A Multivariate Analysis of Crash and Naturalistic Driving Data in Relation to Highway Factors (2013)

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27 C h a p t e r 7 A key objective of this project has been to focus on data analysis coupled to mechanisms and control performance, not just on statistical associations. In Chapter 5 three can- didate surrogates were evaluated, and time to edge crossing (TTEC) was seen to be the best, while the very simple lateral deviation variable provided the worst surrogate. Presumably TTEC works better because it takes account of more relevant variables. However, it may not be optimal and better surrogates may still exist. According to the guiding principles of Chapter 2, a best-case surrogate is expected to be closely connected to the control task and disturbances in the control task. In this sec- tion the aim is to formulate a candidate surrogate and evaluate its performance in a limited set of cases. However, because of time and computing constraints, at this point no formal large- scale analysis using seemingly unrelated regression (SUR) or extreme value distributions is to be carried out. When a driver is engaged in lane keeping, there exists a rela- tively continuous process of adjusting the yaw angle of the vehicle to match that of the road. On a continuous curve, the steer angle is changed so that the yaw angular velocity— the rate of change of directional angle—matches the highway curvature and the vehicle speed. Yaw rate error (YRE) is a pro- posed measure of overall lane-keeping control performance that may supersede simpler measures such as lane position or time to lane crossing discussed previously. While a full sur- rogate analysis based on YRE has not been carried out in this study, the team does focus on the feasibility of defining and computing YRE and seeks indicators of its value as a control- oriented performance indicator. This brings the team back to “what driving is.” Driving is a control task based on visual input; it includes filtering of input for relevance, extracting signals or patterns from that visual information, and hence provides a reference to guide steering and speed control. Control action then involves manual effort by the driver to modulate vehicle motion using further force and acceleration cues (Toffin et al. 2007; Land and Horwood 1995; Chen and Ulsoy 2001). Here the team’s focus is on the visual reference for lane keep- ing in terms of a conflict measure or error criterion. In broad terms, the team seeks a simple measure of the control refer- ence for situations when the driver is concerned with staying in the lane but less concerned with some optimal path within that lane. To this end, YRE, a measure of yaw rate correction required, is introduced. Since no preferred path is known, the YRE is computed for multiple lane boundary points and the most critical of these will represent the overall correc- tion required. This metric has been used previously in driver modeling (Gordon and Magnuski 2006) and applied to colli- sion avoidance (Chang and Gordon 2008). The approach is analogous to longitudinal speed control in traffic, in which control action required can be found in terms of the vehicle deceleration needed to avoid a collision with the vehicle in front. Again, this contrasts with the predicted time to collision (TTC), based on instantaneous positions and velocities of the vehicles (Vogel 2003). While in the speed control problem there is essentially a single target point, the more complex lane-keeping activity involves multiple con- flict points and more complex vehicle kinematics. The team focused on yaw velocity rather than the related variables of path curvature and lateral acceleration because of the importance of visual reference. Yaw velocity is directly available to the driver as the perceived angular rate of distant or peripheral objects across the field of view. Path curvature by contrast requires a constructive element as the driver “imag- ines” the path of the vehicle, something that is surely more appropriate to low speed maneuvering. Again, vehicle lateral acceleration is not a visual input, but rather a feedback for the lower-level manual control of the vehicle. Thus, the empha- sis on yaw rate as the reference is based on its availability through visual feedback. This is analogous to what happens in vehicle stability control (e.g., Trachtler 2004)—vehicle yaw rate is directly measured and compared to a reference— though in this case, it is based on anticipated vehicle response to steering at the current speed. In this case path curvature is Yaw Rate Error

28 not directly measurable, and lateral acceleration is subject to many dynamic disturbances such as body roll; also, the lateral acceleration is dependent on location (whether that is at the driver’s head or in a solid state electronic device). By contrast, the yaw rate is only sensitive to sensor orientation. It is also worth noting that under ideal conditions of con- stant speed, minimal vehicle sideslip (when the vehicle is in a normal stable condition) and negligible body roll angle, the three variables mentioned (path curvature, yaw rate, and lateral acceleration) are simply proportional to each other. So under these simple conditions, any one of these variables might be used for the current purpose. For any point on the road or lane boundary, we are to deter- mine whether a yaw rate correction is needed to avoid going outside of the lane/road. If so, the yaw correction required is a measure of conflict. The maximum magnitude of all such corrections (left or right) is to be the conflict measure, though it is often of interest to analyze “worst right boundary case” and “worst left boundary case” in parallel. Additional information is relevant, namely, the distance and polarity (left, right) of any conflict point, as well as the horizon distance. The horizon distance is the maximum distance or headway for which, under ideal yaw rate, no conflicts occur. The hori- zon distance is a combined measure of position and direction error, as well as road geometry, and arises naturally out of the YRE analysis. As mentioned, YRE and these associated measures are related to time to lane crossing (TTLC), but are expected to incorporate a greater degree of continuity and relevance into the control task. Unlike TTLC, the “angle of attack” of the lane excursion is implicitly included, so it potentially attaches due significance to how severe the predicted lane excursion will be, not just when it will be. For this reason, YRE is expected to be a superior combined metric of lane-keeping performance analysis than TTLC. We now consider how to construct the yaw error criterion by using NDD. In Figure 7.1 we represent the lateral vehicle control relative to a single “conflict point” P. This is presumed to be on the right lane boundary, so the yaw rate (positive in the case shown, with the vehicle curving to the right) should be no more than for the critical case shown. The vehicle point Q required to pass to the left of P, while here it just intersects with P. Using polar coordinates (f, d), f is the azimuth angle and d is the distance-to-target, both computed relative to the velocity vector at the reference point Q. This in turn is oriented at an angle f0 relative to the vehicle axes, and if Q is assumed to be at the outside edge of the front right tire, then f0 is very roughly equal to the steering angle at the right front wheel. The vehicle path is in the form of a circular arc, for which the essential geometry is represented in Figure 7.2. We find that the critical case occurs when the turning radius R satisfies Equation 7.1 sin 2 (7.1) d R φ = which is equivalent to the yaw rate condition 2 sin (7.2)r U d = φ where U equals vehicle speed. Equation 7.2 defines the maxi- mum yaw rate of the vehicle to avoid conflict with a right boundary point P. When driving data are used, there is no direct information on all of the variables used in the above. The absolute coordi- nates of the boundary points are unknown, as are their rela- tive locations to the vehicle. Therefore, they must be inferred from the lane tracker, which estimates lateral position and lane width. Note that while in principle GPS could be used, it is far from being accurate enough to give useful estimation of the lane-keeping performance, so this is not considered. The team proposes a method that is more realistic to estimate instantaneous value of YRE by using multipoint measure- ments of lateral lane position, vehicle yaw rate, and vehicle speed. Essentially this is to distinguish vehicle path curvature from highway curvature by using variations in lane position. The calculations and their derivation are somewhat messy (see Appendix D). However, they turn out to be entirely feasible. As a “free bonus,” the YRE estimation technique provides a potentially useful estimation of underlying road curvature; this is based on vehicle yaw rate, but factoring out any lateral drift of the vehicle within the lane. Such estimation φ φ0 P Q dr Q P φ φ v d 2 d 2 Figure 7.1. Turning kinematics (reference point Q intersects with boundary edge point P during a steady state turn). Figure 7.2. Essential geometry of steady state turning motion.

29 is not applied in this project, but it is worth noting that it is available for future use. The motivation for YRE estimation was to provide a robust and continuous measure of lane-keeping control performance. To test this idea, at least in an informal way, the team consid- ered a small number of driving situations and compared YRE to TTLC and its reciprocal, inverse time to lane crossing (ITTLC). The estimation method described above was used to deter- mine the YRE for driving events recorded in the UMTRI NDD. Event 1, depicted in Figure 7.3, shows a driver negotiating an on-ramp that is in the form of a right-hand curve. The left plot shows the location of the left and right front wheels relative to the lane boundaries. Note that there is some variation in the lane width, but that most of the variations are in the dashed lines, which depict the outside edges of the front tires. This event shows a situation in which the driver maintained a position very close to the lane boundary with several excursions beyond the boundary. From video review, it appeared that the driver’s attention was switching between reading a map and looking at the road ahead. The event rep- resents an example of poor lane keeping. Figure 7.4a shows critical and actual yaw rate time histories, as well as lateral distance within the lane boundary (scaled by a factor 0.1 so that scales are reasonably consistent). All conflicts for this event appear to be right side only, so the YRE in Figure 7.4b is positive whenever the current location and path predict at least one lane boundary conflict within the chosen time horizon (0.5 to 2 s). Note that the YRE is always positive at the start of a lane excursion, and actually -2 0 2 0 5 10 15 20 25 tim e [s] (a) distance [m] 0 100 200 300 0 100 200 300 400 500 (b) dist [m] di st [m ] Figure 7.3. The vehicle path for Event 1. (a) The dotted lines represent the left and right edges of the vehicle with respect to the center of the lane markings (solid lines). (b) The XY position of the vehicle in space. (a) time [s] 0 5 10 15 20 25 30 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 ya w ra te [ra d/s ], d ist [m /10 ] ract. rcrit. sr/10 (b) time [s] 0 5 10 15 20 25 30 -0.04 -0.02 0 0.02 0.04 0.06 ya w ra te [ra d/s ] YRE Figure 7.4. The yaw rate parameters for Event 1. (a) Actual yaw rate, critical yaw rate, and distance to right lane boundary. (b) The calculated YRE through the curve.

30 always becomes positive before a lane excursion occurs. In this sense, as would be expected, YRE is predictive of each lane excursion. Figure 7.5 shows YRE again (lower plot) together with TTLC in the upper plot and also its reciprocal, ITTLC, in the center plot. ITTLC might be preferred as a conflict metric since large values indicate proximity to a lane excursion, in contrast to TTLC, which is large when the vehicle is tracking the lane well. The main features seen in Figure 7.5 are the great variations and major discontinuities in TTLC and ITTLC, as compared to the more continuous form of YRE. This suggests that YRE may connect more directly to the continuous steering control behavior of the driver, especially because lane crossing is not generally a catastrophic event and does not generate a panic response from the driver. In Figure 7.6 this is tested informally by plotting steer response (upper curve) as well as YRE (lower curve). Each local peak of the YRE curve seems to coincide with a sharp nega- tive slope in the steering, and this is the case at the YRE peaks at around t = 2, 7, 16, and 24 s; these sharp reactions seem to correlate with corrective actions by the driver in a way that TTLC, ITTLC, and even lane crossing in Figure 7.4a do not. The distracted driver in this event is not responding to YRE as it reaches positive values, but arguably when attention to the road coincides with a positive value of YRE. The second event considered was a single boundary cross- ing followed by a correction back to the middle of the lane. The vehicle trajectory data can be seen in Figure 7.7. The event is somewhat simpler than Event 1, in that only one major excursion exists. Figure 7.8 shows the event in terms of yaw rate and critical yaw rate, and it is interesting that the conflict most heavily dominated by variations is the critical yaw rate rather than the actual yaw rate. In the upper plot of Figure 7.8, the yaw rate exceeds its critical value at around 7 s, while the first lane excursion takes place around 1 s later, again showing the predictive nature of YRE. In the lower plot, the YRE undergoes a correction at t = 10 s and from the previous analysis we would expect to see a sharp negative slope in the steering angle then. Notice that in Figure 7.9, the previous comparisons with TTLC and ITTLC are consistent: the time-based metrics show large discontinuities, while YRE varies continuously and in a simple way during the event. YRE grows at a very roughly uniform rate until the correction is presumably applied at t = 10 s, then decays uniformly until at around 12 s, it is cor- rected again in the opposite sense. In Figure 7.10, a sharp negative slope is seen at t = 10 s, and a positive slope steering correction takes place at t = 12 s, as expected. Of course there are other steering corrections visible in Figure 7.6, and not all are directly predicted by conflicts with the right lane boundary, but perhaps some involve the right lane boundary. To this end, a modified plot of vehicle yaw rate plotted over the pair of critical boundary cases is considered below. First, however, we consider a third example, also on a curved road section but one where there are no obvious lane bound- ary conflicts (Figure 7.11). It shows a nearly uniform dis- tance from the car to the lane boundaries while negotiating the right-hand curve. Surely in this case the control loop is Figure 7.6. A comparison of the driver-controlled steering angle and the calculated YRE for Event 1. Figure 7.5. A comparison of the driver risk parameters for Event 1. (a) TTLC. (b) ITTLC. (c) YRE. (a) time [s] 0 5 10 15 20 25 -20 -10 0 10 20 tim e [s] TTLC (b) time [s] 0 5 10 15 20 25 -20 -10 0 10 20 1/ tim e [s- 1 ] ITTLC (c) time [s] 0 5 10 15 20 25 -0.04 -0.02 0 0.02 0.04 0.06 ya w ra te e rro r [r ad /s] YREr 0 5 10 15 20 25 30 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 time [s] St ee rin g An gl e [ra d], Y RE [ra d/s ] Steering Angle YREr

31 Figure 7.7. The vehicle path for Event 2. (a) The dotted lines represent the left and right edges of the vehicle with respect to the center of the lane markings (solid lines). (b) The XY trajectory of the vehicle. -2 0 2 0 5 10 15 20 tim e [s] (a) distance [m] (b) dist [m] 0 100 200 300 400 500 0 100 200 300 400 di st [m ] Figure 7.8. The yaw rate parameters for Event 2. (a) The actual yaw rate, critical yaw rate, and distance to the right lane boundary. (b) The calculated YRE through the curve. (a) time [s] 0 2 4 6 8 10 12 14 16 18 20 22 -0.05 0 0.05 0.1 0.15 ya w ra te [ra d/s ], d ist [m /10 ] ract. rcrit. sr/10 (b) time [s] 0 2 4 6 8 10 12 14 16 18 20 22 -0.04 -0.02 0 0.02 0.04 0.06 ya w ra te [ra d/s ] YRE Figure 7.9. A comparison of the driver risk parameters for Event 2. (a) The TTLC. (b) The ITTLC. (c) The YRE. (a) time [s] 0 2 4 6 8 10 12 14 16 18 20 22 -20 -10 0 10 20 tim e [s] TTLC (b) time [s] 0 2 4 6 8 10 12 14 16 18 20 22 -20 -10 0 10 1/ tim e [s- 1 ] ITTLC (c) time [s] 0 2 4 6 8 10 12 14 16 18 20 22 -0.04 -0.02 0 0.02 0.04 ya w ra te e rro r [r ad /s] YREr

32 Figure 7.13 shows the yaw rate versus its two critical limits, where conflict avoidance takes the form < <, left , rightr r rc c All three events are shown, but the most striking is for Event 3 in the lower plot: the vehicle appears to be controlled very precisely within the critical boundaries, with minimal inactive, meaning that the driver has found a stable line and has no need to make multiple corrections to avoid boundary conflicts. Figure 7.12 appears to show otherwise. Again, we are plotting YRE for the right boundary and steering control actions. Far from being random or disconnected from the boundary conflict, the driver appears to be making regular steering corrections (negative slope interventions) whenever YRE approaches a critical (zero or positive) value. 0 2 4 6 8 10 12 14 16 18 20 22 -0.05 0 0.05 0.1 0.15 0.2 time [s] St ee rin g An gl e [ra d], Y RE [ra d/s ] Steering Angle YREr Figure 7.10. A comparison of the driver- controlled steering angle and the calculated YRE for Event 2. -2 0 2 0 2 4 6 8 10 12 14 16 18 20 tim e [s] (a) distance [m] (b) dist [m] 0 100 0 100 200 300 400 500 600 di st [m ] Figure 7.11. Vehicle path for Event 3. (a) The dotted lines represent the left and right edges of the vehicle with respect to the center of the lane markings (solid lines). (b) The XY position of the vehicle in space. Figure 7.12. A comparison of the driver- controlled steering angle and the calculated YRE for Event 3. 0 2 4 6 8 10 12 14 16 18 -0.05 0 0.05 0.1 0.15 0.2 0.25 time [s] St ee rin g An gl e [ra d], Y RE [ra d/s ] Steering Angle YREr

33 overshoot but using the full range. Far from a stable “on cen- ter” steering control tracking the lane center, in “YRE space” the vehicle is bouncing quasiperiodically between its limits. If this interpretation is correct, the YRE provides a simple picture of lane-keeping control actions by the human driver. Turning to the center plot, where a single excursion event was seen, the degradation in control appears to be initiated as early as t = 3 s when the more stable “bouncing between lim- its” is interrupted. After the lane excursion is corrected, nor- mal effective control appears to be regained at around 14 s. Turning back to Figure 7.4a, this same interpretation seems reasonable from the within-lane drift: intuitively the driver is drifting right from about t = 3 s, and only recovers full control at around t = 15 s. The point here is that YRE seems to provide a direct measure of lane-keeping performance, and may even correlate with the error criterion active in the control loop of the human driver. In Figure 7.13a, it appears that the driver does not regain effective control of the vehicle throughout the 15 s, and this is consistent with the distracted nature of the driving event. Finally in the upper two plots, left and right boundaries actually cross over, so no solution to the above equation actually exists. This interesting situation is briefly considered below. As intended, we have defined and evaluated a YRE criterion as the basis of potential new surrogates for single-vehicle road departure crashes. The measure appears to be strongly connected to lane-keeping control, and has several advantages over similar but less clear measures. Note that • YRE behaves in a continuous way, even when lane bound- ary crossings take place, and this is not the case for TTLC and its reciprocal (ITTLC). • YRE excursions correlate strongly with rapid steering interventions by the driver, especially when the driver is providing effective control of lane position. • When left and right critical yaw rate boundaries are con- sidered simultaneously, the normal effective control of lane position appears to operate to constrain between the crucial limits. • YRE may be a useful predictor of actual lane excursions, but, more important, it seems to provide a strong indicator of degraded or ineffective lane keeping. In Events 1 and 2, the lane excursions appear to induce an impossible situation for the driver: the left and right lim- its cross over. This is most easily seen in Figure 7.13b, where crossover takes place between approximately t = 8 and t = 12 s. From Figure 7.7a and Figure 7.8a, this corresponds to the vehicle being outside the lane boundary; the steering task changes from lane keeping to lane recovery, though from Figure 7.13. Comparison between the critical yaw rate for left and right boundary conflicts and the actual yaw rate for (a) Event 1, riding the right boundary; (b) Event 2, single boundary crossing with correction; and (c) Event 3, good lane following. (a) time [s] 0 5 10 15 20 25 30 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ya w [ra d/s ] yawRc,right yawR yawRc,left (b) time [s] 0 5 10 15 20 25 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 ya w [ra d/s ] yawRc,right yawR yawRc,left (c) time [s] 0 2 4 6 8 10 12 14 16 18 0.02 0.03 0.04 0.05 0.06 0.07 0.08 ya w [ra d/s ] yawRc,right yawR yawRc,left

34 such events appear to show that YRE control relationships in lane keeping are robustly followed by most drivers in most conditions. Further work will be needed to expand the num- ber of events and attempt to quantify formally and accurately the relationships hinted at in the three events presented. In Chapter 8, the section Road Boundary Change and Yaw Rate Error briefly considers the application of YRE to “road wid- ening” scenarios, where the right lane boundary becomes ambiguous and one might expect lane-keeping control to be disturbed. Otherwise, the analysis of YRE is limited to the brief exploration presented above. Figure 7.10, the reaction seems to be consistent with a single sharp correction to divert the YRE to a correct linear rate of descent, followed by a second sharp correction in the oppo- site direction at around t = 12 s. Thus it seems that the cross- over is not a major factor to the driver, who perhaps applies focus to one boundary at a time. The preceding results were based on arbitrarily chosen events. There was no selection procedure adopted other than to find events from lane position typical of (a) an extended period of degraded lane control, (b) a single event lane excursion error, and (c) well-controlled lane keeping. Informal reviews of many