A method for safety monitoring in emergency scenarios of autonomous driving

Abstract

This invention belongs to the field of autonomous driving safety perception and intelligent decision-making technology, specifically relating to a method for safety monitoring in emergency scenarios of autonomous driving, including the following steps: Step S1, processing trajectory data, extracting instantaneous driving actions, and clustering to extract the mean and correlation coefficient of the separating modes; Step S2, training a conditional variational autoencoder multimodal prediction model based on the mean and correlation coefficient of the separating modes; Step S3, performing dual-threshold mode filtering on the prediction results according to weights; Step S4, performing online conformal prediction calibration on the filtered results; Step S5, using the calibrated results as constraints to calculate the backward reachability set of multi-vehicle game and online inference to determine the urgency level of the scenario. This invention provides an uncertainty quantification method with strict coverage guarantee under finite sample conditions, taking into account the reliability and coverage of the prediction results as well as the real-time performance of the calculation, and the risk prediction has good interpretability.

Description

Technical Field

[0001] This invention belongs to the field of autonomous driving safety perception and intelligent decision-making technology, specifically involving an emergency scenario safety monitoring method for autonomous driving. This method integrates a deep learning prediction model, a conformal prediction calibration algorithm, and a differential game backward reachable set emergency scenario safety monitoring method. Background Technology

[0002] With the rapid development of Advanced Driving Assistance Systems (ADAS) and autonomous driving technology, vehicle safety monitoring and risk warning have become one of the core technological challenges restricting the large-scale commercialization of autonomous driving. According to the classification standards of the Society of Automotive Engineers (SAE), Level 3 and above autonomous driving systems need to achieve autonomous decision-making in complex traffic scenarios, which places more stringent requirements on the system's safety monitoring capabilities.

[0003] In real-world road traffic environments, autonomous vehicles need to cope with a variety of complex scenarios. How to accurately and quickly assess the urgency of these scenarios and make reasonable safety decisions accordingly has become a core issue for autonomous driving safety systems.

[0004] From a system architecture perspective, a complete autonomous driving emergency scenario safety monitoring system typically includes the following key modules: an environmental perception module responsible for fusing information from multiple sensor sources to construct a dynamic traffic scene around the vehicle; a behavior prediction module predicting the future movement intentions of surrounding vehicles and pedestrians based on historical trajectories and contextual information; a risk assessment module quantifying the degree of danger in the current scenario based on the prediction results; and a decision-making and planning module generating safe and feasible driving strategies based on the risk assessment results. Among these, behavior prediction and risk assessment are the core of the entire monitoring system, directly determining the accuracy and timeliness of the warnings.

[0005] Current mainstream behavior prediction methods are mainly based on machine learning and deep learning techniques, including trajectory sequence prediction based on recurrent neural networks (RNNs), latent variable modeling based on variational autoencoders (VAEs), and multimodal trajectory generation based on generative adversarial networks (GANs). These methods have made significant progress in prediction accuracy, but still face some fundamental challenges.

[0006] Existing methods for assessing the urgency of autonomous driving scenarios can be mainly categorized as follows, and each method has certain technical limitations.

[0007] The first category is direct risk prediction. These methods often employ machine learning or deep learning, directly outputting risk levels from input scene features. For example, traditional machine learning risk classification methods use classifiers such as Support Vector Machines (SVM) and Random Forests to map scene features to discrete risk levels. The advantage is its ability to learn non-linear relationships in the data; the disadvantages are reliance on manually designed feature engineering, limited ability to model long-range dependencies, and inability to provide quantitative information on prediction uncertainty. Deep learning methods use deep neural networks to directly input raw sensor data and output a risk score or urgency level for the scene. The advantages are its ability to automatically learn feature representations and fit complex non-linear relationships; the disadvantages are the need for large amounts of labeled data, poor model interpretability, and a lack of effective modeling of prediction uncertainty.

[0008] The second category is trajectory prediction and evaluation. This type of method first predicts the trajectory, such as using a constant speed model or deep learning model, by predefining a series of safety criteria and threshold rules, such as collision risk measurement based on time-to-collision (TCC) and lane departure risk assessment based on lane departure distance. Its advantages are high computational efficiency and strong interpretability; its disadvantages are that rule design relies on experience, it is difficult to cover all complex scenarios, and its ability to handle boundary conditions is insufficient. When traffic scenarios exceed the scope of the preset rules, the system is prone to missed or false alarms. This type of method is essentially a completely open-loop prediction, without considering the physical characteristics and dynamic response characteristics of the predicted object; therefore, it is usually difficult to demonstrate adversarial capabilities and estimate worst-case scenarios.

[0009] The third category is safety verification methods based on reachability set analysis. These methods, based on system dynamics models and optimal control theory, calculate the safe or hazardous reachability domains of a vehicle. Their advantages include rigorous theoretical guarantees and the ability to handle system uncertainties. Disadvantages include high computational complexity, difficulty in applying to real-time systems, and the assumption that adversary behavior is known and environmental conditions are relatively simple. Modeling a zero-sum game problem allows for closed-loop simulation of the worst-case scenario under closed-loop conditions, thus enabling safety verification. However, for complex scenarios with multiple traffic participants, this approach typically consumes enormous computational resources, making real-time risk assessment difficult.

[0010] The existing technology has the following key technical problems: First, there is the issue of ensuring the effectiveness of the prediction. Existing prediction methods usually focus on prediction accuracy, with less consideration given to the reliability and coverage of the prediction results, which is not conducive to discovering the worst-case scenario.

[0011] Secondly, there is the issue of closed-loop interpretability. Direct risk prediction is completely uninterpretable, trajectory prediction has relatively high interpretability but the result is open-loop, and reachability set method is a closed-loop analysis, but it simplifies the environment too much and does not carefully consider reasonable and foreseeable prediction results, resulting in conservative results.

[0012] Finally, there is the issue of real-time computation. Existing computation methods involving reachable sets are all time-consuming and can only be processed by online table lookup, but the dimensionality explosion problem still exists, making it difficult to handle high-dimensional cases. Summary of the Invention

[0013] To address the problems existing in current technologies, this invention proposes an emergency scenario safety monitoring mechanism based on CVAE prediction, conformal prediction calibration, and game-theoretic backward reachability sets. The core of this technical concept lies in: using a Conditional Variational Autoencoder (CVAE) to predict multimodal actions, rigorously calibrating the predicted ellipse using a conformal prediction algorithm, and then injecting the calibrated predicted ellipse as a constraint into a game-theoretic backward reachability set analysis framework, ultimately achieving reliable assessment and early warning of scenario urgency.

[0014] Technical solution: A method for safety monitoring in emergency scenarios of autonomous driving includes the following steps: Step S1: Process trajectory data, extract instantaneous driving actions, and cluster to extract the mean and correlation coefficient of the separation modes; Step S2: Train the conditional variational autoencoder multimodal prediction model based on the mean and correlation coefficient of the separated modes; Step S3: Perform dual-threshold mode screening on the prediction results based on weights; combine the absolute weight threshold and the cumulative weight threshold to screen out modes with high confidence and physical reasonableness. Step S4: Perform online conformal prediction calibration on the screened results; Step S5: Use the calibrated results as constraints to calculate the backward reachability set of the multi-vehicle game, and infer online to determine the urgency of the scenario.

[0015] Beneficial effects Compared with the prior art, the present invention has the following significant advantages: (1) This invention employs a conformal prediction algorithm for confidence threshold calibration, providing an uncertainty quantification method with strict coverage guarantee under finite sample conditions. Its core advantage lies in the fact that the provided coverage guarantee is strictly valid for finite samples and does not depend on the correctness of the model assumptions. Specifically, for any new test sample, the calibration ellipse output by this invention can guarantee at least... (For example, 95%) of the actual states fall within this range. This strict probability guarantee provides a theoretical basis for setting the warning threshold, avoiding the threshold selection process that relies on experience or trial and error in traditional methods.

[0016] (2) Intelligent screening and boundary determination for multimodal prediction are achieved. This invention designs a dual-threshold modal screening strategy, which filters out low-probability noise modes by using an absolute weight threshold and ensures prediction coverage by using a cumulative weight threshold. This strategy can significantly reduce the conservatism of subsequent reachability set calculations while maintaining a coverage rate of over 95%.

[0017] (3) It balances the reliability of the safety boundary with the real-time performance of the calculation. Traditional methods based on reachability set analysis have high computational complexity and are difficult to apply in real time. This invention proposes an approximate forward reachability set calculation method, which only requires the calculation of a single bivariate nonlinear equation to obtain the non-consistency score. At the same time, it can be proven that the result of the method used is a subset of the actual reachability set, so the calibrated control result has safety conservatism.

[0018] (4) Online continuous calibration and distribution drift adaptation are achieved. This invention designs an online recursive conformal calibration method that updates the confidence threshold in real time through stochastic gradient descent. It can automatically adapt to environmental changes, does not require storing historical calibration data, and has a constant computational cost of O(1). Theoretical analysis shows that, under a reasonable learning rate design, the recursive threshold can almost inevitably converge to the optimal quantile, and the long-term average coverage meets the preset lower bound guarantee.

[0019] (5) The worst-case scenario in multi-agent interaction is fully considered. This invention constructs a chase-and-escape game model between the autonomous vehicle and the surrounding vehicle. The backward reachable set is defined as the set of states in which the autonomous vehicle can still avoid collision under the condition that the surrounding vehicle takes the most unfavorable action. The safety monitoring mechanism designed based on this worst-case analysis can fundamentally guarantee the safety baseline of the autonomous driving system and avoid collision accidents caused by underestimating the threat of the other party.

[0020] (6) A reasonable balance between safety and comfort is achieved. This invention injects the conformally calibrated predicted ellipse as a constraint into the game optimization, so that the circumferential vehicle control strategy considers all reasonable possible action ranges, rather than just typical or average behavior. This design ensures safety in the worst case and avoids false alarms caused by excessive conservatism, thereby improving the overall availability of the system. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the overall process of this invention. Figure 2 This is a schematic diagram illustrating the independent modality cluster centers and correlation coefficients obtained in an embodiment of the present invention. Figure 3This is a network structure diagram of the CVAE model in an embodiment of the present invention; Figure 4 This is a schematic diagram of the top three weighted modes in a certain prediction according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the value function under different relative positions in the relative motion scenario of two vehicles according to an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the evolution trajectory of adversarial game in an embodiment of the present invention. Detailed Implementation

[0022] The technical solution provided in this application will be further described below with reference to specific embodiments and accompanying drawings. The advantages and features of this application will become clearer from the following description.

[0023] This invention aims to solve the following key technical problems existing in current autonomous driving emergency scenario safety monitoring technologies.

[0024] First, there is the issue of reliable quantification and calibration of prediction uncertainty. While existing deep learning prediction models can output multimodal predictions, they lack reliable methods for quantifying prediction confidence. Specifically, the predicted distribution output by the model often exhibits a systematic deviation from the true distribution. For example, the model might predict a vehicle's trajectory within a 95% confidence elliptical region, but in reality, only 80% of the actual trajectory falls within this region. This prediction bias, characterized by either overconfidence or underconfidence, leads to inaccurate subsequent risk assessments. Therefore, there is an urgent need for an uncertainty calibration method that can provide a strict coverage guarantee under limited sample conditions.

[0025] Second, there is the problem of predictive modality selection and boundary determination. In real-world traffic, drivers' behaviors often involve multiple mutually exclusive possibilities, such as going straight, turning left, or turning right at an intersection. Considering only a single modality leads to an excessively large prediction boundary, rendering it unreliable, while considering all possible modalities may introduce noisy modes with extremely low probabilities, resulting in misjudgments. Existing methods lack a systematic strategy for predicting and selecting multiple independent modalities that can achieve a reasonable balance between prediction coverage and prediction accuracy.

[0026] Third, there is the problem of worst-case analysis in multi-agent interactions. Existing methods, when assessing scenario risks, often only consider the "typical" behaviors of surrounding traffic participants, failing to adequately account for the reasonable "worst-case" behaviors they might take. In real traffic, other road users may take dangerous actions for various purposes; therefore, safety monitoring systems need to be designed based on worst-case assumptions. Existing methods lack an effective means to model multi-agent game interactions and solve for the worst-case reachability set.

[0027] Fourth, there is the issue of online learning and continuous calibration. The driving environment is non-stationary; road conditions, weather changes, and driving culture all vary with time and location. Predictive models calibrated based on static datasets experience a significant performance drop when faced with distribution drift. Existing methods lack a mechanism to adapt to environmental changes online and continuously calibrate prediction results.

[0028] Fifth, the dilemma of balancing computational efficiency and security guarantees. While theoretical methods based on reachability set analysis can provide strict security boundary guarantees, traditional methods require solving high-dimensional partial differential equations or performing large-scale grid computing, making their computational complexity insufficient for real-time systems. Furthermore, existing backward reachability set analysis methods are primarily used for autonomous systems; considering the prediction results of deep learning necessitates addressing the computation and processing of reachability sets for non-autonomous systems.

[0029] like Figure 1 As shown, an emergency scenario safety monitoring method for autonomous driving involves inputting surrounding environmental information and vehicle status information collected by sensors of the autonomous vehicle, and outputting a judgment result on the urgency level of the scenario. The method includes the following steps: Step S1: Process trajectory data to extract instantaneous driving actions, and extract the mean and correlation coefficient of the separation modes by clustering; In distribution-based prediction methods, multiple modes are often mixed to fit a complex distribution. However, this does not guarantee that the modes are independent and mutually exclusive (e.g., straight driving and turning / acceleration and deceleration are two independent and mutually exclusive modes). Therefore, it is necessary to obtain the separated modes in advance through cluster analysis.

[0030] First, the natural driving dataset (this example uses the NuScenes dataset released by the autonomous driving company Motional) is preprocessed (e.g., Kalman filtering is applied to the trajectory), and driving actions (longitudinal acceleration) are calculated from the trajectory. -Yaw rate ); Because the kinematic model is differentially flat, the trajectory and driving action are invertible, and the driving action can be obtained from the coordinates (x, y) of the trajectory point. ,as follows: in, x , y The coordinates of the trajectory points in the geodetic coordinate system are represented in meters (m). Heading direction, in rad; a Longitudinal acceleration, unit m / s² 2 ; The yaw rate is expressed in rad / s.

[0031] Next, analyze the driving action phase diagram (in this embodiment, the horizontal axis represents longitudinal acceleration). The vertical axis represents the yaw rate. The modalities are segmented according to different phases, then clustered within each phase to obtain several modalities. The coordinates of the modal cluster centers and the action correlation coefficients are then calculated. Specifically: (1) Roughly classified by speed; Because the calculation error of driving actions at low speeds is relatively large, the driving data is divided into low-speed and high-speed segments according to the speed threshold (1.5m / s). Among them, the low-speed segment is difficult to estimate because the change of driving actions has little impact on the trajectory point at low speeds. Therefore, this invention only considers the case where the vehicle speed is greater than 1.5m / s.

[0032] (2) Phase division in high-speed segment; For high-speed data, calculate the polar coordinates of each sample point on the phase plane of longitudinal acceleration a - yaw rate ω. Based on the action intensity threshold and direction angle, the action space is hard-divided into six phases: cruise, acceleration, braking, left turn, right turn, and mixed phases. Specifically, in the driving action phase diagram (a-ω phase diagram), the greater the distance from the origin, the larger the driver's action amplitude, and different directions represent different action types. The segmentation principle is to first obtain 5 positive phases: Cruise: small acceleration / deceleration and steering actions, i.e., the phase near the origin; Acceleration: small steering actions, positive acceleration / deceleration; Deceleration: small steering actions, negative acceleration / deceleration; Left turn: small acceleration / deceleration, positive yaw rate; Right turn: small acceleration / deceleration, negative yaw rate. Mixed mode: the region remaining after extracting the 5 positive phases.

[0033] (3) Cluster within each phase; For samples within each phase region, if the number of samples accounts for less than 0.1% of the total number of samples, the samples of that type are directly classified into one mode. When the number of trajectory samples is large, Gaussian Mixture Model (GMM) with automatic order determination based on Bayesian Information Criterion (BIC) is used for local clustering to obtain several behavioral modalities. The mean vector of each mode is used as the coordinate of the cluster center; the covariance matrix of the GMM mode is decomposed to obtain the major and minor axes and rotation angle of the ellipse; and the correlation coefficient between longitudinal acceleration and yaw rate is calculated using the off-diagonal elements of the covariance matrix, thereby generating the elliptical coverage of each behavioral mode.

[0034] like Figure 2In this embodiment, a total of 15 clustering modes were obtained, with the following number of modes: 1 cruise, 4 acceleration, 4 deceleration, 1 left turn, 1 right turn, and 4 other mixed modes.

[0035] After segmentation, Gaussian mixture clustering is performed on the phases to obtain M=15 cluster center coordinates and action correlation coefficients.

[0036] Step S2: Train the conditional variational autoencoder multimodal prediction model based on the mean and correlation coefficient of the separated modes; Trajectory prediction is performed using a Conditional Variational Autoencoder (CVAE) multimodal prediction model. Traditional CVAE models predict GMMs without restrictions between different modes, resulting in a single mode being represented by multiple Gaussian distributions. This invention obtains and fixes the mean and correlation coefficient of different modes through pre-clustering, and the distribution prediction model only predicts the variance, thereby ensuring the relative independence of the predicted modes.

[0037] The network structure of the CVAE model is as follows: Figure 3 This includes historical encoder networks, decoder networks, and future encoder networks.

[0038] Prediction model input in This involves encoding historical trajectory information, including the lateral and longitudinal differences of historical trajectory points, speed, heading, and information related to adjacent vehicles. Prediction result labels. out For future trajectory points, including the horizontal and vertical coordinates of the future trajectory points.

[0039] Historical encoder network Input is conditional input in Output to hidden variables z Distribution parameters; future coding networks Simultaneously access conditional input in and future state out This yields the posterior results of the latent variables. Decoder network Based on conditional input in and latent variables obtained by sampling z Distribution parameters for generating future action sequences u (Using a linearized kinematics model to propagate the probability distribution, the spatial location truth labels are converted into a probability distribution for training and propagation of supervisory signals).

[0040] The training objective of the model is to maximize the Evidence Lower Bound (ELBO), which is equivalent to minimizing the weighted combination of the reconstruction loss and the KL divergence loss.

[0041] During the reasoning phase, by starting from the prior distribution... Multiple latent variables are sampled and fed into the decoder network to generate multiple conditionally independent action samples. The number of modalities M, their mean, and correlation coefficients are fixed in the previous clustering step; the model only learns the weights and variances of different modalities. These samples are fitted using Gaussian mixture model parameters to form the final multimodal prediction output.

[0042] The network parameters are trained using large-scale natural driving data to learn the diverse distribution of driving behaviors.

[0043] There are M modes in total (obtained from step S1). The weight of each mode is obtained through the CVAE model, and the mode with the largest weight is... The dominant mode: .

[0044] in, Indicates the first m The weights of each modality .

[0045] Each mode output by the prediction model corresponds to a two-dimensional Gaussian distribution (action). The overall distribution is a mixture of Gaussians: , in, satisfy and Output by the model; The mean value of the actions in the m-th mode; Let m be the action covariance matrix of the m-th mode. , These are the standard deviations of acceleration and angular velocity, respectively. The correlation coefficient between the two is given.

[0046] like Figure 4 These are the top three modes by weight in a given prediction, with the mode m=10 being the dominant mode.

[0047] Step S3: Perform dual-threshold mode screening on the predicted results based on weights; combine the absolute weight threshold and the cumulative weight threshold to screen out modes with high confidence and physical reasonableness.

[0048] Each modality corresponds to an action confidence ellipsoid, defined as: in, The confidence threshold is used to determine the ellipsoid size, which is determined by conformal calibration in step S4.

[0049] In reality, vehicle behavior has one or more reasonable modes. Considering only a single mode will result in an excessively large calibration boundary that includes multiple modal results. Considering all modes will introduce modes with extremely low probabilities, leading to misjudgments downstream.

[0050] Therefore, a dual-threshold mode selection strategy is designed, combining absolute weight thresholds and cumulative weight thresholds to screen out modes with high confidence and physical reasonableness. This includes: 1. Filter low-probability modes to avoid noise interference (step S3-1). 2. Ensure that the cumulative weight of the filtered modalities is large enough to cover the main driving intentions (step S3-2).

[0051] Specifically as follows: S3-1: Absolute weight threshold filtering; Assign weights to the M modes Sort the modalities from largest to smallest to obtain the sorted modal set: The purpose of sorting is to prioritize and retain high-confidence modalities to ensure that the screening results align with the primary driving intent.

[0052] Set absolute weight threshold (recommend ), filtering out those with weights lower than The low-probability modes, the retained mode set is: The core function of this step is to eliminate noise modes that are almost meaningless, reduce the computational load of subsequent conformal calibration, and avoid calibration deviations caused by low-probability modes.

[0053] like (All modal weights are less than) If the modality with the largest weight after sorting is retained, then: S3-2: Cumulative weighted filtering; Set cumulative weight threshold (recommend =0.9~0.95), for The modalities are accumulated in descending order of their weights until the sum of the accumulated weights is not less than 1. This yields a preliminary set of selected modes: like (The cumulative weights of all preserved modes still do not reach) If ), then retain All modes in, i.e. .

[0054] Step S4: Perform online conformal prediction calibration on the screened results; The core of conformal calibration is to calculate the action confidence threshold using actual vehicle data or a small amount of calibration data to be tested. This ensures that the probability of the ellipsoidal set covering the modalities after the real actions are filtered is not lower than the preset confidence level. ( For example, let the significance level be denoted as . (i.e., 95% coverage). This step is based on split conformal, combined with the modalities after dual-threshold screening, to calculate the calibration confidence level.

[0055] S4-1: Calculation of Inconsistent Score; The CVAE multimodal prediction model predicts the constraint range of the control variable (corresponding to a Gaussian distribution in...). In risk monitoring problems, the distance between the vehicle and surrounding vehicles, i.e., the vehicle's positional state, is used to calculate collision risk (an elliptical region under confidence level). The range of the vehicle's positional state is calculated using the forward reachability set method, based on the vehicle's control boundaries. The minimum confidence level is then found by calculating the inconsistency score. This ensures that the location coverage includes the actual trajectory points. The trajectory samples are then verified using a non-consistency score.

[0056] Strict forward reachability set computation is very complex and difficult to meet the requirements of factual computation. This invention proposes a method for calculating under-approximate forward reachability sets with constant boundary control. The calculation steps are as follows (derivation and proof process omitted).

[0057] Based on the definition of the confidence ellipsoid in S3, the constraint equations can be written as follows: in, To control the center of the ellipse.

[0058] Decompose the covariance matrix into The rotation angle is The calculation formula is as follows: in, It is the tangent of the four quadrants. and This represents the standard deviation along the direction of the semi-axis of the ellipse. Therefore, the boundary control input can be written as about Linear parameterization: in To parse the parameters, and To control the center of the ellipse.

[0059] Record the initial values ​​of the vehicle status. The recursive time domain length is T. Using the bicycle model equations, the position is calculated based on the control parameters given the initial position. The bicycle model equations are as follows: , Describe the bicycle model under constant control The following position mapping is: When, the corresponding analytical expression is: when When, the corresponding analytical expression is: Let the actual trajectory point after time T be... Record the displacement Please solve the following problem regarding... Solution of the nonlinear equation system : Obtaining Inconsistent Scores .

[0060] S4-2: Offline calculation of confidence threshold; Calibration requires a certain amount of data, which can be obtained through offline acquisition and recording or online calculation. Assuming n sets of discrete calibration data are collected as the calibration set, the non-consistency score based on the calibration set is calculated first. Then calculate the confidence threshold to ensure that the coverage is greater than or equal to the confidence threshold. The details are as follows: S4-2-1 Inconsistent Score Sort; Sort the inconsistencies in the calibration set in ascending order to obtain an ordered score sequence: in This represents the j-th smallest score after sorting.

[0061] S4-2-2 Calculate quantiles and confidence thresholds; Based on the preset credit level Calculate the quantile position : in This indicates rounding up. The core of this formula is to ensure strict coverage with a limited sample size, avoiding quantile estimation bias caused by the limited sample size.

[0062] Confidence threshold That is, the number after sorting. Small non-consistency score .

[0063] S4-3: Online recursive calculation of confidence threshold; The online recursive operation consists of two steps: first, an initial value is calculated; then, the quantiles are updated recursively based on the initial value, thus continuously updating the correction during the operation. Specifically: S4-3-1 Recursive Initial Values calculate; The following two methods can be used to set it up: (1) Based on a small number of real vehicle calibration samples, the initial threshold is calculated using the method in step S4-2. To ensure initial coverage is close to ; (2) Directly set empirical initial values, such as initially giving the 3-sigma confidence level of the normal distribution, and then quickly converge to the optimal value through recursion.

[0064] S4-3-2 Online Recursion; Calculate the non-uniformity fraction at time t using the S4-1 method. The confidence threshold at time t is calculated recursively using the following formula: in, Let be the confidence threshold at time t; The confidence threshold at time t - 1; For the learning rate, control Update speed guides convergence and avoids oscillations (recommended static learning rate) ); The non-consistent score at time t; This is an indicator function that reflects whether the current frame has been overwritten.

[0065] Step S5: Use the calibrated results as constraints to calculate the backward reachability set of the multi-vehicle game, and infer online to determine the urgency of the scenario; S5-1 constructs the Hamilton-Jacobi-Isaacs (HJI) reachability set problem and trains a value function neural network; The calibrated results are used as constraints to calculate the backward reachability set of the multi-vehicle game. Specifically, S2~S4 first predicts a Gaussian distribution of an action, then filters the multimodal prediction results, and finally calibrates the prediction results (obtaining confidence scores). The control region is determined based on the Gaussian distribution of S2 and the confidence score of S4. This area is the constraint boundary of the control quantity in this step.

[0066] First, a multi-vehicle kinematic model is constructed and a collision risk cost function is designed to quantify the degree of danger during vehicle interaction. Then, the interaction behavior between the two vehicles is modeled as a differential game problem, the definition of the system's Hamiltonian is completed, and the Hamiltonian optimization problem involving minimax operations is decomposed hierarchically. For the self-vehicle, optimal control under the constraint of its own emergency action boundary is solved, and for the surrounding vehicles, suboptimal control under elliptical constraints is solved, thus achieving full-domain analysis and control solution of collision risk in a multi-vehicle game scenario. Finally, a value function neural network is trained using a data-driven method to solve this game problem online.

[0067] S5-1-1 Construction of multi-vehicle kinematic model; The multi-vehicle kinematics model is as follows: Where x and y are the global coordinates of the vehicle's center of mass. For the vehicle's heading, The speed of the vehicle. , , These are the vehicle's acceleration, yaw rate, and steering curvature, respectively; these quantities are the inputs to the system control. The subscript A indicates the vehicle itself. The number i represents the surrounding vehicles (if i is not specified, it means any one of the surrounding vehicles).

[0068] The system equations of the multi-vehicle kinematic model can be simplified as follows: ,in, , , , .

[0069] S5-1-2 Risk Cost Function Design; Considering the worst-case scenario during the two vehicles' journey—that the background vehicle intends to collide—the driver vehicle must ensure that it avoids collision even if the background vehicle has such an intention. Therefore, the cost function... Defined as the minimum distance between the background car and the driver car, the distance is defined as the signed distance function: .

[0070] S5-1-3 Game Theory Problem Construction and Hamiltonian Definition; This is a path minimization functional, where the actions of the two vehicles constitute a zero-sum game, and its value function is: Where t represents time. x Represents system state variables. , is the instantaneous curvature of the vehicle, determined by the instantaneous front wheel angle, and the two satisfy a monotonic one-to-one mapping. The front wheel steering angle of the vehicle, in rad; L This refers to the wheelbase of the vehicle.

[0071] Let the Hamiltonian be: The HJI equation is obtained as follows: While ordinary upper and lower bound constraints reflect physical boundaries to some extent, they are too coarse. Furthermore, completely free zero-sum games do not accurately reflect real-world interactions. Therefore, reasonable constraint design is needed to depict more realistic road conditions.

[0072] Two different constraint description strategies were adopted for the vehicle itself and surrounding vehicles. For surrounding vehicles, a reasonable and foreseeable range of actions was obtained through prediction, while for the vehicle itself, a reasonable constraint range was obtained by defining emergency action boundaries.

[0073] S5-1-4 Decomposition of Hamiltonian Optimization Problem; First, expand the objective function of the Hamiltonian: in, and It is the coefficient matrix expression after rearranging the system equations into the affine form of control.

[0074] Since the constraints on the self-car and the surrounding car are independent, and the objective function is the sum of two terms, the minimax problem can be decomposed into two independent optimization problems, as follows: Maximization problem: , Minimization problem: , in, .

[0075] Both of these problems are linear optimization problems with convex constraints. The optimal solution must lie on the control ellipse constraint boundary defined by S3, and the solution result depends entirely on the constraint conditions.

[0076] 5-1-5 Solving the optimal control solution under emergency boundary constraints for the vehicle; First, the emergency boundaries of the vehicle need to be defined. The constraints of the emergency action boundaries are defined based on the vehicle's adhesion ellipse and action intensity. The main forces during vehicle movement are provided by the interaction between the road surface and the tires; therefore, the combined acceleration between the tires and the ground satisfies the adhesion ellipse constraints. in, g The acceleration due to gravity is usually taken as 9.8 m / s². 2 ; Let be the road surface adhesion coefficient, taken as... .

[0077] Emergency boundaries primarily consider two aspects. Firstly, to handle the current crisis, the driver needs to make significant driving maneuvers to resolve it, indicating an emergency scenario. Secondly, when acceleration approaches the adhesion ellipse boundary, some linearization assumptions of the original model will no longer hold, significantly increasing the vehicle's handling difficulty and thus manifesting as an emergency. Lateral acceleration, based on common linear tire assumptions, typically requires lateral acceleration to be less than 0.4g; exceeding this usually triggers ESP to stabilize the vehicle's attitude and causes noticeable discomfort. Longitudinal acceleration is generally related to road adhesion and can approach the adhesion limit, but approaching this limit increases tire slippage, triggering ABS. Longitudinal acceleration exceeding 0.6g usually causes noticeable discomfort. Considering changes in road adhesion, the emergency boundaries for both lateral and longitudinal acceleration are defined as follows: The boundary ellipse for the vehicle's emergency action constraint can then be defined as: The curvature constraint can be derived from the physical constraints on the front wheel steering angle. Acceleration also has physical constraints, but the physical boundary of acceleration is naturally larger than the elliptical boundary. Therefore, only the curvature constraint needs to be considered. By writing the constraints in matrix form, the optimization problem for vehicle control can be written as: in , .

[0078] The solution to the optimization problem of autonomous vehicle control is: when At this time, the upper and lower limits have no effect and are completely determined by the elliptical boundary.

[0079] Let the direction vector To maximize According to the generalized form of the Cauchy-Schwarz inequality: If and only if , When the value is a scalar, equality is taken. Therefore, the optimal solution... The direction should be with Consistent. Substituting the constraints yields... ,therefore: when When the new boundary is the intersection of an ellipse and a rectangle, this intersection must be a convex set, therefore the optimal solution must be found on the boundary. Thus, points on the original elliptical boundary remain optimal as long as their curvature does not exceed the constraint.

[0080] If the original optimal solution exceeds the boundary, then the optimal solution is obtained at the rectangular boundary. The optimization problem becomes: set up The optimal solution is: .

[0081] Solution of suboptimal control under elliptic constraints for 5-1-6 cycle vehicle; The surrounding vehicles require consideration of two elliptical constraints and one upper and lower boundary constraint. Although all three constraints are convex, the overall problem remains a convex optimization problem. However, it is often difficult to obtain a closed-form solution when both elliptical constraints are activated simultaneously. Iterative solutions using numerical optimization tools typically take more than 100 times longer than simple analytical solutions, which is usually unacceptable when the model is trained with a large number of samples. Therefore, a suboptimal solution was used to solve for the control variables based on the actual situation.

[0082] Specifically as follows: (1) Optimal solution under prediction constraints The k-confidence ellipse for the driving action can be obtained from the prediction: The constraint ellipse of the circumference can then be represented as: in, To constrain the center of the ellipse.

[0083] The problem of minimizing the rook: Similarly, let the direction vector To maximize .make Then we have: because It is unrelated to the optimization variables; we only need to consider According to the Cauchy-Schwarz inequality, if and only if The time is equal. Therefore, the optimal solution is... The direction should be with Consistent. Substituting, we get: get: ; (2) Correction of physical constraint control for the circumferential vehicle In addition to the aforementioned predictive constraints, actions exceeding the limits of the vehicle dynamics attachment ellipse are considered impossible in the real world; therefore, these actions exceeding physical limits require correction. The expression for the attachment ellipse is: In addition, the vehicle steering system has physical constraints: Simultaneously considering the difficulty of obtaining analytical results for optimal solutions under multiple constraints, a heuristic suboptimal strategy is designed here to handle the constraints and maintain the original direction. Let the adjusted solution be: Considering the physical constraints of the ellipse: , Assume the mean satisfies physical constraints Then we get (taking positive values): in, ; ; .

[0084] Considering the turning constraint, the adjusted solution is: Solve , Assume the mean satisfies the constraints Solving for: Finally, the scaling factor is obtained: The adjusted solution is obtained: , The superscript (0) here indicates that no constraint is applied.

[0085] The adjusted solution is no longer optimal, which will lead to the vehicle being at a disadvantage. However, the above adjustment method only produces suboptimal results when it approaches the physical upper limit boundary. In real time, vehicles usually cannot and will not approach the physical upper limit. Therefore, the conservatism of adopting the suboptimal strategy can be accepted.

[0086] The above result is valid only if the mean satisfies the physical constraints. If the mean does not satisfy the physical constraints, then we do not consider solving within the constraints (in real time, the prediction results in the truncation part usually have very small weights and can be ignored). In this case, we directly adopt the truncation strategy to solve the suboptimal solution. This method can ensure the continuity of the strategy and help the robustness of model training.

[0087] First, determine the magnitude of the optimal gradient direction under the prediction constraints. , After the first constraint is processed, the result is The superscript (1) indicates that the process has undergone a constraint.

[0088] The second constraint is handled as follows The superscript (2) indicates that the process has undergone two constraints.

[0089] In summary: In summary, the control strategy after constraint correction is as follows: 5-1-7 Training a value function neural network using a data-driven approach; The above calculation process fully describes the construction of the HJI equation system. By using the HJI equation as supervision, data is generated and then trained, thereby avoiding the need for online solving of game theory problems.

[0090] Specifically, this game problem can be solved quickly online by training the value function using DeepReach.

[0091] S5-2 uses value function neural network-based online inference to obtain vehicle risk; After the above problem is constructed, a value function neural network can be obtained through training. Based on the value function neural network, collision can be determined online. Based on the online solution of the above optimization problem, the trajectory of the vehicle game can be deduced from the optimal control quantity.

[0092] The urgency of the scenario is determined based on the minimum distance between the two workshops within the next T seconds. Specifically, the current state is input into the trained model to obtain the nearest distance within the next T seconds. When the nearest distance is less than 0, it indicates that a collision has occurred; when it is greater than 0, it indicates that no collision has occurred. The magnitude of the nearest distance represents the urgency of the scenario.

[0093] like Figure 5The scene includes a background car and the player car. Both the player car and the background car have a speed of 5 m / s and a relative heading angle of 0. The function represents the relative positions of the two cars, where the black closed curve represents the zero-value function. The inside of the curve indicates a collision, and the outside indicates no collision.

[0094] Furthermore, for specific scenarios, the game process can be deduced using value function networks. Based on value functions and the aforementioned optimal control problem solution process, the vehicle trajectory for the next T seconds can be calculated progressively and can be used for diagnosis and analysis. Figure 6 Given that the surrounding vehicles are positioned at coordinates (-5, -5) relative to the vehicle, the vehicle's speed is 5 m / s, the surrounding vehicles' speed is 5 m / s, and the relative heading angle is 0 rad, the evolution trajectories of the two vehicles 3 seconds later.

[0095] Compared with the prior art, the core improvements of this invention include the following: (1) Independent mode acquisition based on segmentation clustering method. This invention obtains longitudinal acceleration and yaw rate action points by processing natural driving trajectory data, and after segmenting the phase diagram according to angle, performs mixture Gaussian clustering in each phase region to obtain cluster centers and action correlation coefficients.

[0096] (2) A Multimodal Prediction Calibration Method Based on a Dual-Threshold Strategy. This invention applies conformal prediction theory to multimodal behavior prediction calibration in autonomous driving scenarios and designs a dual-threshold screening strategy combining absolute weight thresholds and cumulative weight thresholds. This strategy can systematically filter low-probability noise modes and retain high-confidence intention modes, solving the problem of balancing coverage and accuracy in multimodal prediction. The main improvements include: the method for setting the dual-threshold thresholds (absolute threshold, cumulative threshold); the method for defining inconsistency scores; and the method for calculating quantile positions.

[0097] (3) Online recursive conformal calibration mechanism. This invention transforms batch conformal calibration into real-time stochastic gradient descent optimization and designs an online recursive calibration method with a computational complexity of O(1). This method enables conformal prediction theory to be applied to online deployment on real vehicles, resolving the contradiction between finite sample coverage guarantee and real-time requirements. The main improvements include: recursive update formula ( (); learning rate design methods; and initial value setting strategies.

[0098] (4) Solving the backward reachable set of the pursuit-escape game based on calibration ellipse constraints. This invention uses the conformally calibrated predicted ellipse as the constraint condition for the circumvention control and introduces a game theory framework to solve the backward reachable set. This method allows the safety analysis to fully consider the uncertainty of multi-agent interactions, rather than just typical behaviors. The main improvements include: matrix formalization of ellipse constraints; closed-form solution of optimization problems under ellipse constraints; and heuristic correction strategies for physical constraints (attached ellipse, turning limit).

[0099] Key terms and definitions in this invention: Conditional Variational Autoencoder (CVAE): A deep generative model that combines variational inference and conditional modeling. The model learns the posterior distribution of the input data through an encoder network and generates the output based on latent variables and conditional information through a decoder network. In autonomous driving scenarios, CVAE is used to model the multimodal distribution of driving behavior, enabling the prediction of multiple possible future actions given the current scene state.

[0100] Conformal prediction is a distribution-independent uncertainty quantification method that provides strict coverage guarantees under finite sample conditions. The core idea of ​​conformal prediction is to construct a prediction set that covers a certain proportion of the true values ​​by calculating the inconsistency score and taking its quantile. This method does not rely on the correctness of the model assumptions, has strong theoretical guarantees, and wide applicability.

[0101] Dual-threshold modal filtering: This invention designs a multimodal filtering strategy that achieves a balance between prediction coverage and prediction accuracy by setting two layers of filtering: an absolute weight threshold and a cumulative weight threshold. The first threshold filters out noisy modes with extremely low probabilities, while the second threshold ensures that the filtered modes cover sufficient cumulative probability quality.

[0102] Pursuit-Evasion Game: A typical problem in game theory where one party (the pursuer) attempts to approach or capture another party (the escapee), while the other party tries to avoid being captured. This invention treats the self-vehicle as the pursuer (who needs to avoid collision) and the surrounding vehicle as the escapee (who may take aggressive actions), constructing a zero-sum game framework for security analysis.

[0103] Backward Reachable Set: Given control constraints and adversarial inputs, the backward reachable set is the set of states reachable from the target set through all possible control sequences. It describes which states will ultimately lead to a collision, given that collisions are known to occur, and is an important tool for safety verification and risk assessment.

[0104] The Hamilton-Jacobi-Isaacs (HJI) equations are partial differential equations describing the optimality conditions of a two-player zero-sum differential game. The HJI equations are a generalization of dynamic programming principles within the framework of game theory, and their solutions yield the value function and the optimal control strategy. This invention obtains the optimal strategy and backward reachability set in a chase-and-escape game by solving the HJI equations.

[0105] The Signed Distance Function (SDF) is a function that describes the distance from any point in space to a target set. It returns a positive value (Euclidean distance) when the point is outside the set, a negative value (the opposite of the penetration depth) when the point is inside the set, and zero when the point is on a boundary. This invention uses a signed distance function based on OBB and SAT to accurately describe the relative relationship between two vehicles.

[0106] Zero-Order Hold (ZOH): A discretization method that maintains a continuous-time signal at a constant value within each sampling period. This invention employs the ZOH method to discretize the dynamics of a continuous-time system, facilitating numerical computation and real-time implementation.

[0107] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Those skilled in the art, after reading this specification, can make various modifications or variations to the technical solutions without departing from the concept of the present invention, and all such modifications or variations fall within the protection scope of the present invention.

Claims

1. A method for safety monitoring in emergency scenarios of autonomous driving, characterized in that, Includes the following steps: Step S1: Process trajectory data, extract instantaneous driving actions, and cluster to extract the mean and correlation coefficient of the separation modes; Specifically, the natural driving dataset is first preprocessed to calculate driving actions, including longitudinal acceleration, from the trajectory. and yaw rate The driving action phase diagram is then segmented according to different phases, and clustered within each phase to obtain several modes. The coordinates of the mode cluster centers and the action correlation coefficient are then calculated. Step S2: Train the conditional variational autoencoder multimodal prediction model based on the mean and correlation coefficient of the separated modes; Specifically, a conditional variational autoencoder multimodal prediction model is used for trajectory prediction. The conditional variational autoencoder multimodal prediction model includes a historical encoder network, a decoder network, and a future encoder network. The input in of the prediction model is the encoding of historical trajectory information, and the prediction result label out is the future trajectory point. The training objective of the model is to maximize the variational lower bound. During the inference phase, multiple latent variables are sampled from the prior distribution and fed into the decoder network to generate multiple conditionally independent action samples. The final multimodal prediction output is formed by fitting the hybrid model parameters. Step S3: Perform dual-threshold mode screening on the prediction results based on weights; combine the absolute weight threshold and the cumulative weight threshold to screen out modes with high confidence and physical reasonableness. Specifically, a dual-threshold modality selection strategy is designed, which combines absolute weight threshold and cumulative weight threshold to select high-confidence and physically reasonable modalities, including: (1) filtering low-probability modalities to avoid noise interference; (2) cumulative weight filtering to ensure that the cumulative weight of the selected modalities is large enough to cover the main driving intentions. Step S4: Perform online conformal prediction calibration on the screened results; Specifically, the vehicle's position state range is calculated through the vehicle's control boundary, and the minimum confidence level is found by calculating the inconsistency score. To ensure that the location coverage includes the actual trajectory points, the inconsistency score is used to verify the trajectory samples; firstly, the inconsistency score based on the calibration set is calculated. Then, the confidence threshold is calculated. The online recursive operation is divided into two steps: one is used to calculate the confidence threshold online; the other is to use the inconsistency score to calculate the confidence threshold at time t online. Step S5: Use the calibrated results as constraints to calculate the backward reachability set of the multi-vehicle game, and infer online to determine the urgency of the scenario; specifically, this includes: S 5.1 Constructs the HJI reachability set problem and trains a value function neural network; uses the calibrated results as constraints to calculate the backward reachability set of multi-vehicle game; constructs a multi-vehicle kinematic model and designs a collision risk cost function to quantify the degree of danger in the vehicle interaction process; then models the interaction behavior of the two vehicles as a differential game problem, completes the definition of the system Hamiltonian, and decomposes the Hamiltonian optimization problem involving minimax operations into hierarchical parts; solves the optimal control under the constraint of the self-vehicle's emergency action boundary for the self-vehicle, and solves the suboptimal control under the elliptical constraint for the surrounding vehicles, thereby realizing the global analysis and control solution of collision risk in the multi-vehicle game scenario; finally, uses a data-driven method to train a value function neural network for online solution of this game problem; S5-2 uses value function neural network for online inference to obtain vehicle risk; the urgency of the scenario is determined based on the minimum distance between the two vehicles within the next T seconds.

2. The method according to claim 1, characterized in that, Step 2 specifically involves: Trajectory prediction is performed using a conditional variational autoencoder multimodal prediction model, with the mean and correlation coefficient of the modes fixed, and only the variance is predicted. The conditional variational autoencoder multimodal prediction model includes a historical encoder network, a decoder network, and a future encoder network; The prediction model input in is the encoding of historical trajectory information, including the horizontal and vertical differences of historical trajectory points, speed, heading, and relevant information of adjacent vehicles; the prediction result label out is the future trajectory point, including the horizontal and vertical coordinates of the future trajectory point; Historical encoder network The input is the conditional input *in*, and the output is the distribution parameters of the latent variable *z*; Future Encoding Network Simultaneously, conditional input (in) and future state (out) are input to obtain the posterior result of latent variables; Decoder Network Based on the conditional input in and the latent variable z obtained from sampling, the distribution parameters u of the future action sequence are generated; The training objective of the model is to maximize the variational lower bound, which is equivalent to minimizing the weighted combination of the reconstruction loss and the KL divergence loss. During the reasoning phase, by starting from the prior distribution... Multiple latent variables are sampled and fed into the decoder network to generate multiple conditionally independent action samples; the samples are fitted with Gaussian mixture model parameters to form the final multimodal prediction output; There are M modes in total. The weight of each mode is obtained through the prediction model, and the mode with the largest weight is... The dominant mode: ,in, This represents the weight of the m-th mode. ; Each mode output by the prediction model corresponds to a two-dimensional Gaussian distribution, and the overall distribution is a mixture of Gaussian distributions. ， in, satisfy and Output by the model, symbol Indicates a Gaussian distribution; The mean value of the actions in the m-th mode; Let m be the action covariance matrix of the m-th mode. , These are the standard deviations of acceleration and angular velocity, respectively. The correlation coefficient between the two is given.

3. The method according to claim 1, characterized in that, Step 3 specifically involves: Each modality corresponds to an action confidence ellipsoid, defined as: ， in, The confidence threshold; A dual-threshold mode selection strategy is designed, combining absolute weight thresholds and cumulative weight thresholds to screen out highly confident and physically reasonable modes, including: (1) Filter low-probability modes to avoid noise interference; (2) Cumulative weight filtering ensures that the cumulative weight of the filtered modalities is large enough to cover the main driving intentions; Specifically as follows: S3-1: Absolute weight threshold filtering; Assign weights to the M modes Sort the modalities from largest to smallest to obtain the sorted modal set: Set absolute weight threshold Filter out those with a weight lower than The low-probability modes, the retained mode set is: ； S3-2: Cumulative weighted filtering; Set cumulative weight threshold ,right The modalities are accumulated in descending order of their weights until the sum of the accumulated weights is not less than 1. This yields a preliminary set of selected modes: 。 4. The method according to claim 3, characterized in that, When using absolute weight threshold filtering, if Then the mode with the largest weight after sorting will be forcibly retained; When using cumulative weight filtering, if Then keep All modes in.

5. The method according to claim 1, characterized in that, Step 4 specifically involves: S4-1: Calculation of Inconsistent Score; The CVAE multimodal prediction model predicts the constraint range of the control quantity. In the risk monitoring problem, the distance between the vehicle and surrounding vehicles, i.e. the vehicle's position state, is used to calculate the collision risk. Using the forward reachability set method, the vehicle's position state range is calculated from the vehicle's control boundary; by calculating the inconsistency score, the minimum confidence level is found. This ensures that the location coverage includes the actual trajectory points; and then the trajectory samples are verified through non-consistency scores. S4-2: Offline calculation of confidence threshold; Calibration requires a certain amount of data, which can be obtained through offline acquisition and recording or online calculation. Assuming n sets of discrete calibration data are collected as the calibration set, the non-consistency score based on the calibration set is calculated first. Then calculate the confidence threshold to ensure that the coverage is greater than or equal to the confidence threshold. , Confidence level; S4-3: Online recursive calculation of confidence threshold; The online recursive operation is divided into two steps: first, the initial value is calculated, and then the quantile is updated recursively based on the initial value, thereby continuously updating and correcting during the operation. S4-3-2 Online Recursion; Calculate the non-uniformity fraction at time t using the S4-1 method. The confidence threshold at time t is calculated recursively using the following formula: in, Let be the confidence threshold at time t; The confidence threshold at time t - 1; For learning rate, The non-consistent score at time t; This is an indicator function.

6. The method according to claim 5, characterized in that, The offline calculation of the confidence threshold is as follows: S4-2-1 Inconsistent Score Sort; Sort the inconsistencies in the calibration set in ascending order to obtain an ordered score sequence: in This represents the j-th smallest score after sorting. S4-2-2 Calculate quantiles and confidence thresholds; Based on the preset credit level Calculate the quantile position : , in Indicates rounding up; Confidence threshold That is, the number after sorting. Small non-consistency score .

7. The method according to claim 5, characterized in that, In step S4-1, the under-approximate forward reachable set calculation method with constant boundary control is adopted. The calculation steps are as follows: The constraint equations are: ， in, To control the center of the ellipse; Decompose the covariance matrix into The rotation angle is The calculation formula is as follows: ， in, It is the tangent of the four quadrants. and This represents the standard deviation along the direction of the semi-axis of the ellipse. Therefore, the boundary control input is written as about Linear parameterization: in To parse the parameters, and To control the center of the ellipse; Record the initial values ​​of the vehicle status. The recursive time domain length is T; using the bicycle model equations, the position is calculated based on the control given the initial position; the bicycle model equations are as follows: ， Describe the bicycle model under constant control The following position mapping is: When, the corresponding analytical expression is: ， when When, the corresponding analytical expression is: ， Let the actual trajectory point after time T be... Record the displacement Solve the following about Solution of the nonlinear equation system : Obtaining Inconsistent Scores .

8. The method according to claim 1, characterized in that, The specific steps for constructing a differential game problem are as follows: S5-1-1 Construction of multi-vehicle kinematic model; The multi-vehicle kinematics model is as follows: Where x and y are the global coordinates of the vehicle's center of mass. For the vehicle's heading, The speed of the vehicle; , , These are the vehicle's acceleration, yaw rate, and steering curvature, respectively; these quantities are the inputs to the system control. The subscript A indicates the vehicle itself. This indicates the surrounding vehicles, where i is the number of the surrounding vehicle. If i is not specified, it means any one of the surrounding vehicles. The system equations of the multi-vehicle kinematic model are simplified as follows: ,in, , , ， ； S5-1-2 Risk Cost Function Design; Considering the worst-case scenario during the two vehicles' journey—that the background vehicle intends to collide—the driver vehicle must ensure that it avoids collision even if the background vehicle has such an intention. Therefore, the cost function... Defined as the minimum distance between the background car and the driver car, the distance is defined as the signed distance function: ； S5-1-3 Game Theory Problem Construction and Hamiltonian Definition; This is a path minimization functional, where the actions of the two vehicles constitute a zero-sum game, and its value function is: Where t represents time, and x represents the system state variable. , which is the instantaneous curvature of the vehicle, determined by the instantaneous front wheel angle, and the two satisfy a monotonic one-to-one mapping; The front wheel steering angle of the vehicle is expressed in rad; L is the wheelbase of the vehicle. Let the Hamiltonian be: The HJI equation is obtained as follows: ； S5-1-4 Decomposition of Hamiltonian Optimization Problem; First, expand the objective function of the Hamiltonian: in, and It is the coefficient matrix expression after rearranging the system equations into the affine form of control; Since the constraints on the self-car and the surrounding car are independent, and the objective function is the sum of two terms, the minimax problem can be decomposed into two independent optimization problems, as follows: Maximization problem: , Minimization problem: , in, ; Both of these problems are linear optimization problems with convex constraints. The optimal solution must lie on the control ellipse constraint boundary defined by S3, and the solution result depends entirely on the constraint conditions.

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