A transverse-longitudinal coupling human-machine dynamic game control method

Abstract

The application discloses a transverse and longitudinal coupling human-machine dynamic game control method, which is composed of a desired path module, a space-time risk evolution analysis module, a transverse and longitudinal non-cooperative game module and a human-machine co-driving vehicle module. The space-time risk evolution analysis module combines the desired path sequence output by the desired path module, constructs a transverse risk and longitudinal risk model, dynamically generates transverse and longitudinal control weights in combination with a risk change trend, embeds the transverse and longitudinal non-cooperative game module to obtain a front wheel rotation angle and a longitudinal acceleration, realizes transverse and longitudinal collaborative control of the vehicle, and improves the safety and stability of human-machine co-driving in a signal-free intersection scene.

Description

Technical Field

[0001] This invention belongs to the field of intelligent driving, specifically a human-machine dynamic game control method with horizontal and vertical coupling. Background Technology

[0002] With the rapid development of intelligent driving technology, the level of vehicle intelligence is constantly improving, and current autonomous driving systems are gradually evolving from assisted driving to higher levels of autonomous driving. However, for a considerable period of time, autonomous driving systems will still find it difficult to completely operate independently of the driver in complex and dynamic traffic environments, especially in scenarios with complex conflict relationships and significant traffic game dynamics. The joint participation of the driver and the autonomous driving system in control will remain an important human-machine co-driving mode. In this mode, how to ensure safety while also considering the driver's intentions, reducing human-machine control conflicts, and improving the smoothness and stability of vehicle operation has become a key technical problem that urgently needs to be solved in the field of intelligent driving.

[0003] In unsignalized intersections, the lack of explicit traffic light constraints means vehicle flow often relies on drivers' autonomous judgment, leading to significant time competition and spatial proximity risks within conflict zones. In such complex conflict scenarios, achieving coordinated lateral and longitudinal vehicle control while balancing driver intent with the control requirements of autonomous driving systems remains a key technical challenge.

[0004] Among the existing publicly available technologies, the solutions related to this application can be roughly divided into three categories. The first category is solutions for traffic organization or scheduling at unsignalized intersections. For example, patent CN120088974A discloses a vehicle traffic planning method and system for unsignalized intersections, which focuses on modeling and planning the timing of vehicle traffic and the process of group traffic at the intersection. The second category is solutions for intersection conflict identification or risk assessment. For example, patent CN110363983B discloses a method for real-time trajectory prediction and conflict identification of motor vehicles and non-motor vehicles at unsignalized intersections, and patent CN115547060B discloses a method for calculating intersection traffic conflict indicators considering vehicle contours. This type of solution is mainly used for conflict identification, risk warning, or safety indication calculation. Its core output is the conflict judgment result or risk indicator, and it does not further construct a weight generation mechanism for human-machine collaborative control. The third category comprises human-machine co-driving control allocation or game-theoretic control solutions. For example, patent CN109885040B discloses a vehicle driving control allocation system in human-machine co-driving, and patent CN115071758B discloses a human-machine co-driving control switching method based on reinforcement learning. These solutions primarily target human-machine control allocation or game-theoretic decision-making in general road scenarios, focusing on achieving control switching or human-machine collaborative control based on vehicle status, driver status, or predictive information. However, most existing human-machine collaborative control solutions concentrate on steering control, using steering wheel input to achieve path tracking or obstacle avoidance coordination, while giving relatively little consideration to longitudinal control coordination. In actual vehicle motion control, relying solely on steering adjustment is insufficient to effectively avoid risks in complex conflict scenarios. Vehicle safety control inherently requires lateral and longitudinal coordination; steering alone cannot meet the comprehensive needs of collision avoidance and risk mitigation. Furthermore, if longitudinal control variables such as braking are introduced into the existing human-machine collaborative control framework, the system model will expand from a single lateral control to a lateral-longitudinal coupled control system. Its dynamic modeling, constraints, and control objectives become significantly more complex, no longer a simple superposition or extension of the original steering control strategy. Simultaneously, a strong coupling relationship exists between lateral and longitudinal controls, requiring a complete reconstruction of the control power allocation mechanism, game structure, and weight generation method. The overall control architecture needs systematic design, rather than simply adding a longitudinal control channel to achieve effective collaboration. In summary, while existing technologies cover unsignaled intersection passage decisions, conflict identification, and human-machine co-driving control, they have not yet constructed a unified lateral-longitudinal modeling and collaborative control mechanism specifically for the spatiotemporal risk evolution characteristics of typical conflict scenarios at unsignaled intersections. In particular, they lack weight generation methods and human-machine collaborative decision-making frameworks for lateral-longitudinal coupled control. Summary of the Invention

[0005] To address the limitations of existing human-machine collaborative control methods, which primarily focus on steering and struggle to meet the demands of lateral and longitudinal collaborative control in complex conflict scenarios, this invention provides a dynamic game-theoretic control method based on lateral and longitudinal coupling. This method constructs a joint assessment model of temporal and spatial risks, introduces a risk evolution trend analysis mechanism, and maps temporal and spatial risks and their evolution trends into lateral and longitudinal dynamic control weights. Considering the lateral and longitudinal coupling relationship, these dynamic control weights are embedded into a non-cooperative game model between the driver and the controller, resulting in a collaborative control output that ultimately controls the front wheel angle and longitudinal acceleration. This achieves integrated human-machine collaborative control of steering and braking, improving the safety and stability of human-machine co-driving in complex conflict scenarios.

[0006] The technical solution adopted by this invention to solve the technical problem is as follows:

[0007] This invention presents a horizontally and vertically coupled human-machine dynamic game-theoretic control method. It establishes a closed-loop control system comprising a desired path module, a spatiotemporal risk evolution analysis module, a horizontal and vertical non-cooperative game-theoretic module, and a human-machine co-driving vehicle module, achieving horizontal and vertical collaborative control of the human-machine co-driving vehicle. Specifically, the desired path module generates desired path sequences for the driver and controller; the spatiotemporal risk evolution analysis module analyzes the spatiotemporal relationship of the vehicle in the conflict zone to determine the horizontal and vertical control weights; the horizontal and vertical non-cooperative game-theoretic module combines the horizontal and vertical control weights, desired path sequences, and vehicle dynamic information, and derives the front wheel angle and longitudinal acceleration through three steps: driving behavior modeling, objective function design, and Nash equilibrium solution; the human-machine co-driving vehicle module weights and fuses the driver's and controller's front wheel angles according to the horizontal control weights, and weights and fuses the driver's and controller's longitudinal acceleration according to the longitudinal control weights, thereby generating the final front wheel control angle and longitudinal acceleration, achieving human-machine steering and braking collaborative control.

[0008] The method includes the following steps:

[0009] Step 1: Expected Path Generation and Processing

[0010] The desired path module generates the desired path sequence for the driver and controller. The driver's desired state includes the driver's desired longitudinal acceleration sequence. Driver's desired route sequence And the driver's expected yaw angle sequence The desired controller state includes the desired longitudinal acceleration sequence. Controller desired path sequence and the controller's expected yaw angle sequence .

[0011] To achieve risk assessment and control decision support in conflict scenarios, this invention further predicts the future motion states of the vehicle and surrounding vehicles within the conflict area; the vehicle dynamic information is defined as follows: ;in, and These refer to the longitudinal and lateral positions of the vehicle, respectively. Let the longitudinal speed of the vehicle be denoted as . The yaw angle of the vehicle. Let yaw rate be the yaw rate of the vehicle. The longitudinal acceleration of the vehicle. and These are the longitudinal and lateral positions of the chariot, respectively. Let be the longitudinal velocity of the chariot. The yaw angle of the chariot.

[0012] In this invention, the future trajectory of the vehicle is predicted from the current state information in the vehicle's dynamic information. Let the current discrete time of the vehicle be... The state is ,in and These refer to the longitudinal and lateral positions of the chariot, respectively. Let be the longitudinal velocity of the chariot. Let be the yaw angle of the vehicle. Within the prediction time window, assuming it travels along the current lane direction, and using a uniform speed or uniform acceleration model for short-time trajectory extrapolation, the global position vector of the vehicle at each prediction time is obtained. The prediction results are used to calculate the predicted time for the vehicle to reach the conflict zone. and the minimum spatial distance between the vehicle and surrounding vehicles. .

[0013] Step 2: Spatiotemporal risk evolution analysis and generation of horizontal and vertical control weights:

[0014] The spatiotemporal risk evolution analysis module first obtains the expected state quantity and vehicle dynamic information at the current moment. .

[0015] Step 2.1, Time Risk Calculation:

[0016] To characterize the time competition between the vehicular and surrounding vehicular vehicles within the conflict zone, this invention defines the time difference between their arrival at the conflict zone as a measure of the degree of time conflict. The predicted time for the vehicular vehicle to arrive at the conflict zone is given by equation (1):

[0017]

[0018] in, This represents the predicted time for the vehicle to arrive at the conflict zone at the current discrete moment. It is the longitudinal velocity of the vehicle at the current discrete moment. Let the longitudinal acceleration of the vehicle be the longitudinal acceleration at the current discrete moment. This represents the equivalent path distance from the vehicle's current position to the entrance of the conflict zone at the current discrete moment. At that time, according to the uniformly accelerated displacement relationship Solve for the predicted arrival time of the vehicle at the conflict zone, and take the positive real root as... ;when and At that time, a uniform velocity approximation is used. If the square root term is less than zero or the vehicle does not meet the motion conditions for reaching the conflict area under the current prediction conditions, then... This is recorded as the preset maximum prediction time. This is used to characterize the unreachable state within the current prediction time domain. Similarly, the predicted time for the vehicle to reach the conflict zone is... The longitudinal velocity and longitudinal acceleration of the circumferential vehicle are determined based on its current position, longitudinal velocity, and longitudinal acceleration. When the longitudinal acceleration of the circumferential vehicle is unavailable, it can also be approximated based on its current position and longitudinal velocity.

[0019] To avoid the discontinuity problem caused by traditional methods based on fixed time thresholds, this invention constructs a continuous time risk function, as shown in equation (2):

[0020]

[0021] in, The predicted time for the vehicle to reach the conflict zone. The predicted time for the vehicle to arrive at the conflict zone. Let be the time risk scale parameter, and satisfy . This is used to adjust the range of influence of the time difference on the risk function. The time risk scale parameter characterizes the system's sensitivity to conflict time margin: when... Less than At that time, the time risk remains high; when Much larger At that time, the time risk rapidly diminishes to near zero. Calibration is determined based on scenario type, vehicle speed range, system sampling period, and prediction time domain length; preferably, parameter calibration can be based on joint simulation samples or historical test data, using risk identification accuracy, control smoothness, and false alarm rate as comprehensive indicators. In low-to-medium speed conditions at unsignalized intersections, Desirable .

[0022] Step 2.2, Spatial Risk Calculation:

[0023] To characterize the spatial proximity of the vehicle and the surrounding vehicle in the prediction time domain, this invention calculates the minimum spatial distance between the vehicle and the surrounding vehicle within the prediction time window, as shown in equation (3):

[0024]

[0025] in, Indicates the vehicle at the predicted time. The global coordinate position vector below, This indicates that the chariot is at the predicted time. The global coordinate position vector below, The predicted time window length is used to calculate the potential future collision distance. This represents the minimum distance between the vehicular and circumferential vehicles within the prediction time window.

[0026] The minimum distance reflects the closest possible approach that the two vehicles may reach during future movement. It is obtained by comparing the positional relationship between the vehicle and the surrounding vehicles at each prediction time within the prediction time window, and is used to characterize the potential spatial proximity in the future. A smaller minimum distance indicates a higher probability of a potential collision.

[0027] To achieve a continuous expression of spatial risk, this invention constructs the following spatial risk function. As in equation (4):

[0028]

[0029] in, Let be the spatial risk scale parameter, and satisfy . This parameter is used to adjust the degree of influence of distance on the risk function. This represents the minimum distance between the vehicular and circumferential vehicles within the prediction time window.

[0030] Step 2.3, Judging the trend of risk evolution:

[0031] The spatiotemporal risk evolution analysis module further analyzes the time risk of adjacent discrete moments. Space risks The temporal and spatial risk evolution trends are calculated separately, as shown in equations (5) and (6):

[0032]

[0033]

[0034] To determine the trend of risk evolution, when or When the risk is determined to increase, or The risk was assessed and mitigated in a timely manner.

[0035] The lateral control weight allocation ratio is dynamically adjusted based on the spatial risk function, and the longitudinal control weight allocation ratio is dynamically adjusted based on the temporal risk function. When the risk increases, the controller's dominance in steering control is increased; when the risk is low, the driver remains in control. The controller weights are defined as follows, as in equations (7) and (8):

[0036]

[0037]

[0038] in, and The adjustment parameters representing the horizontal and vertical weights are both positive real numbers. To control the weights horizontally, For vertical control weights, The denominator is a non-zero protection constant. For the evolution trend of space risks, This represents the evolutionary trend of time risk. The weights of the horizontal controller... and vertical controller weights The range of values ​​is limited to Within, the driver's corresponding weight is taken respectively. and When the calculation result exceeds the specified range, a saturation function is used to truncate it to... The parameters and This parameter is used to adjust the sensitivity of the controller weight to changes in risk. A larger parameter value results in a slower increase in the controller weight, while a smaller parameter value makes the controller weight more sensitive to changes in risk. The parameter is calibrated based on the scenario type, vehicle speed range, sampling period, and co-simulation results. Preferably, it can be comprehensively adjusted based on risk response speed, control smoothness, and traffic safety.

[0039] Step 3: Establishment and solution of the horizontal and vertical non-cooperative game control model:

[0040] Step 3.1, Prediction Model Establishment:

[0041] The predictive model uses the vehicle dynamics model to establish a driver-controller interaction model, as shown in equation (9):

[0042]

[0043] in, , , , , .

[0044] in, For state variables, The rate of change of state, For the front wheel steering angle, For longitudinal acceleration, It is a continuous-time state matrix. Continuous-time control input matrix, For the output matrix, For the affine compensation term in the continuous-time locally linearized model, To control the output matrix; , , , , , These are the vehicle's longitudinal velocity, lateral velocity, yaw angle, yaw rate, longitudinal displacement, and lateral displacement. For the overall vehicle quality, Let the longitudinal speed of the vehicle be denoted as . and These are the distances from the center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires, respectively. This is the moment of inertia of yaw rotation.

[0045] Step 3.2, Time-domain discretization of the model:

[0046] The driver-controller interaction model is discretized to convert the continuous system into a finite-time domain, which facilitates non-cooperative game solving, as shown in equation (10):

[0047]

[0048] in, , , , , , , , , .

[0049] in, The discrete-time state matrix, and These are the discrete-time control input matrices for the driver and the controller, respectively. The system sampling period is This is the model compensation term, used to characterize the residual dynamic term generated by the nonlinear vehicle dynamics model after local linearization and discretization at the current sampling time. and These represent the front wheel steering angles of the driver and controller, respectively. and Representing the longitudinal acceleration of the driver and the controller respectively, by introducing This can avoid being solely determined by The control inputs describe the approximate error caused by the dynamic changes of the vehicle. This represents the discrete sampling time index. This implementation uses a zero-order preserved discretization method based on the state transition matrix to discretize the continuous-time model. (Prediction time domain) and control time domain Determined based on system response speed, sampling period, and real-time computing capability, satisfying... .

[0050] The future can be predicted through iterative formula (10). The output of the step; at the same time, actual control can also be obtained in this process. The output of the step is as shown in equation (11):

[0051]

[0052] in, , , , , , To predict the time domain, To control the time domain, and .

[0053] The final discretized prediction output equation can be obtained by rearranging equation (11), as shown in equation (12):

[0054]

[0055] in, , , , , , , .

[0056] in, To predict control output, and These are the control input sequences for the driver and the controller, respectively. The coefficient matrix of the vehicle state variables. and These are the control input coefficient matrices for the driver and the controller, respectively.

[0057] Step 3.3, Objective Function Design:

[0058] After the driver-controller interaction model is established, objective functions for the driver and controller are constructed respectively to quantify the path tracking and speed control requirements, while also taking into account the smoothness of the control input. The objective function mainly includes a tracking error term and a control input penalty term, wherein the tracking error term comprehensively represents the path tracking error and the speed tracking error, as shown in Equation (13):

[0059]

[0060] in, , , , , , , , , , , .

[0061] in, To predict control output, For the driver's reference output, For the reference output of the controller, and These are the control input sequences for the driver and the controller, respectively. and Let these be the objective functions for the driver and the controller, respectively. and These are the output tracking weight matrices for the driver and the controller, respectively. and These are the control input weight matrices for the driver and the controller, respectively. and These are the single-step output tracking weights for the driver and the controller, respectively. and These are the single-step control input weights for the driver and the controller, respectively. , To control the output, and These are the expected outputs of the driver and the controller, respectively. and These represent the front wheel steering angles of the driver and controller, respectively. and These represent the longitudinal acceleration of the driver and the controller, respectively.

[0062] Step 3.4, Solving for Nash Equilibrium:

[0063] The Nash equilibrium solution is used to solve the human-machine steering and braking cooperative control optimization problem, as shown in equation (14):

[0064]

[0065] First, the path tracking error between the driver and the controller is defined as shown in equation (15):

[0066]

[0067] in, and These are the path tracking errors for the driver and the controller, respectively.

[0068] Then, substituting equation (15) into equation (14), we obtain the driver and controller objective functions with the tracking error term added, as shown in equation (16):

[0069]

[0070] in, and These are the structural transformation matrices of the output tracking weight matrix in the objective function of the driver and controller, respectively. and These are the structural transformation matrices of the control input weight matrices in the objective functions of the driver and controller, respectively.

[0071] The sequence of front wheel steering angles between the driver and the controller was obtained by using the least squares method and the convex iteration method. and The first element of each sequence is selected as the front wheel steering angle for the driver and the controller, respectively, as shown in equation (17):

[0072]

[0073] in, and The first element in the front wheel steering angle sequence for both the driver and the controller.

[0074] The longitudinal acceleration sequences of the driver and controller were obtained by using the least squares method and the convex iteration method. and The first element of each sequence is selected as the longitudinal acceleration of the driver and the controller, respectively, as shown in equation (18):

[0075]

[0076] in, and These are the first elements in the longitudinal acceleration sequences of the driver and controller, respectively.

[0077] Step 4: Human-machine collaborative control output fusion:

[0078] Human-machine co-driving vehicles receive the front wheel steering angle from the driver and controller. and longitudinal acceleration of driver and controller and Then, according to the horizontal control weights respectively and vertical control weights The control quantities are weighted and fused to obtain the final front wheel control angle of the human-machine co-driving vehicle. and longitudinal control acceleration This enables coordinated steering and braking control of vehicles driven by both humans and machines.

[0079] The beneficial effects of this invention are as follows: by constructing time risk functions and spatial risk functions, a quantitative assessment of potential environmental conflict risks is achieved, improving the accuracy and pertinence of risk identification; based on the risk evolution trend, lateral and longitudinal control weights are dynamically generated to achieve adaptive weight allocation for steering and braking by the driver and controller, reducing abrupt control switching and improving the smoothness of the human-machine collaboration process; by constructing a non-cooperative game model and solving for Nash equilibrium, the coordinated control quantities of front wheel angle and longitudinal acceleration are obtained, achieving effective coordination between the driver's operating intentions and safety control requirements, improving traffic safety in complex conflict scenarios, and reducing potential collision risks. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the human-machine dynamic game control based on horizontal and vertical coupling in a typical application scenario of an unsignalized intersection. Detailed Implementation

[0081] The present invention will now be described in detail with reference to the accompanying drawings.

[0082] This invention specifically relates to a human-machine dynamic game control method with horizontal and vertical coupling, applicable to complex traffic scenarios with conflict areas, such as unsignalized intersections. In this embodiment, the invention is illustrated using an unsignalized intersection scenario as an example. (Refer to...) Figure 1 The illustration specifically includes the following steps:

[0083] In practice, the vehicle is selected as a specific type of passenger vehicle. The total vehicle mass is taken as... wheelbase is The width of the vehicle body is The vehicle height is The moment of inertia of the yaw is The distance from the center of gravity to the front axle is The distance from the center of mass to the rear axle is The lateral stiffness of the front tire is The rear tire lateral stiffness is The steering system gear ratio is 16. The system sampling period is... The prediction time domain length is 20 steps.

[0084] In this embodiment, the vehicle performs a left-turn at an unsignalized intersection. To illustrate the feasibility of this invention, the specific implementation process of the method is described below, combining the vehicle's dynamic information at a discrete moment, the distance information of the conflict zone, the spatiotemporal risk calculation results, and the human-machine steering and braking cooperative control output. The vehicle state information can be obtained from a real vehicle. Data can be acquired from the bus, inertial measurement unit, steering angle sensor, wheel speed sensor, and environmental perception module, or it can be obtained from... and Output from the co-simulation platform.

[0085] Step 1: System Model Construction

[0086] Step 1.1, Vehicle dynamics model construction:

[0087] This invention focuses on the longitudinal, lateral, and yaw motions of a vehicle. The front wheel steering angle and longitudinal acceleration of the vehicle are used as system inputs for modeling. The left and right wheels of the vehicle have the same motion state. A simplified three-degree-of-freedom vehicle dynamics model is obtained by combining these features. The longitudinal, lateral, and yaw motions of the vehicle are shown in Equation (19).

[0088]

[0089] in, , , , .

[0090] in, For the overall vehicle quality, and These are the longitudinal speed and lateral speed of the vehicle, respectively. Let the first derivative of the vehicle's longitudinal velocity with respect to time be _____. Let be the first derivative of the vehicle's lateral velocity with respect to time. The longitudinal resultant force is the force exerted by the vehicle along the longitudinal direction of its body. Let yaw rate be the yaw rate of the vehicle. Let x be the yaw acceleration of the vehicle. The turning angle of the car's front wheels. The moment of inertia of the yaw motion of the vehicle. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. and These are the lateral forces on the front and rear wheels, respectively. and These are the lateral stiffness of the front and rear tires, respectively. and Let be the slip angles of the front and rear wheels, respectively. Under the condition that the front wheel steering angle is relatively small, take . And ignore higher-order nonlinear terms.

[0091] By deriving equation (19), the vehicle dynamics equation can be obtained, as shown in equation (20):

[0092]

[0093] in, For the overall vehicle quality, and These are the longitudinal speed and lateral speed of the vehicle, respectively. Let the first derivative of the vehicle's longitudinal velocity with respect to time be _____. Let be the first derivative of the vehicle's lateral velocity with respect to time. For longitudinal acceleration, Let yaw rate be the yaw rate of the vehicle. The yaw angle of the vehicle. Let be the first derivative of the yaw angle of the vehicle with respect to time. Let x be the yaw acceleration of the vehicle. The turning angle of the car's front wheels. The moment of inertia of the yaw motion of the vehicle. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. and These are the lateral stiffness of the front and rear tires, respectively. The first derivative of the vertical position in global coordinates. It is the first derivative of the lateral position in global coordinates.

[0094] In this embodiment, the vehicle mass, yaw moment of inertia, distance from the center of mass to the front and rear axles, and tire lateral stiffness parameters in equations (19) and (20) are all assigned values ​​using the parameters mentioned above.

[0095] Step 1.2, Driver Model Construction:

[0096] To simulate the lateral and longitudinal control of a vehicle by a human driver, this invention employs a dual-point pre-aiming driver model and adds a desired acceleration generation module in the longitudinal direction to generate the complete control input vector. The specific control strategy is as follows: During the path tracking task, the driver model generates the desired lateral turning angle based on the current vehicle state using near and far point pre-aiming, as shown in equation (21):

[0097]

[0098] in, and These are the near-point preview line-of-sight angle and the far-point preview line-of-sight angle, respectively. and These represent the lateral deviations of the near and far aiming points, respectively. and These are the close-point aiming distance and the far-point aiming distance, respectively. This represents the vehicle's yaw angle. The aforementioned near-point anti-aiming information, far-point anti-aiming information, and vehicle status together constitute the input to the dual-point anti-aiming driver response model.

[0099] The driver obtains the near-point pre-aiming line of sight through the pre-aiming operation. and the far-point aiming line of sight After the visual information is transmitted and processed by the brain delay module, the desired steering wheel angle can be generated, which is the driver model's desired steering angle, as shown in equation (22):

[0100]

[0101] in, For the driver model to turn the corner, Pre-aiming steering gain for the driver For driver aiming feedback gain, For driver reaction time, These are complex frequency domain variables in the Laplace transform. The anti-steering gain, anti-feedback gain, and reaction time together constitute the driver response parameters.

[0102] In the longitudinal control direction, the driver model generates the desired acceleration. To track the desired speed As in equation (23):

[0103]

[0104] in, The current longitudinal speed of the vehicle, It represents the longitudinal gain, used to smooth acceleration or deceleration responses.

[0105] The lateral and longitudinal control outputs are combined to form the driver control vector, as shown in equation (24):

[0106]

[0107] This vector is compared with the controller control input vector generated by the subsequent controller model. They all have a consistent structural form, including front wheel steering angle control input and longitudinal acceleration control input, which are used for subsequent non-cooperative game solving and realize the coordinated adjustment of lateral and longitudinal channels.

[0108] By modeling and discretizing the vehicle dynamics equation shown in equation (20) using formulas (9), (10), and (11) in the invention, the driver model control output matrix can be obtained. .

[0109] Driver model control output matrix The lateral displacement and yaw angle are extracted from the model to obtain the driver's expected path sequence and driver's expected yaw angle sequence generated by the driver model, as shown in equation (25):

[0110]

[0111] in, and These are the driver's expected path sequence and driver's expected yaw angle sequence generated by the driver model, respectively. For prediction in the time domain.

[0112] Extract the driver's desired path sequence generated by the driver model respectively Driver's expected yaw angle sequence and the driver's desired longitudinal acceleration sequence The first item yields the driver's desired path at the current moment. The driver's expected yaw angle at the current moment And the driver's expected longitudinal acceleration at the current moment .

[0113] Step 1.3, Controller Model Construction:

[0114] To achieve joint regulation of the vehicle's lateral and longitudinal control objectives, the controller model generates a controller control input vector based on the vehicle dynamics model and desired trajectory information. This controller control input vector includes front wheel steering angle control input and longitudinal acceleration control input. By iteratively calculating the controller model in the prediction time domain, the controller desired path sequence, controller desired yaw angle sequence, and controller desired longitudinal acceleration sequence can be obtained. Further, the first term of each of these sequences is extracted to obtain the controller desired path, desired yaw angle, and longitudinal acceleration at the current moment.

[0115] Step 2, Expected Path Generation and Processing:

[0116] Based on the established driver and controller models, the first term of the expected state sequence of the driver and controller is extracted as the expected state quantity at the current moment, which is used for the subsequent calculation of time risk, space risk and control weight.

[0117] Step 3: Spatiotemporal risk evolution analysis and generation of horizontal and vertical control weights:

[0118] The spatiotemporal risk evolution analysis module first obtains the expected state quantity and vehicle dynamic information at the current moment. .

[0119] In this embodiment, the trajectory of the vehicle is predicted in a short time according to the method described in

[0012] of the invention. That is, based on the current vehicle dynamic information, the trajectory is extrapolated using a uniform speed or uniform acceleration model within the prediction time window to obtain the global position vector of the vehicle at each prediction time. Based on this, time risk and space risk are calculated.

[0120] At the discrete time corresponding to the above-mentioned vehicle embodiment Take the current longitudinal speed of the vehicle Lateral velocity is taken yaw rate Horizontal angle The equivalent path distance from the vehicle's current location to the entrance of the conflict zone is taken as... Combining the outputs of the current driver model and controller model, the vehicle's current longitudinal predicted acceleration is taken as... The negative value indicates deceleration control. Based on the parameters, the predicted time for the vehicle to reach the conflict zone can be calculated using formula (1). .

[0121] Zhou Che's current longitudinal speed is taken The equivalent path distance from the current location to the entrance of the conflict zone is taken as... Under uniform velocity prediction conditions, the predicted time for the Zhou vehicle to reach the conflict zone is approximately... The time difference between the arrival of the vehicular and circumstantial vehicles at the conflict zone is approximately The time risk scale parameter is taken as... Substituting the time difference into formula (2), we can obtain that the time risk value at the current moment is at a high level, indicating that the vehicle and the surrounding vehicle have a clear time competition relationship in the conflict area.

[0122] Furthermore, extrapolating the future trajectories of the vehicle and surrounding vehicles within the prediction time domain yields a sequence of relative distances at each future sampling time, where the minimum spatial distance is taken as... The spatial risk scale parameter is taken as... Substituting the minimum spatial distance into equation (4), we can obtain that the spatial risk value at the current moment is also at a high level, indicating that the two vehicles have a strong tendency to approach each other in the short time domain in the future.

[0123] If adjacent discrete time The corresponding time risk value and space risk value are both lower than the current time. Based on equations (5) and (6), it can be determined that the current risk is in a worsening stage. In one example, the horizontal control weight adjustment parameter... Pick Vertical control weight adjustment parameters Pick Then, according to equations (7) and (8) in the invention, the weight of the lateral controller can be further obtained as follows: Lateral driver weights are The weights of the vertical controller are The longitudinal driver weight is This demonstrates that, taking the scenario of a left turn at an unsignalized intersection as an example, when the risk of conflict increases, the method of this invention can increase the participation of the controllers in the lateral and longitudinal lanes of the vehicle, respectively, rather than adopting a fixed control switching method.

[0124] It should be noted that the above embodiments are merely typical parameter examples of the method of the present invention in the scenario of left turn at an unsignalized intersection. Under different vehicle vehicle conditions, the vehicle dynamics model can be recalibrated according to the vehicle's total mass, wheelbase, center of gravity position, tire lateral stiffness, and steering system transmission ratio; under different scenario conditions, the risk scale parameters and control weight adjustment parameters can be adjusted according to the vehicle's operating speed range, the geometry of the conflict area, and the motion state of surrounding vehicles. For straight-through-left-turn conflict scenarios, cross-traffic scenarios, and other low-to-medium speed traffic scenarios with conflict areas, the spatiotemporal risk assessment, control weight generation, and lateral and longitudinal non-cooperative game solving methods of the present invention can be used to complete the cooperative control output.

[0125] Step 3.1, Time Risk Calculation:

[0126] Based on the expected state quantity at the current moment and the vehicle dynamic information, the predicted arrival times of the voluntary vehicle and the surrounding vehicles in the conflict area are calculated, and a time risk function is constructed based on the arrival time difference between the voluntary vehicle and the surrounding vehicles. The specific calculation method is shown in equations (1) and (2) in the invention content. The time risk is used to characterize the degree of time competition between vehicles in the conflict area and serves as the basis for dynamic adjustment of the longitudinal control weight.

[0127] Step 3.2, Spatial Risk Calculation:

[0128] Within the prediction time domain, a continuous spatial risk function is constructed based on the minimum distance between the vehicle and the surrounding vehicle within the prediction time window. The specific calculation method is shown in equations (3) and (4) in the invention content. Spatial risk is used to characterize the potential collision proximity of the two parties in the future time domain and serves as the basis for dynamic adjustment of lateral control weights.

[0129] Step 3.3, Judging the trend of risk evolution:

[0130] After obtaining the temporal and spatial risks, the evolution trend of the current conflict state is further determined based on the rate of change of risk values ​​at adjacent times. The specific calculation method is shown in equations (5) and (6) in the invention content. If the rate of change of risk is greater than zero, it indicates that the corresponding risk is increasing; if the rate of change of risk is less than zero, it indicates that the corresponding risk is mitigating. The risk evolution trend serves as the triggering basis for the dynamic adjustment of horizontal and vertical control weights, respectively.

[0131] Based on the above risk evolution results, the horizontal control weight and the vertical control weight are calculated according to equations (7) and (8) in the invention content, respectively.

[0132] In this embodiment, the horizontal weight adjustment parameter Pick Vertical control weight adjustment parameters Pick Thus, the weights of the lateral controller, the lateral driver, the longitudinal controller, and the longitudinal driver can be obtained.

[0133] Step 4: Establishment and solution of the non-cooperative game control model:

[0134] Based on the established vehicle dynamics model, a non-cooperative game model between the driver and controller is established by combining the lateral and longitudinal control weights, the driver's and controller's desired path sequences, and vehicle dynamic information, and then discretized. Specifically, the continuous-time model is discretized using the vehicle's longitudinal speed, lateral speed, yaw rate, lateral displacement, and yaw angle as state variables, and the driver's control input and the controller's control input as game variables. The model is then expanded in the prediction time domain to obtain the discrete prediction output equation for solving the non-cooperative game, the specific form of which can be found in equations (9) to (12) in the invention content.

[0135] After establishing and discretizing the horizontal and vertical non-cooperative game models, the driver's objective function and the controller's objective function are constructed respectively. The objective function is used to weight the front wheel steering angle and longitudinal acceleration, and its specific expression is shown in Equation (26).

[0136]

[0137] in, , , , , , .

[0138] in, and Let be the objective function for the driver and the controller. and The output tracking weight matrix for the driver and controller. and The control input weight matrix for the driver and controller. To control the output, and These are the expected outputs of the driver and the controller, respectively. and This represents the weight of the lateral state deviation between the driver and the controller. and This represents the weight of the longitudinal state deviation between the driver and the controller. and This indicates the control weights of the driver and the controller for the front wheel steering angle. and This indicates the longitudinal acceleration control weights between the driver and the controller. and They represent the predicted time. The control input vectors for the driver and controller are given, where, and These are the front wheel steering angle control inputs for the driver and the controller, respectively. and These are the longitudinal acceleration control inputs for the driver and the controller, respectively.

[0139] Formula (26) is simplified to facilitate the subsequent Nash equilibrium solution. The simplified result is shown in formula (13) in the invention content.

[0140] The solution to the Nash equilibrium is usually achieved by solving the prediction and control optimization problems of each of the two players in the game, as shown in equation (14) in the invention.

[0141] First, the tracking error between the driver and the controller is defined as shown in equation (15) in the invention.

[0142] Then, substitute equation (15) in the invention into equation (14) in the invention to obtain the driver and controller objective functions with added tracking error terms, as shown in equation (16) in the invention.

[0143] Subsequently, the least squares solution of equation (16) in the invention content is obtained by using the QR algorithm, as shown in equation (27):

[0144]

[0145] In the formula, , , , , , .

[0146] in, and These are the control input sequences for the driver and the controller, respectively. , These are the state reference output mapping matrices for the driver and controller, respectively. , These are the control coupling mapping matrices between the driver and the controller, with subscripts... , Mapping relationships within the same control channel, subscript , The corresponding cross-coupling relationship between front wheel steering angle and longitudinal acceleration, , This is an augmented vector used in the quadratic programming solution in the least squares approach.

[0147] From equation (27), we know that the driver's control input It depends not only on the state variables and driver's expected output sequence It also depends on the controller's desired output sequence. Conversely, this hinders the solution of the Nash equilibrium to some extent. Therefore, the convex iteration method is introduced to solve the Nash equilibrium between the driver and the controller, as shown in equation (28):

[0148]

[0149] in, , , , , and These are control input sequences for the driver and the controller, respectively, and the control input sequences include front wheel steering angle components and longitudinal acceleration components.

[0150] Finally, the front wheel steering angle component and longitudinal acceleration component are taken from the first item of the driver's and controller's control input sequences, respectively, to obtain the driver's front wheel steering angle. Front wheel steering angle of the controller longitudinal acceleration of the driver and the longitudinal acceleration of the controller The extraction method for the front wheel steering angle is shown in Equation (17) in the invention description, and the extraction method for the longitudinal acceleration is shown in Equation (18) in the invention description.

[0151] Step 5: Fusion of human-machine steering and braking coordinated control output:

[0152] Obtain the driver's front wheel steering angle Front wheel steering angle of the controller longitudinal acceleration of the driver and the longitudinal acceleration of the controller Then, based on the horizontal control weights The driver's front wheel steering angle and the controller's front wheel steering angle are weighted and fused. Simultaneously, based on the longitudinal control weights... The driver's longitudinal acceleration and the controller's longitudinal acceleration are weighted and fused. Through this fusion process, the final control front wheel steering angle is generated. and ultimately control longitudinal acceleration This enables coordinated control of the vehicle's lateral and longitudinal directions, as shown in equations (29) and (30):

[0153]

[0154]

[0155] In the above embodiment, through the horizontal and vertical non-cooperative game solving process, the driver's front wheel steering angle at the current moment can be obtained as follows: The controller's front wheel steering angle is The driver's longitudinal acceleration is The longitudinal acceleration of the controller is Furthermore, the driver's front wheel steering angle and the controller's front wheel steering angle are weighted and fused according to the lateral control weights, and the driver's longitudinal acceleration and the controller's longitudinal acceleration are weighted and fused according to the longitudinal control weights. The lateral control weights are then... Lateral driver weights and vertical controller weights longitudinal driver weights Substituting into the final fusion formula, we can obtain the final control front wheel steering angle of the vehicle at the current moment as approximately... The final controlled longitudinal acceleration is approximately .

[0156] The results above show that in the unsignalized intersection left-turn scenario of this embodiment, when the conflict risk is high and in a worsening stage, the final control front wheel steering angle and final control longitudinal acceleration of the vehicle are closer to the safe control values ​​given by the controller, but still retain some influence from the driver's input, thereby avoiding the control abrupt change caused by the complete separation of the driver in traditional hard-switching control. As the temporal and spatial risks gradually decrease in subsequent time steps, the weights of the lateral and longitudinal controllers decrease synchronously, and the driver's dominant role in the corresponding lane gradually recovers, thus demonstrating that the method of the present invention can achieve dynamic game control of human-machine interaction with lateral and longitudinal coupling.

[0157] In summary, this invention proposes a dynamic game-theoretic control method for human-machine interaction that couples horizontally and vertically. Based on the desired path and the dynamic information of the vehicle and surrounding vehicles within the conflict area, this method predicts the vehicle's trajectory in the future time domain and constructs temporal and spatial risk models. Combined with a risk change trend analysis mechanism, it dynamically characterizes the potential conflict risk state. Furthermore, it maps the spatiotemporal risks and their evolution trends into horizontal and vertical dynamic control weights, embedding them into a non-cooperative game model between the driver and controller. By solving the Nash equilibrium, it obtains the coordinated control inputs for the driver and controller regarding steering angle and acceleration, thereby achieving risk-driven human-machine steering and braking collaborative control. Compared to existing human-machine shared control methods based on fixed weights or rules, this invention can dynamically adjust the allocation ratio of steering and braking in horizontal and vertical control according to the conflict risk and its evolution trend, achieving coordinated regulation rather than simple superposition. This improves the consistency and coordination between steering control and speed control, enhancing the stability and safety of human-machine collaborative control in complex conflict scenarios.

Claims

1. A human-machine dynamic game control method with horizontal and vertical coupling, characterized in that, This method constructs a closed-loop control system consisting of a desired path module, a spatiotemporal risk evolution analysis module, a lateral and longitudinal non-cooperative game module, and a human-machine co-driving vehicle module to achieve lateral and longitudinal collaborative control of the human-machine co-driving vehicle. The desired path module generates the desired path sequence between the driver and the controller. The spatiotemporal risk evolution analysis module analyzes the spatiotemporal relationship of the vehicle in the conflict zone and determines the lateral and longitudinal control weights. The lateral and longitudinal non-cooperative game module combines the lateral and longitudinal control weights, the desired path sequence, and the vehicle dynamic information, and obtains the front wheel steering angle and longitudinal acceleration through three steps: driving behavior modeling, objective function design, and Nash equilibrium solution, thereby achieving lateral and longitudinal collaborative control of the human-machine co-driving vehicle. The desired path module is used to generate the desired path sequence between the driver and the controller. ;in , and These are the driver's desired longitudinal acceleration sequence, path sequence, and yaw angle sequence, respectively. , and These are the longitudinal acceleration sequence, path sequence, and yaw angle sequence desired by the controller, respectively. The spatiotemporal risk evolution analysis module extracts the first term of the driver's expected path sequence and the controller's expected path sequence as the expected state quantity at the current moment; simultaneously, it acquires vehicle dynamic information. ;in, and These represent the longitudinal and lateral positions of the vehicle, respectively. Let the longitudinal speed of the vehicle be denoted as . The yaw angle of the vehicle. Let yaw rate be the yaw rate of the vehicle. The longitudinal acceleration of the vehicle. and These are the longitudinal and lateral positions of the chariot, respectively. Let be the longitudinal velocity of the chariot. The yaw angle of the chariot; In both horizontal and vertical risk analysis, the future trajectory of vehicles is predicted within the prediction time window based on vehicle dynamic information; time risk. Characterized by the arrival time difference between the vehicular and peripheral vehicles at the conflict zone, defined as: ， in, and These represent the predicted arrival times of the vehicular and circumferential vehicles at the conflict zone, respectively. Represents the time risk scale parameter, and satisfies ; Space risks It is characterized by the minimum spatial distance between the vehicle and the surrounding vehicles within the conflict area, as shown in the following formula: ， in, This represents the minimum distance between the vehicle and the surrounding vehicle within the prediction time window. Represents the spatial risk scale parameter, and satisfies ; Furthermore, based on the time risk of adjacent discrete moments... Space risks Calculate the trend of risk evolution; Finally, horizontal and vertical control weights are generated based on the aforementioned time risk, spatial risk, and risk evolution trend, as shown in the following formula: ， ， in, and These represent the adjustment parameters for the horizontal and vertical weights, respectively. For non-zero protection constants of letters, For the evolution trend of space risks, As time risk evolves, To control the weights horizontally, For vertical control weights; The horizontal and vertical non-cooperative game module, combining horizontal and vertical control weights, the driver's and controller's desired path sequences, and vehicle dynamic information, establishes a horizontal and vertical non-cooperative game model between the driver and controller, and then discretizes it: ， in, To predict control output, For vehicle state variables, and These are the control input sequences for the driver and the controller, respectively. The coefficient matrix of the vehicle state variables. and These are the control input coefficient matrices for the driver and the controller, respectively; The control inputs for the driver and the controller are defined as follows: ， ， in, , , and These represent the front wheel steering angles of the driver and controller, respectively. and These represent the longitudinal accelerations of the driver and the controller, respectively. The objective functions for the driver and controller are constructed separately, as shown in the following formulas: ， in, and Let these be the objective functions for the driver and the controller, respectively. and These are the tracking weight matrices for the driver and the controller, respectively. and These are the control input weight matrices for the driver and the controller, respectively, used to weight the front wheel angle and longitudinal acceleration; After solving the horizontal and vertical non-cooperative game optimization problem, the least squares method and convex iteration method are used to find the front wheel steering angle sequence of the driver and the controller. and longitudinal acceleration sequence of driver and controller and The first element of each sequence is selected as the driver's front wheel steering angle. and longitudinal acceleration and the front wheel steering angle of the controller and longitudinal acceleration ; Finally, based on the horizontal control weights The driver's front wheel steering angle and the controller's front wheel steering angle are weighted and fused, based on the longitudinal control weights. The longitudinal acceleration of the driver and the longitudinal acceleration of the controller are weighted and fused to generate the final front wheel control angle and control longitudinal acceleration, thereby achieving coordinated control of the vehicle in both the lateral and longitudinal directions.

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