Wheel hub motor drive differential steering intelligent vehicle path tracking and anti-rollover control method

Abstract

This invention discloses a method for path tracking and rollover prevention control in a hub motor-driven differential steering intelligent vehicle. The method comprises the following steps: establishing a path tracking error model, a differential steering dynamics model, and a reference model for the intelligent vehicle; based on the path tracking error model, using an improved sliding mode multi-objective model predictive controller (SMPC) for upper-level control, calculating the reference front wheel steering angle required for tracking the reference path; inputting the reference front wheel steering angle into the reference model to generate a reference yaw rate and a reference roll angle; based on the differential steering dynamics model, using a model predictive-model-free adaptive controller (MPC-MFAC) for lower-level control, calculating and outputting the front wheel differential torque and active suspension control force according to the reference yaw rate and the reference roll angle, thereby achieving tracking of the reference yaw rate and the reference roll angle. This invention can synergistically improve the vehicle's path tracking accuracy and rollover prevention stability, effectively ensuring driving safety and comfort.

Description

Technical Field

[0001] This invention relates to the field of intelligent vehicle control technology, specifically to a method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle. Background Technology

[0002] In-wheel motor-driven electric vehicles have become a research hotspot in the field of intelligent driving due to their advantages such as independent controllable driving torque for each wheel and high transmission efficiency. Differential steering, achieved by adjusting the driving torque of the left and right wheels, can eliminate the need for traditional mechanical steering mechanisms and serve as a redundant backup for steer-by-wire systems, significantly improving vehicle reliability and safety.

[0003] Path tracking is a core technology for autonomous driving, and its control accuracy directly affects vehicle performance. Model predictive control (MPC) is widely used due to its ability to handle multi-constraint optimization problems, but its control effect usually depends on an accurate vehicle dynamics model, and online solution computation is computationally burdensome. Sliding mode control (SMC) is highly robust to model parameter fluctuations and external disturbances, but its inherent chattering problem can affect control smoothness and even actuator life. Although existing research has improved sliding mode control by optimizing reaching laws, research on deeply integrating SMC and MPC to leverage their respective advantages remains relatively insufficient.

[0004] Furthermore, for intelligent vehicles employing differential steering, the vehicle system exhibits strong nonlinearity and time-varying parameters, meaning that model-based control strategies may face insufficient robustness under complex conditions. More importantly, during high-speed cornering, centrifugal force can easily cause body roll. Excessive roll angles can lead to tire load transfer, affecting differential steering performance and posing a risk of rollover. Currently, rollover prevention control research primarily focuses on traditional steering vehicles using active suspension, differential braking, or stabilizer bars. However, for in-wheel motor-driven differential steering intelligent vehicles equipped with active suspension, coordinating path tracking and rollover prevention control to achieve high-performance integrated control remains a pressing technical challenge. Summary of the Invention

[0005] Therefore, the purpose of this invention is to provide a method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle, in order to solve the problems mentioned in the background art.

[0006] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0007] A method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle includes the following steps:

[0008] S1. Establish the path tracking error model, differential steering dynamics model, and reference model of the intelligent vehicle;

[0009] S2. Based on the path tracking error model, an improved sliding mode multi-objective model predictive controller (SMPC) is used for upper-level control to calculate the reference front wheel angle required for tracking the reference path.

[0010] S3. Input the reference front wheel steering angle into the reference model to generate the reference yaw rate and the reference roll angle;

[0011] S4. Based on the differential steering dynamics model, a model predictive-model-free adaptive controller (MPC-MFAC) is used for lower-level control. According to the reference yaw rate and the reference roll angle, the front wheel differential torque and active suspension control force are calculated and output to achieve tracking of the reference yaw rate and the reference roll angle.

[0012] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method of the present invention, the improved sliding mode multi-objective model predictive controller (SMPC) control steps are as follows:

[0013] The sliding surface is designed based on sliding mode control theory and used as the convergence target of the system state. The expression for the sliding surface is as follows:

[0014]

[0015] in, , , , All are weighting coefficients, and all are greater than 0. For lateral error, This represents the rate of change of the lateral error. For heading error, This represents the rate of change of heading error.

[0016] Design an adaptive power-law approach to generate sliding mode reference values. The expression for the adaptive power-approach law is:

[0017]

[0018] in, , , , , , All are constants; The coefficient of the power term;

[0019] Using the sliding surface and the sliding reference value The tracking error and the control increment are used as optimization objectives. A multi-objective cost function is constructed, and the optimal control quantity is solved by rolling optimization of model predictive control to drive the system state to converge to the sliding surface.

[0020] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method described in this invention, the multi-objective cost function expression is as follows:

[0021]

[0022] in, To predict sliding mode variables, This is a sliding mode reference value. To control the increment, , These are the weighting coefficients. To predict the time domain, To control the time domain.

[0023] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method described in this invention, the model prediction-model-free adaptive controller (MPC-MFAC) control steps are as follows:

[0024] Based on the reference yaw rate, the reference roll angle, and the differential steering dynamics model, the MPC controller, under the condition of satisfying the first preset constraint, optimizes the first cost function to obtain the basic front wheel differential torque and the basic active suspension control force.

[0025] The MFAC controller predicts the vehicle state at time k based on the MPC controller. Compared with actual vehicle state quantity Deviation between The front wheel differential torque compensation and active suspension control force compensation are calculated using a model-free adaptive control algorithm.

[0026] The basic front wheel differential torque is added to the front wheel differential torque compensation to obtain the final front wheel differential torque. The basic active suspension control force is added to the active suspension control force compensation to obtain the final active suspension control force.

[0027] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method of the present invention, in the MFAC controller, the model-free adaptive control algorithm calculates the compensation control quantity in the following manner:

[0028] The system is equivalent to a compact-form dynamic linearization model:

[0029] in, The system output vector corresponds to the compensation amount. The system input vector corresponds to the state deviation. , It is a pseudo-Jacobi matrix;

[0030] The pseudo-Jacobi matrix is ​​estimated online using a minimum parameter estimation algorithm with a reset mechanism. ;

[0031] The control input at the current moment is calculated using the following formula.

[0032]

[0033] in, Step size factor As a weighting factor, For the desired output, For system input, This is an estimate of the pseudo-Jacobi matrix.

[0034] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method described in this invention, the pseudo-Jacobi matrix... The estimation algorithm includes a reset mechanism: when the condition is met... or At that time, the pseudo-Jacobi matrix Reset to initial estimate .

[0035] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method of the present invention, in step S1, the differential steering dynamics model includes a front wheel differential steering system dynamics model, the expression of which is:

[0036]

[0037] in, It is the equivalent moment of inertia. It's the front wheel steering angle. It is the equivalent steering damping of the steering system. This is the total self-aligning torque of the front wheels. ΔT is the frictional torque, and ΔT is the difference in steering torque between the front wheels.

[0038] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method of the present invention, in step S3, the reference model is a linear three-degree-of-freedom vehicle model with neutral steering characteristics, and its expression is:

[0039]

[0040] , ,

[0041] in, For reference yaw rate, and These are lateral velocity and longitudinal velocity, respectively. For reference to the front wheel steering angle, and These are the lateral forces of the front and rear wheels, respectively. This is the equivalent tilt stiffness.

[0042] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method described in this invention, the lateral load transfer rate (LTR) and / or occupant-perceived lateral acceleration are also calculated in real time during the control process. As an indicator for evaluating rollover prevention performance and ride comfort;

[0043] The lateral load transfer rate (LTR) is calculated using the following formula:

[0044]

[0045] The occupant sensed lateral acceleration Calculated using the following formula:

[0046] .

[0047] As a preferred embodiment of the wheel hub motor driven differential steering intelligent vehicle path tracking and anti-rollover control method described in this invention, in step S2, the improved sliding mode multi-objective model predictive controller (SMPC) applies constraints to the control quantity and control increment. The control quantity is the front wheel steering angle δ, and its constraint range is ±35°. The control increment is the front wheel steering angle change rate Δδ, and its constraint range is ±10° / s.

[0048] In step S4, the model predictive controller (MPC) applies constraints to the control quantity and control increment, wherein the control quantity includes: the basic front wheel differential torque. Its constraint range is ±800 N·m; basic active suspension control force , i=1,2,3,4, with a constraint range of ±30000 N; the control increment includes: the basic front wheel differential torque change rate, with a constraint range of ±50 N·m / s; the basic active suspension control force change rate, with a constraint range of ±3000 N / s.

[0049] Compared with the prior art, the beneficial effects of the present invention are:

[0050] 1. This invention creatively proposes a hierarchical control architecture, where the upper layer focuses on path tracking and the lower layer is responsible for yaw and roll stability tracking. This architecture uses a reference model to convert the reference front wheel steering angle output by the upper layer into the reference yaw rate and reference roll angle tracked by the lower layer. This allows the vehicle to accurately track the path while actively suppressing the body roll angle within a safe range, fundamentally solving the contradiction between tracking and stability during high-speed cornering.

[0051] 2. The improved sliding mode multi-objective model predictive controller (SMC) used in the upper layer combines the robustness of sliding mode control with the rolling optimization and constraint handling capabilities of model predictive control. Through a designed adaptive power-law approach, it can quickly approach large errors and smoothly slide when errors are small, effectively suppressing the chattering of traditional sliding mode control. Simulations show that, compared to the traditional SMC, this controller reduces the maximum absolute values ​​of lateral displacement error and heading error by 76.09% and 54.55%, respectively, and the output front wheel steering angle command is smoother.

[0052] 3. The lower layer employs a model-predictive-model-free adaptive controller, innovatively combining MPC and MFAC. MPC calculates the basic quantities of front wheel differential torque and active suspension control force based on the model, while MFAC calculates the compensation amount in real time using a data-driven approach based on the deviation between the MPC predicted state and the actual state. This structure allows the controller to maintain the optimization capability of model prediction while possessing the ability to compensate for unmodeled dynamics and parameter uncertainties through model-free adaptive learning, thus improving the robustness of the system. Simulations show that after introducing MFAC, the peak tracking error of yaw rate is reduced by approximately 75%.

[0053] 4. This invention achieves efficient anti-rollover control by directly tracking the reference roll angle through a lower-level controller and coordinating differential torque with active suspension control force. Simulation results under high-speed double lane change conditions at 100km / h show that the peak roll angle of the vehicle using the control strategy of this invention is reduced by approximately 64.6% compared to the case without anti-rollover control, and it can effectively track the reference roll angle; at the same time, the absolute value of the peak value of the lateral load transfer rate, which evaluates rollover risk, is reduced by approximately 52.2%, significantly reducing the risk of tires leaving the ground. Attached Figure Description

[0054] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0055] Figure 1 A schematic diagram of the path tracking error model for an intelligent vehicle provided by the present invention;

[0056] Figure 2 A schematic diagram of the front-wheel differential steering system of the intelligent vehicle dynamics model provided by the present invention;

[0057] Figure 3 A schematic diagram of the planar dynamics model of the differential steering intelligent vehicle dynamics model provided by the present invention;

[0058] Figure 4 A schematic diagram of the vertical and roll dynamics models of the differential steering intelligent vehicle dynamics model provided by the present invention;

[0059] Figure 5 This is a diagram of the path tracking and anti-rollover control architecture for a hub motor driven differential steering intelligent vehicle provided by the present invention.

[0060] Figure 6 This is a block diagram of the MPC-MFAC control provided by the present invention;

[0061] Figure 7 A curve comparison of the tracking reference path for two traditional steering intelligent vehicles using SMPC controllers and SMC controllers, provided for the present invention.

[0062] Figure 8 A comparison chart of lateral error curves for simulation of two types of intelligent steering vehicles using SMPC and SMC controllers, provided for this invention.

[0063] Figure 9 A comparison chart of heading error curves for two types of intelligent steering vehicles using SMPC and SMC controllers, provided for the present invention;

[0064] Figure 10 A comparison chart of the front wheel steering angle curves of two types of intelligent steering vehicles using SMPC and SMC controllers, provided for the present invention;

[0065] Figure 11 The response curves of the intelligent vehicle's actual yaw rate tracking the reference yaw rate under the 54km / h operating condition, when using the SMPC+MPC strategy and the SMPC+MPC-MFAC strategy respectively;

[0066] Figure 12 The comparison diagram of the response curves of the differential torque of the front intelligent wheel under the working condition of 54km / h, when using the SMPC+MPC strategy and the SMPC+MPC-MFAC strategy respectively, is provided for the present invention.

[0067] Figure 13 The SMPC+MPC-MFAC hierarchical control strategy provided by this invention is shown in the trajectory comparison diagram of the intelligent vehicle tracking the double lane change reference path under high-speed conditions at 100 km / h, using two strategies: no rollover prevention control and rollover prevention control.

[0068] Figure 14 The SMPC+MPC-MFAC hierarchical control strategy provided by this invention is compared with the lateral error curve of the intelligent vehicle under high-speed conditions at 100 km / h when using two strategies: no anti-rollover control and anti-rollover control.

[0069] Figure 15 The SMPC+MPC-MFAC hierarchical control strategy provided by this invention is compared with the heading error curves of the intelligent vehicle under high-speed conditions at 100 km / h when using two strategies: no anti-rollover control and anti-rollover control.

[0070] Figure 16 The SMPC+MPC-MFAC hierarchical control strategy provided by this invention is shown in the yaw rate tracking response curve of the intelligent vehicle under high-speed conditions at 100 km / h, when using two strategies: no anti-rollover control and anti-rollover control.

[0071] Figure 17 The graph shows a comparison of the roll angle response curves of the intelligent vehicle under high-speed conditions at 100 km / h when using two strategies: no rollover prevention control and rollover prevention control.

[0072] Figure 18 The graph shows a comparison of the lateral load transfer rate of the intelligent vehicle under high-speed conditions (100 km / h) when using two strategies: no rollover prevention control and rollover prevention control. The SMPC+MPC-MFAC hierarchical control strategy provided by this invention is shown in the graph.

[0073] Figure 19 The diagram shows the comparison of lateral acceleration perceived by the occupants of an intelligent vehicle when using two strategies: no rollover prevention control and rollover prevention control.

[0074] Figure 20 A comparison diagram of the response of four active suspension control forces under high-speed conditions provided by the present invention;

[0075] Figure 21 A comparison chart of the front wheel differential torque response results provided by the present invention. Detailed Implementation

[0076] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0077] See Figure 5 The hub motor driven differential steering intelligent vehicle path tracking and rollover prevention control architecture shown in this invention includes the following specific steps:

[0078] S1. First, establish a mathematical model for the intelligent vehicle, including a path tracking error model for upper-level control, a differential steering vehicle dynamics model for lower-level control, and a reference model for generating the ideal response.

[0079] S2. Based on the established path tracking error model, an improved sliding mode multi-objective model predictive controller is designed and implemented. This controller receives the vehicle's lateral error, which is sensed in real time by sensors (such as cameras and GNSS / IMU integrated navigation systems). With heading error The reference front wheel steering angle required for the vehicle to follow the desired path is obtained through rolling optimization calculation. ;

[0080] S3. The reference front wheel steering angle calculated by the upper layer. The input is fed into a linear three-degree-of-freedom reference model with neutral steering characteristics. This model is based on the vehicle's current longitudinal velocity. Under the given conditions, calculate the reference yaw rate that the vehicle should maintain stable driving under the current steering input. and safe reference roll angle ;

[0081] S4. Based on the established differential steering dynamics model, design and run a model-predictive-model-free adaptive controller. This controller receives a reference yaw rate from the reference model. and safe reference roll angle and the vehicle's actual yaw rate Roll angle, lateral velocity Suspension displacement and other state variables (measured by onboard sensors) are used to calculate the final front wheel differential torque through comprehensive optimization and adaptive compensation. and four active suspension control forces ;

[0082] S5. The calculated front wheel differential torque ΔM is distributed to the hub motors of the left and right front wheels to generate the torque difference required for steering. At the same time, four active suspension control force commands are sent to the corresponding active suspension actuators to generate a force to suppress roll. Through the precise execution of the lower-level control, the actual yaw and roll motion of the vehicle closely follow the reference value, thereby ensuring roll stability during high-speed steering while achieving precise path tracking.

[0083] The following section elaborates on the path tracking and rollover prevention control architecture of a hub motor-driven differential steering intelligent vehicle:

[0084] 1. Mathematical Model of Intelligent Vehicles

[0085] 1.1 Path tracking error model

[0086] Linear two-degree-of-freedom vehicle models can characterize the lateral and yaw motions of a vehicle and are often used to construct traditional steering autonomous vehicle models that achieve path tracking, such as... Figure 1 As shown. Figure 1 middle, The vehicle's heading angle; For reference heading angle; The lateral error is the shortest distance from the vehicle's center of gravity to the road centerline.

[0087] Assuming a constant speed and a small front wheel steering angle, then... Figure 1 The following is a traditional steering autonomous vehicle dynamics model:

[0088]

[0089] Wherein: the front wheel differential torque is the lateral velocity; Longitudinal velocity; and These are the lateral stiffness of the front and rear wheels, respectively. and These are the distances from the vehicle's center of gravity to the front and rear axles, respectively. Indicates yaw rate; The steering angle of the front wheels; For the overall vehicle weight; This is the moment of inertia of the vehicle about the vertical direction.

[0090] Cause heading error Let be the difference between the current heading angle and the reference heading angle of the intelligent vehicle, then:

[0091]

[0092] Assuming the intelligent car travels on a reference path with a turning radius of R, its ideal acceleration is... and actual acceleration It can be represented as:

[0093] (3)

[0094] From equation (3), we can derive:

[0095] (4)

[0096] make , , Then equations (2) and (4) can be rewritten as:

[0097] (5)

[0098] in,

[0099] ; .

[0100] 1.2 Dynamics Model of Differential Steering Intelligent Vehicle

[0101] The established dynamic models mainly include: the front wheel differential steering system, the planar dynamics model, and the vertical and roll dynamics models (such as...). Figures 2-4 (As shown).

[0102] Depend on Figure 2 The dynamic model of the front wheel differential steering system can be obtained as follows:

[0103] (6)

[0104] in, It is the equivalent moment of inertia; It's the front wheel steering angle; It is the equivalent steering damping of the steering system; This is the total return torque of the front wheels; ΔT is the frictional torque; ΔT is the difference in steering torque between the front wheels, and ; It is the kingpin offset. It is the radius of the wheel; , These are the driving torques of the left and right front wheels, respectively. This is the total differential torque of the left and right front wheels.

[0105] Based on the tire brush model, It can be represented as:

[0106] (7)

[0107] in, , This refers to the return torque of the left and right front wheels; The tire's contact patch width is half the width of the ground. and This represents the lateral force on the two front wheels; This refers to the front wheel lateral stiffness. The front wheel slip angle, and .

[0108] Combining equations (6) and (7), the dynamic model of the front wheel differential steering system can be expressed as:

[0109] (8)

[0110] in, It is a distractor, and

[0111] Depend on Figure 3 The planar dynamics model of the differential steering intelligent vehicle can be obtained as follows:

[0112] (9)

[0113] in, It is half the wheel track; Where is the sprung mass; h is the distance from the center of mass to the roll axis; The roll angle; and This refers to the lateral force exerted on the front wheels by the ground. and This refers to the lateral force exerted on the rear wheel by the ground. This is a distractor.

[0114] Depend on Figure 4 The vertical and roll dynamics models of the differential steering intelligent vehicle can be obtained as follows:

[0115] (10)

[0116] ;

[0117] ;

[0118] ;

[0119] ;

[0120] in, This represents the vertical displacement of the vehicle body; , , , These are the suspension forces for the left and right front suspensions and the left and right rear suspensions, respectively. This is the moment of inertia of the roll. , , , Unsprung mass; , , , It represents the vertical displacement of each unsprung mass; , , , The tire stiffness of each wheel; , , , The spring stiffness coefficients for the left and right suspensions; , , , These are the damping coefficients of the left and right suspensions; , , , The control force provided by the active suspension; , , , It is the vertical road surface input for each tire.

[0121] 1.3 Reference Model

[0122] The model serves to provide a reference yaw rate and a reference roll angle, the latter acting as a safety threshold for the roll angle. Considering that a linear three-degree-of-freedom vehicle model with neutral steering characteristics can effectively describe the coupling relationship between lateral, yaw, and roll parameters, it is chosen as the reference model.

[0123] set up , Then the reference model can be expressed as:

[0124] (11)

[0125]

[0126] , , .

[0127] in, For reference yaw rate; and These are the lateral velocity and the longitudinal velocity, respectively. For reference front wheel steering angle; and These are the lateral forces of the front and rear wheels, respectively. This is the equivalent tilt stiffness.

[0128] 2. Rollover Evaluation Indicators

[0129] To comprehensively evaluate the rollover stability and ride comfort of intelligent vehicles, the following evaluation indicators were selected to analyze their motion state from two aspects: load transfer characteristics and lateral dynamic response, so as to achieve a comprehensive evaluation of rollover prevention performance and tracking effect.

[0130] 2.1 Lateral load transfer rate

[0131] For non-tripping rollovers of intelligent vehicles, the Load Transfer Ratio (LTR) is used as a key evaluation indicator. It is defined as the ratio of the difference in vertical load between the left and right tires to the sum of the vertical loads on both sides, i.e.:

[0132] (12) Where n is the number of axles of the vehicle, and n=2; F lj F rj Let |LTR| and |LTR| represent the vertical loads of the tires on the j-th axle, respectively. From equation (12), it can be seen that when the vehicle turns, the normal load on the inner wheel decreases while that on the outer wheel increases; therefore, the range of |LTR| is [0,1]. When 0 ≤ |LTR| < 1, the wheels do not leave the ground and no rollover occurs.

[0133] When |LTR|=1, one wheel leaves the ground, causing a rollover.

[0134] From equations (8) to (10), we can obtain the commonly used expressions for calculating LTR:

[0135] (13)

[0136] 2.2 Occupant-perceived lateral acceleration

[0137] This parameter represents the magnitude of the lateral inertial load acting on the occupants during path tracking. As a crucial indicator of vehicle ride smoothness and passenger comfort, its specific expression is:

[0138] (14)

[0139] The first term is the tangential inertial acceleration generated by the roll angle acceleration; the second term is the component of the lateral acceleration generated in the vehicle roll direction; and the third term is the component of gravity generated in the vehicle roll direction.

[0140] 3 Control System

[0141] 3.1 Control Architecture

[0142] Path tracking and rollover prevention control architecture designed for in-wheel motor driven differential steering intelligent vehicles, such as Figure 5 As shown in the figure, the upper-level SMPC controller calculates the reference front wheel angle required for a conventional steering intelligent vehicle to track the reference path based on lateral and heading errors. The reference model then obtains the reference yaw rate and reference roll angle. The lower-level MPC-MFAC controller outputs the front wheel differential torque and four active suspension control forces to enable the differential steering intelligent vehicle to track the reference yaw rate and reference roll angle.

[0143] 3.2 Upper-layer controller

[0144] This paper proposes an improved sliding mode control (SMC) multi-objective model predictive control (SMPC) to achieve high-precision path tracking. The method uses Model Predictive Control (MPC) as the primary control method to handle system constraints and perform rolling optimization, while embedding the convergence characteristics of SMC. Specifically: first, a sliding surface is designed based on sliding mode control theory and used as the convergence objective of the system state; then, a hierarchical weighted multi-objective cost function is designed, and the convergence requirements of the sliding surface are transformed into constraints in the MPC optimization problem. The optimal control quantity is solved through rolling optimization of MPC, driving the system state to asymptotically converge to the sliding surface, ultimately achieving asymptotic convergence of lateral and heading errors. This master-slave fusion structure retains the ability of MPC to handle multi-constraint optimization while leveraging the variable structure characteristics of sliding mode control to enhance the system's robustness to model uncertainties and external disturbances.

[0145] 3.2.1 Sliding surface

[0146] To minimize lateral error and heading error The sliding surface is designed to converge quickly to zero, as shown below:

[0147] (17)

[0148] in, , , , All are weighting coefficients, and all are greater than 0.

[0149] Traditional discrete sliding mode reaching laws are typically as follows:

[0150] (18)

[0151] in, Boundary layer thickness; The approximation law index; and All are positive numbers.

[0152] As can be seen from equation (18), the positive coefficient Determines the system state towards the sliding surface The rate of convergence. When When it increases, The stronger the effect, the faster the state approaches the sliding surface; but if... If the value is too large, the overshoot of the system state when crossing the sliding surface will increase, which will exacerbate chattering. It is a sign function, when Take +1 at time. When -1 is taken, in A jump will occur at that point. It is the amplitude of this jump. The larger the value, the greater the switching amplitude, and the more severe the resulting jitter; to suppress jitter, the value will be reduced. However, this weakens the effect of the switching term and slows down the system's approach to the sliding surface. Therefore, these two terms are independent in the expression and have no dynamic relationship. To increase the approach speed, it is necessary to increase... or To suppress chattering, it is necessary to reduce it. This inverse relationship can be directly reflected in the structure of the expression.

[0153] Considering that the approach law shown in equation (18) is difficult to balance "approach speed" and "bluster" simultaneously ( and Increasing the value exacerbates chattering, while decreasing it slows down the approach. Therefore, an improved adaptive power-law approaching law is designed as follows:

[0154] (19)

[0155] ; ;

[0156] in, , , , , , All are constants; The coefficient of the power term.

[0157] It can be seen from equation (19) that The larger, The larger it is, the faster it approaches the target size. The smaller, The smaller the value, the better it is at suppressing chattering. Furthermore, this reaching law incorporates a power-law characteristic, enabling "rapid approach for large errors and slow sliding for small errors." Therefore, this reaching law exhibits a large equivalent reaching gain when the error is large, improving the system's convergence speed; when the error is small, the reaching term decreases, effectively reducing chattering amplitude. And... You can get points Sliding mode reference value at time .

[0158] 3.2.2 Model Discretization

[0159] set up , , Then equation (5) can be expressed as:

[0160] (20)

[0161] Since the path tracking error model is continuous, it cannot meet the design requirements of the MPC path tracking controller. Therefore, equation (20) must be discretized. The new state-space expression of the system is:

[0162] (twenty one)

[0163] in,

[0164] ; ; ;

[0165] n and m are the dimensions of the state variables and control variables, respectively, and n=4 and m=1.

[0166] The predicted value of the system output variable can be expressed as:

[0167] (twenty two)

[0168] in, ;

[0169] ;

[0170] ;

[0171] For prediction in the time domain; To control the time domain, and .

[0172] 3.2.3 MPC Optimization with Embedded Sliding Mode Constraints

[0173] To achieve convergence of the sliding surface, smooth control increment, and small tracking error, the following weighted multi-objective cost function is constructed:

[0174] (twenty three)

[0175] in, For the predictive sliding mode variables of the MPC controller; , All are weighting coefficients.

[0176] As can be seen from equation (23), this cost function contains two terms: the first term is the sliding mode tracking error term, which aims to force the system state to converge to the sliding mode surface; the second term is the control increment term, which is used to suppress chattering in sliding mode control.

[0177] In actual control systems, the system state variables and control variables also need to meet certain constraints. The constraints on the control variables, control increments, and sliding surfaces are set as follows:

[0178] (twenty four)

[0179] Where: control quantity Front wheel steering angle Its constraints are Control increment The rate of change of the front wheel steering angle Its constraints are .

[0180] To solve the optimization problems in equations (23) and (24), they are generally transformed into quadratic programming (QP) problems before being solved. This is because quadratic programming is a classic optimization problem in mathematics with relatively mature solution methods. Therefore, the optimization problem for model predictive control can be equivalently transformed into solving the following quadratic programming problem:

[0181] (25)

[0182]

[0183] in, .

[0184] To achieve effective control of the intelligent vehicle's path tracking, the system obtains the optimal control increment sequence through online optimization at each sampling time, and applies the first element of the sequence as the actual control increment to the autonomous vehicle. The closed-loop control process of "state update - sliding mode variable evaluation - SMPC rolling optimization" is repeatedly executed, enabling the path tracking error to gradually converge. This also enhances the robustness against model uncertainties and external disturbances, thereby ensuring the stability and reliability of the control process.

[0185] 3.3 Lower-level controller

[0186] from Figure 5 It can be seen that after the upper-level SMPC controller obtains the front wheel steering angle required for a traditional steering intelligent vehicle to track the desired path, and inputs the reference front wheel steering angle into the reference model to obtain the reference yaw rate and reference roll angle, it is also necessary to design a lower-level controller to control the front wheel differential steering torque and active suspension control force in order to reduce the lateral deviation between the actual path and the reference path of the differential steering intelligent vehicle and reduce the risk of vehicle rollover.

[0187] Therefore, an MFAC controller is introduced into the lower-level MPC controller to predict the state variables of the MPC. With actual state quantity Error between Corrections are made to improve the tracking performance and rollover prevention capabilities of the differential steering intelligent vehicle. The MPC-MFAC control block diagram is shown below. Figure 6 As shown.

[0188] from Figure 6 It can be seen that the MPC controller optimizes the objective function under constraints to obtain the basic quantities of the front wheel differential driving torque and the active suspension control force at the current moment. The MFAC controller obtains the compensation amounts for the front wheel differential drive torque and active suspension control force by tracking the predicted state quantities of the MPC. Therefore, the total control output of the lower-level MPC-MFAC controller for the differential steering vehicle is .

[0189] 3.3.1 MPC Controller

[0190] Pick, Then the state-space equations of equations (6)-(10) can be expressed as:

[0191] (26)

[0192] To balance path tracking accuracy and rollover prevention performance, it is necessary to optimize the vehicle's output and control increment. Furthermore, a relaxation factor is introduced to avoid unsolvable situations. Therefore, the objective function and constraints are as follows:

[0193] (27)

[0194]

[0195] Where Q and R are weight matrices; It is a relaxation factor; These are the weighting coefficients.

[0196] Control quantity Basic front wheel differential torque and basic active suspension control force , Constraints , Constraints Control increment Basic front wheel differential torque rate of change and basic active suspension control force The rate of change of , with constraints as follows: , .

[0197] 3.3.2 MFAC Controller

[0198] To further improve the path tracking accuracy of the lower-level MPC control and compensate for uncertainties in the vehicle dynamics model and external disturbances, an MFAC controller is introduced into the MPC controller. The MFAC input is the predicted state variable of the MPC controller. With actual state quantity State deviation between The output is the compensation amount for the front wheel differential torque and the four active suspension control forces.

[0199] At this point, equations (6) to (10) can be designed as a nonlinear discrete-time system as shown in the following equation:

[0200] (28)

[0201] in, For output vector, For the input vector, For an unknown nonlinear function vector, , These are two integers, representing the lengths of the system's input and output signal sequences, respectively.

[0202] For nonlinear discrete-time systems, the following assumptions can be made:

[0203] Assumption 1: Function Regarding input variables Assumption 2: The partial derivatives of the input and output are continuous, and the state of the intelligent vehicle system changes smoothly with the control input. The control system satisfies the Lipschitz condition, ensuring that the rates of change of the input and output are bounded. Then, for any λ and ... There exists a constant b > 0 that satisfies:

[0204] (29)

[0205] in, ;

[0206] ; It is a 2-norm.

[0207] Theorem 1: For nonlinear discrete-time systems (28) that satisfy the above assumptions, a pseudo-Jacobi matrix is ​​introduced to transform the complex nonlinear discrete-time system into an equivalent compact form dynamic linearization (CFDL) mathematical model:

[0208] (30)

[0209] in, .

[0210] Assumption 3: Pseudo-Jacobi matrix It has no physical meaning; it is merely an equivalent linearization tool that satisfies the boundedness diagonal dominance condition, namely:

[0211] (31)

[0212] in, ,and , All are constants greater than 0.

[0213] With state deviation tracking error and control increment smoothness as optimization objectives, the functional expression of the control input criterion is designed as follows:

[0214] (32)

[0215] in, The vehicle state quantity at time k is predicted by the MPC controller at time k-1. Let K be the actual state of the vehicle at time k; φ is the weighting factor, and φ = 1.6.

[0216] Substituting equation (29) into equation (32), we can obtain... Finding the extreme value and introducing a step size factor, the expression for the MFAC controller is obtained as follows:

[0217] (33)

[0218] in, Let step size be the factor, and take... .

[0219] However, due to the pseudo-Jacobi matrix Since the unknown is time-varying, the minimum parameter estimation method is required for real-time estimation to ensure that the estimated value is dynamically updated with the system state. With the fitting error of the linearized model and the smoothness of the estimated value as objectives, the estimation criterion function is constructed as follows:

[0220] (34)

[0221] in, To estimate the weighting factors, take This is used to suppress abrupt changes in the estimated value.

[0222] Finding the extreme value of equation (34), we get The real-time estimation algorithm expression is as follows:

[0223] (35)

[0224] in, Let step size be the factor, and take... .

[0225] Combining equations (33) and (35), the expression for the MFAC controller can be obtained as follows:

[0226] (36)

[0227] In order to The estimation algorithm has a stronger ability to track time-varying parameters by introducing a reset mechanism: when or At that time, there exists ,in, For a very small positive number, take .

[0228] The compensation control quantity of MFAC is superimposed with the basic control quantity of MPC to obtain the total control quantity of front wheel differential force and active suspension control force. And apply it to the differential steering intelligent vehicle.

[0229] In the final simulation, the MFAC controller and the MPC controller synchronously and discretely sample, completing the closed-loop control process of "state deviation calculation - pseudo-Jacobi matrix estimation - compensation control quantity solution - total control quantity output" in each sampling period.

[0230] 4. Simulation Analysis

[0231] To verify the control effect of the control method of the present invention, a joint simulation comparison analysis of CarSim and Simulink was conducted, with the reference path being a double-sliding curve.

[0232] 4.1 Simulation Analysis of Upper-Level Controller

[0233] To verify the path tracking control effect of the upper-level SMPC controller, a simulation comparison was conducted on two traditional steering intelligent vehicles, one using an SMPC controller and the other using an SMC controller. The vehicle speed was 54 km / h, and the simulation time was 15 seconds. The simulation results are as follows: Figures 7-10 As shown.

[0234] The curve of the autonomous vehicle tracking the reference path is as follows Figure 7 As shown. From Figure 7 It can be seen that both the intelligent vehicles using SMC and SMPC controllers can track the reference path. A closer look at the enlarged view shows that the intelligent vehicle using the SMPC controller tracks the reference path more smoothly.

[0235] The lateral error curves and heading error curves of the intelligent vehicle are as follows: Figure 8 and Figure 9 As shown. From Figure 8 and Figure 9 As can be seen, the maximum absolute value of the lateral error of the intelligent vehicle using the SMPC controller is 0.055m, and the maximum absolute value of the heading error is 0.030rad, while those using the SMC controller are 0.23m and 0.066rad, respectively. Compared to the SMC controller, the maximum absolute values ​​of the lateral displacement error and heading error of the intelligent vehicle using the SMPC controller are reduced by 76.09% and 54.55%, respectively. Overall, the standard deviation of the lateral error of the intelligent vehicle under the SMC controller is 0.056m; while the standard deviation of the intelligent vehicle using the SMPC controller is 0.014m, a reduction of 75% in error fluctuation. This indicates that SMPC allows the vehicle to stay more accurately on the reference path, reducing the risk of lane departure. Under the SMC controller, the standard deviation of the heading error is 0.015rad / s; while that of the SMPC controller is 0.004rad / s, a reduction of 73% in error fluctuation. This shows that SMPC can control vehicle steering more smoothly and stably, improving driving smoothness and ride comfort.

[0236] The front wheel steering angle curve of the intelligent vehicle is as follows Figure 10 As shown. From Figure 10 As can be seen, the front wheel steering angle curve output by the SMC controller exhibits obvious jitter during steering processes of approximately 6-7s and 11-13s. In contrast, the front wheel steering angle curve output by the SMPC controller rises and falls more smoothly, returns to 0deg more quickly, and remains stable.

[0237] In summary, the SMPC controller designed in this invention effectively suppresses the chattering that is easily generated by traditional sliding mode control, and can provide a smoother front wheel steering angle for the lower-level differential steering control, thus laying the foundation for the lower-level control.

[0238] 4.2 Simulation Analysis of Hierarchical Controller

[0239] Section 4.1 has verified the path tracking performance of the upper-level SMPC controller. However, in a hierarchical control structure, the accuracy of the reference front wheel steering angle output by the upper-level controller depends on the control performance of the lower-level controller on the vehicle's yaw motion. To verify the advantages of MPC-MFAC in handling the nonlinearity and model parameter uncertainty of differential steering intelligent vehicles, this paper further designs the following two control strategies for comparative analysis: SMPC+MPC (without MFAC compensation) and SMPC+MPC-MFAC. The vehicle speed remains at 54 km / h, and the simulation results are as follows: Figures 11-12 .

[0240] Figure 11 This represents the tracking response of the intelligent vehicle's yaw rate to a reference yaw rate under two control strategies. From... Figure 11 It can be seen that both control schemes can achieve stable tracking of the reference yaw rate. During the period of intense yaw motion (t≈9.3–9.7s), the peak value of the reference yaw rate is approximately 0.35 rad / s, the peak value of the SMPC+MPC-MFAC controller is approximately 0.345 rad / s, and the peak value of the SMPC+MPC controller is approximately 0.331 rad / s. Therefore, after introducing MFAC compensation, the peak tracking error of the yaw rate is reduced from 0.02 rad / s to 0.005 rad / s, a reduction of approximately 75%.

[0241] Figure 12 The response of the front wheel differential torque under two control strategies is presented. It can be seen that the two control schemes maintain a consistent overall trend, both being able to adjust the front wheel differential drive torque according to the yaw motion requirements, and always within the constraints.

[0242] The above results show that MFAC can effectively compensate for model uncertainties in the yaw dynamics of differential steering autonomous vehicles by correcting the deviation between the MPC predicted state and the actual state online, thereby improving the transient tracking accuracy of yaw rate.

[0243] 4.3 Simulation Analysis of Layered Anti-Rollover Controller

[0244] Building upon this, to further verify the path tracking and rollover prevention integrated control performance of the proposed SMPC+MPC-MFAC hierarchical control strategy under high-speed conditions, this paper increases the longitudinal speed of the intelligent vehicle to 100 km / h and compares the two scenarios of "no rollover prevention control" and "with rollover prevention control". The simulation results are as follows: Figure 13 – Figure 21 As shown.

[0245] Figure 13 This describes the path tracking performance of an intelligent vehicle under high-speed conditions. Figure 13 As can be seen, under both control strategies, the intelligent vehicle can complete the overall tracking task of the dual lane change path without obvious divergence or instability, indicating that the constructed hierarchical control framework still has a good stability foundation under high-speed conditions. Compared with the case without anti-rollover control, the lateral offset amplitude during the path straightening phase is slightly reduced after the introduction of anti-rollover control, indicating that the introduction of anti-rollover control does not reduce the path tracking performance of the upper-level SMPC.

[0246] Figure 14 This is the lateral error curve for an intelligent vehicle. From... Figure 14 As can be seen, without rollover prevention control, the absolute value of the vehicle's lateral error peak reached 0.29m, and the oscillation decayed slowly, still showing slight fluctuations after 8 seconds, indicating poor steady-state accuracy. After introducing rollover prevention control, the peak value of the lateral error decreased to 0.22m, with a maximum error reduction of approximately 24.1%; at the same time, the error oscillation decay rate significantly accelerated, basically converging to near 0 after 7 seconds, resulting in a smaller steady-state error and improved path tracking accuracy.

[0247] Figure 15 This is the heading error curve for the intelligent vehicle. From... Figure 15 As can be seen, compared with vehicles without rollover prevention control, the absolute value of the peak heading error under controlled conditions decreased from 0.06 rad to 0.04 rad, a reduction of approximately 33.3%, and the standard deviation of the heading error decreased from 0.016 rad to 0.012 rad, a reduction of approximately 25%. Furthermore, the error oscillation decayed faster, and the steady-state accuracy was higher. This demonstrates that the designed control strategy achieves improvements in lateral stability and path tracking accuracy, verifying the effectiveness and robustness of the algorithm.

[0248] Figure 16 The figure shows the yaw rate tracking response of the intelligent vehicle. As can be seen from Figure 16, the overall trend and peak position of the yaw rate of the intelligent vehicle are basically consistent with those of the two cases with and without anti-rollover control. The peak value of the yaw rate is 0.661 rad / s, and it can track the reference yaw rate well in both cases. This indicates that the introduction of anti-rollover control has not affected the basic control performance of the lower differential steering system on yaw motion.

[0249] Figure 17 This describes the roll angle response of the intelligent vehicle. Figure 17 It can be seen that without rollover prevention control, the roll angle amplitude of the intelligent vehicle increases significantly during steering, especially with a noticeable peak around 5.5 seconds. The peak amplitude of 0.116 rad is much larger than the reference roll angle of 0.037 rad, indicating that the vehicle body is already in a relatively dangerous roll state at this point, and the risk of rollover increases significantly. However, after introducing rollover prevention control, the reference roll angle can be tracked better, and the peak roll angle is effectively suppressed, with its maximum value significantly reduced to 0.039 rad, a decrease of approximately 64.6%.

[0250] Figure 18 This shows the variation in the lateral load transfer rate. From... Figure 18 It can be seen that without rollover mitigation control, the lateral load transfer rate increases during high-speed steering, with a peak value of 0.891, indicating a significant reduction in the vertical load on the inner wheel and a high risk of tire lift-off for the intelligent vehicle. After introducing rollover mitigation control, the absolute value of the peak LTR decreases to 0.426, a reduction of approximately 52.2%. This demonstrates that the rollover mitigation control strategy can improve tire contact stability of the intelligent vehicle by actively adjusting suspension forces to alleviate the uneven load distribution between the inner and outer tires.

[0251] Figure 19 The comparison results show the lateral acceleration perceived by the occupants. From Figure 19 As can be seen, under high-speed conditions, the overall lateral acceleration of the intelligent vehicle is significantly higher than that at 54 km / h. After introducing anti-rollover control, its peak value is reduced by about 33%. This indicates that the proposed anti-rollover control strategy improves vehicle stability and ride comfort to a certain extent, without introducing additional severe lateral impact.

[0252] Figure 20 This describes the response of the four active suspension control forces under high-speed operating conditions. Figure 20 It can be seen that the intelligent vehicle outputs active suspension control force, forming anti-roll moment on both sides of the vehicle body, and the absolute value of the peak value of the active suspension is 27080N, which is always within the constraint range.

[0253] Figure 21 The results of the front wheel differential torque response are as follows: Figure 21 It can be seen that after the introduction of anti-rollover control, the overall trend of the front wheel differential torque is basically the same as that without anti-rollover control, with a maximum peak value of 485.2 Nm. This indicates that anti-rollover control mainly shares the roll suppression task through active suspension, avoiding the increase in control burden by simply relying on differential steering, thus helping to maintain the working stability of the differential steering system.

[0254] comprehensive Figures 13-21Simulation results show that at 100 km / h, the proposed SMPC+MPC+MFAC hierarchical control strategy reduces the vehicle roll angle by approximately 64.6% while maintaining path tracking and yaw rate tracking performance, and consistently tracks the reference roll angle well. Simultaneously, the absolute value of the peak lateral load transfer rate is reduced by approximately 52.2%, lowering the risk of tire liftoff. Furthermore, the peak value of occupant-perceived lateral acceleration is reduced by approximately 33%, indicating that rollover prevention control improves ride comfort while enhancing driving stability. These results further validate the effectiveness and robustness of the proposed control strategy under extreme high-speed conditions.

[0255] 5. Conclusion

[0256] To address the issues of insufficient path tracking accuracy and poor rollover stability in hub motor-driven differential steering autonomous vehicles, a hierarchical control strategy combining SMPC and MPC-MFAC is proposed. The main research conclusions are as follows:

[0257] (1) The upper-level SMPC controller combines the robustness of sliding mode control with the optimization of model predictive control. By improving the adaptive power-law approaching law, it balances the approaching speed and chattering problem of sliding mode control. Simulation results show that, compared with the traditional SMC controller, the SMPC controller reduces the maximum absolute values ​​of the lateral displacement error and heading error of the intelligent vehicle by 76.09% and 54.55%, respectively, and the output reference front wheel angle is smoother, laying a good foundation for the lower-level control.

[0258] (2) The lower-level MPC-MFAC controller effectively solves the nonlinearity and model parameter uncertainty problems of differential steering intelligent vehicles. By using MFAC to compensate for the prediction state deviation of MPC online, the peak tracking error of yaw rate is reduced by about 75%, improving the tracking accuracy of reference yaw rate. At the same time, the controller integrates active suspension anti-rollover control logic, which can achieve roll angle tracking by controlling the four active suspension control forces.

[0259] (3) Multi-condition simulation verification shows that the proposed hierarchical control strategy exhibits good control performance at 100km / h high speed. The peak roll angle is reduced by about 64.6%, the absolute value of the peak lateral load transfer rate is reduced by about 52.2%, and the peak occupant perceived lateral acceleration is reduced by 33%, without affecting the path tracking and yaw rate tracking performance, thus achieving optimization of stability, tracking accuracy and ride comfort.

[0260] Although the present invention has been described above with reference to embodiments, the features in the disclosed embodiments can be combined with each other in any way. The fact that these combinations are not exhaustively described in this specification is merely for the purpose of saving space and resources. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle, characterized in that, Includes the following steps: S1. Establish the path tracking error model, differential steering dynamics model, and reference model of the intelligent vehicle; S2. Based on the path tracking error model, an improved sliding mode multi-objective model predictive controller (SMPC) is used for upper-level control to calculate the reference front wheel angle required for tracking the reference path. S3. Input the reference front wheel steering angle into the reference model to generate the reference yaw rate and the reference roll angle; S4. Based on the differential steering dynamics model, a model predictive-model-free adaptive controller (MPC-MFAC) is used for lower-level control. According to the reference yaw rate and the reference roll angle, the front wheel differential torque and active suspension control force are calculated and output to achieve tracking of the reference yaw rate and the reference roll angle.

2. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 1, characterized in that, The control steps of the improved sliding mode multi-objective model predictive controller (SMPC) are as follows: The sliding surface is designed based on sliding mode control theory and used as the convergence target of the system state. The expression for the sliding surface is as follows: ;in, , , , All are weighting coefficients, and all are greater than 0. For lateral error, This represents the rate of change of the lateral error. For heading error, This represents the rate of change of heading error. Design an adaptive power-law approach to generate sliding mode reference values. The expression for the adaptive power-approach law is: ;in, , , , , , All are constants; The coefficient of the power term; Using the sliding surface and the sliding reference value The tracking error and the control increment are used as optimization objectives. A multi-objective cost function is constructed, and the optimal control quantity is solved by rolling optimization of model predictive control to drive the system state to converge to the sliding surface.

3. The method for path tracking and rollover prevention control of a hub motor-driven differential steering intelligent vehicle according to claim 2, characterized in that, The expression for the multi-objective cost function is as follows: ;in, To predict sliding mode variables, This is a sliding mode reference value. To control the increment, , These are the weighting coefficients. To predict the time domain, To control the time domain.

4. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 1, characterized in that, The Model Predictive-Model-Free Adaptive Controller (MPC-MFAC) control steps are as follows: Based on the reference yaw rate, the reference roll angle, and the differential steering dynamics model, the MPC controller, under the condition of satisfying the first preset constraint, optimizes the first cost function to obtain the basic front wheel differential torque and the basic active suspension control force. The MFAC controller predicts the vehicle state at time k based on the MPC controller. Compared with actual vehicle state quantity Deviation between The front wheel differential torque compensation and active suspension control force compensation are calculated using a model-free adaptive control algorithm. The basic front wheel differential torque is added to the front wheel differential torque compensation to obtain the final front wheel differential torque. The basic active suspension control force is added to the active suspension control force compensation to obtain the final active suspension control force.

5. The method for path tracking and rollover prevention control of a hub motor-driven differential steering intelligent vehicle according to claim 4, characterized in that, In the MFAC controller, the model-free adaptive control algorithm calculates the compensation control quantity in the following manner: The system is equivalent to a compact-form dynamic linearization model: ;in, The system output vector corresponds to the compensation amount. The system input vector corresponds to the state deviation. , It is a pseudo-Jacobi matrix; The pseudo-Jacobi matrix is ​​estimated online using a minimum parameter estimation algorithm with a reset mechanism. ; The control input at the current moment is calculated using the following formula. ;in, Step size factor As a weighting factor, For the desired output, For system input, This is an estimate of the pseudo-Jacobi matrix.

6. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 5, characterized in that, The pseudo-Jacobi matrix The estimation algorithm includes a reset mechanism: when the condition is met... or At that time, the pseudo-Jacobi matrix Reset to initial estimate .

7. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 1, characterized in that, In step S1, the differential steering dynamics model includes the front wheel differential steering system dynamics model, the expression of which is: ;in, It is the equivalent moment of inertia. It's the front wheel steering angle. It is the equivalent steering damping of the steering system. This is the total self-aligning torque of the front wheels. ΔT is the frictional torque, and ΔT is the difference in steering torque between the front wheels.

8. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 1, characterized in that, In step S3, the reference model is a linear three-degree-of-freedom vehicle model with neutral steering characteristics, and its expression is: ; , , ;in, For reference yaw rate, and These are lateral velocity and longitudinal velocity, respectively. For reference to the front wheel steering angle, and These are the lateral forces of the front and rear wheels, respectively. This is the equivalent tilt stiffness.

9. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 1, characterized in that, During the control process, the lateral load transfer rate (LTR) and / or occupant-perceived lateral acceleration are also calculated in real time. As an indicator for evaluating rollover prevention performance and ride comfort; The lateral load transfer rate (LTR) is calculated using the following formula: The occupant senses lateral acceleration. Calculated using the following formula: 。 10. The method for path tracking and rollover prevention control of a hub motor driven differential steering intelligent vehicle according to claim 1, characterized in that, In step S2, the improved sliding mode multi-objective model predictive controller (SMPC) imposes constraints on the control quantity and control increment. The control quantity is the front wheel steering angle δ, with a constraint range of ±35°, and the control increment is the front wheel steering angle change rate Δδ, with a constraint range of ±10° / s. In step S4, the model predictive controller (MPC) imposes constraints on the control quantity and control increment. The control quantity includes: the basic front wheel differential torque. Its constraint range is ±800 N·m; basic active suspension control force , i=1,2,3,4, with a constraint range of ±30000 N; the control increment includes: the basic front wheel differential torque change rate, with a constraint range of ±50 N·m / s; the basic active suspension control force change rate, with a constraint range of ±3000 N / s.

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