category: literaturenote citekey: weigeneratingriskyrealisticscenarios2025 title: "Generating risky and realistic scenarios for autonomous vehicle tests involving powered two-wheelers: A novel reinforcement learning framework" authors: "Wei, Zhiyuan; Bian, Jiang; Huang, Helai; Zhou, Rui; Zhou, Hanchu" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108038 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108038" zotero_key: XBP8KQQB zotero_storage: VZ9G9WE3 collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Wei, Zhiyuan"

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Generating risky and realistic scenarios for autonomous vehicle tests involving powered two-wheelers: A novel reinforcement learning framework

Zhiyuan Wei a , Jiang Bian a , Helai Huang a , Rui Zhou b ,∗ , Hanchu Zhou a

^a School of Traffic and Transportation Engineering, Central South University, Changsha, 410075, China
^b School of Automation, Central South University, Changsha, 410075, China

A R T I C L E I N F O

Keywords: Traffic safety Autonomous vehicles Safety testing

A B S T R A C T

Emerging technologies have the potential to revolutionize transportation, with Autonomous Vehicles (AVs) enhancing traffic safety, improving efficiency, and reducing emissions by optimizing driving patterns and minimizing idling time. However, despite their great potential, the actual utility and functionality of AVs have yet to be fully realized. Testing remains a critical method for advancing AVs adoption, and given that Powered Two-Wheelers (PTWs) is a major contributor to crashes, this paper proposes a novel scenario generation method for PTWs interactions with AVs. First, we extracted 314 car-to-PTWs crashes from the China In-depth Mobility Safety Study-Traffic Accident (CIMSS-TA) database as the initial state of the test scenarios. Subsequently, Reinforcement Learning (RL) was employed to control PTWs, using a reward function guided by a potential energy function that mirrors human driving characteristics to enhance the risk and realism of the generated scenarios. Finally, the effectiveness and scientific validity of the generated scenarios are verified by comparing and analyzing the risk, realism, and crash severity through multiple indicators. The results demonstrate that our proposed method increases riskiness while maintaining a high level of realism. It is hoped that this process will be applied in the future to not only test AV functions but also encourage AVs to be more mindful of crash severity.

1. Introduction

The development of Autonomous Vehicles (AVs) promises to revolutionize transportation by improving safety, reducing traffic congestion, and mitigating environmental impacts (Neurohr et al., 2020). Although AVs have the potential to eliminate most human errors (Singh, 2015; Ghorai et al., 2024), their safety still needs to be validated through rigorous testing. Virtual simulation is preferred for its cost and time efficiency compared to real-world testing (Kalra and Paddock, 2016). It enables extensive and repeatable testing under diverse conditions without the logistical and financial burdens of public road tests (Chen et al., 2024; Zhou et al., 2024b; Scanlon et al., 2021).

A key aspect of virtual simulation testing is the use of scenariobased testing (Riedmaier et al., 2020; Feng et al., 2020, 2023), which involves creating specific situations AVs might encounter on the road. This allows developers to evaluate and enhance the vehicles' responses to various challenges. However, constructing realistic test scenarios is challenging and requires detailed representations of real-world conditions and interactions (Zhou et al., 2023; Ding et al., 2023). Incorporating interactions in scenario construction is essential, as most existing research focuses on logical scenarios and rarely addresses interactions during the testing process (Zhou et al., 2024a; Sun et al., 2021; Pan et al., 2021).

Powered Two-Wheelers (PTWs), including motorbikes and scooters, are prevalent worldwide, especially in densely populated areas, and are an economical and convenient mode of transport (Li et al., 2023a,b; Venthuruthiyil and Chunchu, 2022). PTWs are among the most vulnerable road users, with a higher risk of serious injury in crashes compared to cars. They can weave through traffic, accelerate and decelerate quickly, and their riders often make split-second decisions that AVs must anticipate and react to Brown et al. (2021), Zhou et al. (2024a), Sui et al. (2019). This unpredictability requires AVs to be tested against a wide range of PTWs behaviors to ensure safety. Incorporating PTWs scenarios in AV testing is essential to improve the robustness and reliability of AVs in mixed-traffic environments.

Interactions between PTWs and AVs are complex and multifaceted, involving unpredictable behaviors that challenge AV decision-making algorithms (Alozi and Hussein, 2024). However, existing studies often ignore interaction behavior during scenario construction (Wei et al., 2024), resulting in scenarios that differ from real-world conditions and may not accurately evaluate AV performance. This study aims to

E-mail address: arayzhou@csu.edu.cn (R. Zhou).

https://doi.org/10.1016/j.aap.2025.108038

^∗ Corresponding author.

ensure that AVs can safely operate alongside PTWs by increasing the intensity of tests targeting AVs and reducing the severity of crashes involving these vulnerable road users. We first extracted crash data from the China In-depth Mobility Safety Study-Traffic Accident (CIMSS-TA) database to generate realistic baseline scenarios, then employ Reinforcement Learning (RL) to control the PTWs and introduce the game relationship between the repulsive and gravitational forces of the molecules in the reward function to capture the decision-making change process of the PTWs driver when responding to the hazards. Finally, we compare these interaction scenarios with the original crash scenarios to illustrate the higher realism and risk associated with dynamic interactions. The main contributions of this paper are as follows:

Proposing an RL-based framework to generate safety-critical and realistic interaction scenarios between PTWs and AVs based on real crashes.
Proposing a molecular model of the interaction process to simplify the simulation of the behavioral changes of PTWs in different relative positions with respect to the AVs without losing realism.
Developing a set of benchmark scenarios that comprehensively cover PTWs behaviors and interactions, thereby enhancing the testing coverage for AVs.

The remaining structure of this paper is as follows: Section 2 summarizes the related research, Section 3 introduces the data and methods, Section 4 presents the experimental results and discussion, and the final section, Section 5, provides the conclusion.

2. Literature review

Testing and evaluation to ensure operational safety are critical steps in the development and deployment of AVs (Neurohr et al., 2020). Both industry and academia use real-world and virtual simulation for vehicle testing. Specifically, real-world tests include shadow driving and track testing, while hardware-in-the-loop and software-in-the-loop tests link vehicle components to simulation software. On the other hand, virtual simulation testing constructs virtual environments to replace real road conditions, simulating and extending real-world scenarios (Li et al., 2023c). It is less costly, more convenient, and highly adaptable compared to traditional testing methods (Enzweiler, 2015; Wachenfeld et al., 2016).

Scenario-based testing is the most effective method (Sun et al., 2021). Multiple approaches are used for scenario generation and extraction, including machine learning, combinatorial testing, and extraction based on driving data and test drivers (Zhou et al., 2024a; Hartjen et al., 2019; Lu, 2023; Rocklage et al., 2017; Zhao et al., 2016). However, AVs face significant challenges in addressing open-world and longtail problems, as testing often requires simulating rare and dangerous situations. The scarcity of valid data in real-world scenarios further complicates these efforts (Ding et al., 2020).

Scenario generation enhances diversity and coverage (Lu et al., 2022; Xinxin et al., 2020; Zhang et al., 2022). Hao et al. (2023) categorized scenario generation into data-driven and knowledge-driven approaches. The knowledge-driven approach uses abstract information, including standards and expert knowledge (Geyer et al., 2014; Nothdurft et al., 2011; Xiong, 2013). However, it is limited by subjective experience and bias. In contrast, the data-driven approach uses real-world or simulated data, generally through machine learning and pattern recognition (Riedmaier et al., 2020). Deep learning methods like Generative Adversarial Nets (GAN) and Variational Autoencoders (VAE) are used in scenario generation (Demetriou et al., 2020; Ding et al., 2018). Several studies have demonstrated the application of these techniques: Krajewski et al. (2018) employed neural networks to model and generate trajectories based on real-world records, while Jenkins et al. (2018) utilized recurrent neural networks to create accident scenarios in road traffic simulators. Zheng et al. (2020) proposed accelerating testing by generating challenging scenarios using adversarial testing techniques. Similarly, O'Kelly et al. (2018) modified GAN architectures to produce risky scenarios, and Rempe et al. (2022) optimized the latent space of VAEs to generate adversarial trajectories. However, most approaches focus on data distributions without considering interaction with AV, leading to scenarios that do not match real-world challenges.

The safety of PTWs has long been a critical focus in transportation safety research. Most studies on PTWs safety emphasize passive and active safety measures, primarily considering driver decision-making, vehicle performance, and structural design (Savino et al., 2020; Barm pounakis et al., 2015; Dubos et al., 2016). Although there are current studies on the interaction between cars equipped with driver assistance systems and PTWs, there is little consideration of the impact of autonomous driving systems on the safety of PTWs riders (Sui et al., 2017; Pan et al., 2024; Zhou et al., 2022). In PTWs scenario studies, Li et al. (2023b) proposed a five-layer scenario architecture for testing Advanced Driver Assistance Systems (ADAS), including Automatic Emergency Braking (AEB) systems interacting with PTWs. Duan et al. (2017) categorized conflicts from naturalistic driving data based on car and two-wheelers motion relationships. Crash data was used to analyze critical scenarios and classify them (Liers, 2013; Atalar and Thomas, 2019) . However, most scenarios are limited to functional and logical layers (Sauerbier et al., 2019; Thorn et al., 2018), insufficient for comprehensive testing.

As AVs market penetration increases, interactions between PTWs and AVs are inevitable. To address this challenge, researchers have explored various methods for scenario generation and analysis. For instance, Wang et al. (2022) used Independent Component Analysis (ICA) to generate virtual crashes from the CIMSS-TA database as a way to expand the scenario library. Zhou et al. (2024a) clustered the pre-crash trajectories to obtain six sets of typical scenarios and generated multiple sets of high-risk scenarios based on the acquired trajectory features. Li et al. (2023a) used a two-layer integrated framework for diverse trajectory prediction considering multiple interactions with complex transportation environments to address challenges in AVs interaction with complex traffic environments. Wang et al. (2020) reconstructed the scenarios based on a simulation platform and invoked PTWs to try to analyze the interaction behavior. However, these methods do not consider dynamic interactions between PTWs and AVs, where riders respond to changing AV behaviors. To tackle this limitation, Alozi and Hussein (2024) examined AVs decisions based on interactions with road users, including pedestrians and cyclists, by using real AVs trajectory data to learn interaction actions and generate utility functions to simulate road user behaviors. However, different behaviors affect AVs decisions, and fixed AVs trajectories may lack the realism of dynamic responses in two-way interactions.

Based on the literature reviewed, several research gaps can be identified. Firstly, while scenario-based testing is acknowledged as the most effective method for evaluating the safety of AVs, current scenario generation methods often lack realism due to their limited consideration of dynamic interactions between AVs and other road users, such as PTWs. Most existing studies focus primarily on data distribution and the generation of typical scenarios without adequately addressing the complexities of real-world interactions that involve adaptive and reciprocal behaviors. Additionally, knowledge-driven approaches are constrained by subjective biases and limited by the availability of comprehensive expert knowledge. In contrast, while data-driven methods are more flexible, they often fail to capture the nuanced interplay between AVs and other road users in complex traffic environments. Furthermore, while various methods have been proposed for creating and testing scenarios involving PTWs, these often do not sufficiently address the dynamic nature of these interactions, where the behavior of PTWs riders can rapidly change in response to AV maneuvers. These gaps highlight the need for more sophisticated scenario generation

Fig. 1. The overall research framework.

techniques that incorporate both the variability of human behavior and the adaptability of AV systems in response to unpredictable and dynamic interactions on the road. Therefore, we will focus on constructing dynamic interaction scenarios between PTWs and AVs, which will be elaborated below.

3. Data and methodology

In this study, we initialize the scenarios using crash slices, where the PTWs involved in the crashes are replaced by PTWs controlled through reinforcement learning, and the AVs takes over the ego vehicle. The PTWs generates adversarial behaviors and creates critical scenarios by interacting with the ego vehicle, in which we use the molecular potential concept to control the PTWs to balance the realism of the scenarios with high efficiency. The overall research framework is outlined in Fig. 1.

3.1. Data processing and scene initialization

We selected 314 car-to-PTWs crashes from the CIMSS-TA database, spanning the years 2017 to 2024, constituting the majority of the 700 scenarios in the dataset, which serve as the basis for scenario initialization. For each case, the motion states and environmental information within the 5 s preceding the crash are recorded. To better describe these scenarios, the coordinate system for each case is standardized. The origin of the coordinate system is set at the midpoint of the ego vehicle's bumper in its initial position. The -axis extends in the direction of travel, while the -axis is perpendicular to the travel direction, extending to the right. Angles are measured clockwise, ranging from 0 to 360 degrees, as shown in Fig. 2.

To reconstruct the pre-crash motion states of the involved vehicles, we use the crash reconstruction software PC-Crash, with key parameters obtained listed in Table 1. Additionally, to facilitate the subsequent adversarial learning of the PTWs, the base scene segments are augmented. Scene slices are extracted from 3 s to 5 s before the crash in a time window of 0.2 s, resulting in 3140 slices. The distribution of the main parameters is presented in Fig. 3.

Fig. 2. 2D coordinates of the ego vehicle.

Environment reproduction builds the environment in Roadrunner by recording original data collected from roads, traffic infrastructure, and weather. The constructed virtual scene is then imported into Unity for rendering as shown in Fig. 4. The basic environment is then edited and imported into the simulator to simulation (Rong et al., 2020).

The car in the original crashes is replaced by the AV, and the initial scenes are set up to include the AV's driving intents: turning left, turning right, and going straight. By setting different driving destinations, the AV's varying driving objectives encourage the PTWs to make different decisions starting from the same initial position.

3.2. Scenario dynamization

3.2.1. Deep deterministic policy gradient

The Deep Deterministic Policy Gradient (DDPG) algorithm is the classical DRL algorithm that uses deep neural networks to estimate optimal policies and is shown to be applicable in continuous action space (Lillicrap et al., 2015; Qiu et al., 2019; Yu et al., 2021). Its use to control the PTWs is applied to the decision problem of throttle and steering selection in continuous space. The controlled PTWs

Fig. 3. Original data distribution.

Fig. 4. Scene construction.

Table 1 Crash variables extracted from PC-Crash.

| Variable | Description | | | | | |-------------|---------------------------------------------------------------|--|--|--|--| | 𝑥𝑒 | The x-coordinate of the ego vehicle | | | | | | 𝑦𝑒 | The y-coordinate of the ego vehicle | | | | | | 𝑥
𝑣
𝑒 | The velocity of the ego vehicle in the x-coordinate | | | | | | 𝑦
𝑣
𝑒 | The velocity of the ego vehicle in the y-coordinate | | | | | | 𝑥
𝑎
𝑒 | The acceleration of the ego vehicle in the x-coordinate | | | | | | 𝑦
𝑎
𝑒 | The acceleration of the ego vehicle in the y-coordinate | | | | | | 𝑥𝑜 | The x-coordinate of the objective vehicle | | | | | | 𝑦𝑜 | The y-coordinate of the objective vehicle | | | | | | 𝑥
𝑣
𝑜 | The velocity of the objective vehicle in the x-coordinate | | | | | | 𝑦
𝑣
𝑜 | The velocity of the objective vehicle in the y-coordinate | | | | | | 𝑥
𝑎
𝑜 | The acceleration of the objective vehicle in the x-coordinate | | | | | | 𝑦
𝑎
𝑜 | The acceleration of the objective vehicle in the y-coordinate | | | | |

interacts dynamically with the AV. The algorithm defines the state and action space and designs the reward function based on the Lennard-Jones potential to simulate real interactions. The DDPG algorithm guides the behavior of PTWs and thus effectively challenges the safety performance of the AV.

In RL, the process by which an agent interacts with the environment is Markov Decision Making (MDP), aimed at obtaining the maximum long-term reward. MDP is defined as a 5-element tuple (, , , , ), where is the state space, is the action space, is the reward function, is the transition function, and is a discount factor representing the impact of future rewards on the current reward. Usually, long-term rewards are defined as:

$$Rt = \sum{i=t}^{T} \gamma^{(i-t)} r(s_t, a_t) \tag{1}$$

where and are the state and action at each time step , respectively. And ( , ) denotes the reward value at the current time step.

DDPG is a deep reinforcement learning framework that addresses the challenge of Q-learning, which can only be applied to discrete actions, through a DPG-based actor-critic approach (Bouhamed et al., 2020). The use of neural network function approximators, while drawing on the features of Deep Q-Network (DQN), allows for the implementation of large state and action spaces for online learning (Lillicrap

Fig. 5. The structure of DDPG.

et al., 2015). In DDPG, the actors represent the Deterministic Policy Gradient (DPG) and the evaluators are the Q-functions. The behavior of an agent is represented by a deterministic policy , where denotes the mapping of states to deterministic actions. Under the current policy, given the instantaneous state and action, the Q-value function is obtained based on the recurrence relation in Bellman's equation:

$$Q^{\mu}\left(s{t}, a{t}\right) = \mathbb{E}{r{t}, s{t+1}} \left[E\left(s{t}, a{t}\right) + \gamma Q^{\mu}\left(s{t+1}, \mu(s_{t+1})\right)\right] \tag{2}$$

When is determined by random initialization, the Q-value function is parameterized with and the minimum loss function is defined to optimize the approximator:

$$L(\theta^{Q}) = \mathbb{E}{s{t} \sim \rho^{\theta}, a{t} \sim \beta, r{t} \sim E} \left[ \left( Q(s{t}, a{t} \mid \theta^{Q}) - y_{t} \right)^{2} \right]$$ (3)

where is the different randomness for the strategy, is the distribution of the state under the currently determined strategy, and is computed as follows:

$$y_t = r(s_t, at) + \gamma Q(s{t+1}, \mu(s_{t+1})|\theta^Q)$$ (4)

To cope with the problem of easy divergence in learning, DDPG uses a replay buffer with a two-layer actor-critic structure to optimize the process of learning values for large nonlinear function approximators. One layer is the network layer and the other is the target network layer, Fig. 5 shows the algorithm structure.

First, select under , we sample noise from the noise process to add to the strategy to help the learning process explore new behaviors:

$$a_t = \mu(s_t) + \mathcal{N} \tag{5}$$

After obtaining the new +1 with the reward value , the set ( , , , +1) is stored in the replay buffer. By randomly sampling a small batch update strategy from it, each set ( , , , +1) is input into the target behavior network to get the behavior ′ (+1) with the structural parameters input into the target criticism network ′ to compute . Update the criticism network and the behavior network with the help of the gradient update formula of the strategy and the gradient update is shown in Eq. (6). Finally, the update of target behavior and target criticism is achieved. The whole algorithmic process is shown in Algorithm 1:

$$\nabla{\theta^{\mu}} J \approx \frac{1}{N} \sum{i} \nabla{a} Q(s{i}, a{i} | \theta^{Q}) \nabla{\theta^{\mu}} \mu(s_{i} | \theta^{\mu})$$ (6)

3.2.2. State and action space

The MDP problem solved by DDPG has state space and action space with a reward structure specifically set up for the PTWs control problem. Based on the above setting, the state of the vehicle is categorized

Algorithm 1 DDPG-based PTWs control model

1: Initialize critic network (, | ) and actor (| ) with random parameters ,
2: Initialize target network ′ ← , ′ ←
3: Initialize replay buffer
4: for episode=1 to M do
5: Initialize a random process for action exploration
6: Receive first observation ¹
7: for t=1 to T do
8: Select action with exploration noise and current policy = ( ) +
9: Obtain reward and new state +1
10: Store transition tuple ( , , , +1) in
11: Sample a random minibatch of N transitions ( , , , +1) from
12: Set = ( , ) + ′ (+1, ′ (+1| )| ′
13: Update critic by minimizing the loss: = ∑ ( − ( , | ))²
14: Update actor policy using the sampled policy gradient: ∇ ≈ ∑ ∇( , | )∇ ( |
15: Update target networks: ′ ← + (1 − ) ′ ; ′ ← + (1 − )
16: end for
17: end for

into lateral and longitudinal in a two-dimensional coordinate system. The state space for setting RL has eight dimensions defined as:

$$x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8$$

where ¹ to ⁴ denote the state of the PTWs and ⁵ to ⁸ denote the state of the ego vehicle.

After initializing the state of the ego vehicle, Baidu Apollo controls the ego vehicle, inheriting the already set state and having different driving tasks. During operation, Baidu Apollo will continuously output its state. The complete trajectory information will be used as an interactive input to guide the PTWs to output the state to complement another portion of the state vector during continuous operation. PTWs are flexible and mutable, and traditional road constraints do not apply (Atalar and Thomas, 2019; Piantini et al., 2022). The state constraints are shown in Eq. (8) (Atalar and Thomas, 2019; Huang et al., 2020; Pan et al., 2021; Sui et al., 2019; Zhou et al., 2022):

$$0 \,\mathrm{m/s} < v_p < 16 \,\mathrm{m/s}$$ (8)

Similarly, in the action space, the control of the PTWs is realized through lateral and longitudinal directions. Simplifying the control process, acceleration replaces the throttle for longitudinal control and yaw rate replaces the steering wheel for lateral control. The state and actions are updated in a cycle of 0.2 s. Given that the purpose of controlling a PTWs is to generate behaviors that are challenging to the AV and conform to real road conditions, we consider only safety in the control, ignoring the effects of comfort and fuel economy. The statistical data and parameter settings for PTWs, with reference to Cao et al. (2019), Zhou et al. (2024a) and others, set the action constraints as shown in Eq. (9):

$$\begin{cases} -4 \,\mathrm{m/s^2} < a_p < 4 \,\mathrm{m/s^2} \ -25^\circ/\mathrm{s} < s_p < 25^\circ/\mathrm{s} \end{cases} \tag{9}$$

3.2.3. Reward

The reward function is the most crucial part of RL and directly determines the training results. Consider the need for intelligent agents to fulfill the goal of rapid testing i.e. generating dangerous scenarios based on crash data. By setting an appropriate reward function, the PTWs is incentivized to execute decisions that can threaten the AV. The interaction between the AV and the PTWs occurs throughout the scenario, with the AV making reasonable decisions based on the challenging behavior of the PTWs to ensure the completion of the driving task. The PTWs also learns to make decisions about dangerous behaviors based on the AV's feedback. During the interaction, the reward function provides guidance based on the latest state and action, causing the safety level of both parties to fluctuate. While aggressive behavior accelerates the generation of critical scenarios, it does not guarantee that the generated scenarios are valid and scientific.

In the test scenarios, we aim to generate scenarios that are fast and efficient. An intuitive representation of this is the relative relationship between the two vehicles. The fast approach of a PTWs to the AV is a quick way to trigger a critical scenario. In reality, every mentally healthy and well-driven driver aims to avoid crashes and maintain a safe gap between vehicles (Wu et al., 2022). It is an instinctive human response to avoid hazards, and drivers will move as far away from the AV as possible when responding to hazards. Therefore, considering only fast targets for critical scenarios does not guarantee driving scenarios that are consistent with human habits and may be ineffective.

The traditional reward function does not focus on the characteristics of variables and reward values that change in relation to each other within a certain range (Yu et al., 2021; Qiu et al., 2019; Xu et al., 2020; Bouhamed et al., 2020; Wei et al., 2024). Therefore, the current setting of the reward function restricts the anthropomorphic nature of PTWs control i.e., it overemphasizes the occurrence of conflicts and ignores irrational behaviors. In order to accurately describe the entire process of driver recognition of hazards while focusing on the generation of critical scenarios, we need to take into account the nature of scenario testing to be fast and realistic.

Krogh and Thorpe (1986) introduced the concept of potential fields in their study of robotics, visualizing the perceptual process as favorable advancement driven by gravity, with repulsive forces impeding unfavorable travel. Hsu et al. (2012) built on the previous research by bringing it into a traditional vehicle following model, where gravity and repulsive forces work together to affect the lateral and longitudinal motion of the vehicle. In this way, the driver and the traffic environment are appropriately incorporated into a unified model, which provides ideas for solving the problem of vehicles following control in dynamic interactions in complex traffic environments. In addition, the environment and AVs in a scenario form a system, and assessing the effect of the system on individual AVs is similar to the concept of field theory (Cheng et al., 2022). Many current studies describe the driving risk of vehicles in operation by introducing the concept of potential field, expecting to optimize the crash avoidance strategies adopted by vehicles when encountering risk in tracking or insertion scenarios by mapping the risk to two or three dimensions using the potential field (Wang et al., 2015, 2016; Wu et al., 2019, 2022).

This study aims to address complex and diverse scenarios in the physical world, i.e., the traffic participants have various short-term objectives such as overtaking, lane changing, and cut-in in its interactions with traffic participants. The diversity of objectives results in potential threats towards the ego vehicle approaching in different ways, in different directions, and at different speeds. Drawing on the generative principles of crash avoidance strategies that utilize potential fields in risk, reverse adoption is used to steer the environment to adjust to a risk amount state, which largely materializes the process of environmentvehicle interaction. Using the molecular potential energy, which has no directionality but only emphasizes the relative distance, not only describes the decision-making process of riders in traffic who perceives danger by virtue of the relative distance, but also simplifies the control so that the model has better robustness. The lateral and longitudinal motions of the PTWs are stimulated by repulsive and gravitational forces to generate high-quality critical scenes.

In a molecular potential energy field, gravitational and repulsive forces interact, causing changes in the field. We hypothesize that the AV and PTWs are analogous to molecules with geometrical dimensions. The AV is set as the object under test. Initially, when the PTWs is far from the AV, the gravitational force is greater than the repulsive force, guiding the PTWs to approach the AV based on the velocity index generated by the scenario. However, as the PTWs get closer to the AV, the effective indicators generated by the scenario become more influential, and the repulsive force exceeds the gravitational force. This prompts PTWs to take measures to avoid danger, simulating the emergency avoidance actions taken by drivers when aware of a potential crash.

A dangerous approach by the PTWs triggers the AV's safety decisionmaking process, and an unavoidable crash prompts the AV to make a drastic emergency response. Both scenarios work together to test the AV's safety features. We use the Lennard-Jones potential in the molecular potential energy formulation to define the reward value, controlling the PTWs to make decisions that mimic human driver characteristics and challenge the AV. When two objects in a potential field are so close that the repulsive force increases, the repulsive effect pushes them apart, which is a positive phenomenon. The details of the visualization approach are shown in Fig. 6.

The specific definition of the Lennard-Jones potential function is as follows:

$$r_d = -4\epsilon \left[ \left( \frac{\sigma}{d} \right)^{\theta} - \left( \frac{\sigma}{d} \right)^{\theta/2} \right] \tag{10}$$

where is the distance between two molecules, and , are parameters set according to different needs. The three driving tasks of the AV divide its motion process into three phases: the go-straight phase, the steering phase, and the steering completion phase, with the go-straight task being in the always unturned stage. There are multiple crash types in the steering phase, covering opposite crashes, rear-end crashes, side crashes, crashes due to right-of-way allocation, etc. Part of the reward function determines the setting of different parameters mainly for this phase. The distance here denotes the distance between the PTWs and the AV, calculated from the shape and the closest point on the AV.

Based on the main objective function considering various constraints and realistic applications, we set the final reward function as:

$$r = \alpha r_d + \beta r_t + \gamma r_p \tag{11}$$

where , and are the magnitude of the effects of the three functions of weight coefficient assignment. By experimental testing, setting them to 0.8, 0.1, and 0.1 respectively. is the reward including guiding the crash at the time level with compliance with traffic rules, and is the penalty i.e. preventing irrational combinations of horizontal and

Fig. 6. Different settings for the reward function.

longitudinal control as well as large movements of PTWs Eqs. (12)–(13) define the variables.

$$r{t} = \begin{cases} f{t} \left( \Delta t \left( S{P}, S{A} \right), T \right) + \beta{1} & \text{if PTWs obeys rules} \ f{t} \left( \Delta t \left( S{P}, S{A} \right), T \right) & \text{otherwise} \end{cases}$$ (12)

$$r{p} = \begin{cases} -f{p}(C{p}, T) - \gamma{1} & \text{if PTWs crosses the border} \ -f{p}(C{p}, T) & \text{otherwise} \end{cases}$$ (13)

where is a function of time, where is the current execution time, and is the time required to predict that the PTWs can conflict with the AV in the current state. , are the states of PTWs and the AV at the current time, respectively. We expect this to decrease as increases. Facilitating the interaction while encouraging the conflict to occur more often at a later time as a way to extend the interaction time. 1 is a reward parameter encouraging the PTWs to follow the traffic rules through the debugging of the experimental training with the limit of the reward function threshold we set it to 15. is a function of conditional judgment where is the number of times it stays in the extremes of acceleration and deceleration. This function decreases as the execution time increases. ¹ is a penalty parameter to discourage the PTWs from fleeing in all directions and we set the value to 40 based on the same requirement. We refer to the algorithm that represents the reward function based on the Lennard-Jones potential transformation as P_DDPG.

3.3. Interaction scenario generation

In the experiment to realize the interaction between PTWs and the AV, we expect to enhance the risk behavior of PTWs through adversarial gaming during the testing of the AV through virtual simulation. We built a joint simulation platform to realize the interaction process between Baidu Apollo and controlled PTWs. The interaction platform we built can be divided into 3 parts. The first is SVL Simulator, which provides the environment for interaction including basic road facilities, weather, road conditions and signal control. The second part is Baidu Apollo, which serves as the AV representative for this experiment and helps the AV avoid potential injuries through black-box decision-making algorithms. The third component is the PTWs, which is controlled by the RL and interacts with the AV trajectory designed above to obtain its continuous state. The AV, which has the function of sensing the environment and driving intention, receives the complete trajectory information of the PTWs in the simulator and interacts and responds to the PTWs. Finally, it outputs the timing trajectory to realize

Fig. 7. The reward of P_DDPG-controlled PTWs.

the training closed loop. It uses different decisions to control the PTWs to generate scenarios that are challenging to the AV (instead of direct attacks such as accelerating towards it) and ultimately realizes the generation of safety-critical scenarios.

4. Experimental results and discussion

4.1. Scenario generation results

We compared the effect of different parameter choices on the reward function, as shown in Fig. 7. As shown in Table 2 when is 4, it is better than the other parameters and the difference is within the acceptable range, although the variance is larger and unsmooth compared to of 2. At the same time, it has the fastest convergence rate and becomes the optimal choice. Convergence is reached when the function is iterated 800 times. We will use surrogate safety metrics to evaluate the quality of the scenarios generated with the help of RL. The AV is expected to respond to threats with extreme decisions, and the analysis of vehicle trajectories should indicate the high quality of the scenarios. The feasibility of the generated scenarios will be demonstrated by maintaining a balance between challenging the AV and ensuring realistic, practical scenarios. The validity of the control model will be verified by comparing the simulation results with real crash data, confirming the accuracy and scientific basis of the generated scenarios.

The trained model was used to generate trajectories and input them into the simulation platform, while the vehicle states were imported

Table 2 Characterization of reward function curves with different parameter settings.

Reward parameters	Mean	Standard deviation	SE of Mean	Variance
𝑟2	66.0325	22.4159	0.5789	502.4719
𝑟4	63.9413	30.5771	0.7895	934.9599
𝑟8	49.3731	31.3790	0.8102	984.6436
𝑟12	37.5993	30.7687	0.7945	946.7144

Fig. 8. Comparison of crash rates across different scenarios.

into the simulation platform to simulate different scenarios resulting from the interaction between the AV and PTWs. In the results shown in Fig. 8, the crash rate of the AV based on the original crashes is only 15.13%, while the values of turn left, turn right, and go straight of the AV in the interaction scenarios increase to 33.48%, 31.08%, and 34.40%, respectively. The average value of 32.98% is twice as much as that of the original crashes.

4.2. Risk analysis

The risk of the entire process for each specific scenario cannot be expressed by the crash rate, and surrogate safety metrics are used to quantify critical scenarios. We use two surrogate safety metrics including Time-based and Deceleration-based to describe the scenarios from different dimensions. Time-To-Collision () (Wang et al., 2021; Rahman and Abdel-Aty, 2018; Rahman et al., 2019b,a) describes the time for a crash between a front vehicle(k) and a rear vehicle(k-1) under the condition of constant speed difference if the vehicle behind is going faster:

$$TTC{k}(t) = \begin{cases} \frac{x{k-1}(t) - x{k}(t) - l}{v{k}(t) - v{k-1}(t)}, v{k}(t) > v{k-1}(t) \ v{k}(t) - v_{k-1}(t) \end{cases}$$

$$(14)$$

where and are the position and velocity of the front vehicle, and −1 and −1 are the position and velocity of the rear vehicle.

Time-Integrated (TIT) and Time-Exposed (TET) (Minder houd and Bovy, 2001) are metrics derived from , and they have been used to assess the safety effects of intelligent vehicles in traffic analysis (Wang et al., 2021; Rahman and Abdel-Aty, 2018). Considering the complexity of the crash due to the variability and randomness of PTWs, their crash safety evaluation with vehicles is presented by Generalized () (Ward et al., 2015):

$$D_{i,j} = \sqrt{(P_m - P_n)^T (P_m - P_n)}$$ (15)

$$D'_{i,j} = \frac{(P_m - P_n)^T (V_m - Vn)}{D{i,j}}$$ (16)

$$GTTC = \begin{cases} \frac{-D{i,j}}{D'{i,j}}, & \text{if } D'{i,j} < 0\ +\infty, & \text{if } D'{i,j} \ge 0 \end{cases}$$

$$(17)$$

where and are the respective positions of the nearest points of the two vehicles, and are the velocity vectors of the two vehicles. While TIT and TET are also converted to be calculated by , see Eqs. (18)–(21).

$$TET(t) = \sum_{k=1}^{N} \delta_t \times \Delta t, \delta_t = \begin{cases} 1, 0 < GTTC_k(t) \le GTTC^* \ 0, else \end{cases}$$ (18)

$$TET = \sum_{t=1}^{T} TET(k)$$ (19)

where is the instantaneous time, is the ID of the vehicle, is the total number of vehicles, is the switching variable at time , is the time step which is 0.2 in the simulation, and is the total simulation time. () is defined similarly to () as the GTTC value of the two vehicles at time . ^∗ is the threshold value of GTTC used to distinguish between safe and unsafe, here we make ^∗ = 1.

$$TIT(t) = \sum_{k=1}^{N} \left[ \frac{1}{GTTC_k(t)} - \frac{1}{GTTC^*} \right] \times \Delta t,$$

$$0 < GTTC_k(t) \le GTTC^*$$ (20)

$$TIT = \sum_{t=0}^{T} TIT(t)$$ (21)

Proportion of Stopping Distance (PSD) (Astarita et al., 2012) is the ratio of the distance to the potential crash point to the minimum acceptable stopping distance, which is used as an indicator based on deceleration since its use is not restricted by the type of following vehicle as shown in Eq. (22).

$$PSD = \frac{d{ij}}{v{ij}^2/2a^*}$$ (22)

where is the distance to the potential crash point, is the approaching speed and is the maximum deceleration.

We compare different scenario generation methods, Wasserstein Generative Adversarial Network (WGAN) (Arjovsky et al., 2017), Timeseries Generative Adversarial Networks (TimeGAN) (Yoon et al., 2019) and DDPG that simply utilizes as the underlying reward function, as shown in Table 3. In WGAN, only the initial state of the scene is generated and the complete temporal scene is generated by sampling the states from the original crashes (Luo et al., 2024). TimeGAN directly generates the complete temporal sequence of the risk scenarios.

Compared to the RL-controlled interaction scenarios, the traditional generative models WGAN and TimeGAN have lower TIT and TET and higher Mean PSD as shown in Table 3. This indicates that the generated scenarios serve the test challenge less effectively. Of the two generative models, while the results for the three WGAN metrics indicate that Baidu Apollo is more dangerous in the generated scenarios, the crash rate of 16.50% is lower than TimeGAN's 21.80%, but is higher than the original's 15.13%. On the other hand, the scenarios obtained using the DDPG have significantly higher crash rates than the generative models, above 30%. The crash rate obtained by GTTC as a parameter-driven reward function is even higher at 33.85% and the comparison of TIT, TET and Mean PSD shows that the scenarios are more threatening, but the difference is not significant and the crash rate is only lower than 1% higher.

Our approach has advantages in terms of risk, as the DDPG-controlled PTWs demonstrates higher risk levels, but subsequent validation will illustrate the importance of the proposed method. The improvement in risk of generating scenarios using P_DDPG relative to the original crashes is analyzed.

The variability in the performance of AVs in the interaction scenarios versus the original crashes is analyzed using surrogate safety metrics

Fig. 9. Distribution of surrogate safety metrics.

Table 3 Effects of different algorithms for generating scenarios.

Methods	TIT(s)	TET(s)	Mean PSD	Crash rate
WGAN	4.11	0.26	6.49	16.50%
TimeGAN	2.02	0.10	7.03	21.80%
DDPG	7.51	0.32	3.52	33.85%
P_DDPG	5.38	0.30	4.29	32.99%

specifically shown in Fig. 9. The distribution of TIT is high around 0 in the original crashes and also has a significant distribution around 0 in the interaction scenario. However, the interaction scenario also has intervals greater than 10 to less than 45, and the distribution at greater than 90 is significantly larger than in the original crashes. Additionally, the mean values are larger, all of which suggest that the interaction raises the overall hazard level.

The TET for the original data is more often around 0. The generated scenarios have distributions around 0, but there are also some distributions above and below 1 with larger mean values. The Mean PSD for each scenario is around 0 for both the generated scenarios and the original crashes. While the generated scenarios are present in the 3–7 range, even with large values, the distributions are lower than those of the original crashes for large values, especially for distributions larger than 5. The comparison of the density distributions of the three metrics indirectly proves that the interaction scenarios are riskier than the original crashes.

The generated scenarios are based on crash data, utilizing crash variables to reproduce the initial state of the ego vehicles and PTWs in a crash and to reconstruct the environment of the scene. By fully utilizing real hazardous scene information, diverse scenarios are generated simply. These scenarios are useful for guided testing because of the threatening nature of crashes.

4.3. Scenario realism

The generated scenarios have been validated as strong threats to the AV. However, their realism in future scenarios is uncertain, as they may produce decisions that do not align with rider behavior. Beneficial testing should iterate the AV improvements, whereas illogical scenarios might mislead the AV functionality. Thus, it is essential to ensure PTWs challenges the AV decision-making while maintaining realism.

The realism of the scenarios can be verified by comparing the behavioral differences in the responses of the ego vehicle in the different scenarios specifically shown in Fig. 10. The AV trained to interact with PTWs using a set reward function decelerates more aggressively and has a higher distribution of all accelerations. The presence of cases with greater acceleration indicates more emergent situations compared to the original crashes of the AV with the PTWs. The distribution of yaw rate suggests that our proposed method forces the AV to perform larger transient steering compared to normal interaction. Compared to the original crash vehicle having a greater range of transverse yaw rate, both AVs show a more concentrated distribution around 0, with more concentration in normal interaction scenarios. The comparison of the

Fig. 10. Ego vehicle's acceleration and yaw rate distributions of different scenarios: (a) acceleration (m∕s² ); and (b) yaw rate ( ◦∕s).

above two metrics proves that the scenarios we obtained cause more intense challenges to the ego vehicle but remain consistent with the ego vehicle's characteristics of motion.

To more accurately illustrate the relationship between the dynamics parameters of the ego vehicle in different scenarios, descriptive statistics were used to quantify them, as shown in Tables 4 and 5.

The deviations of the ego vehicle acceleration distributions when the AV takes over are all slightly larger than the original crashes. In terms of variance and standard deviation, the bias is smaller for the original crashes, AV is larger in different scenarios, and the bias for the interaction crash is larger but within acceptable limits. The distribution of mean values AV in the interaction scenario is 1.7708 is greater than the remaining and its extreme value is smaller relative to the AV in the

Table 4 Descriptive statistics of ego vehicle's acceleration in different scenarios.

Scenario categories	Maximum	Minimum	Mean	Standard deviation	Variance
Vehicles in Original Crashes	6.5000	−6.100	−0.0193	0.1699	0.0289
AV in Original Crashes	6.0076	−5.0063	−0.7598	0.7595	0.5768
AV in Interaction Scenarios	5.4775	−5.4998	−1.2102	1.7708	3.1356

Table 5 Descriptive statistics of ego vehicle's yaw rate in different scenarios.

Scenario categories	Maximum	Minimum	Mean	Standard deviation	Variance
Vehicles in Original Crashes	25.0000	−24.5675	0.0331	5.6540	31.9678
AV in Original Crashes	22.7000	−23.7000	0.0134	1.2992	1.6879
AV in Interaction Scenarios	23.5368	−23.7427	−0.1650	5.0290	25.2907

Fig. 11. Dynamics parameters of the PTWs.

crash scenario, below 6 and above -6, the difference is not significant. For the yaw rate, the extreme values of all three are greater than 22 and less than 25, and the difference between them is small. The mean value of AV in the interaction is less than 0 and the standard deviation and variance are greater than that of AV in the original crashes, which is similar to that of the original crashes and is smaller. The results of the comparison of the two dynamic parameters in the interaction scenarios that the effect of the RL-controlled PTWs on the AV decision is somewhat consistent with the effect of the original PTWs.

The dynamics parameters of the PTWs in the crash data and generated scenarios are shown in Fig. 11. Acceleration and velocity characterize the decision-making of PTWs. In the original crash data, PTWs speeds are high around 7 m/s, with a smaller distribution above 20 m/s. Acceleration is mainly between −3 to 2.5 m/s² , with deceleration predominantly used to avoid crashes, skewed towards negative values. The scenarios generated by P_DDPG show a clear distribution of PTWs with speeds of 0, 5–10 m/s. Extreme speeds above 15 m/s are not common in the generated scenarios compared to the original data. The reward function was designed to bring the PTWs rapidly closer to the critical scenario, resulting in a higher velocity distribution. The acceleration ranges are consistent with the original data, but deceleration increases at higher speeds, indicating the need for an emergency response. The presence of higher decelerations at speeds near 0 for the joint distribution reflects the decision to stop to avoid danger. Overall, the interaction scenarios retain the original characteristics but generate more hazardous situations, satisfying realism.

Unlike P_DDPG, in the scenarios generated by the DDPG-controlled PTWs, the velocities are concentrated between 10 and 15 m/s, with more values around 20 m/s and fewer values close to 0. The acceleration distribution increases between 2–4 m/s² and −4 to −2 m/s² . The joint distribution shows more cases of acceleration at speeds of 12 and 15 m/s, with acceleration peaking at around 2 m/s² . Deceleration is spread from −4 to 0 m/s² , especially above 12 m/s. Simple risk-targeted scenarios drive PTWs to frequent, drastic acceleration and deceleration, differing from human driving. This suggests many scenarios are unrealistic. Thus, the slightly elevated risk leads to less effective scenarios, underscoring the effectiveness of our framework.

The reward function balances speed and scenario effectiveness by modeling gravitational and repulsive forces. Focusing solely on speed leads to ineffective scenarios, defeating the test's purpose and hindering the AV function improvement. The opposing forces in the reward

Fig. 12. DeltaV for different scenarios.

function guide RL, increasing speed while maintaining realism in the AV testing. Modeling and emergency avoidance strategies similar to real riders enhance the test's rationality.

4.4. Crash severity

The critical scenarios of PTWs and the AV are not only about testing the AV, but also concern the damage caused to PTWs. Therefore, we set a metric to measure the severity of the crash. Filtering and comparing the original crashes with the interaction scenario where the crash occurred. Vehicle speed is the main factor affecting crash severity and DeltaV quantifies the severity of the conflict by determining the magnitude of the change in speed of the traffic participants as a result of the crash (Wang et al., 2021; Theofilatos and Yannis, 2015; Venthuruthiyil et al., 2023). For ease of calculation, we assume the masses of the PTWs and the car to remain constant at 200 kg and 1800 kg, respectively. This approach focuses exclusively on the changes in the speeds of the crash-involved parties for comparison purposes, ignoring any effects arising from variations in mass.

The result is shown in Fig. 12, where the Delta V distribution of original crashes is higher between −5 and 15, especially in the 0–8 range, and interaction crashes are more frequent between 5 and 14, with a higher density at 9 and values ranging from −2 to 18. Interaction crashes also occupy a certain density in the 0–3 range. The higher the DeltaV value of the interaction crashes, the more intense the crashes are. The metric demonstrates the severity of the crashes in the generated critical scenarios, implying that the scenarios are a strong guide for testing AV prevention with PTWs crashes.

5. Conclusion

This study presents a novel approach to enhance the realism and effectiveness of testing AV by incorporating interactions with PTWs in virtual simulations. By leveraging the RL framework and utilizing real crash data, we generated safety-critical scenarios that challenge AV decision-making. To further enhance the scenario realism, we introduced a molecular repulsion force model into the reward function. This model ensured a balance between speed and effectiveness, avoiding the pitfalls of unrealistic scenario generation. The molecular repulsion model guided the RL training by simulating the natural avoidance behavior of PTWs, resulting in scenarios that more accurately reflect real-world driving dynamics.

However, several shortcomings have been identified in this research. While interactions involving multiple PTWs and vehicles are common in real-world scenarios, these more complex dynamics have not been adequately considered. Accurate and comprehensive modeling of PTWs is not possible due to its uncertainty and may result in inadequate coverage due to dataset limitations. In addition, differences in road infrastructure especially obstacles and signal control can affect the decision-making of traffic participants. Also, different road structures and road rules can interfere with the behavior of intelligences and riders. These scenario elements have not been fully considered. Therefore, subsequent work will focus on the interaction of multiple targets, considering the use of multiple datasets and the behavioral assessment and reproduction of PTWs. The characterization of different behaviors in situations with multiple static scenario elements will also be a focus of future research.

CRediT authorship contribution statement

Zhiyuan Wei: Writing – original draft, Visualization, Methodology. Jiang Bian: Writing – review & editing, Software. Helai Huang: Supervision, Conceptualization. Rui Zhou: Writing – original draft, Methodology, Data curation. Hanchu Zhou: Writing – review & editing, Conceptualization.

Declaration of competing interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This research was supported in part by the National R&D Program of China (Grant No. 2023YFB2504700), Changsha Major Science and Technology Projects, China (No. kh2401002) and Advanced Technology Interdisciplinary Project, Central South University, China (No. 2023QYC016).

Data availability

The authors are unable or have chosen not to specify which data has been used.

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