**The visually guided interception of a moving target is a fundamental visuomotor task that humans can do with ease. But how humans carry out this task is still unclear despite numerous empirical investigations. Measurements of angular variables during human interception have suggested three possible strategies: the pursuit strategy, the constant bearing angle strategy, and the constant target-heading strategy. Here, we review previous experimental paradigms and show that some of them do not allow one to distinguish among the three strategies. Based on this analysis, we devised a virtual driving task that allows investigating which of the three strategies best describes human interception. Crucially, we measured participants' steering, head, and gaze directions over time for three different target velocities. Subjects initially aligned head and gaze in the direction of the car's heading. When the target appeared, subjects centered their gaze on the target, pointed their head slightly off the heading direction toward the target, and maintained an approximately constant target-heading angle, whose magnitude varied across participants, while the target's bearing angle continuously changed. With a second condition, in which the target was partially occluded, we investigated several alternative hypotheses about participants' visual strategies. Overall, the results suggest that interceptive steering is best described by the constant target-heading strategy and that gaze and head are coordinated to continuously acquire visual information to achieve successful interception.**

*ψ*) is defined as the angle between the direction from the actor toward the target and a reference direction in space, which is some allocentric axis in the environment. The heading angle (

*φ*) is the actor's direction of locomotion relative to the same allocentric reference axis, and the target-heading angle is the difference between these two angles (

*β*=

*ψ*−

*φ*). Thus, the target-heading angle is the angular deviation of the target from the actor's current direction of locomotion. The three interception strategies can now be described in terms of these angles and their rate of change over time during interception.

*β*= 0 and

^{1}Second, whereas the CB strategy predicts a straight interception path, the CTH strategy is consistent with a range of interception paths with different degrees of curvature, including straight paths. The degree of curvature of a single trajectory when considering the CTH strategy is determined by the constant value of the target-heading angle. For example, the actor can produce a curved path when adopting a small target-heading angle as in Figure 1b, but the actor can also produce a straight path with a slightly larger constant target-heading angle as in Figure 1d. Thus, variability across trajectories may be a key factor in finding out which strategy best describes human interceptions.

*β*=

*ψ*−

*φ*), the target-heading angle covaries with the target's bearing. Therefore, observing interception behavior that is consistent with the CB strategy in a speed control task is also consistent with the CTH strategy. Thus, it is fundamentally not possible to distinguish the CB strategy from the CTH strategy based on the observed angular measurements when using speed control tasks.

*i*th frame,

*x*= 0,

*z*= 0 m). The target was a red textured cylinder, 3 m tall with a radius of 0.2 m. The car was 3.6 m long, 1.8 m wide, and 1.5 m tall. At the beginning of each trial, the car appeared at the origin (

*x*= 0,

*z*= 0 m), facing in the

*z*direction, and immediately began moving straight ahead along a green strip (14 m long) on the ground. At the end of the strip (

*x*= 0,

*z*= 14 m), the target appeared 40 m ahead and 12 m to the left of the car (

*x*= −12,

*z*= 54 m, i.e., 16.67° with reference to

*z*-axis) and immediately began moving rightward on a path parallel to the

*x*-axis (Figure 3b). Participants steered the car to intercept the target. The initial location and the moving direction of the target were mirrored left and right about the

*z*-axis in a counterbalanced fashion, and data were collapsed in the analysis. In half of the trials, the target was visible throughout interception, and in the other half of the trials, it was visually occluded 2.5 s after having appeared. A trial ended as soon as the target was within 1.8 m from the car's center, corresponding to an interception, or the car went beyond the line

*z*= 54 m, corresponding to a miss. To prevent a potential influence of landmarks on interception, the surrounding background image and the sky were rotated by an angle chosen uniformly at random between 0° to 270° for each trial.

*x*direction as the allocentric reference axis and computed the target's bearing relative to it in each frame according to the following equation:

*X*,

_{i}*Z*) and (

_{i}*x*,

_{i}*z*) are the coordinates of the target and the car, respectively, in the

_{i}*i*th frame. As heading direction of the car was recorded in each frame (

*φ*on the

_{i}*i*th frame), the target-heading in the

*i*th frame is computed as

*β*=

_{i}*ψ*−

_{i}*φ*. To compute the absolute rate of change of these angles, we divided their absolute difference between two successive frames by the time passed between those two frames.

_{i}*x*and

*z*positions) as well as mean time series of target-heading (

*φ*), bearing (

*ψ*), and their absolute rate of change, respectively.

*SD*= 0.20°) across participants. Within the Vizard software, the 3-D gaze unit vector with reference to the participant's head was read online from the SMI software package. For each frame, this gaze vector as well as position and orientation of the participant's head with respect to the environment were recorded. During analysis, we combined the gaze unit vector with the participant's head position and orientation to calculate the 3-D gaze direction in the environment.

*SD*= 0.08) for target speed 4 m/s, 0.99 (

*SD*= 0.02) for 5 m/s, and 0.99 (

*SD*= 0.03) for 6 m/s; for occluded targets, it is 0.31 (

*SD*= 0.31) for 4 m/s, 0.16 (

*SD*= 0.25) for 5 m/s, and 0.01 (

*SD*= 0.02) for 6 m/s. A two-way, repeated-measures ANOVA on interception rate indicated significant main effects of target visibility,

*F*(1, 17) = 289.17,

*p*< 0.01,

*η*

_{p}

^{2}= 0.94, and target speed,

*F*(2, 34) = 10.13,

*p*< 0.01,

*η*

_{p}

^{2}= 0.37, with a significant interaction between them,

*F*(2, 34) = 19.14,

*p*< 0.01,

*η*

_{p}

^{2}= 0.53. A follow-up simple effect test with Sidak adjustment revealed a significant main effect of target speed for both visible targets,

*F*(2, 16) = 10.99,

*p*< 0.01, and occluded targets,

*F*(2, 16) = 4.56,

*p*< 0.05. The significant main effect of target visibility indicates that target occlusion severely impaired interception performance. The significant interaction confirms that participants intercepted faster targets slightly more than slower targets when targets were visible; by contrast, they intercepted fewer faster targets than slower targets when targets were occluded. Thus, these results show that subjects indeed relied heavily on the visibility of the targets during interception in our experiments, confirming that our experimental setup did indeed investigate primarily online control of interceptive steering.

*SD*= 0.12) for target speed 4 m/s, 7.52 s (

*SD*= 0.37) for 5 m/s, and 12.17 s (

*SD*= 1.08) for 6 m/s; for occluded targets, it is 5.82 s (

*SD*= 0.23) for 4 m/s, 6.14 s (

*SD*= 0.47) for 5 m/s, and 6.61 s (

*SD*= 0.85) for 6 m/s. These analyses confirm than interception durations were longer in the current study compared to most previous studies on visuomotor interception.

*t*test against zero),

*t*(53) = 31.59,

*p*< 0.001,

*d*= 4.30, across all speeds in the visible trials with a mean of 8.80°/s (

*SD*= 2.05°/s) and a 95% confidence interval of [8.26, 9.35]. Similarly, the absolute rate of change of the heading angle, i.e., the absolute turning rates in the visible conditions were significantly different from zero,

*t*(53) = 43.12,

*p*< 0.001,

*d*= 5.87, with a mean turning rate of 8.91°/s (

*SD*= 1.52°/s) and a 95% confidence interval of [8.51, 9.32]. Thus, according to these results, the CB strategy is not a good account of subjects' behavior in our experiments.

*SD*= 5.64°) with a 95% confidence interval of [15.10, 18.11]. Accordingly, a one-sample

*t*test against a mean of zero showed that the target-heading angle was significantly,

*t*(53) = 21.64,

*p*< 0.001,

*d*= 2.95, different from zero. Taken together, the above results suggest that neither the CB nor the pursuit strategy can describe subjects' interception in our experiment.

*SD*= 1.07°/s) with a 95% confidence interval of [2.79, 3.36]. This is significantly different from zero, as the one-sample

*t*test against zero was significant,

*t*(53) = 21.15,

*p*< 0.01,

*d*= 2.88). Noting that subjects adjusted their target-heading angle during the beginning of the interception, some deviation from zero of its rate of change is to be expected. In order to still differentiate between CTH and CB, we compared the absolute rates of change in target-heading and target's bearing by computing their means for each participant as depicted in Figure 5b. Specifically, we averaged the absolute rate of change over each trial, then computed the mean for each target speed. A paired

*t*test indicated that the mean absolute rate of target-heading (

*M*= 2.97°/s,

*SD*= 0.89°/s) was significantly smaller than that of target's bearing (

*M*= 8.70°/s,

*SD*= 2.12°/s) across target speed,

*t*(53) = −15.57,

*p*< 0.01,

*d*= 2.12. We additionally computed the confidence intervals of the final target-heading and bearing angles separately for the three speed conditions in the visible trials. Because of the experimental setup, the initial target-heading angle was 16.67° and the initial bearing angle was 106.67° at the moment when the target appeared. The 95% confidence interval of the final target-heading angle for a target speed of 4 m/s is [14.264°, 21.542°]; for a target speed of 5 m/s, it is [16.249°, 23.756°], and for a target speed of 6 m/s, it is [9.65°, 20.607°]. By contrast, the 95% confidence interval of the final bearing angle for target speeds of 4 m/s is [64.8°, 75.9°]; for target speeds of 5m/s, it is [38.9°, 51.8°]; and for target speeds of 6m/s, it is [14.2°, 28.5°]. This means that the initial target-heading angle was within the 95% confidence interval of the final target-heading angle in all conditions, whereas this was not the case for the bearing angle in any of the three conditions. Thus, taken together, these results provide evidence that interceptive steering is better accounted for by the CTH strategy rather than the CB strategy or the pursuit strategy in the present experiments.

*SD*= 2.12°) for target speed of 4 m/s, 7.54° (

*SD*= 3.08°) for 5 m/s, and 7.18° (

*SD*= 3.71°) for 6 m/s. A one-way, repeated-measures ANOVA indicated that target speed had no significant influence on variability within participants,

*F*(2, 34) = 1.77,

*p*= 0.19. These results indicate a stable pattern of steering within participants in terms of the CTH strategy regardless of target speed.

*SD*= 0.61) and a 95% confidence interval of [−0.298, 0.0239], and the gaze-heading angle was, on average, about 2° off the heading direction toward the target with a mean of 1.91° (

*SD*= 1.79°) and a 95% confidence interval of [1.43, 2.39] at the beginning of the trials.

*SD*= 1.15°) for target speed of 4 m/s with a 95% confidence interval of [−3.04, −1.97], −2.72° (

*SD*= 1.59°) for 5 m/s with a 95% confidence interval of [−3.45, −1.98], and −2.72° (

*SD*= 2.36°) for 6 m/s with a 95% confidence interval of [−3.80, −1.63]. To confirm that these values suggest a stable gaze behavior across participants, velocities, and conditions, we carried out a two-way, repeated-measures ANOVA on subject-wise mean gaze-target angles, which did not show a significant effect of target condition,

*F*(1, 17) = 0.51,

*p*> 0.48, nor a significant effect of target speed,

*F*(2, 34) = 2.48,

*p*> 0.98.

*SD*= 9.3%) in the visible trials within the first 2.5 s. The density function in the second segment indicates that participants visually tracked the target most of the time also after they had observed the target's initial motion in the first segment with a proportion of gaze falling within 5° to the left or to the right of the target of 88% (

*SD*= 8.3%). The lower peak in the density in Figure 9a at about 17° to the right of the target direction for the first segment of both visible and occluded trials can be attributed to participants still looking in the heading direction at the moment of target appearance (see Figure 7) and shifting gaze with a brief delay. Combined with the results about interception strategies in the previous section, the results here suggest that participants visually tracked the target most of the time for picking up current information about target motion and used the CTH strategy to guide their interception.

*r*= 0.80 (

*p*< 10

^{−3}) for 4 m/s,

*r*= 0.81 (

*p*< 10

^{−3}) for 5 m/s, and

*r*= 0.87 (

*p*< 10

^{−3}) for 6 m/s. This is again evidence for the hypothesis that subjects tracked the target during interception and adjusted their gaze continuously in accordance with their steering to intercept the moving target. Note that this establishes a close connection between the direction in which subjects looked and the direction in which they steered.

*SD*= 2.71°) for target speed of 4 m/s, 2.73° (

*SD*= 2.59°) for 5 m/s, and 3.32° (

*SD*= 3.41°) for 6 m/s; in interception of occluded targets, it was 2.09° (

*SD*= 2.11°) for target speed of 4 m/s, 2.18° (

*SD*= 2.27°) for 5 m/s, and 1.70° (

*SD*= 2.78°) for 6 m/s. These results indicate that, in the interception of faster targets, participants oriented their head more toward the target when the target was visible than when it was occluded. To test whether gaze-heading θ angle and facing-heading angle ω were linked, we computed the correlation between the two angles for visible trials with a correlation coefficient of

*r*= 0.69 (

*p*< 10

^{−3}) for 4 m/s,

*r*= 0.72 (

*p*< 10

^{−3}) for 5 m/s, and

*r*= 0.81 (

*p*< 10

^{−3}) for 6 m/s. Thus, gaze and head movements were closely coordinated to accomplish target tracking.

*SD*= 0.26) saccades per second across participants and target speeds, it was 0.38 (

*SD*= 0.26) in visible trials. A paired

*t*test showed that saccade frequency was significantly higher in occluded than in visible trials,

*t*(17) = 7.89,

*p*< 0.01,

*d*= 1.86. This is not easily explainable with the interception location prediction strategy, which would predict only a few saccades to the future interception location and stable gaze at that location thereafter. The off-line tracking hypothesis may predict tracking of the occluded target with smooth pursuit or a sequence of smaller size saccades. Thus, although this result contradicts the trajectory prediction strategy, it cannot rule out the off-line tracking strategy.

*SD*= 11.8), which was significantly smaller than the aforementioned 88% in visible trials,

*t*(17) = −34.85,

*p*< 0.001,

*d*= 8.21. Instead, a larger proportion of gaze fell within 5° to the left and right of the heading direction in occluded trials (39%,

*SD*= 12.31) compared to the visible trials (15%,

*SD*= 10.72). A paired

*t*test showed that this difference was statistically significant,

*t*(17) = 7.01,

*p*< 0.001,

*d*= 1.65. According to the interception location prediction strategy, this is difficult to explain as the possible interception location was not in the direction of current heading of the car but to the right of the heading direction most of the time during interception. Similarly, the off-line tracking hypothesis would predict gaze falling in the believed direction of the occluded target, which, during the visible trials, did not coincide with the heading direction. Although it is not fully possible to exclude that subjects misjudged the putative location of the occluded target to be in the direction of the car's heading, it is highly unlikely, particularly given the experience gained during visible trials.

*SD*= 3.74%) in the second segment of visible trials, which is significantly different from 50%,

*t*(17) = 50.45,

*p*< 0.001,

*d*= 11.89. In occluded trials it was 68% (

*SD*= 19.69%), which is also significantly different from 50%,

*t*(17) = 3.96,

*p*= 0.001,

*d*= 0.93. This result is difficult to reconcile with the trajectory prediction strategy as the possible interception location was to the right of the heading direction in both visible and occluded trials. According to the off-line tracking hypothesis, subjects could have tried to maintain gaze on the believed position of the occluded target, which was to the left of the heading direction both in visible and occluded trials. Similarly, the target position was to the left of the heading direction during visible trials, but subjects directed their gaze to the right of the heading direction 32% (

*SD*= 19.69%) of the time during occluded trials. Thus, these results cannot fully rule out that subjects might have tracked the erroneously believed position of the target during occluded trials, but this is unlikely.

^{−1}to 1.29 ms

^{−1}were comparable across the two conditions, the condition with approaching targets led to relatively shorter interception durations compared to the condition with receding targets. Therefore, due to the inertia in human locomotion (e.g., see Fajen & Warren, 2003, 2007), the interception durations in the former condition might be too short for participants to bring the target-heading angle to a constant value. By contrast, we designed the current experiment so that interceptions usually lasted for about 6–12 s. Additionally, a further difference between these studies is that Fajen and Warren (2004) used the task of interception by walking, and the current study used interception by steering, which involves different end effectors.

*n*times the change in the target-heading,

^{2}that is,

*n*

*n*, this strategy can produce interception paths with different degrees of curvature, which appears consistent with participants' interception paths in the current study. Nevertheless, the value of

*n*is a free parameter and, therefore, not sufficiently constrained in this model with respect to participants' steering behavior in the current study. Specifically, some particular values of

*n*could lead to a target-heading that continuously changes during interception, inconsistent with the current study. Overall, although the average target-heading angle's rate of change was small but significantly different from zero with a value of 3.07°/s (

*SD*= 1.07), the CTH strategy best described participants' steering behavior in this study.

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^{1}This was addressed in detail in Zhao, Straub, and Rothkopf (2017), who examined interception strategies by manipulating the visual information about an allocentric reference.

^{2}It was called target drift in Rushton and Allison (2013), i.e., the change in the target direction with reference to the agent's egocentric reference. It is equivalent to the change in target-heading in the current study.