# Driver Behavioral Classification on Curves Based on the Relationship between Speed, Trajectories, and Eye Movements: A Driving Simulator Study

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Apparatus

^{®}Smart Eye) was used in the experiment (Figure 1). It comprised three front cameras that performed the eye-tracking of the driver and an additional rear camera recording the scenes that the drivers see. The eye-tracking was done by recording eye movements and capturing the direction of the gaze, head position, eyelid opening, blinks, attachment points, pupil size, and other monitoring and measurement. Data on the eye movements of 23 subjects were recorded during the experiment. The simulated environment was projected on a 1.40 × 0.80 m flat panel of 1080 p resolution and 60 Hz projection rate, which also projects rear and lateral mirrors and the speedometer. Speakers reproduce sounds similar to vehicle engines and traffic environments to enhance participant immersion with visual and auditory stimuli.

#### 2.3. Experimental Road

#### 2.4. Database

^{®}software [43].

#### 2.5. Data Analysis

- Description of variables:
- ○
- Dependent variables: driving speed, lateral placement, and eye movement information, such as the number of fixations, fixation duration, pupil diameter, and gaze direction.
- ○
- Independent variables: approach tangent lengths and curve radii.

- Factorial ANOVA is an analysis of variance involving two or more independent variables, which is the case of this experiment, as shown in the descriptions of variables above.
- ANOVA with repeated measures consists of an analysis of variance conducted in any design. The independent (predictor) variables were measured using the same subjects under all conditions, which is the case of our experiment. The F-statistic from a repeated measures ANOVA is reported as F (df, df
_{error}) = F-value, p = p-value. The first degree of freedom (df) was calculated as the number of conditions less one, and the second was the product of the first with the number of subjects less one. The following formula explains the F-ratio:$$F=\frac{explainedvariance}{unexplainedvariance}=\frac{M{S}_{conditions}}{M{S}_{error}}$$

- The following tests were performed to check if the assumptions to proceed with the ANOVA with repeated measures were not violated:
- ○
- The Kolmogorov–Smirnov test evaluates if the distribution of scores is significantly different from a normal distribution. A significant p-value indicates a deviation from normality.
- ○
- The Friedman’s ANOVA is a non-parametric test, also known as the non-parametric version of the one-way repeated measures ANOVA. It compares multiple conditions when the same subjects participate in each condition. The resulting data are not normally distributed.
- ○
- The Levene’s test checks if there is any significant difference between the variances of a group and, thus, a non-significant result indicates that the hypothesis was satisfied.
- ○
- The Mauchly test assesses the hypothesis that the variances of differences between conditions are equal. A significant Mauchly’s statistical test (i.e., when it has a probability value less than 0.05), it is conclusive that there are significant differences between the variances of the differences; therefore, the sphericity condition was violated.
- ■
- The Greenhouse–Geisser correction estimates the distance from sphericity. It was used to correct the degrees of freedom associated with the corresponding F ratio when the Mauchly test causes the sphericity condition to be violated.

## 3. Results and Discussion

#### 3.1. Driving Speed

^{2}(9) = 18.37, p < 0.05). Therefore, the degrees of freedom were corrected by Geisser–Greenhouse spherical estimates (ε = 0.58). The test also revealed a significant main effect of curves radii F (2, 469) = 145.55, p < 0.001, Partial Eta Squared = 0.383, and observed power = 1.000, and a non-significant one for approach tangents F (2, 469) = 0.617, p = 0.540, Partial Eta Squared = 0.003, and observed power = 0.153. The ANOVA showed the interaction effect between radii and approach tangent was not significant F (3.466, 173.28) = 2.894, p = 0.055, Partial Eta Squared = 0.055, and observed power = 0.729.

#### 3.2. Lateral Placement

^{2}(8) = 35.06, p <0.001).

#### 3.3. Driver Classification on Curve Trajectories

^{2}(10) = 51.204 (p < 0.001); however, it accepted the null hypothesis of non-association between approach tangent lengths and trajectories classification χ

^{2}(10) = 9.837 (p = 0.455). Testing the association between the trajectories behaviors with the nine curve configurations classes resulted in lower limits of expected frequencies to rely on the Pearson chi-square test.

^{2}(24) = 33.235 (p < 0.05).

#### 3.4. Eye-Movements Data Analysis

^{®}Smart Eye equipment were the number of fixations, their durations, pupil size, and gaze directions regarding the driver’s visual attention. These were assessed in two different ways, i.e., calculated as the polygon area formed by the drivers’ gaze dispersion for each curve configuration and adopting the relation between the standard deviations of the eye-tracking in the X and Y axes.

#### 3.4.1. Fixations

^{2}(2) = 120.139, p < 0.001) and approach tangents (χ

^{2}(2) = 76.712, p < 0.001).

^{2}(2) = 1.246, p = 0.536) and approach tangents groups (χ

^{2}(2) = 2.094, p = 0.351).

#### 3.4.2. Pupil Diameter Analysis

^{2}(2) = 14.174, p < 0.001) and (χ

^{2}(2) = 29.656, p < 0.001), respectively.

#### 3.4.3. Gaze Analysis

^{2}(8) = 156.664, p < 0.001). In general, the average areas tracked increased with radius and approach tangent increase, as seen in Figure 12. A smaller spread of drivers’ field of view was related to a greater focus while performing, indicating that the observed result is in line with the literature since shorter curves and tangents tend to demand more attention from the drivers.

^{2}(8) = 22.483, p = 0.004).

^{2}(2) = 9.368, p = 0.009) and (χ

^{2}(2) = 17.170, p < 0.001), respectively.

## 4. Conclusions

^{2}(8) = 35.06, p < 0.001). The curve trajectories were classified according to lateral position parameters. The incidence of the most dangerous behavior decreased with the increase in the curve radius, supporting the study conducted by Mauriello et al. [7] and consistent with crash statistics, as reported elsewhere. Such first results are in line with those reported in the literature. The most common indicators for successful horizontal curve negotiation (i.e., speed and lateral position) showed a significant association with curve radius but not with the tangent length approach. This signifies their importance as Papadimitriou et al. ranked curve radius as the riskiest factor related to road alignment infrastructure [45]. Further research is necessary to extend the results (e.g., improvements in trajectory classification parameters and development of a multivariate analysis of the variables, such as ordinal logistic regression and inclusion of socioeconomic variables).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Examples of different driving behavior paths. (

**a**) Ideal behavior, (

**b**) Normal behavior, (

**c**) Intermediate behavior, (

**d**) Cutting, and (

**e**) Correcting behavior. The gray lines represent road edges, the red line is the middle line axis, and the blue one is the vehicle’s center of gravity path.

**Figure 13.**Mean Standard Deviation of gaze distributions per curve radii (

**a**) and approach tangent (

**b**).

Treatments | Length (m) | Deflection Angle (Degrees) | Radius (m) | Approach Tangent (m) | Number of Observations |
---|---|---|---|---|---|

Rs-Ts | 182.17 | 56 | 125 | 50 | 56 |

Rs-Tm | 421.63 | 56 | 125 | 310 | 56 |

Rs-Tl | 661.09 | 56 | 125 | 570 | 56 |

Rm-Ts | 182.17 | 56 | 370 | 50 | 56 |

Rm-Tm | 421.63 | 56 | 370 | 310 | 56 |

Rm-Tl | 661.09 | 56 | 370 | 570 | 56 |

Rl-Ts | 182.17 | 56 | 615 | 50 | 56 |

Rl-Tm | 421.63 | 56 | 615 | 310 | 56 |

Rl-Tl | 661.09 | 56 | 615 | 570 | 56 |

Total | 504 |

Curve Configuration | Radius (m) | Approach Tangent (m) | Speed (km/h) | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 77.10 | 1.38 | 0.20 |

2 | Rs-Tm | 125 | 310 | 80.79 | 1.34 | 0.20 |

3 | Rs-Tl | 125 | 570 | 82.93 | 1.31 | 0.03 * |

4 | Rm-Ts | 370 | 50 | 96.05 | 1.61 | 0.20 |

5 | Rm-Tm | 370 | 310 | 96.06 | 1.79 | 0.20 |

6 | Rm-Tl | 370 | 570 | 94.00 | 1.83 | 0.20 |

7 | Rl-Ts | 615 | 50 | 101.03 | 1.41 | 0.20 |

8 | Rl-Tm | 615 | 310 | 100.48 | 1.54 | 0.20 |

9 | Rl-Tl | 615 | 570 | 101.22 | 1.52 | 0.20 |

Curve Configuration | Speed Change Behavior | |||||
---|---|---|---|---|---|---|

SSD | SS | SSI | ||||

Rs-Ts | 32 | (61.54%) | 16 | (30.77%) | 4 | (7.69%) |

Rs-Tm | 44 | (83.02%) | 4 | (7.55%) | 5 | (9.43%) |

Rs-Tl | 48 | (94.12%) | 2 | (3.92%) | 1 | (1.96%) |

Rm-Ts | 22 | (44.90%) | 13 | (26.53%) | 14 | (28.57%) |

Rm-Tm | 29 | (63.04%) | 9 | (19.57%) | 8 | (17.39%) |

Rm-Tl | 40 | (80.00%) | 8 | (16.00%) | 2 | (4.00%) |

Rl-Ts | 14 | (28.00%) | 16 | (32.00%) | 20 | (40.00%) |

Rl-Tm | 16 | (31.37%) | 11 | (21.57%) | 24 | (47.06%) |

Rl-Tl | 31 | (60.78%) | 11 | (21.57%) | 9 | (17.65%) |

Total | 276 | (60.93%) | 90 | (19.87%) | 87 | (19.21%) |

Curve Configuration | Radius (m) | Approach Tangent (m) | DLP (m) | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 0.20 | 0.13 | 0.015 * |

2 | Rs-Tm | 125 | 310 | 0.32 | 0.22 | 0.013 * |

3 | Rs-Tl | 125 | 570 | 0.32 | 0.22 | 0.006 ** |

4 | Rm-Ts | 370 | 50 | 0.27 | 0.20 | 0.000 *** |

5 | Rm-Tm | 370 | 310 | 0.34 | 0.31 | 0.000 *** |

6 | Rm-Tl | 370 | 570 | 0.29 | 0.25 | 0.000 *** |

7 | Rl-Ts | 615 | 50 | 0.30 | 0.21 | 0.000 *** |

8 | Rl-Tm | 615 | 310 | 0.35 | 0.34 | 0.000 *** |

9 | Rl-Tl | 615 | 570 | 0.33 | 0.25 | 0.000 *** |

Class | Approach Tangent | Curve | Total | |
---|---|---|---|---|

1. Ideal behavior | |LP|max ≤ 0.65 or 2.95 ≤ |LP|max ≤ 4.25 ${\sigma}_{LP}\le 0.35$ | |LP|max ≤ 0.55 or 3.05 ≤ |LP|max ≤ 4.15 ${\sigma}_{LP}\le 0.20$ | ||

2. Normal behavior | |LP|max ≤ 0.9 or 2.7 ≤ |LP|max ≤ 4.5 ${\sigma}_{LP}\le 0.40$ |∆LP|max ≤ 1.2 | |LP|max ≤ 0.9 or 2.7 ≤ |LP|max ≤ 4.5 ${\sigma}_{LP}\le 0.35$ |∆LP|max ≤ 1.2 | ${\sigma}_{LP}\le 0.50$ | |

3. Intermediate behavior | 3.1 Driving close to the centerline | |LP|max ≤ 1.0 or 2.6 ≤ |LP|max ≤ 4.6 ${\sigma}_{LP}\le 0.40$ |∆LP|max ≤ 1.1 | ${\sigma}_{LP}\le 0.30$ LPmean > 0.5 | |

3.2 Driving outside in curve approach | 1.0 < |LP|max < 2.6 or |LP|max > 4.6 | |LP|max ≤ 1.0 or 2.6 ≤ |LP|max ≤ 4.5 ${\sigma}_{LP}\le 0.35$ LPmean ≤ 0.5 | ||

4. Cutting | 4.1 Right curves | |||

lane 1 | LPmin < −3.70 | LPmax > −3.2 | ||

lane 2 | LPmin < −0.10 | LPmax > 0.40 | ||

lane 3 | LPmin < 3.50 | LPmax > 4.00 | ||

4.2 Left curves | ||||

lane 1 | LPmax > −3.50 | LPmin < −4.00 | ||

lane 2 | LPmax > 0.10 | LPmin < -0.40 | ||

lane 3 | LPmax > 3.70 | LPmin < 3.20 | ||

5. Correcting behavior | 5.1 in approach | ${\sigma}_{LP}>0.30$ alat_max > 4 m/s ^{2} | - | |

5.2 on the curve | - | ${\sigma}_{LP}>0.30$ alat_max > 4 m/s ^{2} | ||

5.3 multiple corrections | Combination of behaviors 5.1 and 5.2 |

Behavior | Ts | Tm | Tl | Total | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Rs | Rm | Rl | Rs | Rm | Rl | Rs | Rm | Rl | Rs | Rm | Rl | |

1 Ideal behavior | 5.36 | 3.57 | 1.79 | 5.36 | 7.14 | 5.36 | 3.57 | 7.14 | 0.00 | 3.57 | 5.95 | 3.57 |

2 Normal behavior | 41.07 | 28.57 | 25.00 | 30.36 | 21.43 | 30.36 | 28.57 | 21.43 | 39.29 | 31.55 | 27.38 | 29.76 |

3 Intermediate behavior | 7.14 | 3.57 | 17.86 | 10.71 | 1.79 | 5.36 | 19.64 | 23.21 | 16.07 | 9.52 | 5.95 | 19.64 |

4 Cutting | 32.14 | 44.64 | 35.71 | 41.07 | 50.00 | 46.43 | 37.50 | 39.29 | 35.71 | 37.50 | 45.83 | 37.50 |

5 Correcting behavior | 7.14 | 14.29 | 10.71 | 0.00 | 1.79 | 1.79 | 0.00 | 0.00 | 0.00 | 10.71 | 1.19 | 0.00 |

6 Others | 7.14 | 5.36 | 8.93 | 12.50 | 17.86 | 10.71 | 10.71 | 8.93 | 8.93 | 7.14 | 13.69 | 9.52 |

Total | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

Curve Configuration | Radius (m) | Approach Tangent (m) | Number of Fixations | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 44.34 | 10.87 | 0.077 |

2 | Rs-Tm | 125 | 310 | 41.22 | 9.01 | 0.126 |

3 | Rs-Tl | 125 | 570 | 19.26 | 4.99 | 0.002 ** |

4 | Rm-Ts | 370 | 50 | 64.39 | 12.04 | 0.000 *** |

5 | Rm-Tm | 370 | 310 | 71.39 | 14.98 | 0.000 *** |

6 | Rm-Tl | 370 | 570 | 57.43 | 11.57 | 0.000 *** |

7 | Rl-Ts | 615 | 50 | 79.65 | 16.44 | 0.000 *** |

8 | Rl-Tm | 615 | 310 | 74.34 | 18.44 | 0.000 *** |

9 | Rl-Tl | 615 | 570 | 66.48 | 15.80 | 0.000 *** |

Curve Configuration | Radius (m) | Approach Tangent (m) | Fixation Duration (s) | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 0.752 | 0.137 | 0.200 |

2 | Rs-Tm | 125 | 310 | 0.764 | 0.146 | 0.000 *** |

3 | Rs-Tl | 125 | 570 | 0.793 | 0.152 | 0.011 * |

4 | Rm-Ts | 370 | 50 | 0.778 | 0.171 | 0.003 ** |

5 | Rm-Tm | 370 | 310 | 0.792 | 0.198 | 0.011 * |

6 | Rm-Tl | 370 | 570 | 0.767 | 0.169 | 0.021 * |

7 | Rl-Ts | 615 | 50 | 0.773 | 0.142 | 0.000 *** |

8 | Rl-Tm | 615 | 310 | 0.796 | 0.166 | 0.002 ** |

9 | Rl-Tl | 615 | 570 | 0.772 | 0.162 | 0.000 * |

Curve Configuration | Radius (m) | Approach Tangent (m) | Pupil Diameter (cm) | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 0.418 | 0.023 | 0.200 |

2 | Rs-Tm | 125 | 310 | 0.403 | 0.018 | 0.005 ** |

3 | Rs-Tl | 125 | 570 | 0.382 | 0.011 | 0.004 ** |

4 | Rm-Ts | 370 | 50 | 0.363 | 0.018 | 0.000 *** |

5 | Rm-Tm | 370 | 310 | 0.407 | 0.011 | 0.200 |

6 | Rm-Tl | 370 | 570 | 0.403 | 0.024 | 0.000 *** |

7 | Rl-Ts | 615 | 50 | 0.382 | 0.009 | 0.000 *** |

8 | Rl-Tm | 615 | 310 | 0.398 | 0.015 | 0.005 ** |

9 | Rl-Tl | 615 | 570 | 0.393 | 0.027 | 0.000 *** |

Curve Configuration | Radius (m) | Approach Tangent (m) | Area (m^{2}) | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 0.030 | 0.033 | 0.000 *** |

2 | Rs-Tm | 125 | 310 | 0.040 | 0.073 | 0.000 *** |

3 | Rs-Tl | 125 | 570 | 0.056 | 0.241 | 0.000 *** |

4 | Rm-Ts | 370 | 50 | 0.090 | 0.087 | 0.007 ** |

5 | Rm-Tm | 370 | 310 | 0.091 | 0.113 | 0.000 *** |

6 | Rm-Tl | 370 | 570 | 0.121 | 0.192 | 0.000 *** |

7 | Rl-Ts | 615 | 50 | 0.126 | 0.136 | 0.000 *** |

8 | Rl-Tm | 615 | 310 | 0.167 | 0.316 | 0.000 *** |

9 | Rl-Tl | 615 | 570 | 0.124 | 0.147 | 0.000 *** |

Curve Configuration | Radius (m) | Approach Tangent (m) | StdGD | K–S | ||
---|---|---|---|---|---|---|

Average | SD | p-Value | ||||

1 | Rs-Ts | 125 | 50 | 2.07 | 3.60 | 0.000 *** |

2 | Rs-Tm | 125 | 310 | 1.42 | 0.92 | 0.000 *** |

3 | Rs-Tl | 125 | 570 | 1.36 | 1.02 | 0.000 *** |

4 | Rm-Ts | 370 | 50 | 1.69 | 0.87 | 0.023 * |

5 | Rm-Tm | 370 | 310 | 1.41 | 0.65 | 0.004 ** |

6 | Rm-Tl | 370 | 570 | 1.51 | 1.31 | 0.000 *** |

7 | Rl-Ts | 615 | 50 | 1.56 | 0.81 | 0.009 ** |

8 | Rl-Tm | 615 | 310 | 1.39 | 0.75 | 0.045 * |

9 | Rl-Tl | 615 | 570 | 1.13 | 0.59 | 0.000 *** |

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**MDPI and ACS Style**

Rondora, M.E.S.; Pirdavani, A.; Larocca, A.P.C.
Driver Behavioral Classification on Curves Based on the Relationship between Speed, Trajectories, and Eye Movements: A Driving Simulator Study. *Sustainability* **2022**, *14*, 6241.
https://doi.org/10.3390/su14106241

**AMA Style**

Rondora MES, Pirdavani A, Larocca APC.
Driver Behavioral Classification on Curves Based on the Relationship between Speed, Trajectories, and Eye Movements: A Driving Simulator Study. *Sustainability*. 2022; 14(10):6241.
https://doi.org/10.3390/su14106241

**Chicago/Turabian Style**

Rondora, Maria Emilia Schio, Ali Pirdavani, and Ana Paula C. Larocca.
2022. "Driver Behavioral Classification on Curves Based on the Relationship between Speed, Trajectories, and Eye Movements: A Driving Simulator Study" *Sustainability* 14, no. 10: 6241.
https://doi.org/10.3390/su14106241