## 3 Results
### Quantitative Evaluation (Experimental Results)
In normal driving, all are acceptable (as the vehicle remains within the lane at all times). Yet, the improvement obtained by both LC and SC is very similar and much better than for the LK. Note that the LK only acts when the vehicle approaches the lane limits, while the LC acts all the time, providing feedback about any deviation from the lane center. The SC, on the other hand, provides some freedom around the centerline, but gives feedback as the deviation increases, before approaching the lane limits. A lower authority in SC (\(\lambda_{\text{dim}}\approx 1\) Nm) compared to LC (\(\lambda_{\text{dim}}=3\) Nm, see Figure 8e) in normal driving, seems to produce a similar tracking performance. This should be further studied, as having the same performance but with less intervention is an important characteristic that could result in positive acceptance of the SC mode. During the distraction event, the differences are amplified. In general, all driving modes are able to keep within lane boundaries. As shown by the RMS values, even in MANUAL mode all drivers are able to stay within the lane most of the time, which might lead to a false sense of security while performing the secondary task. However, it is also noted that within the 20 events tested in MANUAL mode, all drivers had at least one out-of-boundaries excursion, which is enough to produce an accident. The feedback given by the LK does help to completely avoid these out-of-boundaries excursions during the distraction event and reduces degradation of the ability to stay closer to the center when compared to the MANUAL mode. On the other hand, the LC and SC driving modes are able to maintain tracking performance during the distraction event. In fact, RMS values for angular and lateral errors are almost identical during the distraction event to those during normal driving, except for the lateral error in SC mode, which shows a reduction consistent with the higher automation authority assigned when the driver is not looking at the road. Note that the RMS lateral error follows the behavior of the automation authority, i.e., as the LC RMS lateral error remains the same, during normal driving, when the SC authority is lower than that of the LC, the SC RMS lateral error is higher, while it is lower during the distraction when the authority is larger. This relationship between the authority and the lateral error found in this exploratory study should be further studied with a larger, more representative driver sample. It is also worth noting that the maximum angular errors for both LC and SC increase similarly during the distraction, while the MAX lateral errors decrease. This might be associated with faster corrections by the automated system, which should be further studied. Overall, when driver and automation are collaborating as a \"team\", the tracking performance is improved in comparison with MANUAL, getting closer to the benefits of Automation-only. The safety indicators of Figures 11 and 12 provide a clearer picture of the system behavior under the different driving modes. As expected, the MANUAL mode had the lowest TLC of all modes both for normal driving and during distraction events, closely followed by the LK mode. The main difference is that during distraction all drivers got to cross the lane (TLC MIN \(\approx 0\)) at least once for MANUAL driving, while the LK mode was able to prevent any lane crossing with a minimum TLC of 0.76 s. The benefits of the LK mode are further evidenced by the fact that the time spent in a riskier condition (i.e., with a TLC below a 3.8 s threshold) is noticeably reduced with respect to the MANUAL mode. This effect seems to be enhanced because, when entering a curve (or, more properly, when approaching a curvature change), the NMPC controller predicts the vehicle will approach the lane borders at a future time, providing the driver with an anticipating haptic torque. Moreover, as expected, all driving modes show a lower TLC during the distraction event than when driving normally.