The rapid development of autonomous driving technology is reshaping the future of transportation, with new energy vehicles (NEVs) emerging as a key platform for its implementation. By integrating electrification with intelligent driving systems, autonomous NEVs offer a sustainable and efficient mobility solution. Compared to conventional internal combustion engine vehicles, NEVs benefit from inherently abundant electrical power, which provides a favorable foundation for supporting the high energy demands of autonomous driving systems, including onboard sensors, computing units, and communication modules. Equipped with sophisticated perception, planning, and control algorithms, autonomous NEVs are designed to operate with minimal human input in complex and dynamic traffic environments. Nevertheless, ensuring safe and reliable autonomous operation across diverse real-world driving scenarios remains a significant challenge. The variability of road geometries, unpredictable behavior of other road users, and complex vehicle interactions call for robust and adaptive safety evaluation frameworks. In this context, accurately assessing local driving risks and enabling risk-aware decision-making are critical to enhancing the safety performance of autonomous NEVs and facilitating their large-scale deployment (Gao et al., 2022; Lu et al., 2022).

Evaluating the safety of a vehicle’s actions is a complex task due to the variety of scenarios an autonomous vehicle may encounter. Each scenario—lane changes, following another vehicle, or navigating through intersections—requires specific safety metrics to assess the risks involved accurately. For example, we evaluate lane-change scenarios using the available gap for a safe transition (Chen et al., 2021; Liu et al., 2021), assess car-following scenarios using metrics such as time to collision (TTC), inverse TTC, time-exposed TTC, time-integrated TTC, and time headway (THW) (Mao et al., 2021; Son et al., 2021; Li et al., 2022; Zhang et al., 2022), and evaluate intersection scenarios based on time to intersection (TTI). These metrics are often discrete and context-specific, making developing a unified safety evaluation method challenging.

The indicators mentioned in longitudinal and lateral contexts represent safety distance methods grounded in vehicle kinematics theory, incorporating both space and time dimensions. These methods primarily calculate driving risk through the vehicle’s state information and the relative motion between two vehicles. The simplicity and physical relevance of the parameters, which closely align with a driver’s intuitive understanding of safety, have made these methods widely used.

However, the rapid advancement of sensors, communication, and intelligent transportation technologies necessitates a breakthrough in critical technologies to advance intelligent vehicles beyond Level 2 (L2) and into Level 3 (L3) and higher levels of autonomous driving. Most current methods only apply to developing intelligent driving technology at Level 2 and below.

Researchers have recently developed quantitative risk assessment methods based on the artificial potential field (APF). They use APF as a typical two-dimensional driving risk assessment approach, incorporating longitudinal and lateral indicators to describe the relationship and risk levels between vehicles and their surrounding environment. This method is now being applied to research on intelligent vehicle safety algorithms.

The APF method, originally introduced by Khatib and Le Maitre (1978) in 1978 for robot control, has since evolved to describe driving risk levels. Researchers from institutions such as Drexel University (Bhatt et al., 1987) and the Georgia Institute of Technology (Arkin and Murphy, 1990) have applied APF to analyze the risk environment for autonomous vehicles. Gerdes and Rossetter (2001) advanced this by creating a risk distribution map and a unified driving assistance system based on APF. Matsumi et al. (2013) used APF to prevent vehicle collisions with pedestrians at intersections and protect vulnerable road users. Huang et al. (2021) developed a dynamic potential field for vehicle decision-making and motion planning using the APF model. Despite these advancements, the application scenarios for APF-based methods remain limited, and the model’s adaptability needs improvement. While APF theory matures and effectively assesses driving risk in areas like car following, path planning, and collision avoidance, previous studies have often overlooked critical factors. These include the driver’s psychological, physiological, and behavioral traits, complex weather and road conditions, and the interaction of various factors within the driver-vehicle-road system. To enhance driving safety assessments, Wang et al. (2016) proposed the “driving safety field (DSF)” model, which considers a comprehensive set of driver, vehicle, and road factors. However, the DSF model faces challenges in establishing a clear physical meaning for the coupling relationships between parameters.

In summary, several studies have been conducted on driving risk assessments, but various deficiencies exist. In this study, we construct a virtual force system from the perspective of autonomous vehicles, presenting a local traffic safety assessment method based on the principle of least action. The main contributions of this study are as follows:

(1) Established a virtual force system centered on the autonomous vehicle that incorporates virtual risk forces, virtual driving forces, and virtual traffic regulation constraint forces.

The remainder of this article is organized as follows. Section 2 analyzes the driving process and establishes a physical model of vehicle motion. In Section 3, we study the virtual force system from the perspective of autonomous vehicles. According to the proposed virtual force system, we set up a local traffic safety assessment method in Section 4. In Section 5, we applied the established method in hazard scenarios by MATLAB’s Driving Scenario Designer to verify the effectiveness of the proposed model. In Section 6, we conclude this study.

The vehicle is influenced by three aspects of the driver-vehicle-road closed-loop system during driving: (1) the driver’s driving goals, (2) the impact of the dynamic traffic environment, and (3) the constraints imposed by traffic regulations. Based on this concept, we can vividly describe the driving process as a small ball rolling down from the top of a U-shaped groove, as shown in Figure 1.

As shown in Figure 1, the ball is subject to three types of forces during its downward rolling: (1) a virtual driving force driven by the driving target; (2) a virtual risk external force influenced by the dynamic traffic environment; (3) a virtual constraint resistance generated by traffic rules. In addition, the inclination angle of the U-shaped groove relates to the driver’s expected speed or expectation of mobility. The ball moves longitudinally when θ i , x ≠ 0 , corresponding to straight driving. The ball moves laterally when θ i , y ≠ 0 , corresponding to lane changing. The angle θ i between the U-shaped groove and the XOY plane reflects the driver’s overall pursuit of efficiency. At the same time, θ i , x and θ i , y correspond to the driver’s pursuit of efficiency in the longitudinal and lateral directions during driving, respectively. According to the principle of Euler angle coordinate system transformation, the relationship between the above three parameters satisfies the following formula: θ i = arccos cos ⁡ θ i , x · ⁡ cos ⁡ θ i , y (1)

We define the virtual driving force as G i , and let G i = m i g ⁡ sin ⁡ θ i . In addition, drivers will inevitably encounter risk scenarios such as obstacles appearing ahead and neighboring vehicles forcibly cutting in while driving. This study describes the risk scenarios as small protrusions in a U-shaped groove, as marked by red circles in Figure 1, and represents them with virtual risk force F j i . Furthermore, due to the existence of traffic rules (such as speed limits), drivers always avoid violating regulations while driving. Therefore, R i represents the virtual constraint resistance imposed by traffic rules on drivers.

This study constructs a virtual force system from the perspective of autonomous vehicle i (hereinafter referred to as vehicle i ) to investigate the safety of the local road traffic environment surrounding autonomous vehicles. As shown in Figure 2, the white vehicle represents the autonomous vehicle i , surrounded by four brown vehicles, j 1 , j 2 , j 3 , and j 4 . These four surrounding vehicles exert virtual risk forces on vehicle i , denoted as F j 1 i , F j 2 i , F j 3 i , and F j 4 i , respectively. The virtual driving force corresponding to vehicle i 's driving intent is G i . The road speed limit rule imposes a virtual constraint force on vehicle i 's behavior, denoted as R s i . Additionally, the constraints from the lane lines on both sides of vehicle i are represented as R l 1 i and R l 2 i . The following sections will provide a detailed introduction to modeling these virtual forces in the local road traffic environment for autonomous vehicles.

In the virtual force system established from the perspective of autonomous vehicles in Section 3, we can analyze the driving safety of autonomous vehicles in the local traffic environment using the principle of minimum action (Wang et al., 2020; Zheng et al., 2021). First, as shown in Figure 2, centered around autonomous vehicle i , we calculate the potential energy exerted on vehicle i by the virtual risk force, virtual driving force, and virtual regulatory constraint force. The virtual risk force generates virtual risk potential energy, which describes the risk situation during the driving process. The greater the virtual risk potential energy, the higher the driving risk. Conversely, the virtual driving force and virtual regulatory constraint force generate virtual driving potential energy, which describes the efficiency of the driving process. The greater the virtual driving potential energy, the lower the efficiency. Therefore, the lower the total potential energy of the vehicle i , the safer and more efficient it is calculated as Equation 16.

Based on Equation 3, the virtual risk potential energy U F j i caused by any other road user on vehicle i is calculated as Equation 16. U F j i = 1 2 M j i V j i 2 R 1 r j i ′ ∈ [ 0 , r min )   1 2 M j i V j i 2 R 2 r j i ′ ∈ r min , r max 0 r j i ′ ∈ r max , + ∞ (16) where the expressions for R ₁ and R ₂ are as Equations 17–18. R 1 = r min − r j i ′ / r e + r 0 1 r min + r min − 2 r max r max 2 (17) R 2 = r 0 1 r j i ′ + r j i ′ − 2 r max r max 2 (18)

Therefore, the total virtual risk potential energy U F exerted on vehicle i by n other road users in the environment is obtained by Equation 19. U F = ∑ j = 1 n U F j i (19)

For simplicity, when modeling the virtual driving potential energy U G generated by the longitudinal virtual driving force and virtual regulatory constraint force, because θ i and θ i x are relatively close, we consider θ i ≈ θ i x . Combining Equations 8, 14, we obtain U_G by using Equation 20. U G = m i g sin ⁡ θ i v l − v i 2 2 v l t e (20) where t e is the unit time.

At the same time, ignoring the influence of G i , y , the virtual constraint potential energy U R generated by the lateral virtual regulatory constraint force is given by Equation 21. U R = k m E i k y ln y m i − y p y p − y p y m i t e (21)

Therefore, in the virtual force system centered around vehicle i , the total potential energy U i experienced by vehicle i in any given scenario is calculated by Equation 22. U i = U F + U G + U R (22)

According to the principle of minimum action, the action equation for the virtual force system centered around vehicle i is constructed as follows as Equation 23. S = ∫ t 0 t f L d t (23) where S is the action of the driving process of vehicle i . Because the virtual force system is centered around vehicle i , T i = 0 , and the Lagrangian L is given by L = T i − U i = − U i .

Theoretically, the lower the total potential energy of vehicle i , the safer and more efficient it is. When vehicle i is driving along the lane centerline at the road speed limit in free flow, U F = U G = U R = 0 , and the action S = 0 , achieving an extremum. This indicates that the vehicle’s driving state is the safest and most efficient. However, in most cases, vehicle i will experience virtual risk forces from other vehicles and cannot always travel at the road speed limit. Therefore, under typical conditions, S < 0 . Thus, this study designs a local traffic safety instantaneous evaluation index D , as shown in Equation 24, such that D = 1 when S = 0 , and D ∈ [ 0 , 1 when S < 0 . D = 2 − a S (24) where a is a constant, with a ∈ 1 , 2 S .

Driving safety is influenced by the vehicle’s motion state. Any vehicle’s hazardous behavior will quickly impact adjacent vehicles’ safety and gradually affect the safety and efficiency of the entire traffic flow. In this section, we design various hazard scenarios from the perspective of autonomous vehicles to demonstrate the effectiveness of the proposed local traffic safety assessment method. These scenarios include rear-end scenarios, a cut-in scenario, and an intersection collision scenario. By calculating the absolute value of the action S and the local traffic safety instantaneous evaluation index D in different scenarios, we analyze the safety of autonomous vehicles during driving. This study ignores vehicle dimensions and uses point masses for calculations for ease of analysis.

Figure 4 shows the designed rear-end (collision) scenario, where autonomous vehicle i and another vehicle j are in the same lane, separated by 120 m. Vehicle i travels at a speed of 30   m / s , and if the motion state remains unchanged, a rear-end collision will occur after 4 s. We use MATLAB’s Driving Scenario Designer to design and simulate the scenario, as shown in Figure 5. The results indicate that, over time, the absolute value of the action S gradually increases, and the local traffic safety instantaneous evaluation index D gradually decreases. A collision occurs after 4 s. If, during this process, autonomous vehicle i detects the risk from vehicle j in front and takes braking or lane-changing actions to avoid the risk, the absolute value of the action S will not continue to increase, meaning the risk will not persist.

First, we design a deceleration to avoid collision scenario with three different deceleration rates: − 4   m / s 2 , − 6   m / s 2 , and − 8   m / s 2 , representing gradual to emergency braking, as shown in Figure 6. To ensure comparability, we set the stopping position of vehicle i to be the same in each case. We use MATLAB’s Driving Scenario Designer to create and simulate these scenarios, and the result is illustrated in Figure 7. In the legend, EB-1, EB-2, and EB-3 correspond to decelerations of − 4   m / s 2 , − 6   m / s 2 , and − 8   m / s 2 , respectively.

From the figure, we can observe that due to the braking of vehicle i , the driving time increases from 4 s to 5.6 s, 6.3 s, and 7.5 s for the respective decelerations. Compared to the rear-end (collision) scenario, the absolute value of the action S significantly decreases, and the local traffic safety instantaneous evaluation index D substantially improves. Additionally, higher deceleration rates result in larger S , indicating higher risk, which aligns with practical observations.

To avoid rear-end collisions, in addition to braking to decelerate the vehicle, lane-changing can also be employed. Therefore, we designed a lane-change avoidance scenario, as shown in Figure 8. For comparison purposes, vehicle i starts changing lanes at distances of 80 m, 60 m, and 40 m from vehicle j , with consistent lane-change trajectory curvature. We use MATLAB’s Driving Scenario Designer to design and simulate these scenarios, and the results are shown in Figure 9. In the legend, LC-1, LC-2, and LC-3 correspond to lane-change starting distances of 80 m, 60 m, and 40 m, respectively.

The figure shows that compared to the rear-end collision scenario, the absolute value of the action S significantly decreases, and the local traffic safety instantaneous evaluation index D shows a notable improvement. Additionally, the results indicate that a longer lane-change starting distance corresponds to greater safety, which aligns with practical observations.

When an obstacle is in front of the vehicle, the vehicle can change lanes to avoid rear-end collisions. However, if the vehicle is too close to other vehicles in the adjacent lane during the lane change, it can pose a risk. Therefore, we designed a cut-in scenario, as shown in Figure 10. For comparison, we designed vehicle j to begin cutting in at distances of 10 m, 15 m, and 20 m from vehicle i , with consistent lane-change trajectory curvature. We used MATLAB’s Driving Scenario Designer to create and simulate these scenarios, and the results are shown in Figure 11. In the legend, CI-1, CI-2, and CI-3 correspond to cut-in starting distances of 5 m, 7.5 m, and 10 m, respectively.

The figure shows that the closer the initial distance between the two vehicles during the cut-in, the greater the risk, which aligns with practical observations. The results also indicate that a vehicle should maintain a sufficient longitudinal distance from vehicles in the adjacent lane before changing lanes.

Research (Zhao et al., 2019) indicates that traffic accidents at non-signalized intersections are generally more severe than those at signalized intersections, and advanced driving assistance systems, such as emergency braking systems, are ineffective in mitigating accidents at non-signalized intersections. Therefore, this study conducts a simulation analysis for non-signalized intersections.

First, we design a collision scenario at a non-signalized intersection, as shown in Figure 12. Vehicles i and j travel at a constant speed of 20   m / s along their respective lanes. If the motion state remains unchanged, they will inevitably collide at point C ( 2 , − 2 ) after 2.5 s. We used MATLAB’s Driving Scenario Designer to create and simulate this scenario, and the results are shown in Figure 13.

The results reveal that as time progresses, the absolute value of the action S gradually increases, and the local traffic safety instantaneous evaluation index D gradually decreases, leading to a collision at 2.5 s. If, during this process, autonomous vehicle i detects the risk from vehicle j and takes braking actions to avoid the risk, the absolute value of the action S will not continue to increase, meaning the risk will not persist.

Assume that autonomous vehicle i detects vehicle j when it is 10 m from the collision point and begins braking. We set the speeds of vehicle i at the trajectory intersection point with vehicle j to be 18   m / s , 16   m / s , and 14   m / s , as shown in Figure 14. We use MATLAB’s Driving Scenario Designer to design and simulate these scenarios, and the results are shown in Figure 15. In the legend, NSI-1, NSI-2, and NSI-3 correspond to the speeds of vehicle i at the trajectory intersection point being 18 m/s, 16 m/s, and 14 m/s, respectively. The results indicate that when vehicle i starts braking at point 2 , − 12 , that is, at simulation time t = 2 seconds, the absolute value of the action S gradually decreases, and the local traffic safety instantaneous evaluation index D gradually increases. Additionally, the lower the speed of vehicle i at the trajectory intersection point, the smaller the absolute value of the action S and the higher the local traffic safety instantaneous evaluation index D , which aligns with practical observations.

In this study, we propose a local traffic safety evaluation method specifically designed for NEVs. By integrating a system of virtual forces to represent driving intentions, regulatory constraints, and interactive dynamics with surrounding vehicles, the method establishes a unified and real-time framework for evaluating driving safety under complex conditions. Through simulations of representative scenarios—including rear-end risks, emergency deceleration, lane changes, cut-ins, and intersection conflicts—the proposed approach effectively predicts and quantifies potential risks. Results demonstrate that timely hazard recognition and the execution of appropriate maneuvers, such as braking or evasive lane changes, substantially reduce local driving risk and enhance overall safety performance. The proposed evaluation framework offers critical support for the design and optimization of autonomous driving algorithms on NEV platforms, contributing to the development of safer, more adaptive, and energy-efficient intelligent transportation systems.