Vehicle stability control method based on DDPG adaptive hyper-super-spiral sliding mode

Abstract

The vehicle stability control method based on DDPG adaptive super-hyper-spiral sliding mode belongs to the lateral stability control field of electric vehicles, and comprises the following steps: step one: a linear 2-DOF reference model is established to obtain ideal yaw angular velocity and mass center side slip angle required for stability control; step two: a sliding mode controller is designed; step three: a super-hyper-spiral sliding mode controller is designed on the basis of step two; step four: a DDPG adaptive super-hyper-spiral sliding mode controller is designed on the basis of step three; and step five: the calculated additional yaw moment is distributed to each wheel to realize vehicle stability control. The second-order sliding mode structure of the STSMC is used to solve the chattering problem of the traditional sliding mode control, and the DDPG dynamic optimization control strategy is used to adaptively adjust the parameters so as to quickly generate accurate yaw moment under complex road conditions and sudden working conditions.

Description

Technical Field

[0001] This invention belongs to the field of lateral stability control of electric vehicles, specifically a vehicle stability control method based on DDPG adaptive superspiral sliding mode. Background Technology

[0002] Distributed drive electric vehicles (DDEVs) have attracted much attention due to their ability to independently control the driving torque of each wheel. As an overdrive system, DDEVs have redundant actuators, making motor torque distribution a core challenge in optimizing vehicle control performance. Improper torque distribution in DDEVs can exacerbate the risks of lateral movement such as skidding and fishtailing. Direct yaw moment is a vehicle stability control technology that generates yaw moment by adjusting the difference in driving torque between each wheel, thereby controlling the vehicle's lateral movement and improving handling and stability. Traditional yaw moment control technology mainly relies on fixed control and adjustment methods, which are difficult to adapt flexibly to dynamic changes in vehicle operating conditions. It cannot dynamically adjust in real time according to the actual driving state and external environment, failing to guarantee system stability and robustness, and is prone to lateral instability. Summary of the Invention

[0003] This invention provides a vehicle stability control method based on DDPG adaptive superspiral sliding mode to address the shortcomings of existing technologies.

[0004] This invention is achieved through the following technical solution:

[0005] The vehicle stability control method based on DDPG adaptive superspiral sliding mode includes the following steps:

[0006] Step 1: Establish a linear 2-DOF reference model to obtain the ideal yaw rate and centroid sideslip angle required for stable control;

[0007] Step 2: Design the sliding mode controller;

[0008] Step 3: Based on Step 2, design a super-spiral sliding mode controller;

[0009] Step 4: Based on Step 3, design the DDPG adaptive superspiral sliding mode controller;

[0010] Step 5: Distribute the calculated additional yaw moment to each wheel to achieve vehicle stability control.

[0011] As described above, the vehicle stability control method based on DDPG adaptive superspiral sliding mode, in step one, by establishing the total lateral force balance equation and the yaw moment balance equation, combined with the linear assumption of tire lateral force and the constraint of road adhesion coefficient, can derive the ideal yaw rate under steady-state steering conditions. and centroid side slip angle The specific formula is as follows:

[0012] (1)

[0013] In the formula, This refers to the front axle wheelbase. This refers to the rear axle wheelbase. For the front wheel deflection angle, The road surface adhesion coefficient, For the longitudinal speed of the vehicle, For safety reasons, , For the lateral stiffness of the front and rear tires, Stability coefficient to describe the steering characteristics of a vehicle , .

[0014] As described above, in the vehicle stability control method based on DDPG adaptive superspiral sliding mode, step two involves adding an additional yaw moment to the linear 2-DOF vehicle dynamics model. The specific formula is as follows:

[0015] (2)

[0016] In the formula, For vehicle quality, Let z be the moment of inertia of the vehicle about the z-axis. To add yaw moment, , These are the yaw rate and its derivative, respectively. , These are the centroid sideslip angle and its derivative;

[0017] Step two defines the yaw rate sliding surface. , center of mass side slip angle of the synovial surface The formulas for expressing them are as follows:

[0018] (3)

[0019] (4)

[0020] In the formula, The yaw rate is the sliding surface parameter. The parameters for the slip surface of the centroid side slip angle are all greater than 0; , These are the yaw rate tracking error and its derivative. , The centroid sideslip angle error and its derivative;

[0021] Step two defines the yaw rate approach rate. centroid side slip angle approach rate The formula for expressing it is:

[0022] (5)

[0023] (6)

[0024] In the formula, The sliding mode approximation coefficient for yaw rate. The sliding mode approximation coefficient is the centroid side slip angle. It is a symbolic function;

[0025] Differentiating formula (3) and substituting formula (5) into formula (2), we obtain the additional yaw torque based on the sliding mode controller as follows: :

[0026] (7)

[0027] Differentiating equation (4) and substituting equation (6) into equation (2), we obtain the additional yaw moment based on the sideslip angle of the center of mass of the sliding mode controller as follows: :

[0028] (8)

[0029] The distribution coefficient method is used in conjunction with formulas (7) and (8) to output the additional yaw moment. The total yaw moment is: :

[0030] (9)

[0031] In the formula, Add gain to yaw rate. Add gain to the centroid sideslip angle.

[0032] As described above, in the vehicle stability control method based on DDPG adaptive superspiral sliding mode, the formula for the superspiral sliding mode approach rate in step three is defined as follows:

[0033] (10)

[0034] In the formula, To control the input, , For the gain of the superspiral sliding mode controller;

[0035] Differentiating formula (3) and substituting formula (10) into formula (2), the yaw rate and additional yaw torque based on the super-spiral sliding mode controller are obtained. The formula for expressing it is:

[0036] (11)

[0037] In the formula, , This is the coefficient for approaching the yaw rate of the superspiral sliding mode;

[0038] Differentiating Formula (4) and substituting Formula (10) into Formula (2) results in the additional yaw moment based on the centroid side slip moment of the super-spiral sliding mode controller. The formula for expressing it is:

[0039] (12)

[0040] In the formula, , It is the approach coefficient of the centroid side deflection angle of the super-spiral sliding mode.

[0041] As described above, in the vehicle stability control method based on DDPG adaptive superspiral sliding mode, step four embeds the DDPG algorithm into the STSMC framework to construct a state space-action space-reward interaction mechanism.

[0042] As described above, in the vehicle stability control method based on DDPG adaptive superspiral sliding mode, the state space is defined as the real-time vehicle dynamic state variables. Its formula is:

[0043] (13)

[0044] In the formula, The sideslip angle is the angle of the centroid. The yaw rate is angular velocity. For yaw rate tracking error, For the centroid sideslip angle tracking error, and It is an integral term;

[0045] The action space is defined as a key parameter of STSMC. Its formula is:

[0046] (14)

[0047] In the formula, the parameters of the super-spiral sliding film yaw rate torque controller are: For sliding surface parameters, The main approach rate coefficient for yaw rate; parameters of the super-spiral sliding film centroid side slip torque controller: For sliding surface parameters, The main approach coefficient for the centroid sideslip angle; Controller allocation coefficients;

[0048] reward function It plays a significant role in DRL, guiding the agent to pursue optimal control performance, and its expression formula is:

[0049] (15)

[0050] In the formula, This refers to the tracking error weighting coefficient.

[0051] The vehicle stability control method based on DDPG adaptive superspiral sliding mode described above uses an Actor-Critic network structure. The Actor network generates parameter adjustment strategies, and the Critic network evaluates the value of the strategies to achieve multi-parameter optimization.

[0052] As described above, in the vehicle stability control method based on DDPG adaptive superspiral sliding mode, the input state in the Actor network is... Output action Through deterministic strategy function The formula for mapping states to optimal actions is as follows:

[0053] (16)

[0054] In the formula, Representing random noise, it enables the agent to have exploratory capabilities; This represents the parameters of the Actor network at the current moment; This indicates that the real-time vehicle dynamics state variables are input through a deterministic policy function. Output its action ;

[0055] Input state in the Critic network With action Output state-action value function Evaluate the long-term benefits of the current strategy;

[0056] The network parameters in the Actor-Critic network structure are as follows: and The Actor network calculates the policy gradient using the backpropagation method. Then, the policy gradient ascent algorithm is used to update the weights of the online actor network. Its formula is:

[0057] (17)

[0058] In the formula, For strategy parameters Find the gradient. Represents the policy function The gradient with respect to its parameters; To obtain the empirical average; This represents the learning rate of the Actor function network;

[0059] The Critic network uses gradient descent to update its parameters. :

[0060] (18)

[0061] in, This indicates the deviation between the predicted value and the target value; To achieve the target value, integrate instant rewards. and future value Discount estimates; As a discount factor, ; This represents the learning rate of the Critic function network.

[0062] To address the instability issue in single-network learning, two networks, an online network and a target network, are deployed in practical applications. The target network parameters are used to calculate the TD target and update the weights of the online reviewer network. After obtaining the online network parameters, the parameters in the target network can be updated according to the soft update principle, the expression of which is:

[0063] (19)

[0064] In the formula, For the target Critic network parameters, For the target Actor network parameters, Indicates the update rate. .

[0065] As described above, in the vehicle stability control method based on DDPG adaptive superspiral sliding mode, step five involves inputting the vehicle state variables, yaw rate, and ideal values ​​of the center of gravity sideslip angle into the top-level controller, i.e., into the DDPG adaptive superspiral sliding mode controller established in step four, to obtain the desired additional yaw moment output. The resulting additional yaw moment The wheels are distributed appropriately to maintain vehicle stability.

[0066] The vehicle stability control method based on DDPG adaptive superspiral sliding mode, as described above, includes the following specific steps in step five:

[0067] Step 1): The four-wheel torque must first meet the additional yaw moment and tire longitudinal force requirements of the upper-level motion tracking controller, expressed by the following formula:

[0068] (20)

[0069] in, , , , The longitudinal forces are those on the left front, right front, left rear, and right rear wheels. The wheelbase is the distance between the wheels. For vehicles in The resultant external force in the direction, For vehicles to bypass The net external torque on the shaft;

[0070] Formula (19) can be rewritten in matrix form as follows:

[0071] (twenty one)

[0072] in,

[0073] ; ;

[0074] Defining minimizing torque distribution error as one of the objectives of torque optimization distribution, the objective function is expressed as follows:

[0075] (twenty two)

[0076] Among them, matrix Indicates the weights of the longitudinal force and yaw moment requirements;

[0077] Step 2): The sum of the squares of the longitudinal and lateral forces of the four wheels is divided by the square of the product of the vertical load and the coefficient of friction to characterize the vehicle's stability margin. For a four-wheel independent drive electric vehicle, the lateral force is uncontrollable under constraints. Therefore, the longitudinal force is chosen as the control variable, and the objective function is expressed as follows:

[0078] (twenty three)

[0079] in, The lateral force of the wheel, For the longitudinal force of the wheel, The vertical load on the wheel;

[0080] Formula (23) can be rewritten in matrix form:

[0081] in,

[0082] ;

[0083] Step 3): Combining the two torque optimization distribution control objective functions, the formula is as follows:

[0084] (twenty four)

[0085] in, These are the weight coefficients of the objective function;

[0086] The constraints were constructed by considering three factors: tire utilization rate, motor output torque, and road surface adhesion conditions. The resulting constraint formula is as follows:

[0087] (25)

[0088] According to the friction ellipse constraint formula (25), the longitudinal force constraint condition can be obtained, and its expression is as follows:

[0089] (26)

[0090] The maximum output torque of the motor should meet the following constraints, expressed by the following formula:

[0091] (27)

[0092] in, is the maximum output torque of the motor, and r is the tire rolling radius;

[0093] Based on formulas (26) and (27), the longitudinal force constraint conditions for each wheel are expressed as follows:

[0094] (28)

[0095] According to formulas (24) and (28), the problem of allocating control variables can be transformed into solving an optimization problem, expressed as follows:

[0096] (29)

[0097] The torque optimization distribution results of a four-wheel motor driven electric vehicle are obtained by solving the QP algorithm.

[0098] The advantages of this invention are: This invention utilizes the second-order sliding mode structure of STSMC to reduce the chattering problem of traditional sliding mode control, and at the same time, through the DDPG dynamic optimization control strategy, it adaptively adjusts parameters to quickly generate accurate yaw moment under complex road conditions and sudden working conditions; Compared with the fixed structure control method, this invention significantly improves the driving stability of distributed drive vehicles and their adaptability to different working conditions. Attached Figure Description

[0099] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0100] Figure 1 This is a schematic diagram of the strategy framework of the present invention;

[0101] Figure 2 This is a schematic diagram of the optimization process of the state space-action space-reward interaction mechanism of the present invention;

[0102] Figure 3 This is the learning and training curve of the DDPG based on plot reward in this invention;

[0103] Figure 4 This is one of the comparison charts of yaw rate at 100km / h on a wet and slippery road surface (road surface adhesion coefficient is 0.3) according to the present invention;

[0104] Figure 5 This is the second comparison chart of the yaw rate at 100km / h on a wet and slippery road surface (road surface adhesion coefficient is 0.3) according to the present invention;

[0105] Figure 6 This is one of the comparison images of the centroid sideslip angle at 100km / h and on a wet and slippery road surface (road surface adhesion coefficient is 0.3) according to the present invention;

[0106] Figure 7 This is the second comparison diagram of the centroid sideslip angle at 100km / h and on a wet and slippery road surface (road surface adhesion coefficient is 0.3) according to the present invention;

[0107] Figure 8 This is a comparison chart of the torque of each wheel at 100km / h on a wet and slippery road surface (road surface adhesion coefficient is 0.3). Detailed Implementation

[0108] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0109] like Figure 1As shown, the vehicle stability control method based on DDPG adaptive superspiral sliding mode includes the following steps:

[0110] Step 1: Establish a linear 2-DOF reference model to obtain the ideal yaw rate and centroid sideslip angle required for stable control;

[0111] Step 2: Design the sliding mode controller;

[0112] Step 3: Based on Step 2, design a super-spiral sliding mode controller;

[0113] Step 4: Based on Step 3, design the DDPG adaptive superspiral sliding mode controller;

[0114] Step 5: Distribute the calculated additional yaw moment to each wheel to achieve vehicle stability control.

[0115] Preferably, in step one of this embodiment, by establishing the total lateral force balance equation and the yaw moment balance equation, and combining the linear assumption of tire lateral force and the limitation of road adhesion coefficient, the ideal yaw rate under steady-state steering conditions can be obtained. and centroid side slip angle The specific formula is as follows:

[0116] (1)

[0117] In the formula, This refers to the front axle wheelbase. This refers to the rear axle wheelbase. For the front wheel deflection angle, The road surface adhesion coefficient, For the longitudinal speed of the vehicle, For safety reasons, , For the lateral stiffness of the front and rear tires, Stability coefficient to describe the steering characteristics of a vehicle , .

[0118] Preferably, in step two of this embodiment, an additional yaw moment is added to the linear 2-DOF vehicle dynamics model. The specific formula is as follows:

[0119] (2)

[0120] In the formula, For vehicle quality, Let z be the moment of inertia of the vehicle about the z-axis. To add yaw moment, , These are the yaw rate and its derivative, respectively. , These are the centroid sideslip angle and its derivative;

[0121] Step two defines the yaw rate sliding surface. , center of mass side slip angle of the synovial surface The formulas for expressing them are as follows:

[0122] (3)

[0123] (4)

[0124] In the formula, The yaw rate is the sliding surface parameter. The parameters for the slip surface of the centroid side slip angle are all greater than 0; , These are the yaw rate tracking error and its derivative. , The centroid sideslip angle error and its derivative;

[0125] Step two defines the yaw rate approach rate. centroid side slip angle approach rate The formula for expressing it is:

[0126] (5)

[0127] (6)

[0128] In the formula, The sliding mode approximation coefficient for yaw rate. The sliding mode approximation coefficient is the centroid side slip angle. It is a symbolic function;

[0129] Differentiating formula (3) and substituting formula (5) into formula (2), we obtain the additional yaw torque based on the sliding mode controller as follows: :

[0130] (7)

[0131] Differentiating equation (4) and substituting equation (6) into equation (2), we obtain the additional yaw moment based on the sideslip angle of the center of mass of the sliding mode controller as follows: :

[0132] (8)

[0133] The distribution coefficient method is used in conjunction with formulas (7) and (8) to output the additional yaw moment. The total yaw moment is: :

[0134] (9)

[0135] In the formula, Add gain to yaw rate. Add gain to the centroid sideslip angle.

[0136] Preferably, the formula for defining the superspiral sliding mode convergence rate in step three of this embodiment is as follows:

[0137] (10)

[0138] In the formula, To control the input, , For the gain of the superspiral sliding mode controller;

[0139] Differentiating formula (3) and substituting formula (10) into formula (2), the yaw rate and additional yaw torque based on the super-spiral sliding mode controller are obtained. The formula for expressing it is:

[0140] (11)

[0141] In the formula, , This is the coefficient for approaching the yaw rate of the superspiral sliding mode;

[0142] Differentiating Formula (4) and substituting Formula (10) into Formula (2) results in the additional yaw moment based on the centroid side slip moment of the super-spiral sliding mode controller. The formula for expressing it is:

[0143] (12)

[0144] In the formula, , It is the approach coefficient of the centroid side deflection angle of the super-spiral sliding mode.

[0145] like Figure 2 As shown, preferably, in step four of this embodiment, the DDPG algorithm is embedded into the STSMC framework to construct a state space-action space-reward interaction mechanism.

[0146] Preferably, the state space described in this embodiment is defined as the real-time vehicle dynamics state quantity. Its formula is:

[0147] (13)

[0148] In the formula, The sideslip angle is the angle of the centroid. The yaw rate is angular velocity. For yaw rate tracking error, For the centroid sideslip angle tracking error, and It is an integral term;

[0149] The action space is defined as a key parameter of STSMC. Its formula is:

[0150] (14)

[0151] In the formula, the parameters of the super-spiral sliding film yaw rate torque controller are: For sliding surface parameters, The main approach rate coefficient for yaw rate; parameters of the super-spiral sliding film centroid side slip torque controller: For sliding surface parameters, The main approach coefficient for the centroid sideslip angle; Controller allocation coefficients;

[0152] reward function It plays a significant role in DRL, guiding the agent to pursue optimal control performance, and its expression formula is:

[0153] (15)

[0154] In the formula, This refers to the tracking error weighting coefficient.

[0155] Preferably, the DDPG algorithm described in this embodiment adopts an Actor-Critic network structure. The Actor network generates parameter adjustment strategies, and the Critic network evaluates the value of these strategies, achieving multi-parameter optimization. Its learning and training curves are as follows: Figure 3 As shown.

[0156] Preferably, the input state in the Actor network described in this embodiment Output action Through deterministic strategy function The formula for mapping states to optimal actions is as follows:

[0157] (16)

[0158] In the formula, Representing random noise, it enables the agent to have exploratory capabilities; This represents the parameters of the Actor network at the current moment; This indicates that the real-time vehicle dynamics state variables are input through a deterministic policy function. Output its action ;

[0159] Input state in the Critic network With action Output state-action value function Evaluate the long-term benefits of the current strategy;

[0160] The network parameters in the Actor-Critic network structure are as follows: and The Actor network calculates the policy gradient using the backpropagation method. Then, the policy gradient ascent algorithm is used to update the weights of the online actor network. Its formula is:

[0161] (17)

[0162] In the formula, For strategy parameters Find the gradient. Represents the policy function The gradient with respect to its parameters; To obtain the empirical average; This represents the learning rate of the Actor function network;

[0163] The Critic network uses gradient descent to update its parameters. :

[0164] (18)

[0165] in, This indicates the deviation between the predicted value and the target value; To achieve the target value, integrate instant rewards. and future value Discount estimates; As a discount factor, ; This represents the learning rate of the Critic function network.

[0166] To address the instability issue in single-network learning, two networks, an online network and a target network, are deployed in practical applications. The target network parameters are used to calculate the TD target and update the weights of the online reviewer network. After obtaining the online network parameters, the parameters in the target network can be updated according to the soft update principle, the expression of which is:

[0167] (19)

[0168] In the formula, For the target Critic network parameters, For the target Actor network parameters, Indicates the update rate. .

[0169] Preferably, in step five of this embodiment, the ideal values ​​of the vehicle state variables, yaw rate, and sideslip angle are input into the top-level controller, i.e., into the DDPG adaptive superspiral sliding mode controller established in step four, to obtain the desired additional yaw moment output. The resulting additional yaw moment The wheels are distributed appropriately to maintain vehicle stability.

[0170] Preferably, step five in this embodiment includes the following steps:

[0171] Step 1): The four-wheel torque must first meet the additional yaw moment and tire longitudinal force requirements of the upper-level motion tracking controller, expressed by the following formula:

[0172] (20)

[0173] in, , , , The longitudinal forces are those on the left front, right front, left rear, and right rear wheels. The wheelbase is the distance between the wheels. For vehicles in The resultant external force in the direction, For vehicles to bypass The net external torque on the shaft;

[0174] Formula (19) can be rewritten in matrix form as follows:

[0175] (twenty one)

[0176] in,

[0177] ; ;

[0178] Defining minimizing torque distribution error as one of the objectives of torque optimization distribution, the objective function is expressed as follows:

[0179] (twenty two)

[0180] Among them, matrix Indicates the weights of the longitudinal force and yaw moment requirements;

[0181] Step 2): The sum of the squares of the longitudinal and lateral forces of the four wheels is divided by the square of the product of the vertical load and the coefficient of friction to characterize the vehicle's stability margin. For a four-wheel independent drive electric vehicle, the lateral force is uncontrollable under constraints. Therefore, the longitudinal force is chosen as the control variable, and the objective function is expressed as follows:

[0182] (twenty three)

[0183] in, The lateral force of the wheel, For the longitudinal force of the wheel, The vertical load on the wheel;

[0184] Formula (23) can be rewritten in matrix form:

[0185] in,

[0186] ;

[0187] Step 3): Combining the two torque optimization distribution control objective functions, the formula is as follows:

[0188] (twenty four)

[0189] in, These are the weight coefficients of the objective function;

[0190] The constraints were constructed by considering three factors: tire utilization rate, motor output torque, and road surface adhesion conditions. The resulting constraint formula is as follows:

[0191] (25)

[0192] According to the friction ellipse constraint formula (25), the longitudinal force constraint condition can be obtained, and its expression is as follows:

[0193] (26)

[0194] The maximum output torque of the motor should meet the following constraints, expressed by the following formula:

[0195] (27)

[0196] in, is the maximum output torque of the motor, and r is the tire rolling radius;

[0197] Based on formulas (26) and (27), the longitudinal force constraint conditions for each wheel are expressed as follows:

[0198] (28)

[0199] According to formulas (24) and (28), the problem of allocating control variables can be transformed into solving an optimization problem, expressed as follows:

[0200] (29)

[0201] The torque optimization distribution results of a four-wheel motor driven electric vehicle are obtained by solving the QP algorithm.

[0202] To verify the feasibility and effectiveness of this method, vehicle stability control simulations were performed using the method of this invention on the CarSim / Simulink platform, and the simulation results were compared with those of the traditional sliding mode control (SMC) method. Table 1 shows the vehicle parameters, using a double lane change condition, a vehicle speed of 100 km / h, and a road adhesion coefficient of 0.3. The simulation test results are as follows. Figures 4-8 As shown.

[0203] Table 1

[0204]

[0205] In summary, the specific implementation steps and content of the DDPG adaptive superspiral sliding mode vehicle stability control method are as follows: The second-order sliding mode structure of STSMC is used to reduce the chattering problem of traditional sliding mode control. Simultaneously, the DDPG dynamic optimization control strategy adaptively adjusts parameters to quickly generate precise yaw moment under complex road conditions and sudden operating conditions.

[0206] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A vehicle stability control method based on DDPG adaptive superspiral sliding mode, characterized in that: Includes the following steps: Step 1: Establish a linear 2-DOF reference model to obtain the ideal yaw rate and centroid sideslip angle required for stable control; Step 2: Design the sliding mode controller; Step 3: Based on Step 2, design a super-spiral sliding mode controller; Step 4: Based on Step 3, design the DDPG adaptive superspiral sliding mode controller; Step 5: Distribute the calculated additional yaw moment to each wheel to achieve vehicle stability control; In step five, the ideal values ​​of the vehicle state variables, yaw rate, and sideslip angle are input into the top-level controller, i.e., into the DDPG adaptive superspiral sliding mode controller established in step four, to obtain the desired additional yaw moment output. The resulting additional yaw moment The wheels are distributed appropriately to maintain vehicle stability.

2. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 1, characterized in that: Step one, by establishing the total lateral force balance equation and the yaw moment balance equation, combined with the linear assumption of tire lateral force and the constraint of road adhesion coefficient, yields the ideal yaw rate under steady-state steering conditions. and centroid side slip angle The specific formula is as follows: （1） In the formula, This refers to the front axle wheelbase. This refers to the rear axle wheelbase. For the front wheel deflection angle, The road surface adhesion coefficient, For the longitudinal speed of the vehicle, For safety reasons, , For the lateral stiffness of the front and rear tires, Stability coefficient to describe the steering characteristics of a vehicle , .

3. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 1, characterized in that: In step two, an additional yaw moment is added to the linear 2-DOF vehicle dynamics model. The specific formula is as follows: （2） In the formula, For vehicle quality, Let z be the moment of inertia of the vehicle about the z-axis. To add yaw moment, , These are the yaw rate and its derivative, respectively. , These are the centroid sideslip angle and its derivative; Step two defines the yaw rate sliding surface. , center of mass side slip angle of the synovial surface The formulas for expression are as follows: （3） （4） In the formula, The parameters of the sliding film surface are the yaw rate. The parameters for the slip surface of the centroid side slip angle are all greater than 0; , These are the yaw rate tracking error and its derivative, respectively. , The centroid sideslip angle error and its derivative; Step two defines the yaw rate approach rate. centroid side slip angle approach rate The formula for expressing it is: （5） （6） In the formula, The sliding mode approximation coefficient for yaw rate. The sliding mode approximation coefficient is the side slip angle of the centroid. It is a symbolic function; Differentiating formula (3) and substituting formula (5) into formula (2), we obtain the additional yaw torque based on the sliding mode controller as follows: : （7） Differentiating equation (4) and substituting equation (6) into equation (2), we obtain the additional yaw moment based on the centroid sideslip angle of the sliding mode controller as follows: : （8） The distribution coefficient method is used in conjunction with formulas (7) and (8) to output the additional yaw moment. The total yaw moment is: : （9） In the formula, Add gain to yaw rate. Add gain to the centroid sideslip angle.

4. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 3, characterized in that: In step three, the formula for expressing the superspiral sliding mode approach rate is defined as follows: （10） In the formula, To control the input, , For the gain of the superspiral sliding mode controller; Differentiating formula (3) and substituting formula (10) into formula (2), the yaw rate and additional yaw torque based on the super-spiral sliding mode controller are obtained. The formula for expressing it is: （11） In the formula, , This is the coefficient for approaching the yaw rate of the superspiral sliding mode; Differentiating Formula (4) and substituting Formula (10) into Formula (2) results in the additional yaw moment based on the centroid side slip moment of the super-spiral sliding mode controller. The formula for expressing it is: （12） In the formula, , It is the approach coefficient of the centroid side deflection angle of the super-spiral sliding mode.

5. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 4, characterized in that: In step four, the DDPG algorithm is embedded into the STSMC framework to construct a state space-action space-reward interaction mechanism.

6. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 5, characterized in that: The state space is defined as the real-time vehicle dynamics state variables. Its formula is: (13) In the formula, The sideslip angle is the angle of the center of mass. The yaw rate is angular velocity. For yaw rate tracking error, For the centroid sideslip angle tracking error, and It is an integral term; The action space is defined as a key parameter of STSMC. Its formula is: (14) In the formula, the parameters of the super-spiral sliding film yaw rate torque controller are: For sliding surface parameters, The main approach rate coefficient for yaw rate; parameters of the super-spiral sliding film centroid side slip torque controller: For sliding surface parameters, The main approach coefficient for the centroid sideslip angle; Controller allocation coefficients; reward function It plays a significant role in DRL, guiding the agent to pursue optimal control performance, and its expression formula is: (15) In the formula, This is the tracking error weighting coefficient.

7. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 5, characterized in that: The DDPG algorithm described above adopts an Actor-Critic network structure. The Actor network generates parameter adjustment strategies, and the Critic network evaluates the value of the strategies, thereby achieving multi-parameter optimization.

8. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 7, characterized in that: Input state in the Actor network Output action Through deterministic strategy function The formula for mapping states to optimal actions is as follows: (16) In the formula, Representing random noise, it enables the agent to have exploratory capabilities; This represents the parameters of the Actor network at the current moment; This indicates that the real-time vehicle dynamics state variables are input through a deterministic policy function. Output its action ; Input state in the Critic network With action Output state-action value function Evaluate the long-term benefits of the current strategy; The network parameters in the Actor-Critic network structure are as follows: and The Actor network calculates the policy gradient using the backpropagation method. Then, the policy gradient ascent algorithm is used to update the weights of the online actor network. Its formula is: (17) In the formula, For strategy parameters Find the gradient. Represents the policy function The gradient with respect to its parameters; To obtain the empirical average; This represents the learning rate of the Actor function network; The Critic network uses gradient descent to update its parameters. : (18) in, This indicates the deviation between the predicted value and the target value; To achieve the target value, integrate instant rewards. and future value Discount estimates; As a discount factor, ; This represents the learning rate of the Critic function network. To address the instability issue in single-network learning, two networks, an online network and a target network, are deployed in practical applications. The target network parameters are used to calculate the TD target and update the weights of the online reviewer network. After obtaining the online network parameters, the parameters in the target network can be updated according to the soft update principle, the expression of which is: (19) In the formula, For the target Critic network parameters, For the target Actor network parameters, Indicates the update rate. .

9. The vehicle stability control method based on DDPG adaptive superspiral sliding mode according to claim 8, characterized in that: The specific operations of step five include the following steps: Step 1): The four-wheel torque must first meet the additional yaw moment and tire longitudinal force requirements of the upper-level motion tracking controller, expressed by the following formula: (20) in, , , , The longitudinal forces are those on the left front, right front, left rear, and right rear wheels. The wheelbase is the distance between the wheels. For vehicles in The resultant external force in the direction, For vehicles to bypass The net external torque on the shaft; Formula (19) can be rewritten in matrix form as follows: (21) in, ； ； Defining minimizing torque distribution error as one of the objectives of torque optimization distribution, the objective function is expressed as follows: (22) Among them, matrix Indicates the weights of the longitudinal force and yaw moment requirements; Step 2): The sum of the squares of the longitudinal and lateral forces of the four wheels is divided by the square of the product of the vertical load and the coefficient of friction to characterize the vehicle's stability margin. For a four-wheel independent drive electric vehicle, the lateral force is uncontrollable under constraints. Therefore, the longitudinal force is chosen as the control variable, and the objective function is expressed as follows: (23) in, The lateral force of the wheel, For the longitudinal force of the wheel, The vertical load on the wheel; Formula (23) can be rewritten in matrix form: in, ； Step 3): Combining the two torque optimization distribution control objective functions, the formula is as follows: (24) in, These are the weight coefficients of the objective function; The constraints were constructed by considering three factors: tire utilization rate, motor output torque, and road surface adhesion conditions. The resulting constraint formula is as follows: (25) According to the friction ellipse constraint formula (25), the longitudinal force constraint condition can be obtained, and its expression is as follows: (26) The maximum output torque of the motor should meet the following constraints, expressed by the following formula: (27) in, is the maximum output torque of the motor, and r is the tire rolling radius; Based on formulas (26) and (27), the longitudinal force constraint conditions for each wheel are expressed as follows: (28) According to formulas (24) and (28), the problem of allocating control variables can be transformed into solving an optimization problem, expressed as follows: (29) The torque optimization distribution results of a four-wheel motor driven electric vehicle are obtained by solving the QP algorithm.

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