Humans Use Predictive Gaze Strategies to Target Waypoints for Steering

A major unresolved question in understanding visually guided locomotion in humans is whether actions are driven solely by the immediately available optical information (model-free online control mechanisms), or whether internal models have a role in anticipating the future path. We designed two experiments to investigate this issue, measuring spontaneous gaze behaviour while steering, and predictive gaze behaviour when future path information was withheld. In Experiment 1 participants (N = 15) steered along a winding path with rich optic flow: gaze patterns were consistent with tracking waypoints on the future path 1–3 s ahead. In Experiment 2, participants (N = 12) followed a path presented only in the form of visual waypoints located on an otherwise featureless ground plane. New waypoints appeared periodically every 0.75 s and predictably 2 s ahead, except in 25% of the cases the waypoint at the expected location was not displayed. In these cases, there were always other visible waypoints for the participant to fixate, yet participants continued to make saccades to the empty, but predictable, waypoint locations (in line with internal models of the future path guiding gaze fixations). This would not be expected based upon existing model-free online steering control models, and strongly points to a need for models of steering control to include mechanisms for predictive gaze control that support anticipatory path following behaviours.


Saccade Time Headways in Experiment 1
We made the observation that the time headway of the guiding fixations in Experiment 1 consistently decreased as the speed increased (see supplementary table ST1 for individual participant results). The limited field of vision of the simulator (and the fact that the participants were not able to rotate the virtual camera other than by rotating the car) is a likely concern here. For example, at the maximum speed of 66 km/h, the maximum visible time headway can be as low as 3 seconds (the maximum visibility varies on the basis of the location and rotation of the vehicle in respect to the path). While the observed time headways were even lower (mean saccade landing point TH: 1.76 s) it seems at least intuitively plausible that the drivers would avoid directing their gaze close to the edge of the screen even if in a more unconstrained setup they would look further. The fact that the trials were ordered from lowest speed to the highest speed is also a possible factor -if the participants increased familiarity with the track has an effect on where they look it would naturally coincide with the increase in speed. In order to test this further, future experiments have to be done with randomized speed profile in virtual reality with free-head movements that correspond to the movement of the virtual camera or in the field, alternatively larger curve radii could elicit higher visibility in terms of time headway.
One other possible explanation involves the increased difficulty of lane keeping with higher speeds (indicated by the higher variation in travel path deviation and increased time spent outside the path, see Steering Performance, below, for details). Land and Horwood [1] demonstrated in a simulator setting that when drivers are only presented with 'far' visual information about the road, i.e. everything else except a small segment of the screen was occluded, the driver's lane keeping ability significantly deteriorated. Vice versa the loss of 'far' information negatively affected the driver's ability to estimate the road curvatures. Similarly, in the steering model of Salvucci and Gray [2] where steering is guided by a near and far travel point, the near-point information is more integral to lane keeping whereas farpoint information is used for greater overall stability. It may be that as the difficulty of lane keeping increases with speed (note that the speed was automatically kept constant, the participants were not able to control it), more guiding fixations fall on the near-vicinity of the driver whereas in easier conditions the drivers are able to distribute more attention to the 'far zone'.
It should also be noted that while the time headways decreased with speed, rather than staying constant or possibly even decreasing, the distance at which saccade landing points fell did increase with speed, just not as much as would be predicted if the time headway stayed constant (see Supplementary Figure S1 ).

Steering Performance
While the gaze behaviour of the drivers was our main interest, we also chose to examine how well the drivers were able to steer in Experiment 2 in comparison to Experiment 1 in terms of both deviation from the track and steering smoothness. The participants (of Experiment 2) mainly stayed on the track or quickly returned if the warning sound started to play, but there were 2 separate occasions on which the participant was unable to return to the track (specifically they drove over 10 meters off the track) after the end of a turn.
Overall however the participants' ability to stay on the lane was comparable to the two higher speed conditions of Experiment 1 (see Supplementary Table ST2 ).  Figures S2 and S3 ). In Experiment 1 the participants appear to steer closer to the inner edge of the road whereas in Experiment 2 the participants appear to steer closer to the outer edge of the road. Note that in contrast to many steering studies, we did not instruct the participants explicitly to steer at the centre of the road (the waypoints in Exp 2 were in the middle, so arguably a central lane position was implied) in either experiment. Thus, constant bias should not be construed as steering error.

Supplementary
The variability (SD) in lane position was about 25-30cm ( Supplementary Figure S4 ). In particular, using only the waypoints in Experiment 2 does not create more lane position variability than the textured fully visible road in Experiment 1, except at the reversal points where the sign of the path curvature changes. When the target information is not available in these transitional locations (when the gap is in the turn position following the curvature zero crossing). The participants cannot then reliably predict that the path will make an S i.e. the turn direction will reverse, and they can get momentarily "lost" (evidenced by peaks in SD, Figure S4 ).