Driver Model C

Fig. 120 to 125 show the results for the mean value of the six adaptable driver parameters, grouped by drivers group, tire and speed.

Figure 120. Mean values of the preview distance ݀௣௥௘௩ଵ of driver model C, grouped by drivers

group, tire and speed.

Figure 121. Mean values of the preview distance ݀௣௥௘௩ଶ of driver model C, grouped by drivers

Figure 122. Mean values of the gain ܭ of driver model C, grouped by drivers group, tire and speed.

Figure 123. Mean values of the lead term time constant W௟௘௔ௗ of driver model C, grouped by

drivers group, tire and speed.

Figure 124. Mean values of the period ܶ_௦௜௡௘ of driver model C, grouped by drivers group, tire and

Figure 125. Mean values of the amplitude ܣ௦௜௡௘ of driver model C, grouped by drivers group, tire and speed.

The results for driver model C show varying speed dependence of the model parameters. The preview distances show similar values as for driver model B, although the values are less speed dependent for the professional drivers. The preview times are speed dependent for both driver groups, with similar values as driver model B as can be seen in Fig. 126 and 127.

Figure 126. Mean values of the preview time ݐ௣௥௘௩ଵ of driver model C, grouped by drivers group,

Figure 127. Mean values of the preview time ݐ௣௥௘௩ଶ of driver model C, grouped by drivers group, tire and speed.

The gain values are all much lower than for driver model B, as could be expected, because there is a feedforward part in the steering wheel angle in model C that forms a large part of the necessary steering wheel angle to follow the path and which is not depending on the path error. Therefore, the driver has to perform smaller additional steering to correct path errors, resulting in this lower driver gain. The speed dependence of the gain is different for the driver groups, the professional drivers have higher gain for higher speed, the nonprofessional drivers have higher gain for lower speed, except for tire 6. The lead term time constant shows different mean values for the both speeds, but not consistent higher or lower for the professional drivers. The feedforward driver parameter period ܶ_௦௜௡௘ is lower for higher speed, as is expected; driving with a higher speed on the same maneuver requires faster steering. Speed dependence of the feedforward amplitude ܣ௦௜௡௘ is only seen for the nonprofessional drivers, being

higher for high speed. This parameter is assumed to be related to the gain, both parameters determine how much the driver steers. The results show that a higher value for ܣ௦௜௡௘ for the nonprofessional drivers is combined with a lower

value for the gain. In contrast, the professional drivers have a higher gain, but almost equal values for ܣ௦௜௡௘. This suggests these two driver parameters can

compensate each other.

Some tire dependency can be seen for the preview distances, but not consistent over the speed and groups. This can also be concluded for the gain parameter. Also here the mutual dependency of this parameter with ܣ_௦௜௡௘ can be seen, a relative high value of the gain is combined with a relative low value of ܣ௦௜௡௘. The lead term time constant does not show the same tire dependency as

with driver model B. The mean values for the professional drivers for low speed show no monotonically in- or decrease and the error bars for the professional drivers are larger. The period ܶ௦௜௡௘ shows tire dependency for the professional

8.3.4 Summary

The results and discussion for the three driver model parameters are summarized here. For every driver model parameter the speed dependency is given by (Table 14.)

- An evaluation symbol, representing the mean driver model parameter values for the tires for low speed with respect to high speed.

- A background color, representing error bars the driver model parameters for a certain speed.

Table 14. Evaluation symbols and ackground color for the speed dependency of the driver model parameters.

Symbol Mean Values for Low Speed w.r.t. High Speed + All higher or lower

 Not all higher or lower

Background color Error Bars for a Certain Speed

No error bars overlap One error bar overlaps More error bars overlap Not relevant

Table 15 gives an overview of the parameters speed dependency evaluated for both drivers groups separately and for both groups together. In addition, the preview time parameters are included, because their speed dependency can differ from the preview distance speed dependency.

Table 15. Summary of Speed Dependency of the Driver Model Parameters grouped by driver group.

Driver Model Parameter Speed Dependency

Professional driver group

Nonprofession

al driver group All drivers

A

preview distance ݀௣௥௘௩௜௘௪ + + +

preview time ݐ௣௥௘௩௜௘௪ + + +

gain + + +

lead time constant ߬௟௘௔ௗ  + 

B preview distance 1 ݀௣௥௘௩ଵ + + + preview distance 2 ݀௣௥௘௩ଶ + + + preview time 1 ݐ௣௥௘௩ଵ + + + preview time 2 ݐ௣௥௘௩ଶ + + + gain ܭ  + 

lead time constant W௟௘௔ௗ + + +

C preview distance 1 ݀௣௥௘௩ଵ + + + preview distance 2 ݀௣௥௘௩ଶ  +  preview time 1 ݐ௣௥௘௩ଵ + + + preview time 2 ݐ௣௥௘௩ଶ + + + gain ܭ +  

lead time constant W௟௘௔ௗ  + 

period ܶ௦௜௡௘ + + +

amplitude ܣ௦௜௡௘  + 

This table shows that preview time is a strong speed dependent parameter for all driver models, having all values higher or lower for different speed and no overlap in error bars. This is also seen for the gain and preview distance of driver model A and the period ܶ௦௜௡௘ of driver model C. The preview distances for the

other models show strong speed dependence only for the nonprofessional drivers. The lead term time constant shows only speed dependency for driver model B, being strong for the nonprofessional drivers.

For every driver model parameter the tire dependency is evaluated in the same way as the speed dependency. Table 16 presents the meaning of the evaluation symbols for the tire dependency, the background color meaning of Table 14 is also used here.

Table 16. Evaluation Symbols for the Tire Dependency of the Driver Model Parameters. Symbol Mean Values for Tires 2, 5 and 6 for Both Speeds

+ Increasing or decreasing  Not increasing or decreasing

Table 17 gives an overview of the parameters tire dependency evaluated for both drivers groups separately and for both groups together, including the preview time parameters.

Table 17. Summary of Tire Dependency of the Driver Model Parameters grouped by driver group.

Driver Model Parameter Tire Dependency

Professional driver group

Nonprofession

al driver group All drivers

A

preview distance ݀௣௥௘௩௜௘௪   

preview time ݐ௣௥௘௩௜௘௪ + + +

gain +  

lead time constant ߬௟௘௔ௗ   

B preview distance 1 ݀௣௥௘௩ଵ    preview distance 2 ݀௣௥௘௩ଶ    preview time 1 ݐ௣௥௘௩ଵ    preview time 2 ݐ௣௥௘௩ଶ    gain ܭ +  

lead time constant W௟௘௔ௗ + (+) +

C preview distance 1 ݀௣௥௘௩ଵ +   preview distance 2 ݀௣௥௘௩ଶ  +  preview time 1 ݐ௣௥௘௩ଵ +   preview time 2 ݐ௣௥௘௩ଶ    gain ܭ   

lead time constant W௟௘௔ௗ   

period ܶ௦௜௡௘ + + +

amplitude ܣ௦௜௡௘ +  

Comparing this table to the table of the speed dependencies, it can be seen that the overall evaluation of the tire dependencies is less good than the speed dependencies. This was to be expected based on the setup of the experiment. The different speed demands were applied to give large differences in driver’s task demand and therefore large differences in driver’s mental workload, the differences between tires being smaller. Validation of this assumption (section 5.3) confirmed this for the nonprofessional drivers, but for the professional drivers the differences were similar. This is confirmed by this table: overall tire dependencies of the parameters are seen more for the professional drivers than for the nonprofessional drivers. Where the preview times all showed strong speed dependency, this is not seen for tire dependency, only for driver model A the preview time shows some tire dependency. The lead term time constant of driver model B is having tire dependency for all drivers. The value for the nonprofessional drivers being put between parenthesis, because this results from the evaluation, but probably due to reaching the lower bound of this

parameter, the error bars are almost zero. The period ܶ_௦௜௡௘ shows tire

dependency, being again stronger for the professional drivers.

8.4 Conclusions

How a driver perceives the tire handling behavior was the main question to be answered in this chapter. The driver model method answered this question by relating tire handling assessment scores to driver’s mental and physical workload and analyzing the optimized driver model parameters representing

driver characteristics like preview time, gain, lead and lag behavior and from this the adapting behavior of the driver. Because of the dependency of the driver parameters, the set of optimized parameters is not unique. By fitting the model steering wheel angle and the driven path of the vehicle at the same time to the measured signals, the variation in the set of optimized driver parameters is reduced to values representing realistic behavior.

To capture complex driver behavior in a few adaptable driver model parameters is no easy task. Driver models A, B and C, used in this driver model method, have an increasing number of adaptable driver model parameters. The more adaptable parameters, the better the model is able to represent the actual driver steering behavior. Analyzing the optimized model parameters revealed that all models could distinguish well between low and high mental and physical workload, seen for the low and high speed demand. Many of the parameters showed clear speed dependence. This was less clear for the workload differences due to different tires. Tire dependency was seen more for the professional drivers than for the nonprofessional drivers, which is in line with the fact that the professional drivers showed larger differences in workload between tires.

The lead term constant for driver model B showed to be the best candidate for both drivers groups, having good tire dependency. Although mutual dependent driver model parameters represent actual driver behavior and are present in all three driver models, too many drive model parameters can make the results less clear. Model A, using a continuous preview path, and model C, having the most adaptable driver model parameters, both seemed to have too much mutual dependencies in their parameters. Driver model B seems to be a good compromise, having a simple, realistic perception part using a discrete preview path, but also having less driver model parameters than model C.

Analysis of the model parameters showed how the driver adapts his perception and control to different workload tasks induced by different speeds and different tires. This also revealed the dependencies between model parameters, which gave insight in dependencies in driver behavior. In addition, differences between the professional drivers and nonprofessional drivers could be explained by looking at the corresponding driver parameters.

This driver model method shows how different driver behavior due to different tires can be explained and how this can be related to the driver’s experienced mental and physical workload.