# Predicting Driver Takeover Time in Conditionally Automated Driving

Jackie Ayoub, Na Du, X. Jessie Yang, Feng Zhou Jackie Ayoub and Na Du
contributed equally. Corresponding author: Feng Zhou.J. Ayoub and F. Zhou are
with the Department of Industrial and Manufacturing, Systems Engineering, The
University of Michigan, Dearborn, 4901 Evergreen Rd. Dearborn, MI 48128 USA
(e-mail: {jyayoub, fezhou}@umich.edu).N. Du is with the Department of
Informatics and Networked Systems, School of Computing and Information,
University of Pittsburgh, 135 N Bellefield Ave, Pittsburgh, PA 15213 USA
(e-mail: na.du@pitt.edu).X. J. Yang is with Industrial and Operations
Engineering, University of Michigan, Ann Arbor, 500 S State St, Ann Arbor, MI
48109 USA (e-mail: xijyang@umich.edu).Manuscript received Nov 17, 2020;
revised xxx 26, 2020.

###### Abstract

It is extremely important to ensure a safe takeover transition in
conditionally automated driving. One of the critical factors that quantifies
the safe takeover transition is takeover time. Previous studies identified the
effects of many factors on takeover time, such as takeover lead time, non-
driving tasks, modalities of the takeover requests (TORs), and scenario
urgency. However, there is a lack of research to predict takeover time by
considering these factors all at the same time. Toward this end, we used
eXtreme Gradient Boosting (XGBoost) to predict the takeover time using a
dataset from a meta-analysis study [1]. In addition, we used SHAP (SHapley
Additive exPlanation) to analyze and explain the effects of the predictors on
takeover time. We identified seven most critical predictors that resulted in
the best prediction performance. Their main effects and interaction effects on
takeover time were examined. The results showed that the proposed approach
provided both good performance and explainability. Our findings have
implications on the design of in-vehicle monitoring and alert systems to
facilitate the interaction between the drivers and the automated vehicle.

###### Index Terms:

Transition of control, predictive modeling with explainability, human-
automation interaction.

##  I Introduction

The SAE Level 3 automation allows drivers to take hands off the wheels, move
feet off the pedals, and engage in non-driving-tasks (NDTs) when the automated
mode is on [2]. However, when the vehicle reaches its operational limit and is
not able to handle the driving scenario, the driver is required to take over
control of the vehicle within a given time to negotiate the scenario safely
(see [3, 4, 5, 6]). Takeover time is one of the critical measures quantifying
the performance of takeover transitions.

Previous literature evaluated takeover timeliness and takeover quality to
assess drivers’ takeover performance [7, 8, 9]. Takeover time assesses the
temporal dimension of takeover performance and is typically defined as the
time between the TOR and the first maneuver of takeover actions, (e.g., gaze
response time, eyes-on-road time, hands-on-wheel response time) [1, 10].
Different thresholds have been used to capture the first takeover maneuver and
the most commonly used threshold is 2∘ of steering rotation or 10% of pedal
inputs, whichever is quick [9, 11, 12]. Previous studies have investigated the
effects of different factors on takeover time [13, 14, 9]. For example,
drivers responded quickly with less cognitive workload [13] and alcohol
consumption increased takeover time [15].

While those relationships provide an estimation on the direction takeover time
changes in different conditions, they did not show what the estimated takeover
time was under different takeover scenarios by examining various variables at
the same time. Without knowing that, the system may not be able to provide
critical situation awareness information needed (e.g., why a TOR is issued and
how the takeover should be handled) at the right time to help negotiate the
takeover process [16]. Thus, it is critical to build a computational model to
accurately predict takeover time during the transitions from automated driving
to manual driving.

In this paper, we developed an explainable machine learning model based on
XGBoost (eXtreme Gradient Boosting) [17] and SHAP (SHapley Additive
exPlanations) [18, 19] to predict takeover time in conditionally automated
driving by aggregating 129 previous studies. XGBoost is one of the most
successful machine learning models based on gradient boosting machines and has
been widely applied in different areas [20, 21]. Thus, we used XGBoost to
predict takeover time with all the possible variables identified in the
literature. However, XGBoost is a black-box machine learning model, which
makes it difficult to understand the contributions of different critical
factors in predicting takeover time. Therefore, in order to explain the
XGBoost model, we used SHAP, which has proved to provide locally accurate and
consistent explanations [19] based on Shaply values in game theory [22]. After
identifying the most important variables, we were able to select only a small
number of critical variables to predict takeover time with better performance
and explainability (globally and locally) compared to previous studies.
Globally, the model was able to rank the involved variables based on their
contributions to takeover time prediction. Locally, the model explained
individual instances with good accuracy. Such insights can be used to develop
an adaptive in-vehicle alert system during the takeover transition period to
improve driving safety in conditionally automated driving. As a summary, the
contributions of this study are:

  * •

We modeled the relationships between numerous predictor variables and takeover
time using explainable machine learning models (i.e., XGBoost and SHAP).

  * •

We used XGBoost to improve the predictive power of the model compared to other
models (e.g., linear regression).

  * •

We used SHAP to improve the explainability of XGBoost by feature selection and
by providing both global (i.e., main and interaction effects) and local
explanations (i.e., individual instance explanations).

  * •

We identified critical relationships between predictor variables and takeover
time, which paves the way to personalize takeover time prediction in specific
scenarios.

##  II Related Work

###  II-A Factors Influencing Takeover Time

Prior research has examined many factors that influence drivers’ takeover
time, such as takeover lead time [13, 23], TOR modality [24, 25], NDTs [14,
26], driving environments [9, 13], and drivers’ characteristics [14, 27, 28].
Takeover lead time refers to the time to collision at the time of the TOR [7].
According to previous meta-analyses [7, 29], an increase of 1 s in takeover
lead time generally led to a 0.2 to 0.3 s increase in takeover time. Yet, such
effects may disappear when the lead time is short. It may be because the short
lead time triggers reflexive and quick responses. With regard to TOR modality,
multi-modal TORs led to shorter takeover time compared to uni-modal ones [24,
25]. Among uni-modal TORs, visual TORs engendered longer takeover time than
auditory or vibrotactile ones [24].

NDTs influence takeover time through different perspectives. Compared to NDTs
involving handheld devices, NDTs with mounted devices led to shorter takeover
time because drivers could directly control the vehicles without putting down
the devices in their hands [23, 26, 30]. While visual NDTs lengthened takeover
time, auditory NDTs produced similar takeover time compared to conditions with
no NDTs [26, 31]. When NDTs induced drivers’ different types of emotions and
cognitive load, their effects on takeover time became complex [8, 12, 13, 14,
32]. For example, some studies found that drivers’ cognitive load and
emotional valence/arousal did not influence takeover time [8, 13, 32], while
others found that higher cognitive load lengthened the reaction time in
steering maneuvers but not braking maneuvers [12, 14]. Further exploration is
needed to address how NDTs interact with other variables to influence takeover
time.

Driving environments such as traffic density, scenario types, and weather are
other important variables that influence takeover time [9, 13, 31, 33, 34].
When the traffic was in the same direction, studies found that heavy traffic
increased takeover time [9, 31]. However, heavy oncoming traffic was found to
reduce eyes-on-road reaction time when drivers were in low cognitive load
[13]. With regard to scenario types, Du et al. [33] found that lane changing
scenarios induced shorter takeover time compared to lane keeping scenarios
because lane changing scenarios had more contextual cues for drivers to
process and the situations looked more urgent.

Drivers’ characteristics, such as age and automation experience, also
influence takeover time [27, 35, 36, 37]. For example, Zeeb et al. [35] found
that repetitive exposure to takeover transitions reduced drivers’ hands-on-
wheel and eyes-on-road reaction time. The effects of age on takeover time were
not consistent. Li et al. [37] found that older adults had longer takeover
time compared to younger adults. In contrast, Korber et al. [36] and Clark et
al. [27] did not found any significant differences of takeover time during
different age groups. Further studies are needed to investigate the effects of
age on takeover time.

Despite the fact that the studies reviewed provided useful information on how
different variables influence takeover time, it is difficult to estimate the
exact takeover time at a specific takeover scenario. Hence, it is necessary to
develop computational models to predict drivers’ takeover time under various
takeover conditions.

###  II-B Existing Models on Takeover Time Prediction

Existing studies have utilized cognitive architecture, linear and non-linear
regression to model driver takeover time [1, 29, 38]. Deng et al. [38] built
the queuing network-adaptive control of thought rational (QN-ACTR) cognitive
architecture to model takeover time. The model used drivers’ task-specific
skills and knowledge as production rules and capacities of human mental
processing as algorithms and parameters. The prediction reached $R^{2}$ of
0.96, root mean square error (RMSE) of 0.5 s, and mean absolute percentage
error (MAPE) of 9% in six empirical experiments. Gold et al. [29] modeled
takeover time using data from six driving simulator experiments (753 takeover
situations). The thresholds of maneuver start were set as 2° steering wheel
angle change or 10% brake pedal actuation. According to variable analysis
results, time-budget, traffic density, repetition, lane position and driver’s
age were selects as predictor variables to model takeover time using a
generalized non-linear model. The model obtained RMSE of 0.81 s, adjusted
$R^{2}$ of 0.43, and deviation of 0.1 - 0.7 s using a validation dataset from
another five additional studies. Zhang et al. [1] reviewed 129 studies (520
takeover events) on takeover time with SAE Level 2 - 3 automation. A linear
mixed model was developed with automation level, TOR modality, NDT modality,
hand occupation, situation urgency, and other road users as dummy variable
inputs. The model showed goodness-of-fit measures (log likelihood) of 132.2,
Akaike’s Information Criterion (AIC) of 136.2, and Schwarz’s Bayesian
Criterion (BIC) of 144.6.

##  III Methodology

###  III-A Dataset

The dataset used in this study was based on a meta-analysis study,
investigating the variables affecting takeover time [1]. A total number of 129
studies were reviewed including conference proceedings, journal articles,
technical reports, posters, and Ph.D. or master theses.

Figure 1: The distribution of 519 takeover time using a bin width of 1 s.

As a result, 18 variables were identified to influence the takeover time as
shown in Table I. The identified variables were related to drivers (i.e., age,
cognitive load, and drivers’ response), automated vehicles systems (i.e.,
level of automation, simulator fidelity), TOR modality (i.e., visual,
auditory, and vibrotactile requests), NDTs (i.e., visual, auditory, and
motoric NDTs), interactions with other road users, and the urgency of the
situation (i.e., urgency, time budget to collision, and time budget to other
boundaries). Only the studies that used the same calculation method of
takeover time were selected. Takeover time was defined as the time interval
between the initiation of the takeover stimulus (i.e., the onset of the TOR or
the start of an environmental event that can initiate driver takeover) and the
moment of driver intervention (by means of braking, steering, or button
pressing). The identified takeover time ranged from 0.69 s to 19.79 s and its
distribution was shown in Fig. 1. Since only one takeover time value was
larger than 8.7 s (i.e., 19.79 s), this value was considered as an outlier and
was excluded from this study.

TABLE I: Variables identified through literature review that influenced
takeover time.

Abbreviation | Feature Description | Scale
---|---|---
AGE | Mean age of the participants. | Years
LAD |  | The level of automated driving where in L2, drivers’ are in charge of the monitoring task and in L3 and above,
---
drivers’ are not needed to monitor the task.
0 = L2; 1 = L3 and above
SIM |  | The low fidelity simulator is either desktop based or computer monitors. The medium fidelity simulator is either
---
a simulator with more than 120 deg horizontal field of view or an
instrumented-cabin simulator.
The high fidelity simulator is either a real car or a simulator with motion
platform.
| 0 = low fidelity; 1 = medium fidelity;
---
2 = high fidelity
TOR_V | Whether a visual TOR exists. | 0 = no; 1 = yes
TOR_A | Whether an auditory TOR exists. | 0 = no; 1 = yes
TOR_VT | Whether a vibrotactile TOR exists. | 0 = no; 1 = yes
TOR_P | Whether a TOR is present. | 0 = no; 1 = yes
NDT_V | Whether the NDT is visual. | 0 = no; 1 = yes
NDT_A | Whether the NDT is auditory. | 0 = no; 1 = yes
NDT_M | Whether a hand operation is needed to perform the NDT. | 0 = no; 1 = yes
NDT_C |  | NDTs requiring working memory are considered as high cognitive load, or they are normal cognitive load.
---
| 0 = normal cognitive load; 1 =
---
high cognitive load
HAND | Whether a device is handheld while performing the NDT. | 0 = hands-free; 1 = handheld
NDT_P | Whether a non-driving task is present. | 0 = no; 1 = yes
TBTC |  | Time budget from the initiation of the TOR until the collision with an obstacle.
---
Seconds
TBTB |  | Time budget from the start of the TOR until reaching the boundaries of the automated system
---
other than collision.
Seconds
URG | Whether a potential urgency exists. |  | 0 = low urgency (TBTC $>$ 15 s);
---
1 = medium urgency (8 s $<$ TBTC $\leq$ 15 s);
2 = high urgency (TBTC $\leq$ 8 s)
DRE |  | Drivers’ response in a low complexity situation include taking over control on a straight road by stabilizing
---
the vehicle in its lane. In a medium complexity situation, the TOR requires a
specific driver response
(e.g., road narrowing, curvy road, road construction, decelerating vehicle
ahead). In a high
complex situation, drivers’ need to decide whether to brake or steer in
response to the event.
| 1 = low complexity; 2 = medium
---
complexity; 3 = high complexity
IRU |  | Whether an interaction with other road users exists during the takeover process.
---
0 = no; 1 = yes

Note the obtained takeover time was the mean takeover time reported in each
condition of the reviewed studies, and it is the response variable to be
predicted in our study using the XGBoost model. The ground truth is the mean
takeover time collected in the meta-analysis study [1]. The corresponding
independent variables associated with that takeover time were considered as
the predictor variables. The prediction process was done by training the
XGBoost model on predicting the ground truth of takeover time using the
corresponding independent variables. The dataset was in a tabular format and
the total number of instances for training and testing was 519. In order to
reduce the percentage of the missing values, dummy variables were used for
many variables. For instance, a visual TOR was coded as ”0” if the TOR was not
visual and ”1” otherwise. Moreover, the time budget to collision and the time
budget to other boundaries variables were combined into one variable since
they both represented the time from the initiation of the TOR to reaching the
longitudinal or lateral boundaries. Finally, missing values accounted for
9.67%.

###  III-B XGBoost Model Development

In this study, we used XGBoost [17] as a regression model to predict the
takeover time. One of the motivations of using XGBoost in predicting the
takeover time is that it provides a great performance with less computational
resources. XGBoost has the advantage to model automatically high order
interaction and to handle missing values in the dataset. Another motivation is
that the predictions of the XGBoost model can be explained using SHAP. The
combination of XGBoost and SHAP provides both good performance and
explainability of the takeover prediction. The XGBoost algorithm is a scalable
learning algorithm composed of an ensemble of decision trees. The learning
process was designed to minimize the objective function by iteratively
splitting each tree and giving more weights to the accurate ones. The main
idea of XGBoost is to build the regression model by adding one tree at a time
to minimize the objective function. The objective function is composed of a
loss function calculated between the predicted and actual values and a
regularization term to avoid over-fitting. XGBoost is scalable to different
applications and is able to handle missing values without an imputation
preprocessing in this study. In addition, XGBoost builds trees using parallel
computing, and thus it runs much faster than the traditional gradient tree
boosting models [39].

Given a dataset $D=\\{x_{i}^{k}$, $y_{i},i=1,...,N,k=1,...,M\\}$, where $M$ is
the number of the predictor variables (i.e., 18 in total in this study) and
$N$ is the number of the observations (i.e., 519 observations in this study),
the XGBoost algorithm aims to minimize the following objective function:

$L^{(t)}=\sum_{i=1}^{n}l(y_{i},\hat{y_{i}}^{(t-1)}+f_{t}(x_{i}^{k}))+\Omega(f_{t}),\\\
$ (1)

where $n$ is the number of the training samples,
$\hat{y_{i}}^{t}=\hat{y_{i}}^{(t-1)}+f_{t}(x_{i}^{k})$ is the prediction at
the $t$-th iteration, $f_{t}(x_{i}^{k})$ is the $t$-th tree to be added, and
$\Omega(f_{t})$ is the regularization term to avoid over-fitting. The learning
process starts by iterating over all the features of the training data. Then,
a split reduction loss is calculated for each tree to obtain the optimal split
having the minimum reduction loss. In order to make predictions, an output
value is calculated for each leaf of the tree to make the final predictions.

In this work, the XGBoost regressor was trained with a 10-fold cross-
validation strategy and using an optimized search for hyperparameters. The
optimized hyperparamters were: subsample, colsample, learning_rate, max_depth,
n_estimators. In addition, we ran the 10-fold cross-validation 100 times
(i.e., random state $=0-99$) to stabilise and obtain optimal results from the
XGBoost regressor.

###  III-C XGBoost Model Evaluation

To compare model performance, four metrics were used including RMSE, Mean
Absolute Error (MAE), Adjusted $R^{2}$ (short for Adj. $R^{2}$), and
correlation coefficient (Corr) between the predicted values and ground truth.
RMSE is defined as the square root of the mean squares of the difference
between the predicted and actual value, and it changes from $0$ to $\infty$
(see Eq. 2). It indicates how close the observed data points are to the
model’s predicted value. The lower the RMSE the better the model fits the
data. MAE is defined as the mean absolute difference between the predicted and
actual values, and it changes from $0$ to $\infty$ (see Eq. 3). It indicates
the average magnitude of the errors in a set of predictions, and the lower the
MAE, the better the model predicts the mean takeover time. Adj. $R^{2}$ is a
revised version of $R^{2}$ by adjusting the number of predictor variables. It
measures the explanatory power of the regression model (see Eq. 4). It usually
changes from 0 to 1, with 0 indicating that the proposed model does not
improve the prediction and 1 indicating perfect prediction. Corr represents
the strength of the linear relationship between the predicted takeover time
and the ground truth. It changes from -1 to +1, with -1 indicating a perfect
negative correlation and +1 indicating a positive correlation.

$RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(y_{i}-\hat{y_{i}})^{2}},\\\ $ (2)

$MAE=\frac{1}{N}\sum_{i=1}^{N}|y_{i}-\hat{y_{i}}|,\\\ $ (3)

$Adj.R^{2}=1-(1-R^{2})\frac{N-1}{N-M-1},\\\ $ (4)

$Corr=\frac{\sum_{i=1}^{N}(\hat{y_{i}}-\bar{\hat{y}})(y_{i}-\bar{y})}{\sqrt{\sum_{i=1}^{N}(\hat{y_{i}}-\bar{\hat{y}})^{2}\sum_{i=1}^{N}(y_{i}-\bar{y})^{2}}},\\\
$ (5)

where N is the total number of the observations, M is the total number of the
predictor variables,
$R^{2}=\frac{\sum_{i=1}^{N}(\hat{y}_{i}-\bar{y})^{2}}{\sum_{i=1}^{N}(y_{i}-\bar{y})^{2}}$,
$y_{i}$ represents the $i$-th actual value, $\mathit{\hat{y}_{i}}$ represents
the $i$-th predicted value, $\mathit{\bar{y}}$ is the average of all the
actual values, and $\bar{\hat{y}}$ is the average of the all the predicted
values.

###  III-D SHAP Explanation

Explanability is key to the adoption of a machine learning model. It improves
people’s trust in model predictions. Ayoub et al. [40, 41] demonstrated that
showing why and how the predictions were made was necessary for users to trust
the model. SHAP explains model predictions by using the Shapley values from
game theory [22]. The Shapley value represents the contribution of each
variable in pushing the model prediction from the expected value (see Eq. 6).
The unit of the SHAP value is the same as the prediction space which is in
seconds in this work. In the case of XGBoost, each predictor variable is
assigned with an importance value based on their contribution to the final
prediction.

$\phi_{i}(\upsilon)=\sum_{S\subseteq
N\backslash\\{i\\}}\frac{|S|!(M-|S|-1)!}{M!}(\upsilon(S\cup\\{i\\})-\upsilon(S)),\\\
$ (6)

where $N$ is the set of all the predictor variables, M is the total number of
the predictor variables, S is a subset of any coalition of the predictor
variables and $\mathit{\upsilon(S)}$ is the contribution of coalition S in
predicting takeover time in our study.

To explain the predictions of XGboost, SHAP provides global and local
explanations of model predictions. Global explanations provide information
about variable importance ranking, main effects of predictor variables on the
response variable, and interaction effects between predictor variables on the
response variable, whereas local explanations help understand individual
predictions by showing the variables contributing to the obtained prediction.
The interaction effect is defined as the effect of the combined variables
minus the main effects of the individual variables in Eq. LABEL:ph.

$\displaystyle\phi_{i,j}(\upsilon)=\sum_{S\subseteq
m\backslash\\{i,j\\}}\frac{|S|!(M-|S|-2)!}{M!}$ (7)
$\displaystyle(\upsilon(S\cup\\{i,j\\})-\upsilon(S\cup\\{i\\})-\upsilon(S\cup\\{j\\})+\upsilon(S)).$

##  IV RESULTS

###  IV-A XGBoost Performance

The performance metrics of the XGBoost prediction model including RMSE, MAE,
Adj. $R^{2}$ and Corr are shown in Table II using 10-fold cross validation for
100 times with different random numbers (0-99) in Python 3.8. In addition, we
took a data-driven method and used feature selection to identify the best
performance of the model with the current dataset by adding one variable at a
time following the importance ranking of the variables identified in Fig. 2.
We continued this process until RMSE stopped decreasing. RMSE was used as our
main performance measure since it is probably the most popular evaluation
metric used in regression analysis. When the RMSE had the smallest value (with
seven most important predictors in the model), all the other metrics,
including MAE, Adj. $R^{2}$, and Corr had the best performance. Finally, we
found that XGBoost performed the best when a combination of seven variables
(i.e., URG, TBTC&TBTB, AGE, HAND, TOR_V, SIM, IRU was used.

TABLE II: Mean value of the model performance measures while using different
variables.

Variables |  RMSE $\downarrow$ |  MAE $\downarrow$ |  Adj. $R^{2}$ $\uparrow$ |  Corr $\uparrow$
---|---|---|---|---
URG | 1.119 | 0.830 | 0.187 | 0.717
URG, TBTC&TBTB | 0.965 | 0.709 | 0.394 | 0.815
URG, TBTC&TBTB, AGE | 0.851 | 0.560 | 0.528 | 0.867
URG, TBTC&TBTB, AGE |  |  |  |
HAND | 0.828 | 0.538 | 0.552 | 0.875
URG, TBTC&TBTB, AGE, |  |  |  |
HAND, TOR_V | 0.826 | 0.533 | 0.554 | 0.877
URG, TBTC&TBTB, AGE, |  |  |  |
HAND, TOR_V,SIM | 0.808 | 0.518 | 0.572 | 0.883
URG, TBTC&TBTB, AGE, |  |  |  |
HAND, TOR_V,SIM, IRU | 0.806 | 0.505 | 0.573 | 0.883

###  IV-B Global Explanation

####  IV-B1 Variable Importance

To understand the importance of the variables in predicting takeover time, we
examined the SHAP summary plot in Fig. 2. The SHAP values represent unique
variable contribution to each prediction. The variables are ranked based on
their global importance, i.e., $\sum_{i=1}^{N}|\phi_{j}^{(i)}|$, where
$\phi_{j}^{(i)}$ represents the SHAP value of the $i$-th instance of the
$j$-th variable. Each dot in the plot represents a SHAP value for its instance
of one variable. It has four characteristics including (1) the color
represents the value of that variable ranging from low (blue) to high (red),
(2) the horizontal location represents the small or large effect of the
variable on the prediction, (3) the vertical location represents the
importance of a particular variable, and (4) the density shows the
distribution of the variable in the dataset [42]. In Fig. 2, we see that URG
is the most important variable in takeover time prediction, followed by
TBTC&TBTB, AGE, and HAND, and so on. For example, a high level of urgency was
shown to reduce the predicted takeover time by almost 1 s, whereas a low level
of urgency increased the predicted takeover time by almost 1.5 s.
Additionally, we saw variations in the tails of the variables, where the
important variables had a wider tail compared to the less important ones with
SHAP values centered around 0 (e.g., NDT_M, NDT_A, LAD, TOR_P).

Figure 2: SHAP summary plot. Figure 3: SHAP main effect plots. (a) URG (b)
TBTC&TBTB (c) AGE (d) HAND (e) TOR_V (f) SIM (g) IRU. Figure 4: SHAP
dependence plots. (a) URG (b) TBTC&TBTB (c) AGE (d) HAND (e) TOR_V (f) SIM (g)
IRU.

####  IV-B2 Main and Interaction Effects

To further understand the effects of the predictor variables on the takeover
time, we explored the main and interaction effects of the most important
variables (see Figs. 3 and 4). The vertical axis represents the SHAP value
that shows the effects of the variables on the prediction and the horizontal
axis represents the actual value of the variables. In the main effect plot for
URG, the takeover time decreased with increased URG (see Fig. 3a). As for time
budget, an increase in TBTC&TBTB increased the takeover time (see Fig. 3b). As
for the variable AGE, an increasing takeover time was shown until AGE reached
45 years old where the takeover time started to decrease after it was larger
than 45 years old (see Fig. 3c). Hand holding a device while performing NDTs
was shown to increase the takeover time (see Fig. 3d). The existence of a
visual TOR was shown to increase the takeover time (see Fig. 3e). Driving
simulators with a high fidelity seemed to reduce the takeover time compared to
those with a low or medium fidelity as seen in Fig. 3f. An interaction with
road users increased the takeover time (see Fig. 3g).

A certain extent of vertical dispersion at single values of the predictor
variables was noticed in the main effect plots. Such dispersion represents the
interaction effect of the predictor variables with other variables
automatically identified by SHAP. To reveal these interaction effects, a
second vertical column was added to the right side of the main effect plots
(i.e., SHAP dependence plots) in Fig. 4. Each dot represents a single
prediction from the dataset. The first vertical axis on the left represents
the SHAP value of the studied variable, which represents how much this
variable can change the output of the takeover time. The horizontal axis
represents the value of the variable. The color corresponds to a second
variable on the right that has an interaction effect with the variable. The
interaction is presented as a distinct vertical pattern of coloring. By
plotting the values of two predictor variables in the dataset, we can see how
they interact. For instance, in Fig. 4a shows that among the situations with a
low or medium level of urgency during the takeover, those with visual TORs
increased the takeover time compared to those with non-visual TORs. However,
among the takeover situations with a high level of urgency, those with non-
visual TORs increased the takeover time compared to those with visual TORs. In
Fig. 4b, among the situations with a low time budget to collision or to other
boundaries (time budget $\leq$ 15 s or so), non-visual TORs increased the
takeover time compared to the visual TOR, while no such effects were observed
when the time budget $>$ 15 s or so. As for the variable AGE, a larger time
budget increased takeover time for those between 30 and 45 years old while a
larger time budget decreased takeover time for those smaller than 30 years old
as shown in Fig. 4c. As for the variable HAND, a larger time budget increased
the takeover time when holding a device in their hands performing NDTs while a
larger time budget tended to decrease the takeover time when the participants’
hands were free during NDTs (see Fig. 4d). In addition, the interaction plot
of TOR_V showed that when the TORs were not visual, a high urgent situation
increased the takeover time compared to a low urgent situation. However, when
the TORs were visual, a high urgent situation decreased the takeover time
compared to a low urgent situation (see Fig. 4e). As for the simulator
fidelity, for takeover scenarios that took place in simulators with a low or
medium fidelity, a high urgency decreased the takeover time while for those
happened in simulators with a high fidelity, a high urgency increased the
takeover time (see Fig. 4f). As for the variable IRU, there was not a clear
interaction effect, possibly due to small effect size, though TOR_V was
selected (see Fig. 4g).

###  IV-C Local Explanation

To explain individual predictions using SHAP, we randomly selected three cases
as illustrated in Fig. 5. The provided explanations show different variables
pushing the predicted takeover time from the base value (i.e., average
prediction over the training data) to the output value (i.e., predicted
takeover time). Thus, each value of a specific predictor variable will either
decrease or increase the predicted value from the base value (e.g., 2.716 in
Fig. 5a). For instance, the variables in red (e.g., TBTC&TBTB=15 in Fig. 5b)
pushed the predicted takeover time higher than the baseline while those in
blue (e.g., HAND = 0 in Fig. 5c) pushed the predicted takeover time lower than
the baseline. By aggregating all the contributions to predicting takeover time
from the base value, the actual prediction for these three particular
instances are obtained as shown in Fig. 5.

In the first example (see Fig. 5a), the predicted takeover time is 0.97 s
(ground truth = 0.89 s) and the variables in blue that push the takeover time
low are “TBTC&TBTB = 3.48”, “URG = 2”, “HAND = 0”, and “IRU = 0” while the
variable in red that pushes the predicted takeover time high is “AGE = 41”. In
the second example, the predicted takeover time is 3.91 s (ground truth = 3.94
s) and the variables that push the takeover time high are “TOR_V = 0”, “URG =
0”, “AGE = 40.9”, and “TBTC&TBTB = 15” while the variables that push the
takeover time low are “HAND = 0” and “SIM = 2” (see Fig. 5b). The third
example illustrates that the predicted takeover time is 7.88 s (ground truth =
8.70 s) and the variables that push the takeover time high are “TOR_V = 1”,
“SIM = 1”, “AGE = 38.5”, “URG = 0”, and “TBTC&TBTB = 30” while the variable
that pushes the predicted takeover time low is “HAND = 0” (see Fig. 5c).

Figure 5: SHAP individual explanations of takeover prediction for (a) ground
truth = 0.89 s, (b) ground truth = 3.94 s, and (c) ground truth = 8.70 s.

##  V DISCUSSION

###  V-A Model Performance

In this work, we showed that XGBoost is an effective and efficient model to
predict takeover time during the control transition period in conditionally
automated driving. Our work used the mean takeover time reported in previous
studies based on a meta-analysis study [1]. Collision risks during takeover
are determined by individual takeover time rather than by the mean of the
takeover time. However, the suggested methods in this work can be used as the
baseline model, which can be personalized to predict individual takeover time
based on the individual drivers’ characteristics and specific takeover
scenarios. The performance of the XGBoost prediction model, including RMSE,
Adj. $R^{2}$, MAE, and Corr is shown in Table III, using a 10-fold cross-
validation strategy. We also performed a 10-fold cross-validation to compare
the performance of XGBoost with other algorithms using Matlab Regression
Learner (See Table III). XGBoost performed the best across all the metrics
among the list of the models, including, linear regression, linear SVM, fine
tree, and random forest. Also, we showed how the XGBoost model performed at
different cumulative time bins (See Table IV). Adj. $R^{2}$ was first
increasing and then decreasing after it peaked at 0.625, while RMSE and MAE
(min/max residual, which is defined as the min or max absolute difference
between predicted takeover time and its ground truth) were increasing and
gradually saturated when more samples with larger takeover time were added.
This is possibly because there are increasingly fewer samples with larger
takeover time (4 samples $>$ 6 s). Corr was consistently good across different
cumulative time bins.

TABLE III: Performance measures comparison between different models.

Models |  RMSE $\downarrow$ |  Adj. $R^{2}$ $\uparrow$ |  MAE $\downarrow$ |  Corr $\uparrow$
---|---|---|---|---
XGBoost | 0.806 | 0.573 | 0.505 | 0.883
Linear regression | 0.887 | 0.412 | 0.672 | 0.642
Linear SVM | 0.917 | 0.372 | 0.655 | 0.630
Fine tree | 1.017 | 0.321 | 0.694 | 0.566
Random forest | 0.958 | 0.392 | 0.677 | 0.648

TABLE IV: Performance measures comparison of XGBoost at different cumulative
time bins.

Models (Samples) |  RMSE $\downarrow$ |  Adj. $R^{2}$ $\uparrow$ |  MAE $\downarrow$ |  Min/Max Residue $\downarrow$ |  Corr $\uparrow$
---|---|---|---|---|---
XGBoost 0-2 s (151) | 0.267 | 0.393 | 0.198 | 0.185/0.212 | 0.828
XGBoost 0-3 s (368) | 0.360 | 0.531 | 0.274 | 0.263/0.292 | 0.869
XGBoost 0-4 s (453) | 0.473 | 0.578 | 0.344 | 0.332/0.358 | 0.884
XGBoost 0-5 s (486) | 0.556 | 0.605 | 0.392 | 0.376/0.410 | 0.892
XGBoost 0-6 s (508) | 0.639 | 0.625 | 0.436 | 0.412/0.460 | 0.899
XGBoost 0-7 s (515) | 0.739 | 0.583 | 0.476 | 0.460/0.502 | 0.887
XGBoost 0-8 s (517) | 0.804 | 0.538 | 0.502 | 0.485/0.529 | 0.874
XGBoost 0-9 s (519) | 0.806 | 0.573 | 0.505 | 0.490/0.534 | 0.883

###  V-B Model Explainability

We used SHAP explainer to understand the effect of the variables on the
takeover time by providing global and local explanations. The provided global
explanation helped us rank the variables based on their importance in the
prediction of the takeover time. The importance of the predictor variables
gave us direct guide in variable selection to improve the performance of
XGBoost. We further explored the main and interaction effects of the most
important variables on the takeover time prediction as evidenced in Figs. 3
and 4. For local explanation, SHAP provided prediction results by comparing
the predicted value to a base value as a reference. Also, it showed the
contributions of each variable-value set in pushing the results close to the
ground truth as shown in Fig. 5. Furthermore, we found that the predictor
variables selected were not exactly the same from [1]. In [1], seven variables
were included in their linear mixed model, i.e., LAD, TOR_A, TOR_VT, NDT_V,
HAND, URG, and IRU. Variables that did not have significant effects ($p>0.05$)
on takeover time were excluded from the model. In our work, we used another
variable selection method based on the importance of variables generated from
SHAP. A sequential method by adding one variable at a time from the most
important one was used to select the variables until RMSE stopped decreasing.
The importance ranking was obtained by their prediction contributions based on
SHAP values with local accuracy and consistency [18, 19], which had a solid
theoretical support from game theory. The XGBoost model selected seven
variables as shown in Table II.

URG (Urgency) was shown to be the most important variable in the prediction of
the takeover time. Similarly, Zhang et al. [1] found that URG had the highest
correlation with the takeover time and a shorter takeover time was associated
with a higher level of urgency of the takeover situation. In addition, we
showed that URG interacted with TOR_V (Visual TOR) (see Fig. 4a). At a high
level of urgency, non-visual TORs increased the takeover time compared to
those with visual TORs. This seemed to be counter-intuitive. We examined other
variables when URG $=2$, TOR_V $=1$ and we found that $44.1\%$ instances were
also with driving simulators with a high fidelity while this percentage was
$19.2\%$ when URG $=2$, TOR_V $=0$. In Fig. 4f, driving simulators with high
fidelity reduced the takeover time compared to those with low or medium
fidelity. This might explain the results. At a low or medium level of urgency,
visual TORs increased the takeover time compared to those with non-visual
TORs. This is consistent with previous research that either auditory or
vibrotactile TORs reduced takeover time compared to visual ones [24, 43].

The second most important variable was TBTC&TBTB (Time budget to collision or
to other boundaries). In agreement with previous studies, an increase in time
budget led to an increase in takeover time [29, 7]. Also, TBTC&TBTB were shown
to interact with TOR_V. At low time budget (i.e., high urgency), TOR_V
decreased the takeover time. The variable URG is negatively correlated with
TBTC&TBTB based on the coding protocol, i.e., it was considered as high
urgency, when the time budget $\leq 8$ s, medium urgency when it was between 8
s and 15 s, and low urgency when it was larger than 15 s. This, to a large
extent, explained the interaction effect between TBTC&TBTB and TOR_V.

The relationships between AGE and the takeover time seems complicated (Fig.
3c), which might be one of the reasons that no consistent results were found
in the literature by comparing old with young participants [27, 37, 36]. We
found that 45 was the turning point that for those younger than 45, age was
positively correlated with the takeover time while for those older than 45,
age was negatively correlated with takeover time. However, the majority of the
participants were younger than 45 in the previous studies. More research
should be conducted to understand the behavior of those older than 45 years
old in the takeover transition period. Furthermore, we found that AGE
interacted with TBTC&TBTB (Fig. 4c) when it was smaller than 45. A smaller
time budget decreased takeover time for those between 30 and 45 years old
while a smaller time budget increased the takeover time for those younger than
30 years old. This result might be explained that compared to those under 30,
those between 30 and 45 were more conservative and careful in automated
driving compared to those below 30 [44].

The next important variable was HAND (Hand holding a device). Consistent with
previous studies (e.g., [1]), NDTs with a device in hands increased takeover
time. In Fig. 4d, we showed that HAND interacted with TBTC&TBTB. A larger time
budget increased the takeover time when performing NDTs with a device in
hands. This was in line with [30, 23, 26]. However, a large time budget
decreased the takeover time compared to a small to medium time budget when the
participants’ hands were free during NDTs. This effect was not big by
examining the SHAP values in Fig. 4d.

Our results showed that visual TORs increased takeover time, which was
consistent with previous literature because visual alerts were less
conspicuous compared to auditory and vibrotactile alerts [24]. The interaction
effect between URG and TOR_V was explained in Fig. 4a.

With regard to the simulator fidelity, a high fidelity reduced the takeover
time compared to a low or medium fidelity, which might be explained by the
difference of ecological validity in different types of simulators. In
addition, we found that high urgency decreased the takeover time in low or
medium fidelity simulators, while high urgency increased the takeover time in
high fidelity simulators (see Fig. 4f). This effect seemed not reasonable for
high fidelity simulators. One possible reason is that other factors
potentially played a role and further studies are needed to investigate it.

For IRU (Interaction with other road users), the model showed that the
surrounding traffic increased the takeover time. This was consistent with
previous literature which investigated the effects of traffic in the same and
opposite direction on takeover time [13, 9, 31]. When there was more traffic
in the surroundings, drivers needed more time to scan the environment,
identify the potential hazards, and negotiate scenarios properly. No clear
interaction effects with others were found.

###  V-C Implications

To achieve reliable takeover time prediction, we recommend that the vehicle
should have a systematic record of the driver’s demographic information and
the vehicle’s settings, as well as interior camera/sensors to detect drivers’
NDT status and exterior camera/sensors to determine environment complexity.

The results of our study provide the automotive industry with recommendations
of the most important variables to predict takeover time. According to the
predicted takeover time, adaptive in-vehicle alert systems can be developed to
help drivers to intervene when necessary. For instance, when the model
predicts that it would take drivers 8 seconds to take over control, advanced
driver assistance systems should be initiated to help drivers identify the
potential hazards in the environment and provide them with suggestions to
shorten takeover time and improve takeover quality.

Meanwhile, our method could be potentially employed to predict stabilisation
time and specific driving behaviors following TORs [34], which provide a more
comprehensive description of takeover performance. Broadly speaking, our
findings can facilitate the interactions between drivers and automated
vehicles, enhance driving safety in intelligent transportation systems, and
improve automated vehicle acceptance across the whole population.

###  V-D Limitations

First, although 18 variables were studied in this work, more variables in
literature were identified that affected takeover time. For instance, drivers’
emotional valence, cognitive load, and vehicle speed were found to influence
takeover time and quality [13, 45]. Also, the vehicle operating state (e.g.
traffic flow, acceleration) is another important factor affecting the takeover
time, which can be included for prediction in the future studies.

Second, the takeover time used in this study is based on the mean value.
Collisions during takeovers are usually determined by individual takeover time
and not by the mean of the takeover time. For instance, if the driver was
sleeping during the ride, it might take him/her more time than usual to take
over control. Thus, our study might not be suitable to identify the exact time
span for a safe takeover. However, the proposed model can be used as the
baseline and can be used to predict individual takeover time when personalized
data is collected specific to the driver and the takeover scenarios in the
future. Also, takeover performance is more than takeover time. Drivers’
stabilisation time of both driver state and driving performance indicators, as
well as different driving behaviors need to be considered to quantify takeover
performance comprehensively.

Third, the majority of the studies were conducted in a driving simulator which
might not reflect the real situations and indicate a low external validity of
the study. For instance, Carsten and Jamson [46] discussed that in driving
simulators people’s perceived risk of the situation was lower compared to a
real driving situation.

Fourth, the interaction effects were only shown between two predictor
variables in Fig. 4 and those involving more than two variables were difficult
to illustrate with SHAP. This might explain some of the counter-intuitive
results shown previously.

##  VI CONCLUSION

In this work, we predicted takeover time using XGBoost and SHAP with good
performance and explainability. Compared to previous studies that investigated
the effects of individual factors on takeover time, our model is able to
examine 18 factors at the same time and identified the most important factors
(i.e., URG, TBTC&TBTB, AGE, HAND, TOR_V, SIM, AND IRU) in predicting takeover
time with better performance. In addition, the model is able to show their
main effects and interaction effects on takeover time. Furthermore, our model
is also able to provide explanations about individual prediction instances,
which paves the way to design in-vehicle monitoring systems to improve
takeover performance in conditionally automated driving.

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|  Jackie Ayoub received her B.E. degree in mechanical engineering from Notre
Dame University, Lebanon, in 2016 and her master degree in Industrial and
Systems Engineering from University of Michigan, Dearborn, in 2017. She is
currently pursuing her Ph.D. in Industrial and Systems Engineering in the
University of Michigan, Dearborn. Her main research interests include human-
computer interaction, human factors and ergonomics, and sentiment analysis.
---|---
|  Na Du is an Assistant Professor in the Department of Informatics and
Networked Systems at the University of Pittsburgh. She received her Ph.D.
degree in Industrial & Operations Engineering from the University of Michigan
and Bachelor’s degree in Psychology from Zhejiang University. Her research
interests include human-computer interaction, transportation human factors,
computational modeling of human behaviors, and human-centered design.
---|---
|  X. Jessie Yang is an Assistant Professor in the Department of Industrial
and Operations Engineering, University of Michigan, Ann Arbor. She earned a
PhD in Mechanical and Aerospace Engineering (Human Factors) from Nanyang
Technological University, Singapore. Dr. Yang’s research include human-
autonomy interaction, human factors in high-risk industries and user
experience design.
---|---
|  Dr Feng Zhou received the Ph.D. degree in Human Factors Engineering from
Nanyang Technological University, Singapore, in 2011 and Ph.D. degree in
Mechanical Engineering from Gatech Tech in 2014. He was a Research Scientist
at MediaScience, Austin TX, from 2015 to 2017. He is currently an Assistant
Professor with the Department of Industrial and Manufacturing Systems
Engineering, University of Michigan, Dearborn. His main research interests
include human factors, human-computer interaction, engineering design, and
human-centered design.
---|---