Formation trajectory prediction method and system based on physical enhanced dynamic graph neural network

Abstract

The embodiment of the application provides a platoon trajectory prediction method and system based on a physically enhanced dynamic graph neural network, comprising: acquiring motion state information and environment perception information of each vehicle in a platoon system, taking each vehicle as a node, dynamically establishing edge connection according to spatial distance, and constructing a dynamic interaction graph; extracting kinematic features, historical trajectory features and road environment features of each node as initial embedding; taking the initial embedding as the starting point of message passing, performing physical constraint message passing of aggregating neighbor messages in the direction of the incoming edge on the dynamic interaction graph layer by layer, and outputting updated embedding after each layer is fused with neural network coding features and physical prior residual by attention weighting, and the updated embedding is used as the input of the next layer, and the target updated embedding of each node is obtained after iteration of multiple layers; and after decoding, the initial prediction trajectory of each vehicle in the platoon in the future time domain is obtained. Through the method, the prediction accuracy and physical consistency in the dynamic platoon scene are significantly improved.

Description

Technical Field

[0001] This application relates to the field of multi-vehicle cooperative control technology, and in particular to a formation trajectory prediction method and system based on a physically enhanced dynamic graph neural network. Background Technology

[0002] Formation trajectory prediction is one of the core technologies of multi-agent cooperative control. It aims to infer the future evolutionary trends of each agent based on the current motion state and environmental information of the formation, providing crucial information for formation decision-making and safety control. Existing prediction methods mainly include: physical model-based methods that use kinematic or dynamic equations to extrapolate states, offering good physical consistency but struggling to accurately model the complex interactions between multiple vehicles; and data-driven methods that directly learn trajectory evolution patterns through neural networks, capable of fitting complex nonlinear relationships, but lacking physical constraints, resulting in low prediction reliability and poor generalization in edge scenarios with insufficient training data coverage.

[0003] To address the aforementioned issues, this invention proposes a formation trajectory prediction method based on a physically enhanced dynamic graph neural network, which improves prediction accuracy and physical consistency in dynamic formation scenarios. Summary of the Invention

[0004] This application provides a formation trajectory prediction method and system based on a physically enhanced dynamic graph neural network, which significantly improves the prediction accuracy and physical consistency in dynamic formation scenarios.

[0005] In a first aspect, embodiments of this application provide a formation trajectory prediction method based on a physically enhanced dynamic graph neural network, including: The motion state information and environmental perception information of each vehicle in the formation system are obtained. The motion state information and environmental perception information are used to dynamically establish edge connections based on the spatial distance between the vehicles in the formation, using each vehicle in the formation as a node, and construct a dynamic interactive graph. The kinematic features, historical trajectory features, and road environment features of each node are extracted as the initial embedding; Using the initial embedding as the starting point for message passing, physical constraint message passing that aggregates neighbor messages along the incoming edge direction is executed layer by layer on the dynamic interaction graph. After attention weighting and fusing neural network encoded features and physical prior residuals, the updated embedding is output as the input for the next layer. After iterating through multiple layers, the target updated embedding of each node is obtained. Decoding the target update embedding yields the initial predicted trajectory of each vehicle in the future time domain within the formation system.

[0006] As can be seen, this invention constructs a dynamic interactive graph, enabling real-time adjustments to the graph connections as the formation topology changes dynamically, thus avoiding prediction biases introduced by static graph structures. By fusing neural network encoding features and physical prior residuals at each layer of message passing, the predicted trajectory is anchored to the physical feasible domain throughout the entire process, avoiding physical inconsistencies in edge scenarios caused by purely data-driven models. By aggregating messages along the incoming edge direction, the interactive information propagates along the physically effective direction in which the preceding vehicle influences the following vehicle, accurately characterizing the unidirectional nature of vehicle-to-vehicle interactions. Through layer-by-layer attention-weighted fusion and iterative updates of the embedding, the interactive influence of multi-vehicle coupling is fully extracted and fused during layer-by-layer propagation, significantly improving the trajectory prediction accuracy and physical consistency in dynamic formation scenarios.

[0007] In one possible implementation, the edge connections of the dynamic interaction graph dynamically adjust the interaction perception radius threshold according to the current vehicle speed and road type. An edge connection is established when the Euclidean distance between the two vehicles is less than or equal to the interactive sensing radius threshold; otherwise, it is not established.

[0008] It is evident that the interaction perception radius adaptively adjusts with vehicle speed and road type. At high speeds, the perception radius is expanded to cover the potential impact of distant vehicles, while at low speeds, the perception radius is reduced to avoid introducing too many redundant connections. At the same time, differentiated threshold configurations are adopted for different scenarios such as highways and urban roads, so that the sparsity of the interaction graph structure matches the communication overhead and computing resources. This avoids the defects of static thresholds in high-speed scenarios, which may lead to prediction bias due to missing key interactions, and in low-speed scenarios, which may introduce noisy connections and increase the computational burden.

[0009] In one possible implementation, the edge connections of the dynamic interaction graph have directional encoding, including: Along the convoy driving direction, when the first vehicle is in front of the second vehicle and the distance between them is less than a preset threshold, a directed edge is established from the first vehicle to the second vehicle.

[0010] As can be seen, by establishing directed edges from the vehicle in front to the vehicle behind, messages are propagated only along the physically effective direction in which the preceding vehicle affects the following vehicle. This accurately portrays the unidirectional nature of vehicle interactions in platooning—the acceleration and deceleration of the preceding vehicle influences the following vehicle's following decision, while the motion state of the following vehicle has almost no feedback effect on the preceding vehicle. Unlike existing undirected graph modeling that treats the interaction influence between vehicles in front and behind as an equivalent bidirectional propagation (where information from the following vehicle propagates back to the preceding vehicle, introducing physically unreasonable noise signals), this scheme, through directional encoding and an incoming edge direction aggregation mechanism, ensures that the target node only receives interaction messages from the vehicle in front of it. This avoids the invalid information flow from the following vehicle to the preceding vehicle in the undirected graph and the resulting prediction bias. From the graph structure level, it guarantees that the direction of information propagation is consistent with the actual physical interaction direction, improving the physical rationality and accuracy of platoon trajectory prediction.

[0011] In one possible implementation, when constructing the dynamic interaction graph, the interaction intensity weights of each edge are calculated based on the Intelligent Driver Model (IDM). The interaction intensity weights are related to the distance between the two vehicles, their relative speed, and the speed of the vehicle itself. The interaction intensity weights are used to weight neighbor messages during message passing.

[0012] As can be seen, by embedding the IDM physical model into the calculation of interaction intensity weights, the edge weights no longer rely on pure data-driven learning or fixed assignments, but instead have clear physical meanings—the greater the expected acceleration amplitude of the current vehicle (i.e., the more drastic the acceleration or deceleration), the higher the corresponding edge weight, and the stronger its interaction influence on the following vehicle; at the same time, the smaller the distance between vehicles and the greater the relative speed, the greater the weight also increases accordingly, accurately reflecting the physical law that "the following vehicle must respond quickly when the vehicle in front changes drastically" in car-following scenarios. Unlike pure data-driven methods that may learn interaction patterns that contradict physics outside the training data distribution (such as assigning low weights when the distance between vehicles is very close and ignoring collision risks), this scheme ensures the rationality and interpretability of the weights in different scenarios through physical prior constraints. Moreover, the IDM prior is independent of the training data distribution, enhancing the model's generalization ability in unseen scenarios such as dense traffic flow and extreme acceleration or deceleration, and avoiding prediction failures caused by insufficient training data coverage in pure data-driven methods.

[0013] In one possible implementation, the method further includes: when there is a lateral cutting motion of a vehicle in an adjacent lane, establishing a directed edge from the cutting vehicle to the target vehicle, wherein the interaction strength weight of the directed edge is dynamically adjusted based on the lateral distance and the relative lateral velocity.

[0014] As can be seen, by extending directional encoding from longitudinal following to lateral cutting-in scenarios, the model can accurately distinguish the different impacts of left-side and right-side cutting-in on the target vehicle. When a cutting-in vehicle approaches the target lane from the left or right, the system establishes corresponding directed edges based on the real-time detected lateral distance and relative lateral velocity. The change in the lateral motion state of the cutting-in vehicle is directly reflected in the dynamic adjustment of the directed edge interaction strength weights: the smaller the lateral distance and the greater the relative lateral velocity (the more obvious the cutting-in intention), the higher the edge weight, the stronger the interaction influence of the cutting-in vehicle on the target vehicle, and the more timely the warning and response signals received by the target vehicle. Unlike the longitudinal following scenario where directional encoding is only transmitted along the driving direction, the directional encoding of directed edges in the lateral cutting-in scenario allows the interaction information to propagate unidirectionally from the cutting-in vehicle to the target vehicle, accurately characterizing the unidirectional disturbance characteristics of the cutting-in behavior—the cutting-in vehicle actively changes lanes to affect the target vehicle, while the target vehicle has almost no feedback influence on the lateral motion of the cutting-in vehicle. Through this lateral directionality encoding, the model can predict the lane-changing intention based on the changing trends of lateral distance and relative lateral speed at the initial stage of lane change, rather than reacting only after crossing the lane boundary. This improves the advance and accuracy of trajectory prediction in lane-changing scenarios and avoids prediction bias caused by ambiguity in lateral interaction direction in undirected graph modeling.

[0015] In one possible implementation, the physical constraint message passing includes: In the current message passing layer, neural network encoded features are extracted from the current layer node representation. At the same time, physical prior residuals are calculated based on the intelligent driver model and the current layer node representation. The prior residuals are the deviation between the intelligent driver model IDM theoretical acceleration and the current predicted acceleration. The neural network encoded features are concatenated with the physical prior residuals and then fused with attention weighting to obtain the fusion message of the current layer. An updated embedding of the current layer is generated based on the fusion message.

[0016] As can be seen, by simultaneously extracting neural network encoded features and calculating physical prior residuals at the current message passing layer, and then concatenating and fusioning them through attention weighting, physical constraints are upgraded from external "soft constraints" applied only to the output layer to intrinsic components embedded in each layer of message passing. The physical prior residuals characterize the direction and magnitude of the current prediction's deviation from physical laws. Concatenated with neural network encoded features and adjusted through attention weights, the model is aware of the physical deviation of the current prediction during the message fusion construction stage, thus prioritizing the correction of feature components deviating from physical laws when generating updated embeddings. Compared to methods that only add physical regularization terms to the loss function or only perform physical verification at the final output layer, this scheme performs physical deviation calculation and correction at each layer, achieving a deep fusion of physical constraints and neural network feature extraction. This fundamentally ensures that intermediate representations are anchored to the physical feasible region at each layer, avoiding the accumulation and amplification of physical deviations during inter-layer propagation, and significantly improving the physical consistency of the predicted trajectory.

[0017] In one possible implementation, the acceleration response of the intelligent driver model (IDM) is jointly determined by the desired speed, maximum acceleration, comfortable deceleration, safe distance, and minimum safe distance, wherein: When the actual speed of the vehicle is closer to the desired speed and the distance between the vehicles is closer to the safe distance determined by relative speed and safe travel distance, the acceleration approaches zero.

[0018] As can be seen, this scheme ensures that even in extreme scenarios where the training data is not covered, the IDM prior can still provide a reasonable acceleration benchmark. This benchmark naturally returns to zero as the speed approaches the expected value and the distance between vehicles approaches the safe distance, so that the predicted trajectory converges to a physically reasonable steady-state car-following state in any scenario. This significantly improves the model's generalization ability and prediction reliability in unseen scenarios such as dense traffic flow and extreme acceleration and deceleration.

[0019] One possible implementation also includes a smooth transition mechanism for edge weights in the Cut-in scenario: when a vehicle in an adjacent lane cuts into the formation, the edge weights between the cutting vehicle and the affected agent are smoothly transitioned from the old value to the new value through interpolation coefficients, which are dynamically calculated based on the lateral distance and relative lateral speed of the cutting vehicle.

[0020] In one possible implementation, the overall kinetic energy conservation constraint of the formation is also incorporated into the message passing process: a kinetic energy conservation regularization term is added during the training phase to ensure that the rate of change of the total kinetic energy of the formation in the predicted trajectory is consistent with the theoretical rate of change of kinetic energy determined by the physical prior model; during the inference phase, when the rate of change of kinetic energy of the predicted trajectory deviates from the theoretical value by more than a preset threshold, trajectory correction based on physical prior is triggered.

[0021] Secondly, embodiments of this application provide a formation trajectory prediction system based on a physically enhanced dynamic graph neural network, including: The construction module is used to acquire the motion state information and environmental perception information of each vehicle in the formation system. The motion state information and environmental perception information are used to dynamically establish edge connections based on the spatial distance between the vehicles in the formation, using each vehicle in the formation as a node, and construct a dynamic interaction graph. An extraction module is used to extract the kinematic features, historical trajectory features, and road environment features of each node as initial embeddings; The message passing module is used to perform physical constraint message passing by aggregating neighbor messages along the incoming edge direction layer by layer on the dynamic interaction graph, with the initial embedding as the starting point of message passing. After each layer is attention-weighted and fused with neural network encoded features and physical prior residuals, the updated embedding is output as the input of the next layer. After multiple iterations, the target updated embedding of each node is obtained. The decoding module is used to decode the target update embedding to obtain the initial predicted trajectory of each vehicle in the future time domain in the formation system.

[0022] The system is used to implement the method corresponding to any embodiment of the first aspect of the present application.

[0023] Thirdly, embodiments of this application also provide an electronic device, which includes: At least one processor; and memory that is communicatively connected to at least one processor; The memory stores instructions that can be executed by at least one processor to cause the electronic device to perform a method corresponding to any embodiment of the first aspect of the present application.

[0024] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement any of the methods described in the first aspect of embodiments of this application.

[0025] Fifthly, this disclosure also provides a computer program product comprising computer-executable instructions, which, when executed by a processor, are used to implement the methods of any embodiment corresponding to the first aspect of this disclosure.

[0026] In summary, this application's embodiments construct a physically enhanced dynamic graph neural network, deeply embedding the IDM car-following physics model into the entire process of formation trajectory prediction—from edge weight calculation during dynamic interaction graph construction to prior residual fusion in physical constraint message passing, and then to kinetic energy conservation global constraints. This ensures that the predicted trajectory is anchored to the physically feasible domain in each layer of message passing, fundamentally avoiding the physically inconsistent predictions of purely data-driven models in edge scenarios. Simultaneously, through adaptive adjustment of distance thresholds, directional encoding, and lateral entry smooth transition mechanisms, the interaction graph structure is reconstructed in real time with changes in formation topology, accurately characterizing the unidirectional characteristics of longitudinal car-following and the directional perturbation characteristics of lateral entry, significantly improving the model's prediction accuracy and physical rationality in dynamic scenarios. Attached Figure Description

[0027] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0028] To more clearly illustrate the technical solutions in the embodiments of this disclosure or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0029] Figure 1 A schematic flowchart of a formation trajectory prediction method based on a physically enhanced dynamic graph neural network is provided in this application embodiment; Figure 2 This application provides a schematic flowchart of a method for constructing a dynamic interaction graph. Figure 3 This is a schematic diagram of a feature fusion method for generating an initial embedding, provided in an embodiment of this application. Figure 4 This is a schematic flowchart of a method for predicting trajectory output provided in an embodiment of this application; Figure 5 A schematic diagram of a formation trajectory prediction method system based on a physically enhanced dynamic graph neural network provided in this application embodiment; Figure 6 This is a schematic diagram of an electronic device for a formation trajectory prediction method based on a physically enhanced dynamic graph neural network, as provided in an embodiment of this application. Detailed Implementation

[0030] In the following description, when referring to the accompanying drawings, the same numbers in different drawings denote the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0031] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0032] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0033] Currently, graph neural network-based methods, which model each agent as a node and relationships as edges for message passing, have become the mainstream paradigm for multi-agent trajectory prediction. However, existing GNN methods still have the following drawbacks: the interaction graph structure is mostly static or fully connected, which cannot reflect the dynamic changes in the topology during formation operation; the edge weights rely on pure data-driven learning, lack physical interpretability, and are difficult to generalize to unseen scenarios; the message passing process does not embed the physical laws of vehicle following, which cannot guarantee that the predicted trajectory is anchored to the physical feasible region, resulting in the prediction results potentially violating basic kinematic constraints under extreme conditions.

[0034] To address the aforementioned issues, this invention proposes a formation trajectory prediction method based on a physically enhanced dynamic graph neural network (IDM). By driving the construction of a dynamic interactive graph through an IDM physical model and fusing the message passing mechanism of physical prior residuals layer by layer, the method embeds the carousel physical laws into the entire prediction process, thereby improving the prediction accuracy and physical consistency in dynamic formation scenarios.

[0035] The terminology involved in this invention will be explained by way of example below.

[0036] (1) Intelligent Driver Model (IDM): It is used to describe the driver behavior of following other vehicles and accelerating and decelerating in traffic flow. It is widely used in autonomous driving simulation, vehicle-road cooperation, commercial vehicle platooning, and traffic flow simulation.

[0037] The core of IDM (Ideal Driving Measurement) is a formula for calculating "ideal acceleration." This acceleration is not fixed but changes in real time according to the current driving conditions. Its core formula is as follows:

[0038] The above formula can be intuitively understood as the difference between two parts: the first part is the free flow term: This represents the driving force a vehicle wants to accelerate to the desired speed under ideal conditions where there are no cars ahead. The second part is interactive. This represents the "resistance" caused by a vehicle in front, which slows the car down. The closer the vehicle is and the slower it is, the greater this resistance becomes.

[0039] In the above formula, Here, is the theoretical acceleration of IDM, and is the final output of the model, which is the recommended acceleration of the vehicle at the current moment. The current speed of the vehicle. The actual distance to the vehicle in front; For the desired speed; This is the maximum acceleration; The acceleration index; The desired safe distance.

[0040] In this embodiment, vehicles can communicate directly via V2V. Communication methods include, but are not limited to, Long Range Radio (LoRa) modules, Narrow Band Internet of Things (NB-IoT) modules, Enhanced Machine-Type Communication (eMTC) modules, mobile communication, LTE-V (LTE-Vehicle-to-Everything), Dedicated Short-Range Communication (DSRC), mobile communication, Cellular Vehicle-to-Everything (C-V2X), and Vehicle-to-Everything (V2X) wireless communication technologies. Understandably, in certain special scenarios, such as in the absence of base station signals in the wild, installing communication modules on transport vehicles creates a local area network (LAN) between convoy vehicles. This allows the lead vehicle and following vehicles to communicate via the LAN, ensuring safe driving.

[0041] In this embodiment of the disclosure, the vehicles in the formation can be, but are not limited to: multiple wheeled mobile robots, wheeled mobile robots, mobile robots, passenger cars, commercial vehicles (e.g., trucks, buses, vans, etc.), special-purpose vehicles (e.g., ambulances, fire trucks, engineering vehicles, rescue vehicles, etc.), agricultural and industrial vehicles (e.g., harvesters, forklifts, etc.), transportation and logistics vehicles (e.g., container trucks, refrigerated trucks, etc.), new energy vehicles (e.g., electric vehicles, hybrid vehicles), and special vehicles (e.g., garbage trucks, water trucks, etc.). In addition to vehicles, the formation may also include drones and flying cars. The formation methods include, but are not limited to, formation between vehicles, formation between vehicles and drones, formation between vehicles and flying cars, and formation between vehicles, flying cars, and drones.

[0042] Figure 1 This is a schematic flowchart illustrating a formation trajectory prediction method based on a physically enhanced dynamic graph neural network, as provided in an embodiment of this application. The method includes steps S101, S102, S103, and S104. Each step is described in detail below.

[0043] Step S101: Obtain the motion state information and environmental perception information of each vehicle in the formation system. The motion state information and environmental perception information are used to dynamically establish edge connections based on the spatial distance between the vehicles in the formation as nodes, and construct a dynamic interaction graph.

[0044] In one possible implementation, Figure 2 This is a schematic flowchart illustrating a method for constructing a dynamic interaction graph, provided in an embodiment of this application. Specifically, in Figure 2 The process includes sub-steps S101a to S101d. Sub-step S101a involves acquiring the motion state information of each vehicle. This is achieved by collecting real-time motion state data such as position, speed, and acceleration of each vehicle through onboard sensors. Sub-step S101b involves acquiring environmental perception information. This involves using the environmental perception module to obtain information about surrounding obstacles and traffic flow. Sub-step S101c involves constructing a dynamic interaction graph. This involves calculating the Euclidean distance between vehicles in the formation and filtering vehicle pairs that are less than a preset threshold. Using vehicles as nodes, edge connections are dynamically generated based on the aforementioned distance relationships, thereby constructing a dynamic graph structure that reflects real-time interaction relationships, providing a structured input data foundation for subsequent trajectory prediction. The following is a detailed explanation of each sub-step.

[0045] Sub-step S101a: Acquire the motion status information of each vehicle. In one possible implementation, each vehicle in the platoon system collects its own motion status data in real time through onboard sensors. These onboard sensors include, but are not limited to, a Global Navigation Satellite System receiver (supporting RTK positioning with centimeter-level accuracy), an inertial measurement unit, wheel speed sensors, and steering wheel angle sensors. Each vehicle broadcasts its own motion status information within the platoon at a frequency of 10Hz via a dedicated short-range communication module (such as DSRC or C-V2X), while simultaneously receiving motion status information broadcast by other vehicles in the platoon.

[0046] The motion status information collected and broadcast by each vehicle includes: the vehicle's two-dimensional position coordinates in the geodetic coordinate system. Velocity vector velocity scalar acceleration scalar (With the vehicle's forward direction as positive and braking as negative), yaw angle (With true north as 0° and clockwise as positive), vehicle length and vehicle width Steering wheel angle and yaw rate .

[0047] After receiving motion status information broadcast by other vehicles in the formation, each vehicle performs timestamp alignment and outlier removal on the received data to form a complete description of the overall motion of the formation. In this embodiment, the formation system consists of four unmanned vehicles. In one possible implementation, they travel in a diamond formation (lead vehicle in front, followed by left, right, and center rear vehicles) on a structured road. The formation travels at a speed of 25 m / s on a highway. The spatial positions of the four vehicles are: lead vehicle (0,0), left rear vehicle (-5,-8), right rear vehicle (5,-8), and center rear vehicle (0,-16) (unit: m, represented in the formation's local coordinate system, with the lead vehicle as the origin, the x-axis as the horizontal axis, and the y-axis as the vertical axis). Each vehicle obtains each other's position, speed, acceleration, and heading angle information through a V2V communication module. In another possible implementation, they travel in a formation (lead vehicle at the head, followed by rear vehicle 1, rear vehicle 2, and rear vehicle 3) on a structured road. The convoy travels at a speed of 25 m / s on a highway. The spatial positions of the four vehicles are: lead car (0,0), rear car 1 (0,-8), rear car 2 (0,-16), and rear car 3 (0,-24) (unit: m, represented in the local coordinate system of the convoy, with the lead car as the origin, the x-axis as the horizontal axis, and the y-axis as the vertical axis). The longitudinal distance between adjacent vehicles is 8 m. Each vehicle obtains each other's position, speed, acceleration, and heading angle information through a V2V communication module.

[0048] Sub-step S101b: Acquire environmental perception information. Each vehicle collects surrounding environmental data through onboard environmental perception sensors and performs fusion processing on the multi-sensor data. The onboard environmental perception sensors include LiDAR (acquiring three-dimensional point cloud data within a 150m range ahead), millimeter-wave radar (detecting the position and relative speed of targets within a 200m range ahead), and cameras (identifying lane lines, traffic signs, and the categories of surrounding traffic participants).

[0049] After each vehicle performs spatial and temporal synchronization of data from multiple sensors, it uses a deep learning object detection algorithm (such as YOLO) for environmental perception processing to extract the following environmental perception information: lane line information (including lane width, number of lanes, and lane curvature). The information includes road boundary locations, road type (highway / urban road / expressway), traffic sign information, and the location, speed, and direction of movement of other road users in the surrounding area. Each vehicle shares this environmental perception information within the convoy via its onboard communication module. After being aggregated and integrated by the lead vehicle, a unified perception description of the convoy's environment is formed.

[0050] Sub-step S101c: Construct a dynamic interaction graph. In one possible implementation, the edge connections of the dynamic interaction graph dynamically adjust the interaction perception radius threshold based on the current vehicle speed and road type; An edge connection is established when the Euclidean distance between the two vehicles is less than or equal to the interactive sensing radius threshold; otherwise, it is not established.

[0051] It is evident that the interaction perception radius adaptively adjusts with vehicle speed and road type. At high speeds, the perception radius is expanded to cover the potential impact of distant vehicles, while at low speeds, the perception radius is reduced to avoid introducing too many redundant connections. At the same time, differentiated threshold configurations are adopted for different scenarios such as highways and urban roads, so that the sparsity of the interaction graph structure matches the communication overhead and computing resources. This avoids the defects of static thresholds in high-speed scenarios, which may lead to prediction bias due to missing key interactions, and in low-speed scenarios, which may introduce noisy connections and increase the computational burden.

[0052] For example, a dynamic interaction graph can be constructed using each vehicle in the formation as a node. ,in N is the set of nodes (N is the total number of vehicles in the platoon). Let be the set of edges at time t. Each node... The attribute encoding includes normalized position coordinates, velocity vector, acceleration, and heading angle.

[0053] For any two vehicles i and j in the formation, calculate the Euclidean distance based on their spatial positions at time t:

[0054] when An edge connection is established only if the condition is met; otherwise, it is not established. The interactive sensing radius threshold is determined in substep S101c-1. The attributes of each edge include the relative distance between the two vehicles. Relative velocity and relative heading angle .

[0055] In this embodiment, the spatial positions of the four vehicles in the formation are: lead vehicle (0,0), follower vehicle 1 (0,-8), follower vehicle 2 (0,-16), and follower vehicle 3 (0,-24). The calculated distance between adjacent vehicles is 8m, and the distances between non-adjacent vehicles are 16m (leader vehicle and follower vehicle 2), 24m (leader vehicle and follower vehicle 3), and 16m (follower vehicle 1 and follower vehicle 3). Under the coverage of the perception radius threshold (the threshold is determined below), the distance between all pairs of vehicles is less than the threshold. Therefore, a fully connected dynamic interaction graph containing all six edges is initially constructed. The constructed dynamic interaction graph will be recalculated and updated at each time step to ensure that the graph structure always reflects the true topological relationship of the formation at the current moment.

[0056] In the process of constructing the dynamic interaction diagram in this application embodiment, the sub-step S101c is further refined, wherein the sub-step S101c includes sub-steps S101c-1, S101c-2, and S101c-3. The following is a detailed description of each step.

[0057] Sub-step S101c-1: Dynamically adjust the interactive perception radius threshold. The interactive perception radius threshold is not a fixed value, but is adaptively adjusted in real time based on the current average speed of the platoon and the road type. Its calculation method is as follows:

[0058] in, This is the preset baseline sensing radius. For vehicle speed adjustment factor, The current average speed of the convoy. This is the road type adjustment factor, where r is the current road type identifier. The function limits the threshold to a preset minimum sensing radius. and maximum sensing radius between.

[0059] Vehicle speed adjustment factor, The setting principle is as follows: at high speeds, vehicle braking distances increase and the potential interaction range expands, requiring an expanded perception radius; at low speeds, the effective interaction distance between vehicles shortens, necessitating a smaller perception radius to avoid introducing excessive redundant connections. The vehicle speed adjustment factor is configured as follows:

[0060] in, For reference speeds (15 m / s for urban roads and 30 m / s for highways). To adjust the sensitivity coefficient (value range 0.2 to 0.5).

[0061] Road type adjustment factor Configure based on the interaction characteristics of different road types: In highway scenarios, vehicle speeds are high and long-distance interactions have a significant impact, so configure to a larger value ( =1.2); In urban road scenarios, traffic density is high and speed is low, so a smaller value is configured ( =0.8); the configuration for expressway / elevated road scenarios is the baseline value ( =1.0).

[0062] Specifically, in this embodiment, four unmanned vehicles are traveling at 25 m / s on a highway, with a baseline perception radius of... =45m, reference speed =15m / s, adjustment sensitivity coefficient α=0.3, highway road type factor =1.2. Calculate the vehicle speed adjustment factor. =1+0.3×(25 15) / 15=1.2, thus obtaining the interactive sensing radius threshold. =45×1.2×1.2=64.8m. At this point, the maximum distance between any two vehicles in the platoon is 24m, which is less than 64.8m, thus initially constructing a fully connected graph structure. If the platoon enters an urban road scenario, the vehicle speed drops to 10m / s, and the road type factor... =0.8, then the threshold is reduced to =45×0.9×0.8=32.4m, avoiding the introduction of excessive redundant connections in low-speed, high-density scenarios. (Calculated value) The threshold for determining edge connection establishment at each time step.

[0063] In one possible implementation, the edge connections of the dynamic interaction graph have directional encoding, including: Along the convoy driving direction, when the first vehicle is in front of the second vehicle and the distance between them is less than a preset threshold, a directed edge is established from the first vehicle to the second vehicle.

[0064] As can be seen, by establishing directed edges from the vehicle in front to the vehicle behind, messages are propagated only along the physically effective direction in which the preceding vehicle affects the following vehicle. This accurately portrays the unidirectional nature of vehicle interactions in platooning—the acceleration and deceleration of the preceding vehicle influences the following vehicle's following decision, while the motion state of the following vehicle has almost no feedback effect on the preceding vehicle. Unlike existing undirected graph modeling that treats the interaction influence between vehicles in front and behind as an equivalent bidirectional propagation (where information from the following vehicle propagates back to the preceding vehicle, introducing physically unreasonable noise signals), this scheme, through directional encoding and an incoming edge direction aggregation mechanism, ensures that the target node only receives interaction messages from the vehicle in front of it. This avoids the invalid information flow from the following vehicle to the preceding vehicle in the undirected graph and the resulting prediction bias. From the graph structure level, it guarantees that the direction of information propagation is consistent with the actual physical interaction direction, improving the physical rationality and accuracy of platoon trajectory prediction.

[0065] Sub-step S101c-2: Directional Encoding. Edge connections in the dynamic interaction graph are directionally encoded. For any two vehicles i and j in the formation, when determining whether to establish an edge connection, the heading angles of the two vehicles are first considered. and Determine the main direction of convoy driving, and then calculate the azimuth angle of vehicle j relative to vehicle i:

[0066] If azimuth angle Falling within the preset forward perception range Inside( If the forward sensing half-angle is set to 30° in this embodiment, then vehicle j is determined to be in front of vehicle i. Simultaneously, the distance between the two vehicles along the platooning direction is calculated. When satisfied and When the value is greater than 0, construct a directed edge (j,i) from vehicle j (the vehicle in front) to vehicle i (the vehicle behind).

[0067] Specifically, assuming the formation is traveling due north (heading angle 0°) ), threshold =64.8m, forward sensing half-angle =30 The positions of the four cars are: lead car (0,0), rear car 1 (0,-8), rear car 2 (0,-16), and rear car 3 (0,-24).

[0068] For the following vehicle 1 (0,-8), the azimuth angle of the lead vehicle (0,0) relative to the following vehicle 1 is atan2(0,8)=0. Within the forward perception range, with a longitudinal distance of 8m ≤ 64.8m, a directed edge is established from the lead vehicle to the following vehicle 1.

[0069] For the following vehicle 2 (0, -16), the azimuth angle of the lead vehicle (0, 0) relative to the following vehicle 2 is 0. Within the forward sensing range, with a longitudinal distance of 16m ≤ 64.8m, a directed edge is established from the lead vehicle to the following vehicle 2; the azimuth angle of the following vehicle 1 (0, -8) relative to the following vehicle 2 is 0. Within the forward sensing range, with a longitudinal distance of 8m ≤ 64.8m, a directed edge is established from rear vehicle 1 to rear vehicle 2.

[0070] For the following vehicle 3 (0, -24), the azimuth angle of the lead vehicle (0, 0) relative to the following vehicle 3 is 0. Within the forward sensing range, with a longitudinal distance of 24m ≤ 64.8m, a directed edge is established from the lead vehicle to the following vehicle 3; the azimuth angle of the following vehicle 1 (0, -8) relative to the following vehicle 3 is 0. Within the forward sensing range, with a longitudinal distance of 16m ≤ 64.8m, establish a directed edge from rear vehicle 1 to rear vehicle 3; the azimuth angle of rear vehicle 2 (0, -16) relative to rear vehicle 3 is 0. Within the forward sensing range, with a longitudinal distance of 8m ≤ 64.8m, a directed edge is established from rear vehicle 2 to rear vehicle 3.

[0071] If the convoy enters an urban road scenario, the threshold is reduced to 32.4m. At this time, the distance between the lead vehicle and the following vehicle is 24m, which is still less than the threshold, so an edge connection is still established. If the convoy further expands the distance or lowers the threshold, when the distance between non-adjacent vehicles exceeds the threshold, the corresponding edge connection is automatically disconnected, and only the edge connection between adjacent vehicles is retained.

[0072] In platooning, directional coding is also used to filter out erroneous edges caused by lateral offset between vehicles in the same row. Since all vehicles in the platoon are arranged longitudinally in the same lane and have the same lateral position, all vehicles behind are within the perception range directly in front of the vehicle in front. Therefore, the role of directional coding is mainly to ensure that the direction of the edge is consistent so that the vehicle in front points to the vehicle behind.

[0073] In one possible implementation, when constructing the dynamic interaction graph, the interaction intensity weights of each edge are calculated based on the Intelligent Driver Model (IDM). The interaction intensity weights are related to the distance between the two vehicles, their relative speed, and the speed of the vehicle itself. The interaction intensity weights are used to weight neighbor messages during message passing.

[0074] Sub-step S101c-3: Interaction intensity weight calculation. When constructing the dynamic interaction graph, the interaction intensity weights of each edge are calculated based on the Intelligent Driver Model (IDM). The acceleration response of the IDM model is:

[0075] The desired vehicle spacing is:

[0076] In the formula, s is the actual distance between the vehicle and the vehicle in front. For the vehicle's speed, The speed difference between the vehicle and the vehicle in front. For maximum acceleration, To reduce speed for comfort, For the desired speed, The minimum safe distance is T, where T is the safe time interval.

[0077] Based on the IDM model, the interaction strength weight of the directed edge (j,i) from the vehicle j in front to the vehicle i behind is:

[0078] in, As the normalization factor, The sigmoid activation function limits the weight values ​​to the interval (0,1).

[0079] With the established directed edge of the navigator Rear vehicle 1, Rear vehicle 1 Rear car 2, rear car 2 Taking car 3 as an example, assume the current speeds of each car are: lead car 24 m / s (declining), follower car 1 24.5 m / s, follower car 2 25 m / s, follower car 3 25 m / s, and the distance between all cars is 8 meters. The IDM model parameters are set as follows: =3m / s², =2m / s², =30m / s, T=1.5s, s0=2m, =50m / s². The navigator vehicle was calculated using the above formula. The edge weight of the rear vehicle 1 is 0.84. The edge weight of the second car is 0.85. The edge weight of the rear vehicle 3 is 0.82.

[0080] The interaction strength weight is attached to each directed edge. During subsequent message transmission, when the target node aggregates messages from its neighbors, the contribution of each neighbor message is multiplied by the weight of its corresponding directed edge, thus achieving the physical prior guidance that "the stronger the interaction, the more attention it receives." For example, when the following car 3 aggregates messages, the edge weight from the following car 2 is 0.82, the edge weight from the following car 1 is 0.85 (but the directional encoding has already established a directed edge from the following car 1 to the following car 3, with a weight of 0.85), and the edge weight from the lead car is 0.84 (the directional encoding has established a directed edge from the lead car to the following car 3). All three are weighted and aggregated, with the following car 1 having the highest weight (0.85) for the following car 3, reflecting the strongest interaction response generated by the combination of the relative speed difference and the distance between the following cars 1 and 3.

[0081] As can be seen, by embedding the IDM physical model into the calculation of interaction intensity weights, the edge weights no longer rely on pure data-driven learning or fixed assignments, but instead have clear physical meanings—the greater the expected acceleration amplitude of the current vehicle (i.e., the more drastic the acceleration or deceleration), the higher the corresponding edge weight, and the stronger its interaction influence on the following vehicle; at the same time, the smaller the distance between vehicles and the greater the relative speed, the greater the weight also increases accordingly, accurately reflecting the physical law that "the following vehicle must respond quickly when the vehicle in front changes drastically" in car-following scenarios. Unlike pure data-driven methods that may learn interaction patterns that contradict physics outside the training data distribution (such as assigning low weights when the distance between vehicles is very close and ignoring collision risks), this scheme ensures the rationality and interpretability of the weights in different scenarios through physical prior constraints. Moreover, the IDM prior is independent of the training data distribution, enhancing the model's generalization ability in unseen scenarios such as dense traffic flow and extreme acceleration or deceleration, and avoiding prediction failures caused by insufficient training data coverage in pure data-driven methods.

[0082] In one specific implementation of this application, based on the dynamic interaction graph constructed in step S101, multidimensional features are extracted for each node in the graph and encoded into an initial embedding vector, which serves as the input for subsequent graph neural network message passing.

[0083] Step S102: Extract the kinematic features, historical trajectory features, and road environment features of each node as the initial embedding. In one possible implementation, Figure 3 This is a schematic diagram illustrating a feature fusion method for generating an initial embedding, provided in an embodiment of this application. Specifically, in Figure 3 The process includes sub-step S102a: extracting kinematic features. For each vehicle node in the formation... The kinematic feature vector for the current moment is extracted from the real-time motion state information obtained in step S101. The kinematic features include the vehicle's velocity scalar. acceleration scalar (With the vehicle's forward direction as positive and braking as negative), yaw angle yaw rate and steering wheel angle .

[0084] Kinematic eigenvectors Represented as:

[0085] To improve model training efficiency and generalization ability, each dimension of the kinematic features is normalized. (Velocity) At the desired speed of the formation Normalization is performed based on the baseline, i.e. Ensure that the velocity characteristic remains in the 0-1 range; acceleration At maximum acceleration Normalization is performed based on the baseline, i.e. Heading angle Normalized to [ The interval π,π]]; yaw rate With maximum yaw rate For baseline normalization; steering wheel angle With the maximum turning angle Normalization is applied to the baseline. Kinematic features are mapped to a fully connected encoding layer. Dimensional embedding space:

[0086] in, The weight matrix is ​​a learnable matrix. This is a bias term.

[0087] Sub-step S102b: Extract historical trajectory features. To capture vehicle motion trends and driving intentions, extract historical trajectory features for each vehicle in the past. Each time step (in this embodiment) =10, corresponding to the historical trajectory sequence within the past 1 second (time step 0.1 seconds). The historical trajectory features include the position coordinates and velocity vectors at each historical moment.

[0088] For vehicle i, its historical trajectory sequence is as follows:

[0089] in, For vehicles in Position coordinates at that moment This corresponds to the velocity vector. The historical trajectory sequence is processed by a gated recurrent unit (GRU) encoder to extract historical motion patterns:

[0090] The last hidden state output by the GRU encoder is used as an embedding representation of the historical trajectory features. The GRU encoder can effectively capture long-range dependencies in time series and extract the vehicle's historical motion patterns.

[0091] Sub-step S102c: Extract road environment features. From the environmental perception information obtained in step S101, extract the road environment features of each vehicle's location. These road environment features include the lane curvature of the lane in which the vehicle is located. Lane width and road type identification (Using one-hot encoding, representing highways, urban roads, expressways, etc.)

[0092] Road environment feature vector Represented as:

[0093] Similarly, the continuous value features are normalized: lane curvature With maximum curvature (In this embodiment, it is set to 0.1 m) - ¹) is normalized to a baseline; lane width is normalized to a standard lane width of 3.5m. In this embodiment, road environment features also include: speed limit information (used to verify the rationality of the desired speed setting) and signs indicating whether there are curves or ramps ahead.

[0094] Road environment features are mapped to a fully connected coding layer. Dimensional embedding space:

[0095] in, The weight matrix is ​​a learnable matrix. This is a bias term.

[0096] Sub-step S102d: Feature fusion to generate initial embeddings. The embedding representations of the three types of features are fused to generate the initial embedding vectors for the nodes. .

[0097] In this embodiment, three types of embeddings are fused using feature concatenation, and the final initial embedding is generated after passing through a fusion coding layer:

[0098] in, This represents a vector concatenation operation. To fuse the weight matrix, The bias term, after concatenation, is reduced to a dimensionality of 1 / 2 after a fusion coding layer. dimension.

[0099] Initial embedding vectors of each node This serves as the starting point for message passing in the graph neural network in subsequent step S103, specifically the node representation of layer 0 (the starting point of message passing). For N nodes in the array, their initial embedding matrix is... .

[0100] Step S103: Using the initial embedding as the starting point for message passing, perform physical constraint message passing layer by layer on the dynamic interaction graph, aggregating neighbor messages along the incoming edge direction. After each layer is attention-weighted and fused with neural network encoded features and physical prior residuals, the output updated embedding is used as the input for the next layer. After iterating through multiple layers, the target updated embedding of each node is obtained.

[0101] In one possible implementation, the physical constraint message passing includes: In the current message passing layer, neural network encoded features are extracted from the current layer node representation. At the same time, physical prior residuals are calculated based on the intelligent driver model and the current layer node representation. The prior residuals are the deviation between the intelligent driver model IDM theoretical acceleration and the current predicted acceleration. The neural network encoded features are concatenated with the physical prior residuals and then fused with attention weighting to obtain the fusion message of the current layer. An updated embedding of the current layer is generated based on the fusion message.

[0102] In one specific implementation of this application, the initial embedding matrix of each node obtained in step S102 is used as the basis. The dynamic interaction diagram constructed in step S101 The system performs multi-layer physical constraint message passing. In each layer, each node aggregates messages from its neighbors along the incoming edge direction (i.e., the direction from the vehicle in front towards itself). The message content combines neural network encoded features with physical prior residuals, and is then weighted by attention to update the node embedding. After iterating through L layers, the target update embedding for each node is obtained, which serves as the input for subsequent trajectory decoding.

[0103] Specifically, initialize the node representation of the current layer. Initially embed the nodes output in step S102 as the node representation of layer 0:

[0104] Where i is the node index. A set of nodes. Current layer index. Starting from 0, message passing is executed layer by layer until the Lth node. The first layer (out of L layers) is used to output the node representation of the Lth layer as the target to update the embedding.

[0105] Constructing a fused message—concatenating neural network encoded features with physical prior residuals. In the first... layer( =0,1,…,L 1) For each directed edge (j,i) in the dynamic interaction graph... (Indicates pointing from vehicle j in front to vehicle i behind), construct the fusion message passed from neighbor node j to target node i. .

[0106] First, based on the current layer representation of source node j. Extracting neural network encoded features:

[0107] in, For the first The multilayer perceptron encoder maps node embeddings to the message feature space. In this embodiment, It contains two fully connected layers, with a hidden layer dimension of 128 and an output dimension of 32.

[0108] Simultaneously, based on the current layer representation of source node j, the current predicted acceleration of that node is calculated. Specifically, from Decode the current prediction speed and acceleration :

[0109] Then, obtain the velocity information of target node i. (Motion state information obtained from step S101), combined with the actual vehicle distance between source node j and target node i Calculate the theoretical acceleration of IDM:

[0110] The expected vehicle spacing is:

[0111] Based on the deviation between the IDM theoretical acceleration and the current predicted acceleration, the physical prior residual is calculated:

[0112] The sign of the residual indicates the direction in which the prediction deviates from the physical laws—when When the value is >0, it indicates that the predicted acceleration is lower than the theoretical value of IDM (i.e., the predicted braking is insufficient), and it needs to be adjusted upwards; when A value less than 0 indicates that the predicted acceleration is higher than the theoretical value of IDM (i.e., the predicted acceleration is excessive) and needs to be adjusted downwards. The magnitude of the residual characterizes the extent of the deviation, and subsequent attention-weighted fusion is used to prioritize the correction of predicted components that deviate from the physical laws.

[0113] The neural network encoded features are concatenated with the physical prior residuals to obtain the fused message:

[0114] Aggregate neighbor messages along the incoming edge direction. For target node i, its set of all incoming edge neighbors is: (That is, all vehicles pointing ahead of node i). Node i is at the... The aggregation message of the layer is a weighted sum of the merged messages of all incoming edge neighbors:

[0115] in, The attention weight is determined by two parts: semantic relevance of the query-key-based dot product attention and interaction strength based on physical distance.

[0116] (1) Semantic relevance attention: Calculate the query vector of target node i Key vector of source node j dot product:

[0117] in, , , The dimension of the key vector.

[0118] (2) Physical distance attention: Physical relevance weights are calculated based on vehicle spacing, relative speed, and road curvature.

[0119] in, The distance between the two vehicles. For relative velocity, β1, β2, and β3 are the road curvature, and β1, β2, and β3 are the weighting coefficients (set to 0.5, 0.3, and 0.2 respectively in this embodiment). and This is the normalization factor.

[0120] (3) Final attention weight: Multiply the semantic relevance by the physical distance attention and combine it with the IDM edge weight calculated in step S101c-3. :

[0121] in, The directed edge interaction strength weights calculated based on the IDM model in step S101c-3 serve as a further constraint on the attention weights based on physical priors, so that neighbors with higher interaction strengths occupy a larger proportion in the aggregation.

[0122] Generate the current layer update embedding. Target node i is at the... Layer aggregation receives messages Then, combined with its current layer representation The next layer node representation is generated through a gating update mechanism. :

[0123] in, For the first The gated recurrent unit (GRU) of the layer is used to fuse aggregated neighbor messages with its current representation. The GRU unit can adaptively control the fusion ratio of historical and new information, which is beneficial for training stability. Updated embedding As the first Layer node representation.

[0124] Repeat the above process, iteratively executing message passing layer by layer until all L layers are completed. In each layer, the node representation is continuously updated, and interactive information propagates layer by layer backward along the directed edges from the vehicle in front—in layer 1, vehicle 1 obtains information from the lead vehicle, vehicle 2 obtains information from vehicle 1 and the lead vehicle, and vehicle 3 obtains information from vehicle 2, vehicle 1, and the lead vehicle; in layer 2, vehicle 2 obtains deeper information from the updated vehicle 1, and vehicle 3 obtains deeper information from the updated vehicle 2, with information propagating sequentially from front to back along the formation. After L layers of iteration, the target update embedding of each node is output. .

[0125] As can be seen, by simultaneously extracting neural network encoded features and calculating physical prior residuals at the current message passing layer, and then concatenating and fusioning them through attention weighting, physical constraints are upgraded from external "soft constraints" applied only to the output layer to intrinsic components embedded in each layer of message passing. The physical prior residuals characterize the direction and magnitude of the current prediction's deviation from physical laws. Concatenated with neural network encoded features and adjusted through attention weights, the model is aware of the physical deviation of the current prediction during the message fusion construction stage, thus prioritizing the correction of feature components deviating from physical laws when generating updated embeddings. Compared to methods that only add physical regularization terms to the loss function or only perform physical verification at the final output layer, this scheme performs physical deviation calculation and correction at each layer, achieving a deep fusion of physical constraints and neural network feature extraction. This fundamentally ensures that intermediate representations are anchored to the physical feasible region at each layer, avoiding the accumulation and amplification of physical deviations during inter-layer propagation, and significantly improving the physical consistency of the predicted trajectory.

[0126] Step S104: Decode the target update embedding to obtain the initial predicted trajectory of each vehicle in the future time domain in the formation system.

[0127] In one possible implementation, the method further includes: when there is a lateral cutting motion of a vehicle in an adjacent lane, establishing a directed edge from the cutting vehicle to the target vehicle, wherein the interaction strength weight of the directed edge is dynamically adjusted based on the lateral distance and the relative lateral velocity.

[0128] In one specific implementation of this application, the embedding is updated based on the target update of each node output in step S103. (i=1,2,…,N), the predicted trajectories of each vehicle in the future time domain are generated through the decoder network.

[0129] In one possible implementation, Figure 4 This is a schematic flowchart illustrating a trajectory prediction output method provided in an embodiment of this application. Specifically, in Figure 4 The process includes sub-step S104a: constructing a trajectory decoder. The trajectory decoder employs a multilayer perceptron (MLP) architecture, embedding the target update of each node into a mapping of the future... The position sequence at each time step. The input to the decoder is the target updated embedding. The output is a prediction of the future trajectory:

[0130] in, For vehicle i in The predicted position coordinates at time τ = 1, 2, ... , To predict the temporal length, the decoder network consists of two fully connected hidden layers, each with a dimension of 128 and a ReLU activation function. The output layer has a dimension of 2×128. .

[0131] Sub-step S104b: Formation Consistency Correction. Since the decoding processes of each node are independent, directly decoding the output trajectory may disrupt the overall formation consistency (e.g., the predicted trajectories of adjacent vehicles in the same lane intersect, or the distance between them is less than the safe distance). This application introduces a formation consistency correction layer after decoding to fine-tune the predicted trajectory. Based on the predicted positions of each vehicle in the formation, the correction layer calculates the distance loss and smoothness loss between adjacent vehicles, and iterates through gradient descent.

[0132] Sub-step S104c: Multi-step prediction and autoregressive strategy. To obtain the complete trajectory in the future time domain, this application employs a multi-step prediction strategy. After obtaining the predicted position sequence, it is used as input again into the message passing and graph neural network to generate the prediction for the next stage.

[0133] Specifically, the prediction time domain is defined as =30 steps, implemented using a sliding window approach: In each prediction, the model outputs the trajectory for the next 15 steps (1.5 seconds), and then uses this prediction result as input to update the graph structure, predicting the next 15 steps again, and so on until all 30 prediction time domains are covered. This rolling prediction method can dynamically update the dynamic interaction graph using intermediate prediction results, making the predicted trajectory better adapt to changes in formation motion.

[0134] Specifically, in the above formation embodiment, after the target update embeddings of following vehicle 1, following vehicle 2, and following vehicle 3 are decoded, each outputs its predicted position for the next 30 time steps, forming three longitudinally arranged predicted trajectories. Since directional encoding ensures that message propagation is along the direction from the preceding vehicle to the following vehicle, the predicted trajectory of following vehicle 3 naturally responds later than that of following vehicle 2 during the acceleration phase, and following vehicle 2 responds later than following vehicle 1, forming a progressive response pattern that conforms to the physical laws of real car-following.

[0135] Sub-step S104d: Directional encoding extension for lateral cutting-in scenarios. In one possible implementation, the method further includes: when there is lateral cutting-in movement between adjacent lanes, establishing a directed edge from the cutting-in vehicle to the target vehicle, wherein the interaction strength weight of the directed edge is dynamically adjusted based on lateral distance and relative lateral velocity.

[0136] Specifically, in the dynamic interaction graph construction process of step S101, in addition to establishing a longitudinal directed edge from the vehicle in front to the vehicle behind in the same lane, the perception module also detects in real time whether there is lateral cutting-in movement of vehicles in adjacent lanes. When it is detected that the vehicle c in the adjacent lane has the intention to cut in or is cutting into the lane, a lateral directed edge (c,i) from the cutting-in vehicle c to the target vehicle i is established.

[0137] Intent detection is based on lateral distance. and relative lateral velocity When the lateral distance of the merging vehicle relative to the target lane continues to decrease ( < 0.2m / s) and lateral distance Less than the preset cut-in detection threshold At that time, it was determined that there was an intention to make inroads.

[0138] Interaction strength weights of lateral directed edges (c,i) Dynamically adjusted based on lateral distance and relative lateral velocity:

[0139] in, The lateral distance (lateral offset) between the cutting vehicle c and the target vehicle i. This is the parameter for the lateral influence range (set to 1.0m in this embodiment). As the normalization factor, This is the lateral velocity gain coefficient (set to 0.5 in this embodiment). It is the relative lateral velocity (the lateral velocity of the cutting vehicle relative to the target vehicle). The sigmoid activation function is used, and the weight values ​​are limited to the interval (0,1). The closer the lateral distance of the cutting vehicle and the greater its lateral cutting speed, the higher the weight, and the stronger the interaction between the cutting vehicle and the target vehicle.

[0140] Lateral directed edges and longitudinal directed edges exist in parallel in the dynamic interaction graph. During subsequent message passing, the target vehicle ii will simultaneously aggregate longitudinal messages from vehicles ahead of it and lateral messages from vehicles cutting in from adjacent lanes. The two types of messages are then fused at the target node through attention weighting to generate an updated embedding, enabling the predicted trajectory to respond simultaneously to the dual effects of longitudinal following and lateral cutting.

[0141] Sub-step S104e: Predicted trajectory output. The predicted trajectories, after formation consistency correction, are output in chronological order as the predicted trajectory matrix for each vehicle in the future time domain. For each node in the formation, the set of predicted trajectories for each node serves as the final output of step S104, which is further used for subsequent formation decisions, path planning, or safety assessments.

[0142] As can be seen, by extending directional encoding from longitudinal following to lateral cutting-in scenarios, the model can accurately distinguish the different impacts of left-side and right-side cutting-in on the target vehicle. When a cutting-in vehicle approaches the target lane from the left or right, the system establishes corresponding directed edges based on the real-time detected lateral distance and relative lateral velocity. The change in the lateral motion state of the cutting-in vehicle is directly reflected in the dynamic adjustment of the directed edge interaction strength weights: the smaller the lateral distance and the greater the relative lateral velocity (the more obvious the cutting-in intention), the higher the edge weight, the stronger the interaction influence of the cutting-in vehicle on the target vehicle, and the more timely the warning and response signals received by the target vehicle. Unlike the longitudinal following scenario where directional encoding is only transmitted along the driving direction, the directional encoding of directed edges in the lateral cutting-in scenario allows the interaction information to propagate unidirectionally from the cutting-in vehicle to the target vehicle, accurately characterizing the unidirectional disturbance characteristics of the cutting-in behavior—the cutting-in vehicle actively changes lanes to affect the target vehicle, while the target vehicle has almost no feedback influence on the lateral motion of the cutting-in vehicle. Through this lateral directionality encoding, the model can predict the lane-changing intention based on the changing trends of lateral distance and relative lateral speed at the initial stage of lane change, rather than reacting only after crossing the lane boundary. This improves the advance and accuracy of trajectory prediction in lane-changing scenarios and avoids prediction bias caused by ambiguity in lateral interaction direction in undirected graph modeling.

[0143] In one possible implementation, the acceleration response of the intelligent driver model (IDM) is jointly determined by the desired speed, maximum acceleration, comfortable deceleration, safe distance, and minimum safe distance, wherein: When the actual speed of the vehicle is closer to the desired speed and the distance between the vehicles is closer to the safe distance determined by relative speed and safe travel distance, the acceleration approaches zero.

[0144] Specifically, the IDM model calculates the vehicle's desired acceleration using the following acceleration response formula:

[0145] Where s is the actual distance between the vehicle and the vehicle in front. For the vehicle's speed, The speed difference between the vehicle and the vehicle in front. For maximum acceleration, For the desired speed, For comfortable deceleration, the desired vehicle spacing is... Defined as:

[0146] in, The minimum safe distance is T, where T is the safe time interval.

[0147] When the actual speed of the vehicle approaches the desired speed, and the distance to the preceding vehicle approaches the safe distance determined by relative speed and safe headway, both of these parameters tend to 1, and the acceleration approaches zero, indicating that the vehicle enters a steady-state following or free-cruising state. In the calculation of physical prior residuals, this zeroing characteristic makes... The deviation from the predicted acceleration directly reflects whether the prediction has converged to a physically reasonable steady state, thus guiding the model to prioritize correcting the predicted components that deviate from the steady state during message passing.

[0148] As can be seen, this scheme ensures that even in extreme scenarios where the training data is not covered, the IDM prior can still provide a reasonable acceleration benchmark. This benchmark naturally returns to zero as the speed approaches the expected value and the distance between vehicles approaches the safe distance, so that the predicted trajectory converges to a physically reasonable steady-state car-following state in any scenario. This significantly improves the model's generalization ability and prediction reliability in unseen scenarios such as dense traffic flow and extreme acceleration and deceleration.

[0149] One possible implementation also includes a smooth transition mechanism for edge weights in the Cut-in scenario: when a vehicle in an adjacent lane cuts into the formation, the edge weights between the cutting vehicle and the affected agent are smoothly transitioned from the old value to the new value through interpolation coefficients, which are dynamically calculated based on the lateral distance and relative lateral speed of the cutting vehicle.

[0150] Specifically, during the process of vehicles from adjacent lanes joining a platoon, the interaction between the joining vehicle and the target lane vehicle is not established instantaneously, but gradually strengthens as the joining process progresses. If the edge weights were to jump directly from zero to the target value at the moment the joining is completed, it would cause a sudden change in the graph topology, leading to violent oscillations in the predicted trajectory. To address this, this application introduces an edge weight smoothing transition mechanism: as the joining vehicle moves from the adjacent lane to the target lane, the edge weights are adjusted according to the lateral distance of the joining vehicle. and relative lateral velocity The interpolation coefficient α(t) is calculated in real time. The interpolation coefficient is defined as:

[0151] in, Let be the lane width, and `smoothstep` be the smooth step function. When the merging vehicle is located in the center of the adjacent lane, α≈0 (no interaction). When the merging vehicle crosses the lane line to enter the target lane, α≈1 (full interaction). The intermediate states are achieved through a smooth step function for continuous transition. The edge weight transition formula is:

[0152] in, The initial edge weights before the cut (usually zero or a very small value). The target edge weights are calculated based on the IDM model after the cutting process is completed. Through this interpolation mechanism, the edge weights change smoothly with the cutting process, avoiding abrupt changes in the graph topology, ensuring the continuity and stability of the predicted trajectory during the cutting process, and providing a temporal buffer for edge reconstruction at the moment of cutting.

[0153] In one possible implementation, the overall kinetic energy conservation constraint of the formation is also incorporated into the message passing process: a kinetic energy conservation regularization term is added during the training phase to ensure that the rate of change of the total kinetic energy of the formation in the predicted trajectory is consistent with the theoretical rate of change of kinetic energy determined by the physical prior model; during the inference phase, when the rate of change of kinetic energy of the predicted trajectory deviates from the theoretical value by more than a preset threshold, trajectory correction based on physical prior is triggered.

[0154] Specifically, as a whole system, the change in the total kinetic energy of the formation should conform to the law of conservation of energy—the increase in kinetic energy comes from the work done by the engine, and the decrease in kinetic energy comes from braking and drag dissipation; there should be no unreasonable situations where energy is created or disappeared out of thin air. This application introduces a kinetic energy conservation regularity term during the training phase:

[0155] Among them, the total kinetic energy of the formation , The theoretical kinetic energy is determined by the physical prior model (considering the work done by the net external forces on the entire formation). This regularization term constrains the rate of change of the total kinetic energy of the formation in the predicted trajectory to be consistent with the physical prior, thereby guiding the predicted trajectory of each node to satisfy the energy conservation law of the entire formation during model training.

[0156] During the inference phase, the total kinetic energy of the formation and its rate of change for the predicted trajectory are calculated and compared in real time with the theoretical rate of change of kinetic energy determined by the physical prior model. When the deviation exceeds a preset threshold, trajectory correction based on the physical prior is triggered. By using global kinetic energy conservation constraints, the deficiency of lacking overall consistency verification in node-by-node prediction is compensated for, ensuring that the predicted trajectory also satisfies the law of conservation of physical energy at the overall formation level, significantly improving the physical reliability and long-term stability of multi-vehicle collaborative prediction.

[0157] As can be seen, this invention constructs a dynamic interactive graph, enabling real-time adjustments to the graph connections as the formation topology changes dynamically, thus avoiding prediction biases introduced by static graph structures. By fusing neural network encoding features and physical prior residuals at each layer of message passing, the predicted trajectory is anchored to the physical feasible domain throughout the entire process, avoiding physical inconsistencies in edge scenarios caused by purely data-driven models. By aggregating messages along the incoming edge direction, the interactive information propagates along the physically effective direction in which the preceding vehicle influences the following vehicle, accurately characterizing the unidirectional nature of vehicle-to-vehicle interactions. Through layer-by-layer attention-weighted fusion and iterative updates of the embedding, the interactive influence of multi-vehicle coupling is fully extracted and fused during layer-by-layer propagation, significantly improving the trajectory prediction accuracy and physical consistency in dynamic formation scenarios.

[0158] Figure 5 This is a schematic diagram of a formation trajectory prediction method system based on physically augmented dynamic graph neural networks, provided as an embodiment of this application. It includes: Module 501 is used to acquire motion state information and environmental perception information of each vehicle in the formation system. The motion state information and environmental perception information are used to dynamically establish edge connections based on the spatial distance between the vehicles in the formation, taking each vehicle in the formation as a node, and construct a dynamic interaction graph. Extraction module 502 is used to extract the kinematic features, historical trajectory features and road environment features of each node as initial embedding; The transmission module 503 is used to take the initial embedding as the starting point of message transmission, and perform physical constraint message transmission by aggregating neighbor messages along the incoming edge direction layer by layer on the dynamic interaction graph. After attention weighting and fusing neural network encoded features and physical prior residuals, the updated embedding is output as the input of the next layer. After iterating through multiple layers, the target updated embedding of each node is obtained. The decoding module 504 is used to decode the target update embedding to obtain the initial predicted trajectory of each vehicle in the future time domain in the formation system.

[0159] The apparatus is used to implement the method corresponding to any embodiment of the first aspect of the present application.

[0160] The relevant explanations can be understood by referring to the corresponding descriptions and effects in the method embodiments, and will not be repeated here.

[0161] Figure 6 This is a schematic diagram of an electronic device for a formation trajectory prediction method based on a physically enhanced dynamic graph neural network, as provided in an embodiment of this application. Figure 6 As shown, the electronic device 600 includes a memory 610 and a processor 620.

[0162] The memory 610 stores a computer program that can be executed by at least one processor 620. This computer program is executed by at least one processor 620 to cause the electronic device to perform the methods provided in any of the above embodiments.

[0163] The memory 610 and the processor 620 can be connected via a bus 630.

[0164] The relevant explanations can be understood by referring to the corresponding descriptions and effects in the method embodiments, and will not be repeated here.

[0165] One embodiment of this application provides a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to perform the following: Figures 1 to 4 The method provided in any corresponding embodiment.

[0166] The computer-readable storage medium may be ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, and optical data storage device, etc.

[0167] One embodiment of this application provides a computer program product comprising computer-executable instructions, which, when executed by a processor, are used to implement, as described above. Figures 1 to 4 The method provided in any corresponding embodiment.

[0168] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0169] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope of this application is indicated by the claims.

Claims

1. A formation trajectory prediction method based on physically augmented dynamic graph neural networks, characterized in that, include: The motion state information and environmental perception information of each vehicle in the formation system are obtained. The motion state information and environmental perception information are used to dynamically establish edge connections based on the spatial distance between the vehicles in the formation, using each vehicle in the formation as a node, and construct a dynamic interactive graph. The kinematic features, historical trajectory features, and road environment features of each node are extracted as the initial embedding; Using the initial embedding as the starting point for message passing, physical constraint message passing that aggregates neighbor messages along the incoming edge direction is executed layer by layer on the dynamic interaction graph. After attention weighting and fusing neural network encoded features and physical prior residuals, the updated embedding is output as the input for the next layer. After iterating through multiple layers, the target updated embedding of each node is obtained. Decoding the target update embedding yields the initial predicted trajectory of each vehicle in the future time domain within the formation system.

2. The method according to claim 1, characterized in that, The edge connections of the dynamic interaction graph dynamically adjust the interaction perception radius threshold according to the current vehicle speed and road type. An edge connection is established when the Euclidean distance between the two vehicles is less than or equal to the interactive sensing radius threshold; otherwise, it is not established.

3. The method according to claim 1 or 2, characterized in that, The edge connections of the dynamic interaction graph have directional encoding, including: Along the convoy driving direction, when the first vehicle is in front of the second vehicle and the distance between them is less than a preset threshold, a directed edge is established from the first vehicle to the second vehicle.

4. The method according to claim 3, characterized in that, When constructing the dynamic interaction graph, the interaction intensity weight of each side is calculated based on the Intelligent Driver Model (IDM). The interaction intensity weight is related to the distance between the two vehicles, their relative speed, and the speed of the vehicle itself. The interaction intensity weight is used to weight neighbor messages during message transmission.

5. The method according to claim 3, characterized in that, The method further includes: when there is a lateral cutting motion of vehicles in adjacent lanes, establishing a directed edge from the cutting vehicle to the target vehicle, wherein the interaction strength weight of the directed edge is dynamically adjusted based on the lateral distance and the relative lateral velocity.

6. The method according to any one of claims 1-5, characterized in that, The physical constraint message passing includes: In the current message passing layer, neural network encoded features are extracted from the current layer node representation. At the same time, physical prior residuals are calculated based on the intelligent driver model and the current layer node representation. The prior residuals are the deviation between the intelligent driver model IDM theoretical acceleration and the current predicted acceleration. The neural network encoded features are concatenated with the physical prior residuals and then fused with attention weighting to obtain the fusion message of the current layer. An updated embedding of the current layer is generated based on the fusion message.

7. The method according to claim 6, characterized in that, The acceleration response of the Intelligent Driver Model (IDM) is determined by the desired speed, maximum acceleration, comfortable deceleration, safe distance, and minimum safe distance, where: When the actual speed of the vehicle is closer to the desired speed and the distance between the vehicles is closer to the safe distance determined by relative speed and safe travel distance, the acceleration approaches zero.

8. A formation trajectory prediction system based on physically augmented dynamic graph neural networks, characterized in that, include: The construction module is used to acquire the motion state information and environmental perception information of each vehicle in the formation system. The motion state information and environmental perception information are used to dynamically establish edge connections based on the spatial distance between the vehicles in the formation, using each vehicle in the formation as a node, and construct a dynamic interaction graph. An extraction module is used to extract the kinematic features, historical trajectory features, and road environment features of each node as initial embeddings; The message passing module is used to perform physical constraint message passing by aggregating neighbor messages along the incoming edge direction layer by layer on the dynamic interaction graph, with the initial embedding as the starting point of message passing. After each layer is attention-weighted and fused with neural network encoded features and physical prior residuals, the updated embedding is output as the input of the next layer. After multiple iterations, the target updated embedding of each node is obtained. The decoding module is used to decode the target update embedding to obtain the initial predicted trajectory of each vehicle in the future time domain in the formation system.

9. A computer-readable storage medium, characterized in that, It stores a computer program thereon, which is executed by a processor to implement the method of any one of claims 1 to 7.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 7.

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