A game theory-based pedestrian trajectory prediction method for right-turn intersection without signal

Abstract

This invention belongs to the field of pedestrian trajectory prediction technology, and particularly relates to a method for predicting pedestrian trajectories at unsignalized right-turn intersections based on game theory. The method includes the following steps: S1, acquiring historical data on pedestrians and vehicles at unsignalized right-turn intersections; S2, analyzing the human-vehicle game factors at unsignalized right-turn intersections and constructing a corresponding human-vehicle game model; S3, inserting the human-vehicle game model into a pre-set S-GAN model to obtain an SDG-GAN model for predicting pedestrian trajectories; S4, training the SDG-GAN model using the historical data acquired in S1; S5, using the trained SDG-GAN model to predict pedestrian trajectories at unsignalized right-turn intersections in real time. This invention ensures the accuracy of pedestrian trajectory prediction at unsignalized right-turn intersections and the effectiveness of assisted driving decisions at such intersections, thus balancing the efficiency and safety of vehicles passing through unsignalized right-turn intersections.

Description

Technical Field

[0001] This invention belongs to the field of pedestrian trajectory prediction technology, and in particular relates to a method for predicting pedestrian trajectories at unsignaled right-turn intersections based on game theory. Background Technology

[0002] In the field of driver assistance systems, the efficiency and safety of vehicles crossing intersections are crucial considerations. At intersections with traffic lights, the system provides clear directions, allowing for autonomous or assisted driving simply by following the lights, thus minimizing the probability of conflicts between pedestrians and vehicles.

[0003] However, at special intersections without traffic lights, such as unsignaled right-turn intersections, the relationship between pedestrians and vehicles becomes particularly complex. Their behavior is both uncertain and interconnected, often influenced by multiple unpredictable factors, such as individual personalities and environmental factors. When vehicles pass through unsignaled right-turn intersections, their right turns are not subject to traffic signal control. The arbitrary movement of right-turning vehicles and the interaction of traffic flows from different directions interfere with pedestrians, significantly increasing the danger for pedestrians. Regarding pedestrians, their crossing at unsignaled right-turn intersections is highly random and maneuverable, and the intentions of different pedestrians vary significantly. Relying solely on the driver's subjective judgment is inaccurate and cannot reduce the risks associated with pedestrian-vehicle interactions.

[0004] Therefore, to balance efficiency and safety when assisted driving / autonomous driving through unsignalized right-turn intersections, accurate prediction of pedestrian trajectories is crucial. Only in this way can the effectiveness of assisted driving decisions at unsignalized right-turn intersections be guaranteed. Currently, pedestrian trajectory prediction is mainly divided into model-driven prediction and deep learning prediction based on historical data. Model-driven methods include social force models, Markov models, and Kalman filter models. Because deep learning can effectively address some shortcomings of model-driven prediction methods, deep learning prediction based on historical data has gradually become the mainstream research direction. For example, the S-GAN model (Social-GAN, Social Generative Adversarial Network) used for assisted driving incorporates the idea of ​​human-vehicle interaction and game theory on top of deep learning prediction.

[0005] Game theory, an important branch of modern mathematics, studies the decision-making process of two or more players in a mutually influential environment. It provides a precise perspective for analyzing cooperative and competitive states and the gains and losses of mutual decisions. However, existing research on pedestrian-vehicle conflicts at intersections primarily focuses on safety, traffic styles, and interactive behaviors. There is a lack of incorporation of game theory into the analysis of various risk factors in pedestrian-vehicle conflicts, particularly methods for predicting pedestrian trajectories. In real-world scenarios, pedestrian-vehicle interaction is a dynamic process requiring consideration of motion factors and macro-level game theory decision-making. This results in a general need to improve the accuracy of existing research, making it difficult to apply to assisted driving decisions at unsignalized right-turn intersections.

[0006] In summary, how to ensure the accuracy of pedestrian trajectory prediction at unsignalized right-turn intersections, thereby guaranteeing the effectiveness of assisted driving decisions at unsignalized right-turn intersections and balancing the efficiency and safety of vehicles passing through unsignalized right-turn intersections, has become an urgent problem to be solved. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, this invention provides a method for predicting pedestrian trajectories at unsignalized right-turn intersections based on game theory. This method can ensure the accuracy of pedestrian trajectory prediction at unsignalized right-turn intersections and the effectiveness of assisted driving decisions at such intersections, thereby balancing the efficiency and safety of vehicles passing through unsignalized right-turn intersections.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] A method for predicting pedestrian trajectories at unsignalized right-turn intersections based on game theory includes the following steps:

[0010] S1. Obtain historical data on pedestrians and vehicles at unsignaled right-turn intersections;

[0011] S2. Analyze the factors in the pedestrian-vehicle game at an intersection with no signal right turn and construct the corresponding pedestrian-vehicle game model;

[0012] S3. Insert the human-vehicle game model into the preset S-GAN model to obtain the SDG-GAN model, which is used to predict the trajectory of pedestrians.

[0013] S4. Use the historical data obtained in S1 to train the SDG-GAN model;

[0014] S5. Use the trained SDG-GAN model to predict pedestrian trajectories in real time at intersections with no right turn signal.

[0015] Preferably, in S2, the construction process of the human-vehicle game model includes:

[0016] S21. Divide the game into stages, design an observation area and a conflict area. Once pedestrians and vehicles enter the observation area, the game is considered to have started. The post-intrusion time is used to characterize the degree of danger of the human-vehicle conflict. The post-intrusion time is the time difference between pedestrians and vehicles entering the conflict area. The shorter the post-intrusion time, the higher the degree of danger.

[0017] S22. Based on the decision-making strategies of pedestrians and vehicles in the game, construct a human-vehicle game payoff matrix; the decision-making strategies include pedestrians and vehicles passing simultaneously, pedestrians waiting for vehicles to pass, pedestrians passing while vehicles wait, and pedestrians and vehicles waiting simultaneously.

[0018] S23. Based on the characteristics of the human-vehicle game payoff matrix, the expectation function and corresponding loss function of the human-vehicle game model are obtained.

[0019] S24. Based on the expectation function and loss function obtained in S23, construct a human-vehicle game model.

[0020] Preferably, in S22, when pedestrians and vehicles pass simultaneously,

[0021] The pedestrian's payment function is:

[0022] The vehicle's payment function is:

[0023] Among them, v v Indicates the pedestrian crossing speed, a v Represents the pedestrian's acceleration v p Indicates the vehicle's speed, a p α1 represents the vehicle acceleration, α2 represents the combined influence factor of the vehicle's velocity and acceleration, and σ represents the combined influence factor of the pedestrian's velocity and acceleration. v The collision severity factor, σ, represents the severity of a vehicle collision. p A factor representing the severity of a pedestrian collision, and:

[0024]

[0025]

[0026] The pedestrian's payment function is as follows:

[0027] In the formula, α4 is the waiting inhibition coefficient when passing through, and t p Waiting time for pedestrians;

[0028] The vehicle's payment function is:

[0029] In the formula, α3 is the velocity excitation coefficient when passing through;

[0030] When pedestrians cross while vehicles wait, the pedestrian's payment function is:

[0031] In the formula, α3 is the velocity excitation coefficient when passing through, v p For pedestrian crossing speed;

[0032] The vehicle's payment function is:

[0033] In the formula, α4 is the waiting inhibition coefficient when passing through, and t v The vehicle waiting time is 0.75 seconds, and the driver's reaction time is 0.75 seconds.

[0034] When pedestrians and vehicles are waiting simultaneously, the pedestrian's payment function is:

[0035] The vehicle's payment function is

[0036] Where α5 is the waiting inhibition coefficient of the vehicle under common loss; α6 is the waiting inhibition coefficient of the pedestrian under common loss; k is the regret factor of both parties. The regret factor is related to the starting acceleration during the waiting process and represents the degree of regret for taking the waiting strategy. The greater the starting acceleration, the greater the degree of regret.

[0037] The human-vehicle game payoff matrix is ​​as follows:

[0038]

[0039] Preferably, in S23, the expected function is the combined expected benefit of both the vehicle and the pedestrian when the Nash equilibrium point of the mixed advantage strategy of vehicle passing through waiting and pedestrian passing through vehicle waiting is reached.

[0040] Among them, the expected benefit when the vehicle chooses to pass. for:

[0041] in, Indicates the probability of a pedestrian crossing. The probability of waiting for pedestrians;

[0042] Expected benefits when vehicles choose to wait for:

[0043]

[0044] Analyze the pure strategy payoff for pedestrians, and the expected payoff when pedestrians cross the road. for:

[0045] in, Indicates the probability of a vehicle passing through. This indicates the probability of a vehicle waiting.

[0046] Expected benefits when pedestrians choose to wait for:

[0047]

[0048] Expected benefits when the vehicle passes With waiting expected returns When the Nash equilibrium is reached, the probability combinations of pedestrians crossing and waiting are as follows:

[0049]

[0050]

[0051] When pedestrians pass through, the expected benefits With waiting expected returns When the Nash equilibrium is reached, the probability combinations of a vehicle passing and waiting are as follows:

[0052]

[0053]

[0054] Preferably, when the SDG-GAN model predicts the trajectory of a pedestrian, the pedestrian trajectory is defined as the change of two-dimensional coordinate position in a time series, and the coordinates of pedestrian u at time t are... The coordinates of vehicle j at time t are The set of historical trajectories X for pedestrian u at each step length from 1 to to u for:

[0055]

[0056] In the formula, 1 to to are the observation frames of the pedestrian's historical trajectory, and to is the length of the observation frame;

[0057] Pedestrian u from to+1 to t p The set of predicted trajectories for each step size for:

[0058]

[0059] In the formula, to+1~to+t p For the predicted frames of the pedestrian's historical trajectory, t p To predict the frame length.

[0060] Pedestrian u from to+1 to tp The set of true historical trajectories Y for each step size u for:

[0061]

[0062] Pedestrian u from 1 to t p The true historical trajectory within With predicted trajectory generation They are respectively [X u ,Y u ]and

[0063] Preferably, in S3, the SDG-GAN model includes a human-vehicle game model, a trajectory generator, and a trajectory discriminator; the trajectory generator is used to encode and decode the output of the human-vehicle game model and the historical trajectory of the pedestrian, and output the predicted trajectory of the pedestrian; the trajectory discriminator is used to discriminate the probability that the predicted trajectory of the pedestrian is the real trajectory.

[0064] Preferably, the trajectory generator includes a trajectory encoder, a game mechanism module, a pooling module, and a trajectory decoder;

[0065] The trajectory encoder embeds the pedestrian and vehicle coordinates at each time step into an embedding function φ containing a ReLU nonlinear activation function to obtain a fixed-length vector. and Then, the pedestrian historical trajectory feature vector is obtained through LSTM unit encoding. With vehicle historical trajectory feature vector

[0066]

[0067]

[0068] In the formula, the embedding function φ represents the fully connected neural network layer. The weight parameters of the embedding function, These are the weight parameters of the LSTM unit;

[0069] The game mechanism module is used to extract game-related data of both the driver and the vehicle based on the game payoff function of both parties. The game-related data includes speed, acceleration, relative distance, and waiting time. It is also used to obtain the post-intrusion time at each time step by using the speed of both parties and the distance between them and the conflict area. The post-intrusion time value is used to determine the degree of danger of the interaction between the two parties at this time step. And the position coordinates of both parties at this time are used to determine whether they are in the observation area or the conflict area.

[0070] The game theory mechanism module is also used to calibrate based on the interactive decisions of people and vehicles in the real world, and to obtain the specific expected gains and losses of both parties under the decision. and The specific expected gains and losses influence the feature vectors of the historical trajectories of both the driver and the vehicle, thus obtaining the game-theoretic feature vectors of both parties. And merged into a feature vector of human-vehicle hybrid game.

[0071]

[0072] In the formula, Let x be the collision severity factor for pedestrian u and vehicle j respectively. Let f be the real-time coordinate region for pedestrian u and vehicle j respectively. pet Let f be the collision severity determination function. R For real-time region determination function, t pet Post-intrusion time during human-vehicle interaction, ω pet ω is the collision severity weighting parameter. R For real-time regional weight parameters;

[0073]

[0074]

[0075]

[0076] In the formula, f pay For game theory calculation functions, f represents the specific payment function under different strategies of both parties. inf Let f be the game influence function. mix For game theory mixture functions;

[0077] The pooling module is used to embed the relative distance between people and vehicles into the embedding function φ to obtain the feature vector of the relative position of people and vehicles. Feature vectors of hybrid human-vehicle game The game pooling vector is obtained by connecting the data and passing it through a multilayer perceptron.

[0078]

[0079]

[0080] In the formula, Mlp GP For pooling modules in a multilayer perceptron network, Cat is used to connect feature vectors. These are the weight parameters corresponding to their respective network layers;

[0081] The trajectory decoder is used to convert game pooling vectors Pedestrian historical trajectory feature vector Establish a connection and use the decoder module multilayer perceptron Mlp GD The feature vector of the decoder is finally obtained by connecting it to random Gaussian noise Z in the network. Compared with the pedestrian coordinate vector after embedding function encoding Initialize the cell zero vector The vectors are input together into the LSTM neural network layer. Finally The pedestrian trajectory prediction coordinates are finally obtained after the decoder and multilayer perceptron.

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, ω λ These are the weight parameters for the corresponding network layer.

[0087] Preferably, in S3, the operation of the trajectory discriminator includes: converting the pedestrian predicted trajectory output by the trajectory generator into a single trajectory. And the actual pedestrian historical trajectory Y u The inputs are fed into the discriminator neural network, and a high-dimensional feature vector is output through the embedding of a fully connected neural network layer. Then, the path is passed through an LSTM neural network layer and a discriminator multilayer perceptron in sequence, and finally the probability of the path being the true trajectory is output.

[0088]

[0089]

[0090]

[0091] In the formula, This is the output vector of the LSTM network layer. P corresponds to the weight parameters of each network layer. real This represents the probability of identifying it as a true trajectory.

[0092] Preferably, in S3, the loss function L of the SDG-GAN model SDG - GAN The cross-entropy loss function L includes the generator and discriminator. GAN(G,D) is the minimum difference loss function L between the actual pedestrian trajectory and the predicted pedestrian trajectory. L2 (G);

[0093] L SDG-GAN =L GAN (G,D)+L L2 (G);

[0094]

[0095]

[0096] In the formula, E is the expected value, r is the input pedestrian real trajectory data, S is the number of samples based on the model generation result, Z is the input Gaussian noise distribution, D represents the discriminator, and G represents the generator.

[0097] Preferably, in S1, the historical data includes: the number of video frames, the pedestrian's coordinates, the pedestrian's acceleration, the pedestrian's waiting time, the vehicle's coordinates, the vehicle's acceleration, the vehicle's waiting time, the distance between the pedestrian and the vehicle, and the time of subsequent intrusion; the distance between the pedestrian and the vehicle is the Euclidean distance between the pedestrian and the vehicle.

[0098] Compared with the prior art, the present invention has the following beneficial effects:

[0099] 1. This invention, based on S-GAN, utilizes micro-level data and game theory to analyze and derive the macro-level interaction strategies between pedestrians and vehicles at unsignalized right-turn intersections at different times. It also divides the pedestrian-vehicle interaction into stages, including observation and conflict zones. When in the observation zone, the payoffs for both parties are obtained probabilistically. When in the conflict zone, existing decisions are determined, and the payoffs for both parties' strategies are directly obtained, enabling a more detailed analysis of the pedestrian-vehicle game process. Based on this, an SDG-GAN model is constructed. Subsequently, the SDG-GAN model is driven by both micro-level pedestrian-vehicle interaction data and macro-level pedestrian-vehicle game strategy payoffs to predict pedestrian trajectories. In this way, this invention combines micro-level motion factors and macro-level game decision-making in real-world interaction scenarios, incorporating game theory into the pedestrian-vehicle interaction state, enabling accurate prediction of pedestrian trajectories at unsignalized right-turn intersections.

[0100] In summary, this invention can ensure the accuracy of pedestrian trajectory prediction at unsignaled right-turn intersections and the effectiveness of assisted driving decisions at unsignaled right-turn intersections, thereby balancing the efficiency and safety of vehicles passing through unsignaled right-turn intersections.

[0101] 2. The SDG-GAN algorithm constructed in this invention integrates macroscopic game theory and microscopic motion parameters, which takes into account the relationship between people and vehicles more comprehensively. It can express the true reaction of pedestrians under the game state and improve the accuracy and interpretability of predicting pedestrian trajectories.

[0102] 3. This invention analyzes the specific human-vehicle game factors in the special interactive scenario of unsignaled right-turn intersections, divides the game into stages, and uses the post-violation time index to distinguish the degree of danger of human-vehicle conflict. It also uses a "regret factor" associated with starting acceleration to characterize the regret degree of both parties, comprehensively considering various factors of both sides as much as possible, and establishes a human-vehicle game payoff matrix based on this. Furthermore, it incorporates the Nash equilibrium concept of complete information games into a deep learning network model to predict pedestrian trajectories. This approach ensures the accuracy of pedestrian trajectory prediction at unsignaled right-turn intersections. Attached Figure Description

[0103] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0104] Figure 1 The flowchart in the embodiment is shown below;

[0105] Figure 2 This is a schematic diagram of the game scenario in the embodiment;

[0106] Figure 3 This is a schematic diagram of the SDG-GAN model in the embodiment;

[0107] Figure 4 This is a schematic diagram of the data acquisition scenario in the embodiment. Detailed Implementation

[0108] The following detailed explanation illustrates the specific implementation methods:

[0109] Example:

[0110] like Figure 1 As shown, this embodiment discloses a method for predicting pedestrian trajectories at unsignalized right-turn intersections based on game theory, including the following steps:

[0111] S1. Obtain historical data on pedestrians and vehicles at unsignalized right-turn intersections.

[0112] In specific implementation, the historical data includes: the number of video frames, the pedestrian's coordinates, the pedestrian's acceleration, the pedestrian's waiting time, the vehicle's coordinates, the vehicle's acceleration, the vehicle's waiting time, the distance between the pedestrian and the vehicle, and the time of subsequent intrusion; the distance between the pedestrian and the vehicle is the Euclidean distance between the pedestrian and the vehicle.

[0113] Based on the collected historical data, a human and vehicle dataset was established:

[0114] (frame, id, x P ,y P ,v P ,a P ,w P ,x V ,yV,v V ,a V ,w V ,R,PET), where v and p in the subscript refer to vehicles and pedestrians respectively, frame represents the number of frames in the video, x / y represents the coordinates, v represents the velocity, a represents the acceleration, w represents the waiting time, R represents the distance between the person and the vehicle, and PET represents the intrusion time (i.e., the time difference between the pedestrian and the vehicle arriving at the conflict area).

[0115] S2. Analyze the factors of the pedestrian-vehicle game at an intersection with no signal right turn and construct the corresponding pedestrian-vehicle game model.

[0116] Through observation and data collection in real-world scenarios, it was found that, according to local traffic regulations, vehicles must slow down when turning right in specific interactive scenarios. Because right-turning vehicles travel slower than straight-going vehicles, pedestrians do not feel a strong sense of danger, and most pedestrians have a very strong intention to cross and are unwilling to waste time waiting. Statistical analysis of pedestrian behavior revealed that at unsignalized right-turn intersections, due to the lack of a clear right-of-way distribution, pedestrians generally choose to cross directly, while drivers generally choose to slow down and yield. Because vehicles lose this "game," their delay time is significantly longer than that of pedestrians.

[0117] This invention proposes a human-vehicle game model, establishes a game formula, gives macro-decision probabilities, and specifically analyzes the influencing factors when pedestrians pass through.

[0118] Model definition. (1) Pedestrians and drivers engage in rational thinking and will choose strategies based on their own circumstances. (2) The game begins once pedestrians and vehicles enter the decision area. (3) Pedestrians and drivers decide whether to follow the static game of complete information simultaneously. (4) A conflict occurs when pedestrians and vehicles enter the conflict area at the same time.

[0119] Model Establishment. (1) Players: There are two players in the game, i=1 and i=2, where i=1 represents a pedestrian and i=2 represents a vehicle. (2) Strategies: In the game between pedestrians and vehicles, both have two identical strategies: {passgae, wait}. (3) Benefits: During the game, each player will receive the impact of other players on themselves and the results of their own decisions. This includes the delay loss when waiting, the loss under conflict between the two sides, and the benefit when one side waits for the other to pass, etc. The benefits of players under different situations will be analyzed in detail.

[0120] In the game, pedestrians and vehicles will produce four possible decision outcomes, denoted as s. n Let n ∈ [1,2,3,4], corresponding to simultaneous passage of pedestrians and vehicles, pedestrians waiting for vehicles to pass, pedestrians passing while vehicles wait, and simultaneous waiting of pedestrians and vehicles, respectively. When pedestrians and vehicles enter the observation area simultaneously, the driver and pedestrian begin to analyze and choose strategies, and then execute those strategies in the next step. Both sides will eventually enter the conflict area, and the relative time difference between their entry into the conflict area is the post-intrusion time, symbolizing the degree of danger in this game, such as... Figure 2 As shown.

[0121] Based on the above analysis, in specific implementation, the construction process of the human-vehicle game model in S2 includes:

[0122] S21. Divide the game into stages, design an observation area and a conflict area. Once pedestrians and vehicles enter the observation area, the game is considered to have started. The post-intrusion time is used to characterize the degree of danger of the human-vehicle conflict. The post-intrusion time is the time difference between pedestrians and vehicles entering the conflict area. The shorter the post-intrusion time, the higher the degree of danger.

[0123] S22. Based on the decision-making strategies of pedestrians and vehicles in the game, construct a human-vehicle game payoff matrix; the decision-making strategies include pedestrians and vehicles passing simultaneously, pedestrians waiting for vehicles to pass, pedestrians passing while vehicles wait, and pedestrians and vehicles waiting simultaneously.

[0124] When pedestrians and vehicles are crossing at the same time

[0125] The pedestrian's payment function is:

[0126] The vehicle's payment function is:

[0127] Among them, v v Indicates the pedestrian crossing speed, a v Represents the pedestrian's acceleration v p Indicates the vehicle's speed, a p α1 represents the vehicle acceleration, α2 represents the combined influence factor of the vehicle's velocity and acceleration, and σ represents the combined influence factor of the pedestrian's velocity and acceleration. v The collision severity factor, σ, represents the severity of a vehicle collision. p A factor representing the severity of a pedestrian collision, and:

[0128]

[0129]

[0130] The pedestrian's payment function is as follows:

[0131] In the formula, α4 is the waiting inhibition coefficient when passing through, and t p Waiting time for pedestrians;

[0132] The vehicle's payment function is:

[0133] In the formula, α3 is the velocity excitation coefficient when passing through;

[0134] When pedestrians cross while vehicles wait, the pedestrian's payment function is:

[0135] In the formula, α3 is the velocity excitation coefficient when passing through, v p For pedestrian crossing speed;

[0136] The vehicle's payment function is:

[0137] In the formula, α4 is the waiting inhibition coefficient when passing through, and t v The vehicle waiting time is 0.75 seconds, and the driver's reaction time is 0.75 seconds.

[0138] When pedestrians and vehicles are waiting simultaneously, the pedestrian's payment function is:

[0139] The vehicle's payment function is

[0140] Where α5 is the waiting inhibition coefficient of the vehicle under common loss; α6 is the waiting inhibition coefficient of the pedestrian under common loss; k is the regret factor of both parties. The regret factor is related to the starting acceleration during the waiting process and represents the degree of regret for taking the waiting strategy. The greater the starting acceleration, the greater the degree of regret.

[0141] The human-vehicle game payoff matrix is ​​as follows:

[0142]

[0143] From the payoff matrix of the vehicle-pedestrian game, it can be seen that the strategies of vehicles choosing to wait through pedestrians and pedestrians choosing to wait through vehicles are more reasonable. Since these two strategies are more advantageous, they are not stable in the evolutionary process. According to the Nash equilibrium principle, if there is a combination of mixed advantageous strategies in the game, there must be a Nash equilibrium point. Calculations can reveal the mixed expected payoffs for both vehicles and pedestrians.

[0144] S23. Based on the characteristics of the human-vehicle game payoff matrix, the expectation function and corresponding loss function of the human-vehicle game model are obtained.

[0145] In specific implementation, the expected function is the combined expected benefit of both vehicles and pedestrians when the Nash equilibrium point of the mixed advantage strategy of vehicles choosing to wait for passage and pedestrians waiting for passage through vehicles is reached.

[0146] Among them, the expected benefit when the vehicle chooses to pass. for:

[0147] in, Indicates the probability of a pedestrian crossing. The probability of waiting for pedestrians;

[0148] Expected benefits when vehicles choose to wait for:

[0149]

[0150] Analyze the pure strategy payoff for pedestrians, and the expected payoff when pedestrians cross the road. for:

[0151] in, Indicates the probability of a vehicle passing through. This indicates the probability of a vehicle waiting.

[0152] Expected benefits when pedestrians choose to wait for:

[0153]

[0154] Expected benefits when the vehicle passes With waiting expected returns When the Nash equilibrium is reached, the probability combinations of pedestrians crossing and waiting are as follows:

[0155]

[0156]

[0157] When pedestrians pass through, the expected benefits With waiting expected returns When the Nash equilibrium is reached, the probability combinations of a vehicle passing and waiting are as follows:

[0158]

[0159]

[0160] S24. Based on the expectation function and loss function obtained in S23, construct a human-vehicle game model.

[0161] S3. Insert the pedestrian-vehicle game model into the pre-defined S-GAN model to obtain the SDG-GAN model, which is used to predict pedestrian trajectories. The structure of the SDG-GAN model is as follows: Figure 3 As shown.

[0162] When the SDG-GAN model predicts pedestrian trajectories, the pedestrian trajectory is defined as the change of two-dimensional coordinate position in a time series. The coordinates of pedestrian u at time t are... The trajectory coordinates of vehicle j are the same as those of the pedestrian. The coordinates of vehicle j at time t are: The set of historical trajectories X for pedestrian u at each step length from 1 to to u for:

[0163]

[0164] In the formula, 1 to to are the observation frames of the pedestrian's historical trajectory, and to is the length of the observation frame;

[0165] Pedestrian u from to+1 to t p The set of predicted trajectories for each step size for:

[0166]

[0167] In the formula, to+1~to+t p For the predicted frames of the pedestrian's historical trajectory, t p To predict the frame length.

[0168] Pedestrian u from to+1 to t p The set of true historical trajectories Y for each step size u for:

[0169]

[0170] Pedestrian u from 1 to t p The true historical trajectory within With predicted trajectory generation They are respectively [X u ,Y u ]and

[0171] In practice, the SDG-GAN model includes a human-vehicle game model, a trajectory generator, and a trajectory discriminator. The trajectory generator is used to encode and decode the output of the human-vehicle game model and the historical trajectory of pedestrians, and output the predicted trajectory of pedestrians. The trajectory discriminator is used to discriminate the probability that the predicted trajectory of pedestrians is the real trajectory.

[0172] The trajectory generator includes a trajectory encoder, a game mechanism module, a pooling module, and a trajectory decoder;

[0173] The trajectory encoder embeds the pedestrian and vehicle coordinates at each time step into an embedding function φ containing a ReLU nonlinear activation function to obtain a fixed-length vector. and Then, the pedestrian historical trajectory feature vector is obtained through LSTM unit encoding. With vehicle historical trajectory feature vector

[0174]

[0175]

[0176] In the formula, the embedding function φ represents the fully connected neural network layer. The weight parameters of the embedding function, These are the weight parameters for the LSTM unit.

[0177] The game mechanism module is used to extract game-related data of both the driver and the vehicle based on the game payoff function of both parties. The game-related data includes speed, acceleration, relative distance, and waiting time. It is also used to obtain the post-intrusion time at each time step by using the speed of both parties and the distance between them and the conflict area. The post-intrusion time value is used to determine the degree of danger of the interaction between the two parties at this time step. And the position coordinates of both parties at this time are used to determine whether they are in the observation area or the conflict area.

[0178] The game theory mechanism module is also used to calibrate based on the interactive decisions of people and vehicles in the real world, and to obtain the specific expected gains and losses of both parties under the decision. and The specific expected gains and losses influence the feature vectors of the historical trajectories of both the driver and the vehicle, thus obtaining the game-theoretic feature vectors of both parties. And merged into a feature vector of human-vehicle hybrid game.

[0179]

[0180] In the formula, Let x be the collision severity factor for pedestrian u and vehicle j respectively. Let f be the real-time coordinate region for pedestrian u and vehicle j respectively. pet Let f be the collision severity determination function. R For real-time region determination function, t pet Post-intrusion time during human-vehicle interaction, ω pet ω is the collision severity weighting parameter. R For real-time regional weight parameters;

[0181]

[0182]

[0183]

[0184] In the formula, f pay For game theory calculation functions, f represents the specific payment function under different strategies of both parties. inf Let f be the game influence function. mix For game theory mixture functions;

[0185] The pooling module is used to embed the relative distance between people and vehicles into the embedding function φ to obtain the feature vector of the relative position of people and vehicles. Feature vectors of hybrid human-vehicle game The game pooling vector is obtained by connecting the data and passing it through a multilayer perceptron.

[0186]

[0187]

[0188] In the formula, Mlp GP For pooling modules in a multilayer perceptron network, Cat is used to connect feature vectors. These are the weight parameters corresponding to their respective network layers;

[0189] The trajectory decoder is used to convert game pooling vectors Pedestrian historical trajectory feature vector Establish a connection and use the decoder module multilayer perceptron Mlp GD The feature vector of the decoder is finally obtained by connecting it to random Gaussian noise Z in the network. Compared with the pedestrian coordinate vector after embedding function encoding Initialize the cell zero vector The vectors are input together into the LSTM neural network layer. Finally The pedestrian trajectory prediction coordinates are finally obtained after the decoder and multilayer perceptron.

[0190]

[0191]

[0192]

[0193]

[0194] In the formula, ω λThese are the weight parameters for the corresponding network layer.

[0195] The trajectory discriminator's operation includes: converting the pedestrian predicted trajectory output by the trajectory generator... And the actual pedestrian historical trajectory Y u The inputs are fed into the discriminator neural network, and a high-dimensional feature vector is output through the embedding of a fully connected neural network layer. Then, the path is passed through an LSTM neural network layer and a discriminator multilayer perceptron in sequence, and finally the probability of the path being the true trajectory is output.

[0196]

[0197]

[0198]

[0199] In the formula, This is the output vector of the LSTM network layer. P corresponds to the weight parameters of each network layer. rea l represents the probability of identifying it as a true trajectory.

[0200] The loss function L of the SDG-GAN model SDG - GAN The cross-entropy loss function L includes the generator and discriminator. GAN (G,D) is the minimum difference loss function L between the actual pedestrian trajectory and the predicted pedestrian trajectory. L2 (G);

[0201] L SDG-GAN =L GAN (G,D)+L L2 (G);

[0202]

[0203]

[0204] In the formula, E is the expected value, r is the input pedestrian real trajectory data, S is the number of samples based on the model generation result, Z is the input Gaussian noise distribution, D represents the discriminator, and G represents the generator.

[0205] S4. Use the historical data obtained in S1 to train the SDG-GAN model.

[0206] S5. Use the trained SDG-GAN model to predict pedestrian trajectories in real time at intersections with no right turn signal.

[0207] In the actual implementation of the technical solution, the inventors selected a signalless right-turn intersection on X Avenue in BN District of City C as the data collection location, primarily collecting basic indicators of pedestrians and vehicles. Due to the high pedestrian traffic and frequent pedestrian-vehicle interactions at this location, the frequency of pedestrian-vehicle conflicts is relatively high. Furthermore, the first right-turn lane in this scenario has parking spaces, and right-turning vehicles can only enter the second lane, further refining the pedestrian-vehicle interaction area. Therefore, this location is more suitable for capturing the pedestrian-vehicle interaction process, such as... Figure 4 As shown.

[0208] The collected pedestrian and vehicle datasets were input into the SDG-GAN model for training, yielding the results. In the observed area, neither vehicles nor pedestrians made decisions. The SDG-GAN algorithm derived the pedestrian's expected payoff from the actual passage probability and combined this with the relative positions of pedestrians and vehicles to influence the pedestrian trajectory prediction, resulting in a more comprehensive prediction mechanism and thus good prediction results. When the pedestrian wins the game and the vehicle waits, the pedestrian's dynamic game payoff is positive, while the vehicle's dynamic game payoff is negative. The game mechanism indicates a reduction in vehicle danger and incentivizes pedestrians to move forward. When the pedestrian loses the game and waits, the pedestrian's dynamic game payoff is negative, while the vehicle's dynamic game payoff is positive. The game mechanism inhibits pedestrians from continuing forward and increases the danger of vehicle passage. When a conflict occurs between pedestrians and vehicles, both the pedestrian and vehicle dynamic game payoffs are negative. The game mechanism indicates that the probability of conflict between the two parties increases rapidly and influences pedestrian trajectories by further refining the severity of the conflict based on the micro-data of both parties. When pedestrians and vehicles wait simultaneously, traffic congestion occurs, traffic efficiency decreases, and the dynamic game payoff for both parties is negative. The game mechanism influences pedestrian trajectory prediction through the regret factor.

[0209] This invention, based on S-GAN, utilizes micro-data and game theory to analyze and derive macro-level interaction strategies between pedestrians and vehicles at unsignalized right-turn intersections at different times. It also divides the pedestrian-vehicle interaction into stages, including observation and conflict zones. When in the observation zone, the expected payoff for each party is obtained probabilistically. When in the conflict zone, existing decisions are determined, and the payoffs for both parties are directly obtained, enabling a more detailed analysis of the pedestrian-vehicle game process. Furthermore, this invention analyzes specific pedestrian-vehicle game factors in the special interaction scenario of unsignalized right-turn intersections, divides the game stages, and uses the post-violation time indicator to distinguish the degree of danger of pedestrian-vehicle conflict. It also uses a "regret factor" associated with starting acceleration to characterize the regret degree of both parties, comprehensively considering various factors of both parties as much as possible, and establishing a pedestrian-vehicle game payoff matrix based on this. Moreover, it incorporates the Nash equilibrium concept of complete information games into a deep learning network model to predict pedestrian trajectories. Based on this, an SDG-GAN model is constructed. The SDG-GAN algorithm integrates macroscopic game theory and microscopic motion parameters, taking a more comprehensive view of the relationship between pedestrians and vehicles. It can express the true reactions of pedestrians under game conditions, improving the accuracy and interpretability of pedestrian trajectory prediction. Subsequently, the SDG-GAN model is driven to predict pedestrian trajectories by combining microscopic pedestrian-vehicle interaction data and macroscopic pedestrian-vehicle game strategy rewards. In this way, this invention combines microscopic motion factors and macroscopic game decision-making in real-world interaction scenarios, incorporating game theory into the pedestrian-vehicle interaction state, enabling accurate prediction of pedestrian trajectories at unsignalized right-turn intersections. This invention ensures the accuracy of pedestrian trajectory prediction at unsignalized right-turn intersections and the effectiveness of assisted driving decisions at such intersections, thus balancing the efficiency and safety of vehicles passing through unsignalized right-turn intersections.

[0210] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory, characterized in that, Includes the following steps: S1. Obtain historical data on pedestrians and vehicles at unsignaled right-turn intersections; S2. Analyze the factors in the pedestrian-vehicle game at an intersection with no signal right turn and construct the corresponding pedestrian-vehicle game model; S3. Insert the human-vehicle game model into the preset S-GAN model to obtain the SDG-GAN model, which is used to predict the trajectory of pedestrians. S4. Use the historical data obtained in S1 to train the SDG-GAN model; S5. Use the trained SDG-GAN model to predict pedestrian trajectories in real time at intersections with no right turn signal. In S2, the construction process of the human-vehicle game model includes: S21. Divide the game into stages, design an observation area and a conflict area. Once pedestrians and vehicles enter the observation area, the game is considered to have started. The post-intrusion time is used to characterize the degree of danger of the human-vehicle conflict. The post-intrusion time is the time difference between pedestrians and vehicles entering the conflict area. The shorter the post-intrusion time, the higher the degree of danger. S22. Based on the decision-making strategies of pedestrians and vehicles in the game, construct a human-vehicle game payoff matrix; the decision-making strategies include pedestrians and vehicles passing simultaneously, pedestrians waiting for vehicles to pass, pedestrians passing while vehicles wait, and pedestrians and vehicles waiting simultaneously. S23. Based on the characteristics of the human-vehicle game payoff matrix, the expectation function and corresponding loss function of the human-vehicle game model are obtained. S24. Based on the expectation function and loss function obtained in S23, construct a human-vehicle game model; In S22, when pedestrians and vehicles are crossing at the same time... The pedestrian's payment function is: ; The vehicle's payment function is: ; in, Indicates pedestrian crossing speed, Indicates pedestrian acceleration, Indicates the speed at which the vehicle passes, Indicates vehicle acceleration, The factor representing the combined influence of vehicle speed and acceleration. The factor representing the combined influence of a pedestrian's speed and acceleration. The collision severity factor indicates the severity of a vehicle collision. A factor representing the severity of a pedestrian collision, and: ； ； The pedestrian's payment function is as follows: ; In the formula, The waiting inhibition coefficient when passing through. Waiting time for pedestrians; The vehicle's payment function is: ; In the formula, The velocity excitation coefficient during passage; When pedestrians cross while vehicles wait, the pedestrian's payment function is: ; In the formula, The velocity excitation coefficient during passage is... For pedestrian crossing speed; The vehicle's payment function is: ; In the formula, The waiting inhibition coefficient when passing through. The vehicle waiting time is 0.75 seconds, and the driver's reaction time is 0.75 seconds. When pedestrians and vehicles are waiting simultaneously, the pedestrian's payment function is: ; The vehicle's payment function is ; in, The waiting inhibition coefficient for vehicles under shared losses; The waiting inhibition coefficient for the common loss of the downline; The regret factor is the degree of regret for both parties. The regret factor is related to the initial acceleration during the waiting process and represents the degree of regret for adopting the waiting strategy. The greater the initial acceleration, the greater the degree of regret. The human-vehicle game payoff matrix is ​​as follows: 。 2. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 1, characterized in that: In S23, the expected function is the combined expected benefit of both the vehicle and the pedestrian when the vehicle chooses to wait for the pedestrian and the pedestrian chooses to wait for the vehicle, which are both Nash equilibrium points. Among them, the expected benefit when the vehicle chooses to pass. for: ;in, Indicates the probability of a pedestrian crossing. The probability of waiting for pedestrians; Expected benefits when vehicles choose to wait for: ； Analyze the pure strategy payoff for pedestrians, and the expected payoff when pedestrians cross the road. for: ;in, Indicates the probability of a vehicle passing through. This indicates the probability of a vehicle waiting. Expected benefits when pedestrians choose to wait for: ； Expected benefits when the vehicle passes With waiting expected returns When the Nash equilibrium is reached, the probability combinations of pedestrians crossing and waiting are as follows: ； ； When pedestrians pass through, the expected benefits With waiting expected returns When the Nash equilibrium is reached, the probability combinations of a vehicle passing and waiting are as follows: ； 。 3. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 2, characterized in that: When the SDG-GAN model predicts pedestrian trajectories, it defines a pedestrian trajectory as the change of two-dimensional coordinate positions over time. exist The coordinates at time t are ,vehicle exist The coordinates at time t are ;pedestrian From 1 to The set of historical trajectories for each step size for: ； In the formula, For observation frames of pedestrian historical trajectories, The length of the observation frame; pedestrian from arrive The set of predicted trajectories for each step size for: ； In the formula, For the predicted frames of the pedestrian's historical trajectory, To predict frame length; pedestrian from arrive The set of real historical trajectories for each step size for: ； pedestrian from arrive The true historical trajectory within With predicted trajectory generation They are respectively and .

4. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 3, characterized in that: In S3, the SDG-GAN model includes a human-vehicle game model, a trajectory generator, and a trajectory discriminator. The trajectory generator is used to encode and decode the output of the human-vehicle game model and the historical trajectory of the pedestrian, and output the predicted trajectory of the pedestrian. The trajectory discriminator is used to discriminate the probability that the predicted trajectory of the pedestrian is the real trajectory.

5. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 4, characterized in that: The trajectory generator includes a trajectory encoder, a game mechanism module, a pooling module, and a trajectory decoder; The trajectory encoder is used to embed the pedestrian and vehicle coordinates at each time step into an embedding function containing a ReLU nonlinear activation function. In the process, a fixed-length vector is obtained. and ; Then, the pedestrian historical trajectory feature vector is obtained through LSTM unit encoding. Vehicle historical trajectory feature vector ; ； ； In the formula, the embedding function For a fully connected neural network layer, The weight parameters of the embedding function, These are the weight parameters of the LSTM unit; The game mechanism module is used to extract game-related data between the driver and the vehicle based on the game payoff function between the two parties; the game-related data includes speed, acceleration, relative distance and waiting time; it is also used to obtain the post-intrusion time at each time step using the speed of both parties and the distance between them and the conflict area; The danger level of the interaction between the two parties at this time step is determined by the value of the intrusion time; and the location coordinates of the two parties at this time are used to determine whether they are in the observation area or the conflict area. The game theory mechanism module is also used to calibrate based on the interactive decisions of people and vehicles in the real world, and to obtain the specific expected gains and losses of both parties under the decision. and The specific expected gains and losses affect the feature vectors of the historical trajectories of both the driver and the vehicle, thus obtaining the game feature vectors of both parties. , And merged into a feature vector of human-vehicle hybrid game. ; ； In the formula, For pedestrians With vehicles Their respective collision severity factors For pedestrians With vehicles Each of their respective real-time coordinate regions Here is the collision severity determination function. This is a function for real-time region determination. Post-intrusion time during human-vehicle interaction For collision degree weighting parameters, For real-time regional weight parameters; ； ； ； In the formula, For game theory calculation functions, For the specific payment functions under the different strategies of both parties, Let be the game influence function. For game theory mixture functions; The pooling module is used to embed the relative distance between people and vehicles into the embedding function. The feature vector of the relative position of the person and the vehicle is obtained. Feature vectors of hybrid human-vehicle game The game pooling vector is obtained by connecting the data and passing it through a multilayer perceptron. ; ； ； In the formula, For pooling modules, multilayer perceptron network layer, Used to connect feature vectors, , These are the weight parameters corresponding to their respective network layers; The trajectory decoder is used to convert game pooling vectors Pedestrian historical trajectory feature vector Establish a connection and use the decoder module of the multilayer perceptron. With network random Gaussian noise The final result after concatenation is the decoder feature vector. ; Compared with the pedestrian coordinate vector after embedding function encoding Initialize the cell's all-zero vector The vectors are input together into the LSTM neural network layer. Finally The pedestrian trajectory prediction coordinates are finally obtained after the decoder and multilayer perceptron. ; ； ； ； ； In the formula, , , These are the weight parameters for the corresponding network layer.

6. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 5, characterized in that: In S3, the trajectory discriminator's operation includes: converting the pedestrian predicted trajectory output by the trajectory generator... and real pedestrian history trajectory The inputs are fed into the discriminator neural network, and a high-dimensional feature vector is output through the embedding of a fully connected neural network layer. Then, the path is passed through an LSTM neural network layer and a discriminator multilayer perceptron in sequence, and finally the probability of the path being the true trajectory is output. ； ； ； In the formula, This is the output vector of the LSTM network layer. , , For the weight parameters of their respective network layers, This represents the probability of identifying it as a true trajectory.

7. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 6, characterized in that: In S3, the loss function of the SDG-GAN model Cross-entropy loss function including generator and discriminator Minimum difference loss function between the actual pedestrian trajectory and the predicted pedestrian trajectory ; ； ； ； In the formula, The expected value is obtained. The input is the actual trajectory data of pedestrians. The number of samples based on the model-generated results. Let D be the input Gaussian noise distribution, and let G be the discriminator and G be the generator.

8. The method for predicting pedestrian trajectories at signalless right-turn intersections based on game theory as described in claim 7, characterized in that: In S1, historical data includes: video frame count, pedestrian coordinates, pedestrian acceleration, pedestrian waiting time, vehicle coordinates, vehicle acceleration, vehicle waiting time, distance between pedestrian and vehicle, and intrusion time; the distance between pedestrian and vehicle is the Euclidean distance between pedestrian and vehicle.

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