Driving Risk Field and Control Strategies for Autonomous Vehicles at a Signalized Intersection

. Driving pattern has been increasingly researched to improve driving safety and develop autonomous vehicles. Oriented towards the complex infrastructures at signalized intersections, this research digs into the risk sources brought by diferent kinds of road elements, including road lane markings, road curbs, median separators, signal timing, and neighboring vehicles around the ego car. Referring to vehicle speed both in the longitudinal and latitudinal dimensions, risk scope and distribution are quantifed with the vehicle position of a torus with a Gaussian cross-section. Ten, the risk is summed over all the road elements across all the points involved by the ego car, the level of which should be controlled within the threshold value when the ego vehicle explores to minimize trip delay. Tus, autonomous driving strategies are developed with respect to vehicle speed and steering angle. Te proposed model is validated with NGSIM data, where a signalized intersection on Peachtree Street is selected and vehicles moving in diferent directions are analyzed. It is found that the proposed model manages to control vehicles with risk at the accepted level and to enhance the speed level as well as reduce acceleration fuctuations. Tis research contributes to improving autonomous driving against complex driving conditions for driving safety and efciency.


Introduction
Driving through signalized intersection is a complex task, where drivers are required to pay close attention to many interruptions and obstacles, either from the road infrastructures (e.g., the yellow/white solid/dotted lanes) or from the neighboring vehicles [1,2]. Ego vehicles observe and immediately respond to these road elements with vehicle state adjustment in both speed and steering angle for safe driving, from which driving patterns can be explored for the development of autonomous driving. With the accumulated literature on signalized intersection safety, driving risk evaluations and controls through signalized intersections are increasingly improved to promote more efcient response strategies.
Driving risks at signalized intersections have long been explored for driving safety and accident reduction. Statistically, there are over 50% injuries and fatalities that occur near the signalized intersections, where driver errors are the leading cause [3]. Based on the k-means cluster analysis and hierarchical Bayesian random intercept models, driver injury severity patterns of intersection-related crashes fnd that drivers' behavioral adjustment to sophisticated external environmental conditions may compensate for crash loss but to unstable degrees. Motivated by the complex interactions between the driver and the environment, studies have been increasingly accumulated, e.g., for the risk perception of roundabouts [4]. Safety performance functions have been established to predict crash frequencies and reductions with countermeasures on risk exposure. To explore the impact of driving behaviors, negative binomial models are developed to explore the relationships of driving crash frequency with the factors of average annual daily trafc, speed, deceleration, acceleration, right-turn lanes, left-turn signal phase, and red-light camera, where right-turn lanes are negatively correlated to crash frequency, while left-turn signal phase has a positive association with crash frequency [5]. On the confict between right-turn vehicles and pedestrian at signalized intersection, male and young pedestrians as well as the ones that have waited for a long time take more risks [6]. At the onset of yellow light at signalized intersections, drivers may behave with low-risk or high-risk, where the former are only slightly disturbed by phone calls and more prone to stop when close to the stop line [7].
Referring to the theory of feld and potential, driving risk feld (DRF) has been introduced into the evaluation of vehicle operation risk. DRF is validated to be correlated to the driver's perceived risk and manual driving behaviors in terms of steering angle and speed [8]. Based on the framework of artifcial feld theory to treat all the obstacles to the subject vehicle as a fnite scalar risk feld, a better basis to access driving safety is established, which considers the uncertainty over future ambient trafc state and the magnitude of crash consequences with the target vehicle in some position at a certain speed [9]. At signalized intersections, the efect of yellow light on driving risk feld has been carefully addressed [10]. Consequently, the vehicle trajectory planning model is developed to address driver's dilemma at yellow light. With the advancement of connected automated vehicles, we may employ the DRF method based on accurate real-time data to help adjust vehicle states by considering the inhomogeneous coefcients of vehicle geometry and direction [11]. Simulation-based confict analyses have also been established for signalized intersection, where comparison is implemented between the simulated and feldmeasured conficts for safety assessment [12].
Te response strategies to the risks at intersections have also been extensively studied. For minimal fatalities and property loss in crashes, infrastructure-cooperative intersection accident warning system has been developed to predict vehicle state evolution based on dynamic Bayesian networks for temporal stochastic process, with the input of the factors of trafc light state, vehicle position, speed, acceleration/deceleration, and heading, as well as driver's behavioral variable. Te model is validated to warn the driver when potentially dangerous driving behaviors are detected [13]. For driving safety and efciency as well as fuel saving, deep reinforcement learning is employed to train the connected and automated vehicles, which can accurately communicate with the surrounding vehicles and signal light, from the scratch for cooperative vehicular operation at signalized intersections on the simulation platform [14]. A generalized critical turning point-based hierarchical decision-making and planning method is developed in various shapes of intersections with median strips and multiple road lines, which is calibrated with real-driving dataset [15]. Furthermore, to examine whether the advanced driving warning system has increased risky behaviors, the hierarchical logistic regression model and the random forest algorithm are developed to fnd that, when the driver is distracted, speeding, or driving in high-density trafc, the likelihood of hard-braking behaviors can be signifcantly increased [16]. Te motion-planning method with intelligent driver model for autonomous vehicles has also been developed to drive through unsignalized intersections, where future vehicle states are predicted with appropriate clearance and time of collision [17].
When looking onto the complex driving conditions on the urban roads, we are motivated to examine the combined efects of all kinds of road elements, including road lane lines, median barriers, road signs, access, intersection geometry, and signal control, in addition to the moving elements such as neighboring vehicles [18,19]. Despite the accumulated research in driving risk, still there are few works attempting to reveal the vehicle risk at signalized intersection, a typical motorized environment [20]. Te response strategies to the established risks from the abovementioned road elements are also called for to fexibly address all kinds of obstacles to the ego vehicle [21,22], that is, the vehicle should follow the pipe defned by road furniture or road markings and to keep distance from the neighboring vehicles on the same or diferent lanes, under the objective of minimal trip delay with driving risk at the reasonable level [23]. Tus, a comprehensive analysis framework is established to decode the efect of diferent types of road elements on driving risks and lay a foundation for the development of autonomous driving for safety and efciency.
Te contributions of the research are three-fold. First, all the basic elements at a typical signalized intersection are analyzed with respect to the possible risks they bring about. Tese elements include the static ones, including multiple road-lane lines, road curbs, median separators, turning curves, and signal timing. Risk from each element is decoded, which decreases as the ego vehicle moves away from them, with the probability of the ego vehicle at each neighboring point obeying Gaussian distribution. Second, response strategies from the ego vehicle are established to avoid the abovementioned obstacles, where the signal driving strategy is developed to address the dilemma caused by yellow light, and the longitudinal and latitudinal driving strategies are proposed for vehicle state adjustment. Furthermore, the proposed risk quantifcation method and the obstacle response strategies are validated with the NGSIM data [24], proving its accuracy and efciency of guiding the vehicle to move downward safely.
Te remaining of the research is organized as follows: Section 2 illustrates the risks source of all kinds of road elements at a typical signalized intersection and risk distribution against vehicle state of direction, speed, and steering angle, Section 3 establishes the response strategies of vehicles against diferent scenarios, considering the operation constraints to the ego vehicle of either road geometry, road markings, signal timing, and neighboring vehicles, Section 4 employs NGSIM data to validate the proposed risk evaluation method and obstacle response strategies, and Section 5 briefy concludes the study with the research plan in future.

2
Journal of Advanced Transportation Figure 1 shows the layout of typical signalized intersections, including both static and moving road elements. It is observed that the lane lines on the approach change from dotted white to solid white around tens of meters upstream of the stop line. Amber double solid lane lines are employed to separate the vehicles of opposite directions. Signal light controls the movement of straight and left-turning vehicles, while the movement of right-turning vehicles is not controlled. Here, the interruptions from pedestrians and bicyclers are not specifcally considered for model simplifcation. Instead, we focus on the movable elements of neighboring vehicles either on the same or diferent lanes. Te basic assumptions of the research are as follows:

Conceptual Framework and Basic Assumptions.
(1) Only vehicles are considered for moving road elements, while pedestrians and bicycles are not considered. Signal control includes green light, amber light, and red light, without fashing light. (2) Autonomous driving system may accurately observe the dynamics of neighboring vehicles and the design of the road infrastructures against stable communication conditions, based on which driving risks can be accurately calculated to develop vehicle control strategies. (3) Autonomous driving system explores to minimize travel delay through the signalized intersection with driving risk not higher than the threshold. Figure 2 gives the basic procedure of implementing the analyses of driving risk feld at the signalized intersection. First, the research scope is defnes vehicle trajectories, which are extracted for left-turning, straight, and right-turning trafc. Ten, the static and moving road elements around the ego vehicle are identifed as risk source, the risk distribution of which is quantifed in proportion to the distance between the ego vehicle and each road element. In the following, we will dig into the efects of each road element on driving adjustments for driving safety and efciency.

Lane Markings.
Lane markings can be categorized into various types, which can be yellow or white and solid or broken. Yellow lines separate trafc in the opposite directions, whereas the broken yellow lines can be crossed if necessary, while solid yellow lines should never be crossed. White lines separate the lanes in the same direction, whereas the broken white lines mean that one may move across it when safe, while the solid white lines require one to stay in the lane. Figure 3 shows the cost of crossing diferent lane markings. It is observed that, crossing white broken lines brings the least cost, followed by crossing yellow dotted lines, while crossing the white solid lane brings appreciable cost due to the penalty of violating trafc rule and crossing a yellow solid line corresponds to even higher cost [25]. Parameters C ws and C ys are employed to represent the cost of wheel rolling on the solid white lane line and solid yellow lane line, respectively; and parameters C wd and C yd mean the cost of moving onto white dotted and yellow dotted lines.

Median Separator and Road Curb Stone.
Vehicle collision with median separator can cause serious damage to both the vehicle and separator, the cost of which is demonstrated in Figure 4 against diferent kinds of road median separators. Hitting the green division or metal division may cause the vehicle's serious deformation and wheel damage, similar to the collision with the curb stone in Figure 5.
Note in the literature, one may introduce the defnition of road boundary potential fled, which extends to infnity as the ego vehicle approaches the road curb or median separator [26]. Actually, the cost of colliding with the road boundary can be quantifed with the average cost, instead of being set infnite. Tat is closely related to vehicle class and speed. Te confict severity can be given by the following: where M represents the expected confict severity and v represents the vehicle speed. Tat is, the larger the vehicle's actual mass and the higher the vehicle's speed, the higher the expected confict severity. Te cost of colliding with road boundary is given by the following: where parameter E b represents the unit cost of colliding with road boundary per equivalent vehicle weight.

Road Signs.
Road signs guide vehicles to operate on the proper path at suitable state, including vehicle weight, height, and speed. For example, if one vehicle runs at the speed higher than the limit, it may receive a speeding ticket or fail to be controlled in case there is emergency. Terefore, vehicles may only operate not higher than the speed limit and always keep the rule. Te cost of breaking the trafc rules by road signs can be given by the following: where n refers to the nth signs faced by the ego car, E sn refers to the unit cost from violating the trafc rule given by sign n, and d sn means the degree level of violating trafc rules. For example, if the speed limit is set at 50 km, 10% higher than the limit is not punished, while speeding between 10% and 20% is punished to a lesser degree than that between 20% and 30%, etc.

Signal Light.
Te potential feld of signal light starts ahead of the stop line. Te frst road segment involving driving cost is the dilemma zone, where vehicles have diffculty in both moving through and stopping ahead of the stop line [27]. If the vehicle chooses to stop ahead of the stop line at the yellow light, the distance that the vehicle drives through can be given by the following: where v 0 is the initial vehicle speed, τ 1 represents the reaction time to brake, and d means the maximum deceleration speed. Instead, if the vehicle chooses to move through the intersection, the maximum distance that the vehicle can drive through is given by the following: where τ 2 is the reaction time to decide to drive through, a is the maximum acceleration, τ is the yellow time interval, W is the intersection width, and L is the vehicle length. Te dilemma emerges when X s > X c , as shown in Figure 6. In contrast, if X s ≤ X c , the driver may choose to stop or to move downstream of the stop line.
In the case of X s > X c , when amber light is on, if the ego vehicle is more than X s from the stop line, the ego vehicle should choose to stop. Tus, the cost of moving past the stop line at the second that yellow light turns on (i.e., C syr ) is set sufciently large. Otherwise, if the distance of it from the stop line is less than X s , the ego vehicle may adjust the driving state to seize the chance to move through the stop line. Tus, the risk from yellow light is given by the following: where X d represents the distance of the target vehicle from the stop line. Parameters C M and C X represent randomly large driving cost, and adjustable driving risk, respectively.

Moving Road Elements and Potential Field.
Here, we focus on the vehicular dynamics for simplifcation because the description of pedestrian and bike crossings can make the model much more complex. Referring to the Yukawa potential [28] proposed in physics, short-range force is employed here to describe the interactions among the surrounding vehicles, risks from which pose direct efect on the driving strategy of the ego vehicle. Figure 7 shows the vehicles that directly interact with the ego car (i.e., the green one). In addition to the leading and following vehicles of the ego car on the same lane, the vehicles most close to the ego vehicle on the adjacent lanes are also included, that is, the vehicles not behind and the vehicle immediately behind the ego car on the adjacent lane are considered as the related moving elements. Note the moving elements may change from time to time as vehicles change lanes. Tus, the related moving elements should be selected each time interval.
Note the collision cost between the ego and the neighboring vehicles is also dependent on the vehicle speed, which is given by the following: where the parameters M e and M n refer to the equivalent mass of the ego vehicle and its neighboring vehicles, considering their speed, and parameter e v refers to the unit cost of vehicle collision per equivalent vehicle weight.

Risk Distribution of Road Elements.
With vehicle longitudinal and lateral speed, if the driver fails to control the vehicle in time, it may run onto road obstacles or markings and be involved with diferent driving costs. Tus, the risk source of road elements can be delivered to the ego vehicle when their distance is shorter than the following: where d x0 and d y0 are the distances traveled by the ego vehicle after it recognizes the driving cost and manages to brake to stop in the lateral and longitudinal direction, respectively, parameters v x and v y are the vehicle speeds in the lateral and longitudinal directions, respectively, T represents driver's reaction time, and ε is the stop distance between the ego vehicle and road elements.
Parameters v x and v y are given by the following: where parameter δ is the vehicle heading angle, which is initiated with the road angle and updated using the following: where δ 0 refers to the vehicle heading angle in the previous step, parameter k represents the coefcient of vehicle angle adjustment, and ∆δ means the diference from vehicle heading to road direction. Te longer the distance between Journal of Advanced Transportation the ego vehicle and the road obstacle, the smaller the cost that can be added to the vehicle. Tus, driving risk from diferent road elements to the ego vehicle is given by the following: where parameter C n refers to the cost from the n th road elements in the previous section, d x and d y are the actual distance between the edge of the road cost and the ego vehicle in the lateral and longitudinal directions, respectively. Te fnal risk incurred by the ego vehicle is given by the following:

Probability Distribution of Vehicle Position.
Tis research takes the method of a torus with Gaussian crosssection to calculate the probability of the ego vehicle moving to the position (x, y), which is then multiplied with the risks caused by diferent road elements. Tat is, the total risk for the ego vehicle can be given by the following: where z xy represents the probability of the ego vehicle moving to point (x, y), given by the following [29]: which is a torus with a Gaussian cross-section. Parameter a is the height of the Gaussian, d xy is the distance between the risk point and the ego car point, R is the vehicle turning radius, and σ is the Gaussian width. Gaussian height a is given by where p is the slope of Gaussian curve, s is the curve length between the risk point and the car position, and v is the vehicle speed. Curve length is given by where R represents the circle radius of the ego vehicle, and θ is the angle intersected by the lines connecting the circle center (x c , y c ) and the ego vehicle position (x, y) or connecting the circle center and the risk position (x′, y′). Circle radius R is given by the following:    Journal of Advanced Transportation where φ is the vehicle steering angle to be updated with the new vehicle heading angle, given by the following: where φ 0 refers to the vehicle heading angle in the previous step and dt means the length of the control step. Te distance between the vehicle and the risk point in equation (14) is given by the following: Gaussian width σ is given by the following: where i represents the inner and outer side of the vehicle, i.e., i � 1 for the inner side and i � 2 for the outer side, parameter q is Gaussian width slope, k i is the slope of the variability brought by vehicle steering angle of the inner and outer side of i � 1 or i � 2, and parameter c is the Gaussian width at the vehicle location, which is related to the car width (w) and takes the value of w/4 to make ± 2σ account for 95% risk. Figure 8 shows the logic framework for vehicle response strategies against the potential feld from various road elements. For the trajectory of the ego vehicle, the involved trafc elements, static or moving, are outlined with their potential risks. Ten, the critical problem of evaluating the driving strategy at signalized intersection is to identify the phase switch from green light to yellow light, at which the driving risk increases greatly if the vehicle cannot move through the remaining distance from the stop line. Tus, the signal driving strategy is developed frst to examine the cost exerted by the start of yellow light. In the following, the longitudinal driving strategy is developed to guide the vehicles to operate on the same lane or change onto the adjacent lanes. Ten, the latitudinal driving strategy takes the decisions from signal and longitudinal driving strategies to return the vehicle speed and steering angle. Figure 9 shows the relationship of signal, longitudinal, and latitudinal driving strategies. First, the signal driving strategy explores to take stronger acceleration or smaller headway. Ten, the longitudinal driving strategy explores vehicle intention of car-following, lane-changing, and accelerating based on the current vehicle state. Te requirements from signal and longitudinal driving strategies are incorporated into latitudinal driving strategy against the objective of minimal driving delay and proper risk level via adjustment in vehicle speed and steering angle. Figure 10 illustrates the signal's driving strategy. When yellow light turns on, if the ego vehicle is following some car, it may explore for smaller headway if possible. If the ego vehicle is the leading car, it may take stronger acceleration than in the general case as long as the speed is not higher than the speed limit to seize the yellow light. Figure 11 shows the longitudinal strategy to control vehicle states in diferent situations. Referring to road conditions, the driving state of the ego vehicle is extracted, to which the adoption of signal driving strategy is judged frst. If there is no additional driving strategy, we come to the point to judge if there is leading vehicle of the ego car. If the ego car is leading on the current lane, it will explore for the possibility of acceleration; if the ego car is following another car, it will search for a faster lane, which means that the leading vehicle on the adjacent lane runs at a higher speed. If there is a faster lane and the lane-change gap is available, the ego car will come to the latitudinal driving algorithm; otherwise, the ego vehicle continues to follow the leading car on the current lane.

Driver's Algorithm.
Taking the decisions from signal driving strategy and longitudinal driving strategy, latitudinal driving strategy is developed together with speed adjustment. Tat is, driving strategies from signal and longitudinal state just add general guide to the vehicles, instead of accurate directions on vehicle state changes. When it comes to latitudinal driving strategies, vehicle speed and steering angle are optimized against the specifc driving risk feld. Figure 12 shows the framework of latitudinal driving strategy. When the perceived driving risk is lower than the threshold and vehicle speed is lower than the speed limit, the algorithm explores to enhance vehicle speed within the speed limit, where parameter ∆ vn means the increase in the rate of vehicle speed in the n th situation; if the signal driving strategy is adopted to require more stronger acceleration, ∆ vn can be set at a larger value as indicated with n � 1; if not, ∆ vn takes a small value with n � 2. If the perceived driving risk is higher than the threshold, while the speed limit is not reached, we may explore the necessity of deceleration, i.e., whether steering itself may reduce driving risk to the expected level. Tis is achieved by performing grid search, an optimization algorithm that is computationally efcient to return a satisfying solution, especially to the sophisticated  Is the car following some car?
Follow the leading car.
Take stronger acceleration Is speed higher than limit?
Keep the acceleration Release accelerator and stay at the limit problems with noise or nonsmoothness. Grid search frst generates uniform grid inputs for the objective function to identify the areas of the search space that deserve more attention. Ten, each variable is enumerated in turn, from which the best performing point is identifed and reported.
Tus, the optimal steering angle at the vehicle's current speed is explored and returned. If the optimal θ manages to reduce the risk lower than the threshold and deceleration is not necessary, vehicle steering angle is updated for risk equal to threshold, and vehicle speed increases within the limit. Otherwise, if deceleration is necessary, vehicle speed decreases in proportion to the gap between risk threshold and risk at current, and steering angle takes the value to reduce risk to the risk threshold. Furthermore, if vehicle risk is higher the threshold and speed is higher than the limit, vehicle decelerates proportional to the gap both in risk and speed.

Scenario Design.
NGSIM database is adopted on Peachtree Street (Atlanta) for detailed car trajectory, which was collected between 12:45 p.m. and 13:00 p.m. on November 8,2006. Vehicle trajectories are recorded, with realtime speed, acceleration, x and y position, the following/ leading car, time headway, spacing headway, and time stamp with the interval of one-tenth second. Figure 13  Taking the northbound approach for example, solid yellow line is set in the road center to separate the vehicles in the opposite direction. Te frst lane on the northbound approach is exclusively for left turning, which is marked with the central solid yellow line and the right-side white solid lane. Te second lane is exclusively for straight vehicles, which is separated with dotted lane line from the third lane that serves both straight and right-turning vehicles. Te frst lane connects to the left-turning curve, which starts immediately downstream of the pedestrian crossing, while the third lane connects to right-turning curve, which is parallel to the curb stone. Figure 14 shows the trajectory of vehicles on each lane of the selected intersection, where the coordinates of road elements are identifed. Figure 15 gives the signal timing control of the four phases, the cycle of which is 95 s with all-red time being 1.9 s. Note the green light for left turning on the 10 th street starts at the 36 th time interval. Figure 16 shows the procedure to preprocess vehicle data and to extract vehicle trajectory. Data preprocessing is implemented with respect to the vehicle speed change, vehicle displacement, and vehicle steering angle. Te range of reasonable steering range is calculated with the maximum steering angle of 20 degrees, and the ratio of steering wheel and wheel turning being 50. With the processed data, data are selected with vehicle position on y axis no more than 400 feet, which fully covers the selected intersection. Vehicles are

Journal of Advanced Transportation
Next step until the last step identifed with the attributes of vehicle ID, total frames count, vehicle length, vehicle width, vehicle origin, and vehicle destination. Te frame count of each vehicle is calculated with the last frame ID minus the frst frame ID. Table 1 summarizes the parameters of risk modeling of diferent road elements, with the parameter values of the Gaussian torus borrowed from the literature [23]. Table 2 gives the parameter values of driver's algorithm, which are obtained with grid search by establishing support vector machine for the regression of these model parameters for maximal likelihood. In this step, 70% of the selected data are employed for model training, while the remaining 30% are employed to test the proposed model.

Results and Discussions.
Tis section analyzes the results of the proposed driving strategy against the developed driving risk feld from the comprehensive road elements at the signalized intersection. Figure 17

Data filter for the selected intersection
Position on Y axis y≤400 (feet) Intersection ID ≤1

Data pre-processing
Is speed change in the reasonable range [-30,15]  Save data from n1 to (n2-1) as the trajectory of one vehicle Y N Figure 16: Te framework for extracting vehicle trajectory and data preprocessing.    open to more freedom to adjust operation trajectory. Tus, there is smaller space for the autonomous driving strategies to make use of higher speed of left-turn vehicles, where acceleration fuctuation is the most reduced with persistent and reliable control.

Conclusions
Driving safety is basic to every driver, for whom driving efciency is also pursued. In this process, drivers must respond to various interruptions and follow the constraints posed by all kinds of road elements, either movable or nonmovable. With the increasing research on driving risk evaluation and driving assistance system, the comprehensive model of driving risk feld has been developed to refect the efect of various road elements on vehicle operation, instead of being limited to one or a few elements. Tis research extends the theory of driving risk feld at the signalized intersection, where driving risks from all kinds of road lane lines, neighboring vehicles, and signal timings are analyzed systematically. Te cost of each kind of road lane lines is analyzed based on the possible cost from touching or crossing the road element. Specifcally, the cost of passing the solid lane line is evaluated with the penalty of violating the trafc rule, while the cost of colliding with the road curb is evaluated with the cost to vehicle damage and to road furniture repair. Te cost of signal timing is carefully addressed since the start of the yellow light, when the vehicle may have difculty in deciding to move across the stop line to stop upstream of it. Moreover, the cost from the  neighboring vehicles is calculated with reference to the short-distance force theory, where the nearby vehicles are recognized to be following or leading the ego vehicle on the same lane or on the right/left-side lane.
In the following, driving strategy against various driving risks is developed. First, the control framework is developed to examine vehicle's distance to diferent road elements and the state of signal light. Ten, the longitudinal and latitudinal driving strategies are developed to respond to the constraints on vehicles' downward movement and to the constraints on vehicles' adjustment within or beyond one lane. Model calibration and validation is implemented based on NGSIM data of an urban street, where a typical four-legged signalized intersection is selected. After preprocessing of the selected data, the parameters are calibrated for the proposed model. Te accuracy of the proposed model is evaluated with RMSE for the vehicles on all the legs of the selected intersection. It is found that, the accuracy of the proposed model is lower on the intersection approach compared to that on the exit, with RMSE being 14.2%, 19.3%, and 11.6% for vehicle speed, longitudinal position, and latitudinal position on the approach, compared to 16.9%, 19.7%, and 23.1% on the exit. Tis can be explained with more driving freedom on the intersection exit.
Limitations of the research are three-fold. First, driving behavior and driver's characteristics are not specifcally considered in the proposed model, which may afect drivers' perception and evaluation of road risks to cause the difference in the driving strategy adoptions. Second, the infuence of pedestrians and bicyclers is not addressed for model simplicity, which may radically change the driving mechanism. For example, when the driver senses the possibility of colliding with a man or a rider, he may change driving trajectory much earlier and fully secure the gap between the planned trajectory and the predicted confict points. Tird, the proposed model should be further validated in extensive road conditions, validating its performance against diferent driving environments.
Future research may extend the research to incorporate the impact of driver's characteristics into the evaluation of and response to the driving risk feld, to better refect driving dynamics along the selected road. Another fruitful avenue is to integrate driving assistance system into the driving risk feld to guide vehicles to better adapt to the changing road environment for safety enhancement, especially against immediate interruptions.

Conflicts of Interest
Te authors declare that they have no conficts of interest.