Braking transverse stability control method for four-wheel independent drive vehicle

By calculating the vehicle's yaw angular velocity and sideslip angle during cornering and braking, and combining PID or fuzzy control methods to adjust the braking force of each wheel to apply a yaw torque, the instability problem of four-wheel independent drive electric vehicles during cornering and braking is solved, and the vehicle's lateral stability control is achieved.

CN120606818AActive Publication Date: 2025-09-09LIAONING UNIVERSITY OF TECHNOLOGY
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Patent Information

Application Number
CN202511024941.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-07-24
Publication Date
2025-09-09
Estimated Expiration
2045-07-24

AI Technical Summary

Technical Problem

Four-wheel independent drive electric vehicles are prone to becoming extremely unstable during cornering and braking due to the sideways deviation characteristics of the tires. Existing technologies make it difficult to effectively adjust the vehicle's lateral stability.

Method used

By obtaining the vehicle's speed and steering wheel angle during cornering and braking, the desired yaw rate and sideslip angle of the center of mass are calculated. PID or fuzzy control methods are selected in combination with the road adhesion coefficient to calculate the required braking force for each wheel to apply the yaw moment and improve the vehicle's lateral stability.

Benefits of technology

During the turning and braking process of a four-wheel independent drive electric vehicle, the braking force of each wheel is adjusted and a yaw torque is applied to avoid problems such as understeering or oversteering, thereby improving the vehicle's lateral stability.

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Abstract

The invention discloses a four-wheel independent drive vehicle braking lateral stability control method which comprises the following steps: step 1, acquiring the vehicle speed and the steering wheel angle of a vehicle in actual driving through a sensor, and calculating the expected yaw velocity and the expected side slip angle of the vehicle; 2, the difference between the expected side slip angle and the actual side slip angle and the difference between the expected yaw velocity and the actual yaw velocity serve as input, yaw moment needing to be added serves as output, and a direct yaw moment control strategy is selected according to the road adhesion coefficient; wherein when the road adhesion coefficient s is less than or equal to 0.6, a PID control method is adopted; when the road adhesion coefficient s is larger than 0.6, a fuzzy control method is adopted; and 3, the braking force needed by each wheel of the four-wheel independent drive vehicle is calculated based on the yaw moment needing to be added. In the turning braking process, yaw moment can be applied to a vehicle by adjusting the braking force of each wheel, and the transverse stability of the vehicle is improved.
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Description

Technical Field

[0001] The invention relates to a method for controlling the braking lateral stability of a four-wheel independent drive vehicle, and belongs to the technical field of electric vehicle braking. Background Art

[0002] During cornering and braking, four-wheel independent drive electric vehicles are affected by the side slip characteristics of the tires. When the vehicle reaches the tire adhesion limit, it will enter an extremely unstable state. At this time, the direct yaw moment control system (DYC) can actively adjust the vehicle body posture by judging the driver's intention, avoiding problems such as understeer or oversteer.

[0003] Fuzzy control is an intelligent reasoning control method based on fuzzy set theory, fuzzy logic reasoning and fuzzy language variables. The fuzzy control system mainly consists of variable definition, fuzzification, fuzzy reasoning, clarification and other parts. The fuzzy controller is the experience gained from a large number of input and output. The main operation method is to fuzzify, define fuzzy rules and clarify the input variables, summarize the obtained data, and determine the appropriate output variable process.

[0004] The direct yaw moment control provided by the present invention calculates the additional yaw moment required by the vehicle through feedback regulation, and further calculates the braking force required to be applied to each wheel, thereby adjusting the lateral stability of the four-wheel independent drive vehicle. Summary of the Invention

[0005] The present invention designs and develops a method for controlling the braking lateral stability of a four-wheel independent drive vehicle. During cornering braking, the braking force of each wheel is adjusted to apply a yaw moment to the vehicle, thereby improving the vehicle's lateral stability.

[0006] The technical solution provided by the present invention is:

[0007] A method for controlling lateral stability of a four-wheel independent drive vehicle by braking, comprising:

[0008] Step 1: Obtain the vehicle's actual speed and steering wheel angle during driving, and calculate the vehicle's expected yaw rate and expected sideslip angle;

[0009] Step 2: Obtaining the road adhesion coefficient, the actual vehicle yaw rate, and the actual vehicle center of mass slip angle, using the difference between the desired and actual center of mass slip angles and the difference between the desired and actual yaw rates as inputs, and using the required additional yaw moment as output, and selecting a yaw moment control strategy based on the road adhesion coefficient;

[0010] Among them, when the road adhesion coefficient s≤0.6, the PID control method is adopted;

[0011] When the road adhesion coefficient s>0.6, the fuzzy control method is used;

[0012] Step 3: Calculate the additional yaw moment required based on the difference between the actual vehicle center of mass slip angle and the desired center of mass slip angle, and the difference between the actual vehicle yaw rate and the desired vehicle yaw rate;

[0013] Calculate the braking force required for each wheel of the four-wheel independent drive vehicle based on the additional yaw moment required;

[0014] The expression for calculating the braking force of each wheel of the four-wheel independent drive vehicle is:

[0015]

[0016] Where m is the mass of the four-wheel independent drive vehicle, in kg; h g is the distance between the center of mass of the vehicle and the ground, in meters; b is the horizontal distance between the rear axle and the center of mass of the four-wheel independent drive vehicle, in meters; L is the wheelbase of the four-wheel independent drive vehicle, in meters; F ua Braking force provided by the front axle brake, F ub The braking force provided to the rear axle brake, in N.

[0017] Preferably,

[0018] The vehicle's desired yaw rate γ _NO The calculation formula is:

[0019]

[0020] Where, v x is the actual speed of the vehicle, in m / s; δ f is the front wheel angle of the four-wheel independent drive vehicle, unit: deg; i is the steering system transmission ratio; V ch is the vehicle longitudinal speed reference value, unit is m / s;

[0021] The vehicle's center of mass sideslip angle β _NO The calculation formula is:

[0022]

[0023] Where a is the horizontal distance between the four-wheel independent drive vehicle and the center of mass, in meters, and k2 is the cornering stiffness of the rear axle, in Newtons / rad.

[0024] Preferably, the vehicle longitudinal speed reference value V ch The calculation formula is:

[0025]

[0026] Where k1 is the cornering stiffness of the front axle of the vehicle, in N / rad.

[0027] Preferably, the wheelbase of the four-wheel independent drive vehicle is L=2.776m, the horizontal distance between the four-wheel independent drive vehicle and the center of mass is a=1.11m, the horizontal distance between the rear axle of the four-wheel independent drive vehicle and the center of mass is b=1.666m, and the vehicle mass of the four-wheel independent drive vehicle is m=1370kg.

[0028] Preferably, in step 2, the fuzzy control in the direct yaw moment control strategy includes:

[0029] The difference Δβ between the expected and actual sideslip angles and the difference Δγ between the expected and actual yaw rates are converted into quantization levels in the fuzzy domain respectively;

[0030] Inputting the difference Δβ between the desired and actual sideslip angles and the difference Δγ between the desired and actual yaw rates into the fuzzy control model, wherein the difference Δβ between the desired and actual sideslip angles is divided into five levels, and the fuzzy set is {NB, NS, Z, PB, PS}; and the difference Δγ between the desired and actual yaw rates is divided into five levels, and the fuzzy set is {NB, NS, Z, PB, PS};

[0031] The output of the fuzzy control model is the additional yaw moment ΔM required. The additional yaw moment ΔM is divided into 7 levels, and the fuzzy set is {NB, NM, NS, Z, PB, PM, PS};

[0032] The membership functions of both input and output are triangular membership functions.

[0033] Preferably, in the fuzzy control, the domain of the difference Δγ between the expected and actual yaw rate is {-1, 1}, the domain of the difference Δβ between the expected and actual sideslip angle is {-1, 1}, and the domain of the additional yaw moment ΔM is {-1, 1}.

[0034] Preferably,

[0035] The calculation formula for the difference between the expected and actual yaw angular velocity of the four-wheel independent drive vehicle is:

[0036] Δγ=γ _NO -γ;

[0037] The formula for calculating the difference between the expected and actual sideslip angles of the center of mass of the four-wheel independent drive vehicle is:

[0038] Δβ=β _NO -β;

[0039] Where γ is the actual yaw rate of the four-wheel independent drive vehicle, and β is the actual sideslip angle of the center of mass of the four-wheel independent drive vehicle.

[0040] Preferably, the PID control is a continuous closed-loop control system, and the system state expression is:

[0041]

[0042] Where, e(t) is the difference in yaw rate Δγ and sideslip angle Δβ at each step, μ(t) represents the output value of the PID system at each step, and K p is the proportionality coefficient, K i is the integral coefficient, K d is the differential coefficient.

[0043] The beneficial effects of the present invention are as follows: the method for controlling the braking lateral stability of a four-wheel independent drive vehicle provided by the present invention adjusts the braking force of each wheel during the turning braking process of a four-wheel independent drive electric vehicle, thereby applying a yaw torque to the vehicle to improve the lateral stability of the vehicle and avoid problems such as understeering or oversteering. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a framework diagram of the fuzzy control system described in the present invention.

[0045] Figure 2 It is the membership function of the fuzzy controller input variable Δγ and difference Δβ described in the present invention.

[0046] Figure 3 It is the membership function of the fuzzy controller output variable ΔM described in the present invention.

[0047] Figure 4 This is a framework diagram of the PID control system described in the present invention.

[0048] Figure 5 This is a relationship diagram between the braking force applied to the wheel and the yaw moment generated according to the present invention.

[0049] FIG6( a ) is a schematic diagram showing a comparison of yaw angular velocities according to the present invention.

[0050] FIG6( b ) is a schematic diagram showing a comparison of the sideslip angle of the center of mass according to the present invention.

[0051] FIG6( c ) is a lateral acceleration curve according to the present invention.

[0052] FIG6( d ) is a schematic diagram of the vehicle driving trajectory according to the present invention. DETAILED DESCRIPTION

[0053] The present invention will be described in further detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0054] like Figure 1As shown in FIG-6 , the present invention provides a method for controlling the lateral stability of a four-wheel independent drive vehicle by braking. During a turning braking process, the method applies a yaw moment to the vehicle by adjusting the braking force of each wheel to improve the lateral stability of the vehicle, including:

[0055] Step 1: Obtain the vehicle's actual speed and steering wheel angle through sensors, and calculate the vehicle's expected yaw rate and expected center of mass deviation angle;

[0056] In the present invention, as a preference, the vehicle speed and steering wheel angle during actual driving of the vehicle are input using carsim software simulation data.

[0057] The vehicle's desired yaw rate γ _NO The calculation formula is:

[0058]

[0059] Where, v x is the actual speed of the vehicle, in m / s; δ f is the front wheel angle of the four-wheel independent drive vehicle, in degrees; i is the steering system transmission ratio; V ch is the vehicle longitudinal speed reference value, in m / s;

[0060] Vehicle center of mass sideslip angle β _NO The calculation formula is:

[0061]

[0062] Where a is the horizontal distance between the four-wheel independent drive vehicle and the center of mass, in meters; k2 is the lateral stiffness of the rear axle, in Newtons per degree.

[0063] Vehicle longitudinal speed reference value V ch The calculation formula is:

[0064]

[0065] Where k1 is the cornering stiffness of the front axle of the vehicle, in N / deg.

[0066] In the present invention, as a preference, the wheelbase of the four-wheel independent drive vehicle is L=2.776m, the horizontal distance between the four-wheel independent drive vehicle and the center of mass is a=1.11m, the horizontal distance between the rear axle of the four-wheel independent drive vehicle and the center of mass is b=1.666m, and the vehicle mass of the four-wheel independent drive vehicle is m=1370kg.

[0067] Step 2: Obtain the road adhesion coefficient, the actual vehicle yaw rate, and the actual vehicle center of mass slip angle. The difference between the desired and actual center of mass slip angles and the difference between the desired and actual yaw rates are used as inputs. The required additional yaw moment is used as output. A yaw moment control strategy is selected based on the road adhesion coefficient.

[0068] The formula for calculating the difference between the desired and actual yaw rate of a four-wheel independent drive vehicle is:

[0069] Δγ=γ _NO -γ;

[0070] The formula for calculating the difference between the expected and actual sideslip angles of the center of mass of a four-wheel independent drive vehicle is:

[0071] Δβ=β _NO -β;

[0072] Where γ is the actual yaw rate of the four-wheel independent drive vehicle, and β is the actual sideslip angle of the center of mass of the four-wheel independent drive vehicle.

[0073] When the road adhesion coefficient s≤0.6, the PID control method is used;

[0074] PID control is a continuous closed-loop control system, and the system state expression is:

[0075]

[0076] Where, e(t) is the difference in yaw rate Δγ and sideslip angle Δβ at each step, μ(t) represents the output value of the PID system at each step, and K p is the proportionality coefficient, K i is the integral coefficient, K d is the differential coefficient.

[0077] When the road adhesion coefficient s>0.6, the fuzzy control method is used

[0078] Fuzzy control includes:

[0079] The difference Δβ between the expected and actual sideslip angles and the difference Δγ between the expected and actual yaw rates are converted into quantization levels in the fuzzy domain respectively;

[0080] The difference between the expected and actual sideslip angles Δβ and the difference between the expected and actual yaw rates Δγ are input into the fuzzy control model. The difference between the expected and actual sideslip angles Δβ is divided into five levels, and the fuzzy set is {NB, NS, Z, PB, PS}. The difference between the expected and actual yaw rates Δγ is divided into five levels, and the fuzzy set is {NB, NS, Z, PB, PS}.

[0081] The output of the fuzzy control model is the additional yaw moment ΔM, which is divided into 7 levels and the fuzzy sets are {NB, NM, NS, Z, PB, PM, PS};

[0082] In the present invention, as a preference, triangular membership functions are selected as both input and output membership functions.

[0083] The domain of the difference between the desired and actual yaw rate Δγ is {-1, 1}, the domain of the difference between the desired and actual sideslip angle Δβ is {-1, 1}, and the domain of the required additional yaw moment ΔM is {-1, 1}.

[0084] Step 3: Calculate the additional yaw moment required based on the difference between the actual vehicle center of mass slip angle and the desired center of mass slip angle, and the difference between the actual vehicle yaw rate and the desired vehicle yaw rate;

[0085] The braking force required for each wheel of the four-wheel independent drive vehicle is calculated based on the additional yaw moment required;

[0086] Among them, the expression for calculating the braking force of each wheel of a four-wheel independent drive vehicle is:

[0087]

[0088] Where m is the mass of the four-wheel independent drive vehicle, in kg; h g is the distance between the center of mass of the vehicle and the ground, in meters; b is the horizontal distance between the rear axle and the center of mass of the four-wheel independent drive vehicle, in meters; L is the wheelbase of the four-wheel independent drive vehicle, in meters; F ua Braking force provided by the front axle brake, F ub The braking force provided to the rear axle brake, in N.

[0089] The relationship between the additional yaw moment and the braking force of each wheel is as follows: Figure 5 The braking force distribution rule curve is determined in .

[0090] The yaw moment is controlled by a yaw moment controller, which is composed of a fuzzy controller and a PID controller.

[0091] like Figure 1 As shown in the figure, the fuzzy control system takes the difference between the expected and actual yaw rate and the difference between the center of mass sideslip angle as input, and outputs the target torque required by the vehicle after inference calculation by the fuzzy controller. The braking force required for each wheel is then calculated based on the target torque and distributed to the motor control system.

[0092] The domain of the input variables of the fuzzy controller, the difference Δγ between the actual yaw rate and the expected value of the vehicle, and the difference Δβ between the actual sideslip angle of the vehicle and the expected value is {-1, -0.5, 0, 0.5, 1}. The domain of the output variable yaw moment ΔM of the fuzzy controller is {-1, -0.35, -0.75, 0, 0.35, 0.75, 1}. The fuzzy language set of the input variables is: NB (negative large), NS (negative small), Z (zero), PB (positive small), PS (positive large); the fuzzy language set of the output variables is: NB (negative large), NM (negative medium), NS (negative small), Z (zero), PB (positive small), PM (positive medium), PS (positive large); the membership diagrams of the input variables and output variables all adopt triangular function distribution, such as Figure 2 and Figure 3 The fuzzy control rules are shown in Table 1.

[0093] Table 1 Fuzzy control rules table

[0094]

[0095] If the fuzzy levels corresponding to the difference in vehicle yaw rate Δγ and the difference in vehicle center of mass sideslip angle Δβ are both "PB" or "PS", then the fuzzy level corresponding to the vehicle's additional yaw moment ΔM is "PS", that is, the additional yaw moment output by the vehicle is the largest and its direction is positive.

[0096] If the fuzzy levels corresponding to the difference in vehicle yaw rate Δγ and the difference in vehicle center of mass sideslip angle Δβ are both "NB" or "NS", then the fuzzy level corresponding to the vehicle's additional yaw moment ΔM is "NS", that is, the additional yaw moment output by the vehicle is the smallest and its direction is negative.

[0097] If the vehicle's additional yaw moment ΔM output participation degree is "NB, NM or NS", the direction of the output additional yaw moment is negative; if the vehicle's additional yaw moment ΔM output participation degree is "PB, PM or PS", the output additional yaw moment is positive; if the vehicle's additional yaw moment ΔM output participation degree is "NB or PB", the output additional yaw moment is maximum; if the vehicle's additional yaw moment ΔM output participation degree is "NM or PM", the output additional yaw moment is moderate; if the vehicle's additional yaw moment ΔM output participation degree is "NS or PB", the output additional yaw moment is small; if the vehicle's additional yaw moment ΔM output participation degree is "Z", the output additional yaw moment is zero, and the vehicle does not need additional yaw moment.

[0098] like Figure 4As shown in the figure, the PID control system takes the difference in yaw rate and the difference in sideslip angle of the center of mass as input. After calculation, the PID controller outputs the target torque required by the vehicle, and then calculates the braking force required for each wheel based on the target torque and distributes it to the motor control system.

[0099] Assume that the car's left turning direction is the positive direction, and the counterclockwise yaw moment is the positive direction, such as Figure 5 As shown in the figure, when the braking force gradually increases, the yaw moment curves of the outer front wheel and the inner rear wheel fluctuate greatly; when the outer front wheel of the vehicle is subjected to braking force, the vehicle body will generate a clockwise yaw moment; when the inner rear wheel of the vehicle is subjected to braking force, the vehicle body will generate a counterclockwise yaw moment; when the outer rear wheel and the inner front wheel are subjected to the same braking force, corresponding yaw moments can also be generated, but the generated yaw moments are smaller than those of the outer front wheel and the inner rear wheel. Therefore, the outer front wheel and the rear inner wheel are used as the controlled wheels of DYC control. It is only necessary to control these two wheels to ensure vehicle stability.

[0100] When the vehicle has an oversteering tendency, the corresponding braking force is applied to the wheels outside the front to generate a compensatory yaw moment in the opposite direction of the vehicle's yaw rate. When the vehicle has an understeering tendency, the corresponding braking force is applied to the rear inner wheels to generate a compensatory yaw moment in the same direction as the vehicle's yaw rate, thereby ensuring the vehicle's stability during cornering. The specific selection rules are shown in Table 2.

[0101] Table 2 Selection rules for controlled wheels

[0102]

[0103] The present invention provides a method for controlling the lateral stability of a four-wheel independent drive vehicle by braking. During the turning braking process of a four-wheel independent drive electric vehicle, the braking force of each wheel is adjusted, thereby applying a yaw torque to the vehicle to improve the lateral stability of the vehicle and avoid problems such as understeering or oversteering.

[0104] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for controlling lateral stability of a four-wheel independent drive vehicle during braking, characterized in that: include: Step 1: Obtain the vehicle's actual speed and steering wheel angle during driving, and calculate the vehicle's expected yaw rate and expected sideslip angle; Step 2: Obtain the road adhesion coefficient, the actual vehicle yaw rate, and the actual vehicle center of mass slip angle, use the difference between the expected and actual center of mass slip angles and the difference between the expected and actual yaw rates as input, use the required additional yaw moment as output, and select a direct yaw moment control strategy based on the road adhesion coefficient; Among them, when the road adhesion coefficient s≤0.6, the PID control method is adopted; When the road adhesion coefficient s>0.6, the fuzzy control method is used; Step 3: Calculate the additional yaw moment required based on the difference between the actual vehicle center of mass slip angle and the desired center of mass slip angle, and the difference between the actual vehicle yaw rate and the desired vehicle yaw rate; Calculate the braking force required for each wheel of the four-wheel independent drive vehicle based on the additional yaw moment required; The expression for calculating the braking force of each wheel of the four-wheel independent drive vehicle is: Where m is the mass of the four-wheel independent drive vehicle, in kg; h g is the distance between the center of mass of the vehicle and the ground, in meters; b is the horizontal distance between the rear axle and the center of mass of the four-wheel independent drive vehicle, in meters; L is the wheelbase of the four-wheel independent drive vehicle, in meters; F ua Braking force provided by the front axle brake, F ub The braking force provided to the rear axle brake, in N.

2. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 1, characterized in that: The vehicle's desired yaw rate γ _NO The calculation formula is: Where, v x is the actual speed of the vehicle, in m / s; δ f The front wheel angle of a four-wheel independent drive vehicle, unit: deg; i is the steering system transmission ratio; V ch is the vehicle longitudinal speed reference value, unit is m / s; The vehicle's center of mass sideslip angle β _NO The calculation formula is: Where a is the horizontal distance between the four-wheel independent drive vehicle and the center of mass, in meters, and k2 is the cornering stiffness of the rear axle, in Newtons / rad.

3. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 2, wherein: The vehicle longitudinal speed reference value V ch The calculation formula is: Where k1 is the cornering stiffness of the front axle of the vehicle, in N / rad.

4. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 3, wherein: The wheelbase of the four-wheel independent drive vehicle is L=2.776m, the horizontal distance between the four-wheel independent drive vehicle and the center of mass is a=1.11m, the horizontal distance between the rear axle of the four-wheel independent drive vehicle and the center of mass is b=1.666m, and the vehicle mass of the four-wheel independent drive vehicle is m=1370kg.

5. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 4, characterized in that: In the step 2, the fuzzy control in the direct yaw moment control strategy includes: The difference Δβ between the expected and actual sideslip angles and the difference Δγ between the expected and actual yaw rates are converted into quantization levels in the fuzzy domain respectively; Inputting the difference Δβ between the desired and actual sideslip angles and the difference Δγ between the desired and actual yaw rates into the fuzzy control model, wherein the difference Δβ between the desired and actual sideslip angles is divided into five levels, and the fuzzy set is {NB, NS, Z, PB, PS}; and the difference Δγ between the desired and actual yaw rates is divided into five levels, and the fuzzy set is {NB, NS, Z, PB, PS}; The output of the fuzzy control model is the additional yaw moment ΔM required. The additional yaw moment ΔM is divided into 7 levels, and the fuzzy set is {NB, NM, NS, Z, PB, PM, PS}; The membership functions of both input and output are triangular membership functions.

6. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 5, characterized in that: In the fuzzy control, the domain of the difference Δγ between the desired and actual yaw rate is {-1, 1}, the domain of the difference Δβ between the desired and actual sideslip angle is {-1, 1}, and the domain of the additional yaw moment ΔM is {-1, 1}.

7. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 6, wherein: The calculation formula for the difference between the expected and actual yaw angular velocity of the four-wheel independent drive vehicle is: Δγ=γ _NO -c; The formula for calculating the difference between the expected and actual sideslip angles of the center of mass of the four-wheel independent drive vehicle is: Δβ=β _NO -b; Where γ is the actual yaw rate of the four-wheel independent drive vehicle, and β is the actual sideslip angle of the center of mass of the four-wheel independent drive vehicle.

8. The method for controlling lateral stability of a four-wheel independent drive vehicle under braking according to claim 7, characterized in that: The PID control is a continuous closed-loop control system, and the system state expression is: Where, e(t) is the difference in yaw rate Δγ and sideslip angle Δβ at each step, μ(t) represents the output value of the PID system at each step, and K p is the proportionality coefficient, K i is the integral coefficient, K d is the differential coefficient.

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