tennis, the ball travels in the order of 25 m between the server and receiver. In baseball, the ball travels roughly 17 m between the pitcher’s hand and the plate. Given its high speed, therefore, a ball typically reaches the service receiver or baseball batter in approximately 400 and 800 ms. In Figure 1, the time is 425 ms. In this brief period, the batter must execute the movement, which takes 150 ms in Figure 1, leaving 275 ms to complete the preparatory processes needed before moving. Nevertheless, a skilled batter is capable of hitting the ball, an action that requires movements to be exquisitely timed and precisely directed in space. For example, hitting a baseball with the bat’s “sweet spot” typically requires a spatial accuracy of within approximately ± 2 cm and a temporal accuracy of within approximately ± 10 ms. Hitting a home run off of a 40 m·s−1 fastball may require temporal accuracy to be within ± 2.5 ms (9).

Figure 1.
Figure 1.:
A batter (left) is ready to strike a ball pitched to him by a pitcher (right). In the example shown (not to scale), the ball leaves the pitcher’s hand with a speed of 40 m·s−1 and travels approximately 17 m (along the dashed path) before being hit. The time between the ball being released by the pitcher and struck by the batter is approximately 425 ms. The batter begins his swing 150 ms before the ball arrives.

The ability of skilled sports people to achieve high degrees of spatiotemporal accuracy perhaps is made more remarkable given well-established experimental results concerning people’s behavior when aiming at stationary targets. These show that a movement’s spatial accuracy and precision is better when it is of longer duration, leading to the type of speed versus accuracy tradeoff described by Fitts’ law (10). Temporal accuracy and precision, in contrast, is better for movements of shorter duration (10). Thus, spatial and temporal accuracy seem to place conflicting demands on performance—make longer duration movements when spatial accuracy is required, and briefer movements when temporal accuracy is required.

Two questions arise from the foregoing considerations:

  1. How is the conflict between spatial and temporal accuracy demands resolved for interceptive actions?
  2. What sensory information and mode(s) of control does a person use to achieve the high degree of spatiotemporal accuracy demanded by many interceptive tasks?

Recent empirical work on rapidly executed, interceptive aiming movements is beginning to suggest answers to these questions. Herein, the basic results of the work are described and their implications for underlying control strategies for interception are outlined.

RESPONSES TO VARIATION IN THE TEMPORAL CONSTRAINTS

The example of hitting a baseball (Fig. 1) illustrates the two basic types of temporal constraint that interception places on performance. First, the time available to the performer is limited—the moving target is seen for only a short time. Second, interception typically demands some degree of temporal accuracy. In many circumstances, these constraints are not independent; a task in which they are and can be manipulated experimentally is shown in Figure 2. In this task, the performer is constrained to move a manipulandum along a straight path perpendicular to the path of target motion. For this reason, we refer to the task as the one degree-of-freedom (1-df) hitting task (11,14).

Figure 2.
Figure 2.:
The one degree-of-freedom hitting task. (a) Schematic illustration of the task. The target (length; L) moves to the right at speed V. The intercepting manipulandum (bat; width, W) moves along the straight path between the two dashed lines starting a distance D from the target’s path. The target can be struck when it is within the strike zone, which is a distance Z from the point where the target can be first seen by the participant. (b) Definition of the timing error. Zero error (middle) is defined to occur when the middle of the target (black) is struck by the middle of the bat (gray). An early error (negative) occurs when the center of the target is to the left of the center of the bat when a strike occurs (left).

In the 1-df task, the time available is (for a constant speed target) equal to the distance Z divided by target speed (V), called the view time (VT). The temporal accuracy constraint can be quantified using a variable called the time window. The target can only be intercepted while part of it is within the strike zone (Fig. 2A). If the target’s leading edge reaches the strike zone at time t1 and its trailing edge leaves the strike zone at time t2, the target is within the zone for a time t2 − t1, which defines the time window (equal to [L + W] / V). To hit the target, the manipulandum must arrive at the strike zone between the times t1 and t2, and so the time window can be regarded as a measure of the temporal accuracy constraint: the narrower the time window, the greater the accuracy required.

A recent series of experimental investigations studied how performance of the 1-df task is influenced by the temporal constraints (11–13). The main dependent measures were movement time (MT), peak movement speed and the temporal error (Fig. 2B). Herein, discussion is restricted to the MT and temporal variable error (VE, the standard deviation of the temporal error). The independent variables were target speed (V; Fig. 2A) and length (L), bat width (W), viewing time (VT) and distance (D). In one experiment (11), L and V were varied while D, W, and VT were held constant. The basic pattern of results obtained is summarized schematically in Figure 3 (the results were similar in the same experiment but with L held constant and W changed). Figure 3A shows how MT was found to vary as a function of target length (with bat width constant) at different target speeds; four different speed are shown (separate lines) and four different target lengths (different symbols). If the same data are plotted as a function of the time window ([L + W] / V), the pattern is as shown in Figure 3B. There was a clear interaction between target length and speed (Fig. 3A)—the slope of the MT length relationship was steeper at slower speeds—and an offset, the intercept with the MT axis was larger for slower speeds. The pattern can be summarized by saying that MT was found in increase in direct proportion to the time window (MT ∝ [L + W] / V, interaction) and to decrease in proportion to target speed independently of the time window (MT ∝ − V, different intercepts) (11). MTs of individuals in this experiment ranged between 80 to 400 ms, similar to those observed other laboratory hitting tasks and baseball batting (1–3,9,10).

Figure 3.
Figure 3.:
Illustration of the pattern of results obtained in experiments with the 1-df task shown in Figure 2. This is the pattern produced by equation 1 (with D and W held constant at 22 cm and 0.5 cm, respectively) and confirmed by experiment. (a) Movement time as a function of target size (L). In these experiments, four different values of L were used (from 4–14 cm) and four different speeds from 1.0 m·s−1 (slowest) to 2.2 m·s−1 (fastest). Representative mean MTs shown (experimental MTs lay in the range of 80–400 ms). (b) MT as in (a) but plotted against the time window [L + W] / V. Data from (11).

In another experiment, the effect of target speed (V) on MT was examined for five different view times (VTs) between 400 and 1000 ms (W = 0.5 cm and L = 6.0 cm were constant) (11). The results of the experiment are reproduced in Figure 4. When there is a reasonable amount of time available (larger VTs) there is a strong effect of target speed on MT, but when there is very little time available, the effect of speed is practically absent. This presumably is because there is some minimum MT that people can achieve, and as the VT decreases, they approach this minimum restricting the extent to which they can vary MT in response to changes in target speed. Note that making a briefer movement when the VT is shorter also increase the time for which the target can be viewed before movement begins (10).

Figure 4.
Figure 4.:
Mean results (N = 8) in which VT and target speed were covaried. Five different VTs were used (0.4, 0.5, 0.6, 0.8, 1.0 s) shown as different symbols joined by lines and four different speeds (1.0, 1.33, 1.67, 2.0 m·s−1). (Reprinted from Tresilian, J.R., and J.H. Houseman. Systematic variation in performance of an interceptive action with changes in the temporal constraints. Quart J. Exp. Psychol. A(in press). Copyright © 2004 Taylor & Francis. Used with permission.)

In some of our experiments, we examined the effect of time window on the variability of the strike times (the temporal VE) (13). It was found that as the time window increased so did the temporal VE (13). Thus, when greater temporal accuracy and precision was required, people were more temporally precise, and this was associated with briefer, faster movements. When less accurate timing was required, people were less precise and this was associated with slower movement. These results are consistent with those obtained in temporally constrained aiming tasks in which participants aim to move a certain prescribed distance (no moving target) in an MT specified for them by the experimenter (10). As noted earlier, in these tasks people have been found to produce brief MTs more precisely than longer MTs (MT variability increases in proportion to MT). The finding that people produce briefer movements when the time window is narrower can, therefore, be interpreted as a strategy for exploiting the greater temporal controllability of briefer movements (see below).

Effects of Other Factors in the 1-df Task

There are other task variables that may influence performance of the 1-df task. These include the distance to move (D; Fig. 2A) and the distance the target moves while visible to the participant (Z). Previous work on interception established that the distance Z has a negligible effect on performance (reviewed in (11)); VT is by far the more important factor (Fig. 4). In contrast, D (Fig. 2A) has been found to have a large effect on performance in interception tasks, with MT increasing in direct proportion to the distance (10,12,15). Overall, the effects of the independent variables (D, L, V, W) on MT in the 1-df task can be summarized by the following empirical relationship:

where a through d are empirical parameters, some of which clearly must depend on the view time given the results summarized in Figure 4. This is reminiscent of the Fitts’ law relationship for movements aimed at stationary targets, which is usually written as (10)

where D is the distance to the target, S is a measure of the target’s size, and a and b are empirical parameters (this is the textbook form of Fitts’ law in which S is a measure of the target’s actual physical size). The quantity log2(2D / S) is referred to as the index of difficulty. Equation 1 describes the finding that MT decreases as the need for temporal accuracy increases. Fitts’ law describes the finding that MT increases as the need for spatial accuracy increases. This highlights the conflict that can arise when successful performance requires both spatial and temporal accuracy. How people resolve this apparent conflict is discussed below.

RESPONSES TO VARIATIONS IN SPATIAL ACCURACY CONSTRAINTS

A task that allows independent control over spatial and temporal accuracy constraints is shown in Figure 5 and is referred to as the two degree-of-freedom (2-df) hitting task (14). In this task, the performer moves in a plane oriented normal to the path of the moving target. In Figure 5, the plane of movement corresponds to that of the page, and the target moves perpendicular to the page and toward it. The x-direction in Figure 5 corresponds to the direction along which the performer is constrained to move in the 1-df task (Fig. 2A). The fact that the performer is free to move up and down (y-direction) means that in the 2-df task, target height constrains the spatial accuracy of aimed movement: in fact, height (H) and distance (D) codetermine the directional accuracy demands (14).

Figure 5.
Figure 5.:
The 2-df hitting task. The target moves along a straight path perpendicular to and toward the plane of the page. The target is flat and rectangular of height, H, and is shown mounted on a rod (vertical, black). The base of the manipulandum is a flat magnetic block that can move freely over a plane steel surface (constraining plane). The participant grasps a cylindrical handle (out of the plane of the page) mounted to the base of the manipulandum and attempts to strike the target with the tip (1.0-cm diameter) of the strike shaft. In the starting position, the tip of the strike shaft is at a distance D from the plane of target motion. (Reprinted from Tresilian, J.R., A. Plooy, and T.J. Carroll. Constraints on the spatio-temporal accuracy of interceptive action: Effects of target size on hitting a moving target. Exp Brain Res. 155:509–526, 2004. Copyright © 2004 Springer-Verlag. Used with permission.)

Using the 2-df task spatial (directional) accuracy demands can be varied while keeping the temporal constraints constant. This strategy was used in a study recently reported (14). Target height could take one of four values (2, 4, 8, 16 cm), whereas the time window and viewing time were held constant. This simple experiment was run at two different values of the time window (70 ms and 35 ms; V = 2.0 m·s−1 or 1.14 m·s−1) and with stationary targets as a control (W = 1.0 cm, L = 7.0 cm in all conditions); separate groups of eight people performed in these three conditions at three distances (D = 8, 20, and 32 cm; Fig. 5). Fitts’ law would predict that when plotted as a function of the index of difficulty, log2(2D / H), the MTs from all conditions should lie on a single straight line with a significant positive slope. Figure 6A shows a plot of the mean data from the two moving target conditions against the index of difficulty, and it is clear that the Fitts’ law prediction is not fulfilled: the data from different distances lay on different lines and the slopes were indistinguishable from zero. The target height had no detectable effect on MT. Even the results from the stationary target condition did not conform to Fitts’ law (Fig. 6B). In these conditions, there was a significant positive slope (although it was small in magnitude, just a few milliseconds per centimeter change in H) and the data conform to Welford’s alternative form for Fitts’ law in which the effects of distance (D) and size (S) are independent (MT = a + blog2D − c log2S; a, b, c positive).

Figure 6.
Figure 6.:
Summary of movement time results in which target height (H) and distance (D) were independent variables. (a) Mean MT as a function of the ID (log2[2D / H]) in the two moving target conditions (N = 16). (b) MT as a function of the Index of Difficulty in the stationary target condition (N = 8). ▾, D = 32 cm; ○, D = 20 cm; •, D = 8 cm. Data from (14).

The results shown in Figure 6A indicate that when hitting a moving target, people hardly altered the timing of movement in response to variations in the spatial accuracy demands. There were also no detectable variations in either movement speed or spatial variability of the strike location (spatial variable error). This strategy led to a greater proportion of missed targets (failures to hit) when the target was small. Participants hit nearly 100% of the 8-cm and 16-cm tall targets, but missed between 20% and 60% of the 2-cm targets, although they were attempting to hit as many as possible. A high proportion of misses is also characteristic of baseball (3). In the next section, we consider how the observations described so far may be explained.

SPEED, ACCURACY, AND CONTROL.

Making briefer, faster movements when there is a greater need for temporal accuracy and precision can be interpreted as the result of a strategy used when corrective sensory feedback plays no significant role in movement control. In the absence of feedback control, temporal accuracy and precision can be improved by making briefer movements for two reasons. First, as mentioned above, briefer open-loop movements are more temporally controllable (10) because there is less time for internal noise and external disturbances to affect performance. Second, making briefer movements means that it is possible to watch the moving target for longer and so to obtain better information about its motion (10) (see next section).

The second reason just mentioned could relate to spatial as well as to temporal control: the spatial accuracy of an open-loop interceptive movement also may be improved if the target were watched for longer. However, the participants in our experiments did not, on average, make briefer movements when greater spatial accuracy was required (Fig. 6A), although a few did (14). Nevertheless, the data of Figure 6 are consistent with the idea that visual feedback played little or no role in the control of movement. A body of data examining movements aimed at stationary visual targets executed in visually open-loop conditions showed that spatial accuracy and precision hardly changes at all with brevity and speed (for MTs between approximately 200 and 500 ms (10, 14). Thus, in the absence of visual feedback, there is not necessarily any significant spatial accuracy advantage to moving more slowly. When feedback is available, there is clearly an advantage because spatial errors can be detected and corrected, and this is the likely reason for the Fitts’ law type speed versus accuracy trade-off (10).

In baseball, the swing times of batters typically lie in the range of 150 to 200 ms (3,10), and for aimed movements involving the whole arm, it takes between 120 and 200 ms for a visually detected error even to start to have an effect on performance (7). Thus, moving slowly enough to make effective use off feedback may not be an option, either because there is too little time available (Fig. 1) or because the task requires that the target be struck hard with the bat moving at high velocity. Under these circumstances, the way to improve accuracy and precision is not to adapt performance so that more effective use can be made of corrective feedback (i.e., increasing movement duration), but to adapt performance so that preprogrammed control results in better performance. Making briefer and faster movements in response to demands for greater accuracy and precision is what such a strategy predicts for temporal control. When greater spatial accuracy is required, there is a possibility that briefer movements may aid performance in some circumstances (by allowing the performer to see the target for longer), but we found little evidence for this in our experiments (14) (Fig. 6A).

The strategy of responding to greater accuracy requirements in a way that enhances the accuracy of preprogrammed movements can be referred to as the preprogrammed strategy (14). Use of this strategy does not necessarily mean that feedback does not influence performance—it may do if there is sufficient time. It simply means that performance adaptations to increased accuracy demands are those that improve the accuracy of preprogrammed movements while reducing (or at least not increasing) the opportunity to use corrective feedback. The preprogrammed strategy can be viewed as involving a kind of tradeoff, not between speed and accuracy as in Fitts’ law, but between accuracy and some concept of physical comfort or effort. When people do not need to be accurate temporally, they move relatively slowly, because such movements are physically less demanding and have a lower metabolic cost. Thus, when you need to be accurate, you make a faster, more effortful movement; when you do not need to be so accurate, you move more slowly and are correspondingly less accurate. The possible organization of underlying sensorimotor control processes is discussed next.

Sensorimotor Control

For an interception to occur, it is necessary that the target object and intercepting effector be at the same location (spatial coincidence) at the same time (temporal coincidence). To use a preprogrammed movement to intercept a target, the performer therefore must be able to anticipate quite accurately both when and where the interception will occur. This can be done using sensory information, available mainly through vision (3,8,9). Experimental data demonstrate that people can make very accurate visual estimates of when a moving target will arrive at a particular location (3,9) (see below), but it is not yet completely clear that people can make correspondingly accurate estimates of where it is going (3,8,9). For the present purposes, we assume that they can.

The functional organization of our proposed preprogrammed scheme (11,14) is shown in Figure 7. The remaining discussion focuses on timing control; the interception location is assumed to have been selected based on information about the target’s path (although it should be remembered that people’s ability to do this accurately remains to be demonstrated directly). The condition for temporal coincidence is that the target and bat be at the interception location at the same time with a margin for error determined by the time window (Fig. 2). Alternatively, we can say that the time remaining until the bat reaches the interception location (its time-to-contact [TTCbat]) must be less than or equal to the time remaining until the target reaches that location (TTCtgt) to within the error margin. If TTCbat is less than TTCtgt, then the bat must stop and wait for the target. This is not possible in hitting, where the temporal coincidence condition is TTCbat = TTCtgt.

Figure 7.
Figure 7.:
Functional organization of component processes in the preprogrammed control scheme for interception described in the text. MT is programmed based on information from the visual stimulus, advance information and expectations, and on the performer’s internal state (goals, motivation). The programmed MT determines the criterion TTC value for movement initiation (TTCc) as MT + RT. The motor pattern generator receives information about the amplitude and direction of the required movement and about the required MT. It begins to issue a descending command when a go signal is received indicating that TTCtgt = TTCc.

To meet the temporal coincidence condition, a preprogrammed hitting movement must start when TTCtgt is equal to the predetermined MT. To do this, the controller must be able to measure TTC from the stimulus input and to use it to initiate movement at the correct moment. In Figure 7, a specific criterion value of TTCtgt is used to trigger the motor pattern generator (also known as a generalized motor program (10)) into issuing descending motor commands. The criterion value must be matched to the MT, which varies as a function of task variables (e.g., equation 1), the person’s goals (e.g., to hit hard or soft), and their expectations (3). Given a particular MT, the value of the criterion value should be MT + RT, where RT (reaction time) is the time taken for a change in the stimulus to influence performance. Figure 8 shows a time line for the processes involved in the scheme of Figure 7. Initially, the person adopts a state of readiness to perform the action (the mechanism of panel a is activated)—they adopt an appropriate posture (e.g., the batter in Figure 1) and are prepared to execute a movement in a manner that depends on their goals, motivational state, expectations, and information obtained about the likely trajectory of the moving target in advance of seeing it (advance information). As soon as the moving target is visible, information is available to fine tune the prepared state, and this involves precisely programming the MT and determining the criterion TTC value. It takes a short time (labeled perceptual processing time) to determine from the stimulus input that the criterion TTC has been reached, some more time to trigger the motor pattern generator and for the descending command to reach the muscles (labeled transmission time), and finally some time for the limb to move in response (labeled neuromotor lag).

Figure 8.
Figure 8.:
Time line of events associated with the scheme in (a). See text for more detail.

In Figure 7, internal noise is shown as two lumped, multiplicative processes (sensory noise and central motor noise; there is also some peripheral motor noise that is not shown). The sensory noise is responsible for Weber’s law-type behavior, such as has been observed for visual TTC discrimination (3,9). The ability to discriminate TTC differences can be expressed as a percentage of the TTC (the Weber fraction). In TTC discrimination, the Weber fraction is between 2% and 5% (3,9), indicating that a TTC of 300 ms, for example, can be estimated to within ± 7.5 ms. Thus, the shorter the TTC, the smaller the error in estimating it. This means that you can determine when to initiate your movement using the preprogrammed scheme of Figure 7 more accurately when the criterion TTC value (and hence the MT) is smaller.

Use of Visual Feedback in Controlling Interceptive Action

In recent years, many researchers have proposed that interceptive actions, even very rapid ones, are controlled using visual feedback (1,2,5,6,8). Models for movement production that involve continuous feedback control have been particularly influential, the primary examples being the τ-coupling model of Lee et al. (5) and the required velocity control model of Peper et al. (8). There is, however, no evidence for feedback control of hitting fast moving targets when MTs are less than approximately 400 to 500 ms. Evidence does exist for feedback control in tasks with MTs larger than 400 to 500 ms (6, 8) and for feedback control of movements with durations in the range of 200 to 400 ms when hitting very slowly moving targets (between 0.06 and 0.2 m·s−1) (1,2). The data from the latter experiments suggest that there was some on-line control of movement direction, but that timing was not controlled on-line (1,2). Thus, timing seems likely to be controlled open-loop, but control of movement direction can involve some on-line control, at least for slow-moving targets.

Apart from the lack of direct empirical evidence, feedback control schemes for rapid interception lack the logic of the preprogrammed scheme because they offer no a priori reasons for expecting the pattern of behavior shown in Figures 3 and 5. If feedback control were important, it would be expected that performance strategies adopted would be such as to increase the opportunity to make use of it (cf., Fitts’ law). In several models of interception, the central command signal is derived from sensory feedback, the idea being that sensory information drives movement production in a continuous fashion (5,8). It is notable that these models do not take into account transmission time delays and peripheral musculoskeletal dynamics. There is evidence to suggest that for rapid arm movements such as those observed in hitting tasks, the central command may be complete even before the movement has begun because of the presence of neural transmission time delays and of significant lags resulting from muscle contraction dynamics and limb and manipulandum inertia (4,7). Under these circumstances, the attractive concept of driving movement using a continuous sensory-motor coupling looses much of its appeal, because the movement is not actually being continuously driven by a sensorially derived signal.

SUMMARY

The high degree of spatiotemporal accuracy and precision needed to hit a fast-moving target is probably achieved using a preprogrammed strategy. A preprogrammed strategy implies that people will try to maximize their chances of hitting the target in advance of starting to move. Thus, a person responds to demands for high levels of spatiotemporal accuracy in a way that tends to improve the accuracy and precision of open-loop movements while restricting use of on-line perceptual feedback. This strategy is appropriate for hitting tasks in which the target must be struck with the manipulandum (hand, bat, or racquet) moving at high speed. Different strategies evidently are used in other interceptive tasks that do not require high-impact speeds. Examples would include the pursuit and capture of a slow-moving target, many catching tasks (particularly when there is plenty of time available), and some laboratory tasks that use computer displays (6).

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Keywords:

aimed movement; timing; anticipation; Fitts’ law; human

©2004 The American College of Sports Medicine