The objective of this paper is to examine the driver’s mental workload experience during extreme nonlinear high slip driving conditions, i.e. with the tyres being close to saturation. This is done for the ISO Double Lane Change manoeuvre, based on extensive test data from two professional test drivers, for different speeds, and with varying tyres. Optimal double lane change closed loop performance is defined and determined and compared to the actual test performance, showing and explaining differences in this performance. A path-tracking driver model has been applied to examine the driver model parameters steering gain and preview time. It is shown that these parameters, which can easily be derived from the closed loop vehicle handling data, vary with mental workload as experienced by these test drivers. This correlation has been demonstrated in previous research for normal driving conditions, where workload, in this paper determined through RSME (Rating Scale Mental Effort) scores, is affected by traffic conditions, where fatigue, experience and learning effects play a significant role. Hence, this paper shows that this, i.e. using the driver model as a virtual sensor to estimate mental workload, can be extended to high slip conditions.

Driver model parameters vary in time, and are not independent. Different combinations of preview time and steering gain lead to the same closed loop performance. We have extended the application of the driver model, the relationship between the driver model parameters and closed loop stability to high slip conditions, before we applied it to severe, i.e. high slip lane change performance.

Moving a vehicle is largely controlled by a driver. The roadmap towards ultimately safe driving by taking the driver completely out of the loop, as described by the hierarchy of autonomous driving as derived by SAE-International (

As discussed by Joop Pauwelussen (

An approach to understand the driver state during this transition phase is by matching the driver performance with a driver model and to adjust the model parameters for best closed loop performance, with these parameters typically being a delay or lead time, a gain, a preview time and alike. It is then of interest to see whether these model parameters vary during this transition phase. Saskia Monsma (

In case of linear vehicle behaviour, this relationship is independent of the curve radius. As a consequence, if a vehicle is not in the situation of extreme steady state conditions (high slip), this relationship between preview time (with which the driver model is observing path deviations ahead of the vehicle) and steering gain (the ratio between the steering action and the observed path deviation) still holds, and is therefore applicable for much more different handling conditons than only steady state. In addition, it was observed that this relationship is almost invariant with respect to speed. This is a great advantage in judging driver performance under practical conditions, when vehicle speed will definitely not be constant. Other studies treat handling performance of experienced vs. inexperienced drivers on a public road (

Most of these studies assume driving conditions, not being very critical, in the sense that tyre behaviour is still far from slip saturation. In the research by Saskia Monsma however, this assumption does not hold. It therefore makes sense to investigate to what extent the approach in driver state assessment as introduced by Joop Pauwelussen could be used likewise under high slip conditions. This may allow a better understanding of the relationship between the extreme driving behaviour and driver’s judgement of vehicle performance based on the ISO Double Lane Change (DLC) test (

The paper is organized as follows. In the next chapter, we will review the path tracking model under linear, almost steady state conditions, as treated by Pauwelussen (

A path tracking model as treated in this paper assumes that a vehicle aims to follow a certain path, with the driver observing the path deviation over a preview distance L_{p} from the vehicle CoG (Centre of Gravity). The path deviation D_{p} is transferred to a steering action with a steering gain K_{p}, and a lag time τ. This lag is assumed to cover both the actual (neuromuscular) lag and the driver reaction time. Lead effects are neglected. See Figure _{p}). In most cases, the initial deviation of the vehicle y(t) is much smaller than the deviation due to yaw behaviour, and we will neglect the first one. In the time domain, the front axle steering angle δ(t) satisfies the following differential equation:

A simple path tracking model.

This is the most simple version of this model. Extensions of this model exist, such as including more preview lengths (e.g. Salvucci & Gray (_{p} and K_{p}, from the time history of the vehicle states. In general, the contribution of y(t) in D_{p} is small compared to the contribution from ψ_{p}

Under steady state conditions, following a circular path with radius R, equation (1) reduces to:

We have indicated this situation in Figure _{p}/R is assumed to be small. Note that L_{p} is usually in the order up to 25 meter.

Steady state path tracking under different slip conditions.

It has been shown (_{p} and L_{p} satisfy a hyperbolic relationship, given by the following expression

with

with vehicle parameters a and b (longitudinal distance between CoG and front and rear axle, respectively), mass m, wheelbase L, acceleration of gravity g, understeer coefficient η, rear axle cornering stiffness C_{α2}, and vehicle speed V. Data for vehicle parameters as used in model analysis are given in annex A1. Observe that this relationship does not include the curve radius, as indicated earlier. As a consequence of relationship (3), a higher preview length leads to a smaller steering gain. This can also be explained from Figure

Functional relationship driver model with vehicle and path observation.

In case of nonlinear axle characteristics, we use the Magic Formula (MF) model, also known as the Pacejka model (

for lateral axle force F_{yi} in terms of slip angle α_{i} where i = 1, 2 for front and rear axle respectively, and for axle Magic Formula parameters C, B_{i}, D_{i} and E_{i}. Our interest is in the impact of the change from linear axle (with cornering stiffnesses C_{αi} = B_{i}.C.D_{i}) to nonlinear axle characteristics. Tests were carried out for three different tyres, one (1) being a winter tyre and two (2, 3) being summer tyres. The MF-axle data were determined by matching test results with model results, see also annex A1.

It can be shown that, in the case of nonlinear axle characteristics (e.g. for high slip), the parameters K_{p} and L_{p} are also related according to (3) but with A_{1} and A_{2} depending on the steady state lateral acceleration a_{y} (= V^{2}/R):

and where the slip angles are derived from:

We have determined the relationship between preview time T_{p} (= L_{p}/V) and steering gain K_{p} for vehicle speed V = 95 km/h for linear and nonlinear axle characteristics. Results are shown in Figure _{p} – K_{p} curves for linear axles are the same and shown with one curve. Figure _{p} – K_{p} relationship is depending on the nonlinear bodyslip gain β/δ. If that is high, the steering gain is expected to reduce for increasing ay, as indicated in Figure

Preview time versus steering gain for linear and nonlinear axle characteristics and for different lateral accelerations.

Steady state vehicle performance up to large slip.

An important question is how the model parameters can be used for driver state estimation. Large steering gain could be interpreted as a situation of higher workload, or likewise, small preview time. One might assume constant values for gain and preview time throughout a manoeuvre, which is often done. The closed loop simulation is able to follow experimental results more accurately when steering gain and preview time are allowed to change during a manoeuvre, where the combination of steering gain and preview time is expected to follow the hyperbolic relationship cf. (3), or at least be close to it. It was suggested by Pauwelussen (_{p}^{2}. As discussed earlier, we applied equation (1), i.e. we neglected y(t) and took the vehicle path as the path to be tracked. To be more specific and to justify replacing the intended path by the _{p} was found to be small. For shorter preview lengths, the error increases (because the relative contribution of the vehicle path deviation y(t) becomes larger), but the ranking for different driver behaviour in terms of this metric appeared to be maintained.

Matching a linear vehicle model to the test results and taking account of (1), we were able to identify the driver parameters with results as shown in Figures

Preview time vs. steering gain; inexperienced driver (left), experienced driver (right).

Preview time frequency distributions; inexperienced driver (left), experienced driver (right).

A number of observations was made from the previous results:

The results for the experienced driver confirms the hyperbolic relationship defined by (3), whereas the inexperienced driver shows more deviations from that curve. This may indicate that the latter driver needs more time to build up an effective steering response, also yielding larger path deviations.

The average steering gain for the inexperienced driver exceeds that of the experienced driver, and likewise the preview time will be less, also demonstrated in Figure _{p} – frequency distribution moved more to lower T_{p}-values.

Repeating the same path several times resulted for the inexperienced driver to move, in his behaviour, to the experienced driver, i.e. to higher average T_{p}, which could be interpreted as a learning effect.

The second application deals with driving simulator tests where elderly drivers had to follow a route of about 8 km, repeatedly, up to a total driving time between 1 and 1.5 hours. Within this route, the driver had to pass six cornering situations with curve radii of approximately 250 m. The route was equipped with various traffic lights, with (randomly) one of these lights turning red, once per complete round where the driver had to stop. Lateral accelerations were always below 5 m/s^{2}.

In addition to the elderly drivers (age over 70 years), also young drivers (age 20–24 years) and drivers with intermediate age (50–70 years) were participating. For most of the tests, the average preview time tended to increase slightly during the first round, and reduce again at the end of the test (after 1 hour of driving). This might be interpreted as getting familiar with the test at the beginning, and getting tired at the end. On the other hand, there may be an effect of giving information to the driver that the end of the test is near. Test results were not discriminative enough to draw clear conclusions on this. In Figure

Preview time versus average cornering speed, for different drivers (young drivers in red, elderly > 70 in blue, and intermediate between 50 and 70 years in magenta), from Pauwelussen (

Please note that the two examples treated in this chapter 2 are not comparable in the sense that we distinguished between experienced and inexperienced vs. young and elderly. The first example describes driving on a public road, whereas the second example is based on very specific driving simulator tests. Learning effects may be at hand, being not accounted for in the second example.

In this chapter, closed loop performance for the ISO double lane change (DLC, see ISO (_{i}, I = 1, 2, 3) is different for the three different DLC-parts, ranging from 2.5 m at the start up to 3.12 m at the end. The possible path for the vehicle’s CoG (Centre of Gravity) is indicated by a red line.

The Double Lane Change.

The driver should prevent to hit any cone. This means that the vehicle’s CoG should remain at the right side of points A_{1} and A_{4} and to the left of points A_{2} and A_{3} where these points are at least half of the vehicle-width away from the cones. With a vehicle width of 1.81 m (BMW 320i Touring), the first part is quite narrow whereas the final part offers more manoeuvring space, which can be exploited to keep the lateral acceleration low. With additional vehicle drifting, more space is needed to prevent hitting cones. We have chosen a vehicle half-width of w_{1} = 1 m for the first DLC part, and w_{2} = w_{3} = 1.1 m for part 2 and 3, respectively. Consequently, the lateral position of the vehicle’s CoG path has to remain:

The DLC includes two lane-transitions, transition 1 (from first lane to second lane) and transition 2 (back to the first lane). With different geometrical parameters for the three DLC parts, the optimal vehicle behaviour will show a different lateral acceleration history at the two transitions. During each of the transitions, the lateral acceleration a_{y} shows two peaks, with opposite sign. A fair guess is that these peak-values are more or less equal in absolute value for each transition. Starting from that situation, suppose we could reduce one of these absolute values, then one would expect the other peak-value to increase, reducing the maximum allowable vehicle velocity to pass the DLC due to increased tyre slip. In addition, one would like to have the maximum lateral acceleration values to spread out along a larger part of the transition. A more local extreme a_{y} means a higher |a_{y}| – value, which we try to avoid. This brings us to the suggestion of a piecewise constant lateral acceleration history for each transition, which is expected to be close to a real optimal a_{y} – performance. For the path between DLC part 1 and part 2, this means that it consists of two circular arcs with the same radius, assuming a constant vehicle speed. We call this the theoretical path. Hence, we define as the

The path connecting part 1 and part 2 of the DLC, just hitting points A_{1} and A_{2}, satisfying the conditions under (8), consisting of two circular arcs with radius R_{1}, with the value of R_{1} as large as possible.

In the same way, one can define the theoretical path for the second transition with circular arc radius R2, where both parts of the total theoretical parts must match smoothly (position and orientation). It is assumed that the vehicle starts at lateral position y = 0 while entering the lane change. At the end of the lane change, ending at position y = –h_{3} + w_{3} will result in the lowest R_{2} – value. We have determined the theoretical path based on these circular arcs and their radii, as shown in Figure ^{2}/R = 5.23 and = 4.48 m/s^{2}. Observe in Figure

The theoretical path, based on circular arcs. Red lines indicate the positions of the cones. Blue lines are the boundaries for the vehicle CoG as defined in (8).

Clearly, no driver can steer a vehicle through a DLC with piecewise constant a_{y}. What we have done next is follow this theoretical (target) path with the vehicle with nonlinear axle characteristics (cf. annex A1) and driver model cf. (1), with τ = 0.05 s, and with model parameters K_{p} and L_{p} chosen such that the final vehicle path is just (not) hitting the points A_{1} – A_{4} from Figure

The total test period lasted several days where both experienced test drivers and nonprofessional (but highly skilled) drivers would carry out the DLC-test for different tyres. In order to make the manoeuvre more challenging at not too high speed, most tests were carried out where the offset between the lanes was set at 5.5 m instead of 3.5 m. During the first day, however, when professional test drivers would carry out this task, the track humidity was judged to be too high for this increased offset and the offset remained 3.5 m. With the intention to restrict ourselves for this paper to professional drivers, we have decided to focus only on the 3.5 m tests, and such that the axle characteristics cf. annex A1 could be used in comparison with the test results. The speed during these tests did not exceed or was close to 95 km/h.

The optimal path is shown in Figure ^{2}), and the axle steering angle in degrees. Observe the optimal path just ‘touching’ the blue boundaries at the points A_{1} – A_{4}, remaining nicely between these boundaries during the DLC, and showing overshoot at the final part of the lane change before arriving at a straight line condition.

Optimal and theoretical (target) path for tyre 2 during the DLC for 95 km/h (left) and the resulting steering angle and lateral acceleration (right).

The lateral acceleration shows peaks slightly above 5 m/s^{2} during the first transition, and slightly lower values (larger circular arc radius of the theoretical path) during the second transition. This analysis has been repeated for tyres 1 and 3, with results for the three tyres given in Table

Optimal path data for the three different tyres.

Description | Tyre 1 | Tyre 2 | Tyre 3 | |
---|---|---|---|---|

_{y}| [m/s^{2}] |
Maximum lateral acceleration | 5.88 | 5.41 | 5.43 |

_{1} [m] |
Radius circular parts target path, first transition | 117.0 | 96.8 | 105.6 |

_{2} [m] |
Radius circular parts target path, second transition | 131.3 | 151.7 | 153.7 |

_{p} [m] |
Preview length for minimum a_{y} – peak value |
13.6 | 15.0 | 13.6 |

_{p} [rad/m] |
Steering gain for minimum a_{y} – peak value |
0.054 | 0.033 | 0.044 |

For tyre 1 (winter tyre, used under non-winter conditions), one observes that both curve radii (i.e. for the transition from lane 1 to lane 2, and back again) for the target (theoretical) path have reduced, with likewise a higher lateral acceleration value than expected from these curve radii. With 95 km/h, a curve radius of 133.1 m (corresponding to the curve in Figure _{y} = 5.32 m/s^{2}. With R = 117.0 m during the first transition, that would change to 5.95 m/s^{2} being close to the value for the optimal path. For tyres 2 and 3, this situation is different. The ‘calculated’ value V^{2}/R is now in the order of 6.6 – 7.2 m/s^{2} whereas the maximum a_{y} - value for the optimal path is much lower. We have plotted the optimal paths for tyres 1 and 2 in Figure

Optimal paths for tyres 1 and 2.

After the tests, Rating Scale Mental Effort (RSME) scores were determined by the driver. This is a rating scale with 150 mm line marked with several anchor points with a descriptive label such as 26: a little effort, 72: considerable effort. It was stated by Monsma (_{y} – value for the optimal DLC path. In other words, tyres 2 and 3 allow you to pass the DLC with a lower a_{y} (i.e. with a higher speed), which is likely to contribute to a lower driver assessment for tyre 1. According to Monsma (

RSME scores per tyre, test driver and test-speed.

Tyre | Driver | Velocity | RSME |
---|---|---|---|

1 | 1 | Low | 72 |

High | 82 | ||

2 | Low | 36 | |

High | 45 | ||

2 | 1 | Low | 34 |

High | 68 | ||

2 | Low | 30 | |

High | 41 | ||

3 | 1 | Low | 39 |

High | 34 | ||

2 | Low | 14 | |

High | 25 |

Now that we have determined the optimal manoeuvres for the three tyres, let us see how that compares to the actual driving performance from the tests. Remember that the optimal path corresponds to 95 km/h whereas the actual speed will be different and, in most cases, lower. For all test-histories, we have varied the initial lateral position and yaw angles such that the path remains between the blue boundaries as indicated in previous figures and described in (8), with a minimum error with (i.e. as close as possible to) the optimal path for that tyre.

We have selected four representative tests as shown in Table

Selected tests for comparison with optimal path.

Test nr. | Average speed |
Driver | Tyre |
---|---|---|---|

21 | 93.72 | 1 | 1 |

34 | 91.36 | 2 | 2 |

71 | 95.95 | 1 | 3 |

61 | 91.72 | 2 | 3 |

We show the actual vehicle path compared to the optimal path, and the lateral acceleration compared to the lateral acceleration for the optimal path. Tests and optimal path were set to start at time = zero at a distance 50 m before the end of the first part of the DLC (x = –50). We start with the first two tests, see Figures _{y} values. Compared to tyre 1 and 2, tyre 3 was rated for a lower workload as indicated in Table

Test results compared to optimal performance for test 21 (tyre 1, driver 1).

Test results compared to optimal performance for test 34 (tyre 2, driver 2).

Test results compared to optimal performance for test 71 (tyre 3, driver 1).

Test results compared to optimal performance for test 61 (tyre 3, driver 2).

We conclude that a significant difference is observed between optimal performance and the test-results for the different tyres and drivers. The humid conditions may have played a role, but the resulting axle characteristics have been determined by matching with the vehicle test results under the same conditions. For driver 1, the variation in RSME scores and in test performance seem to be consistent where, for the best rated tyre, the test performance was close to optimal performance.

In chapter 2, we described the impact of high slip on the steady state relationship between closed loop driver model parameters K_{p} (steering gain), L_{p} (preview length) and T_{p} (preview time). The examples showed applications, where the combinations of steering gain and preview time were discussed, with possible attribution to closed loop stability. It was shown by Pauwelussen (_{y} for fixed vehicle speed of 95 km/h, and for the nonlinear vehicle parameters from annex A1 for tyre 2, see Figure

Closed loop stability boundaries for different ay-values and fixed curve radius.

Let us next apply the driver model (1) to the double lane change manoeuvre where we allow the preview time and steering gain to vary along the lane change, to be determined by comparing the real steering angle with the steering angle following from (1). In more detail, we have determined the preview time and steering gain parameters for each following 0.1 second during the double lane change, for all tests, where we have determined T_{p} and K_{p} from time periods of 0.25 second (

Typical output is shown in Figures _{p} correspond to the situation where the driver is approaching the end of the first part of the lane change before moving to the second lane, and the second part of the lane change at the second lane, just before moving back to the first lane. In Figure _{p} vs. K_{p} assuming linear axle characteristics. One observes that the (T_{p} – K_{p}) values during the lane change closely follow this hyperbolic relationship closely, according to our findings in chapter 2, with some outliers. Please note that the values for T_{p} and K_{p} correspond to different lateral accelerations and therefore different closed loop stability boundaries during a DLC manoeuvre.

Variation of preview time during the double lane change.

Preview time T_{p} vs. steering K_{p}.

The driver model response can be illustrated by plotting the preview position together with the vehicle path and the lane change path. The lane change path is taken as the mid-points between the cones, with a smooth (sinusoidal) transition between the lanes. The preview position corresponds to point A in Figure _{p} in Figure

Preview positions for the ISO double lane change for a professional driver.

Each combination of driver, tyre and speed was applied at least six times, and we have determined the mean of the average T_{p} value for these six tests, denoted as T_{p}-average. Please note that the T_{p} score is not a judgement by the driver but a result of the manoeuvring during the lane change. One could say that this is a kind of ‘footprint’ of the driver, whereas the RSME scores is based on subjective judgement. That means that we are comparing the driving performance (the ‘footprint’) of the driver with his own judgement.

Lower preview time leads to higher steering gain. If, under extreme lane change conditions, a higher steering gain can still be interpreted as higher workload, one would expect a negative correlation between average preview time and the RSME scores. Both T_{p}-average and RSME are shown in Figure _{p} average and RSME. We have also considered the results for the afternoon, when the road had become less humid, resulting in a less challenging testing task for these professional test drivers. RSME scores varied between 10 and 82 in the morning with a score of 80 corresponding to considerable to great effort, see also Table _{p} was found to be reduced (from [0.45–0.62] to [0.41–0.53]).

RSME versus T_{p} (average), professional test drivers, day 1, morning.

The correlation between RSME and T_{p} was found to be significant in the morning. Values were found of –0.81 for driver 1 and –0.66 for driver 2, determined from tests with low and high speed. In the afternoon, the correlation for driver 2 has totally disappeared. But also the variation in RSME values has become very low (less than half of the variation in the morning), confirming the fact that weather conditions were too good to be discriminative for the three different tyres.

If one considers T_{p}-average and RSME scores for the different tyres and the speed conditions, as shown in Figures _{p} scores show in general an increasing score and a good distinction between low and high speed. Tyres 2 and 3 resulted in higher average preview time, compared to tyre 1. For tyre 3, the T_{p} scores were lower than those for tyre 2. Tests for tyre 3 were carried out when the road was getting more dry. As a result, the workload was rated as low, shown by the RSME scores being less than 40. These low RSME scores were not only due to the possibly better performance by tyre 3, but also by the improved test conditions. The T_{p} values appear all to be quite similar, near 0.55 s. The standard deviation for the T_{p} score varied for most of the tests between 0.01 and 0.03 s. Consequently, some overlap between low and high speed scores, especially for driver 1 could be expected.

T_{p} (average) scores for different tyres, and speeds (professional drivers).

RSME scores for different tyres and speed (professional drivers).

The RSME scores for the professional drivers tend to overlap as well, as also reported by Monsma (

We give some results for the nonprofessional drivers, having carried out the DLC with a larger offset, and for better road conditions. The values for T_{p}-average were determined by a single set of average tyre characteristics for the different tyres. Nonprofessional drivers were divided in different groups, with drivers no. 5 and 6 testing at day 3, drivers 7 and 8 testing at day 4, and drivers 9 and 10 carrying out the severe DLC at day 5 (notation cf. Monsma (_{p} for day 3 is shown in Figure _{p} corresponding to low speed. Especially for driver 6, the correlation is very good. Observe that driver 5 tends to score at higher level than driver 6. Unfortunately, the results of drivers 9 and 10 showed less correlation, especially driver 10. This may be driver specific, since they are less experienced. For these drivers, further analysis revealed that the T_{p}-value gives a good distinction between low and high speed, and between tyre 1 and both tyres 2 and 3, but not between the two summer tyres 2 and 3. The RSME scores appeared not to show such clear distinction, especially for high speed (with RSME scores almost all close to 70). In terms of the research by De Waard, one could say that, for high speed, these drivers are in the overload region with maximum workload, i.e. no variation to lower workload values.

RSME vs. T_{p} (average), nonprofessional test drivers, day 3.

We have examined double lane change behaviour for professional drivers, with the objectives to understand optimal lane change performance and the difference between this optimal performance and the driver test results. In addition, we have examined driver model parameters as a possible indication of driver mental workload by comparing them with the so-called RSME ratings. The experimental part of these investigations is based on tests, carried out within the scope of the PhD research by Saskia Monsma (

It is possible to determine optimal lane change performance, i.e. the performance for minimum lateral acceleration.

Test drivers do not always follow the optimal path. Sometimes they do and sometimes they don’t, in the latter case with larger lateral acceleration than necessary. Tests were carried out under humid road conditions (being accounted for in the axle characteristics). Results suggest the match with the optimal path to be improved for a drier road.

Under non-extreme conditions, path tracking driver model handling parameters such as steering gain and preview time are related to one another. They follow a hyperbolic relationship where different combinations yield the same closed loop handling behaviour. For extreme conditions with high slip, a similar hyperbolic relationship is found (confirmed by the test results), being close to the relationship for low slip. Preview time is observed to vary during the lane change, which can be interpreted as the driver model to switch attention to the next lane, at both transitions of the lane change.

Closed loop stability drops quite dramatically with increasing slip.

It appears that mental workload has an effect on the driver model parameters preview time and steering gain, even under extreme handling conditions. This has been observed earlier under normal driving conditions where experienced and non-experienced drivers were compared. It has also been observed during simulator experiments where the driving skills of elderly drivers were examined. Hence, the path tracking driver model can be used as a virtual sensor to estimate mental workload, which has now been extended to high slip conditions.

We have introduced a predictive parameter T_{p}-average. This is the mean of the average preview time values for repeated Double Lane Change tests for a specific combination of test driver, selected tyres and speed. Increased workload (characterized by RSME-scores) appeared to correspond to reduced T_{p}-average. This was true for tests discriminating between low and high workload conditions (i.e. with sufficient range in the RSME scores). Some situations occurred where the test conditions were not challenging enough. Also in case of overload for the driver (i.e. high workload for all tests, as occurred for a set of tests with non-professional drivers), no clear relationship between RSME and T_{p}-average was found. In both cases, the range of RSME was small. This confirms the findings of De Waard (

Professional test drivers are experienced in judging tyres in a reproducible way. We noticed that most batches of tests for a specific tyre showed a high level of reproducibility but some did not. It is therefore recommended to collect and analyse more similar data under DLC conditions, including the available non-professional DLC data.

We close this paper with the statement that the presented approach (i.e. using the driver model as virtual sensor, in the sense that driver model parameters are determined by matching a closed loop driver-vehicle model with the actual vehicle performance, and applying them as a measure for mental workload) has a significant value for driver state assessment under every day practical traffic conditions. Interpreting high steering gain as increased workload indicating a potentially risky situation, one might be able to support the driver effectively to relax such situations. Think of special target groups such as elderly drivers. The paper shows that even for an extreme double lane change manoeuvre, this approach gives meaningful results.

The additional file for this article can be found as follows:

Vehicle parameters and double lane change data. DOI:

For this research, we are indebted to Saskia Monsma of the HAN University of Applied Sciences, for using the test data that have been derived earlier through her PhD research. I also like to thank one of the reviewers for suggesting to include figure

The author has no competing interests to declare.