Flight height control and trajectory tracking method for hovercar in land-air dual mode

Abstract

The invention discloses a flying height control and trajectory tracking method for an aerocar in a ground-air dual mode, and the method comprises the following steps: 1, building a four-rotor aerocar dynamics model in a flying state; 2, designing a height controller based on adaptive RBF neural network sliding mode control according to the four-rotor aerocar dynamics model established in the step 1, and controlling the flight height by dynamically adjusting the rotating speed of a motor; and step 3, in a ground driving state, establishing a vehicle trajectory tracking model, designing a linear model prediction control algorithm, and outputting a required front wheel turning angle to realize trajectory tracking control. According to the method, air-ground dual-mode control of the hovercar is innovatively provided, and operation and control of the hovercar are well achieved.

Description

Technical Field

[0001] This invention belongs to the field of flying car technology, specifically relating to a method for flight altitude control and trajectory tracking of a flying car in both land and air modes. Background Technology

[0002] Flying cars, with their strong adaptability and ability to perform various tasks, have not only become a new option for future urban transportation, but also play a vital role in sustainable mobility and transportation systems. However, the power system of flying cars makes their control strategies more complex, which places higher demands on their control effectiveness and modeling accuracy.

[0003] Dual-mode control of flying cars refers to how to control the stable altitude of the flying car in flight and its tracking along a planned path when driving on the ground. Scholars both domestically and internationally have conducted extensive research in this area, proposing many advanced control methods such as optimal control, robust control, and active interference rejection control. For example, Chinese patent CN118810311A discloses a flying car and its control method, which uses redundant rotors and engine switching to provide emergency lift in the event of a main flight system failure. While this invention has a certain effect on improving flight safety, it fails to fully consider the system reliability risks caused by redundant system start-up delays, engine power response lags, and fuel dependence, and its overall survivability under extreme flight conditions remains insufficient.

[0004] Despite the numerous methods proposed, many shortcomings remain in the control of flying cars, and many unresolved issues persist in the control of dual-mode (land and air). This demonstrates that the flying car control system within this technology exhibits significant technological immaturity. Summary of the Invention

[0005] The purpose of this invention is to provide a method for flight altitude control and trajectory tracking in dual-mode (land and air) operation of a flying car, in order to solve the problems of model uncertainty and external disturbances existing in the existing dual-mode operation control methods for flying cars.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for flight altitude control and trajectory tracking of a flying car in both land and air modes includes the following steps:

[0008] Step 1: Establish a dynamic model of the quadcopter flying car in flight mode;

[0009] Step 2: Based on the quadcopter flying car dynamics model established in Step 1, design an altitude controller based on adaptive RBF neural network sliding mode control, and control the flight altitude by dynamically adjusting the motor speed.

[0010] Step 3: Under ground driving conditions, establish a vehicle trajectory tracking model, design a linear model predictive control algorithm, output the required front wheel steering angle, and realize trajectory tracking control.

[0011] Furthermore, in step 1, the quadcopter flying car dynamics model includes a flying car structural model, a motor model, and a propeller model.

[0012] Furthermore, step 1 includes the following sub-steps:

[0013] Step 1.1, establish the flying car structural model:

[0014] In the force analysis of flying cars, Indicates the geodetic coordinate system. The vehicle body coordinate system is represented; the relationship between these two systems is expressed as:

[0015]

[0016] in, , , , , , , Indicates the position within the system. Indicates the position in the geodetic coordinate system. Represents the transfer matrix. , and Representing the coordinates in the geodetic coordinate system , and The included angle of the axis;

[0017] definition ,in, , and These represent the flying car orbiting in the vehicle's fixed coordinate system. , and The angular velocity vector of the axis; by express:

[0018]

[0019] The lift of a propeller is expressed as:

[0020]

[0021] in, This indicates the distance between the propeller and its main body. This represents the lift of the four propellers. ;

[0022] The torque of a force is expressed as:

[0023]

[0024] In the formula, Indicates the motor speed. , Indicates the reaction torque coefficient. , and These represent the aerodynamic drag coefficients in the three directions of the geodetic coordinate system. Indicates lift torque. Indicates the propeller reaction torque. Indicates air resistance torque;

[0025] The control input of the flying car is determined by the lift generated by the propeller, and is expressed as... , These inputs are represented as:

[0026]

[0027] in, , and Representing the coordinate system of the flying car around its body , and Moment of inertia of the shaft;

[0028] By combining the above equations, the translational motion of the flying car can be expressed as:

[0029]

[0030] The rotation of a flying car is written as:

[0031]

[0032] in, , and These represent the lift interference from the flying car in three directions. , and These represent the disturbances to the rotational torque in three directions of the flying car;

[0033] Step 1.2, establish the motor model:

[0034] The flying car uses a brushless DC motor, and the motor's motion equation is expressed as:

[0035]

[0036] Among them, subscript The variable representing armature voltage, subscript The variable representing the excitation voltage. , , and These represent resistance, inductance, current, and voltage, respectively. Represents the electromotive force coefficient. Indicates magnetic flux. Indicates the motor's rotational speed. This represents the moment of inertia of the motor. It represents the electromagnetic torque of the motor, used to accurately calculate the thrust of the propeller;

[0037] Step 1.3, Create a propeller model:

[0038] The propeller thrust is obtained by varying the rotational speed:

[0039]

[0040] in, Indicates air density, Indicates the propeller coefficient. Indicates the propeller diameter. This represents the thrust coefficient.

[0041] Furthermore, in step 2, an altitude controller based on adaptive RBF neural network sliding mode control is designed, including a system description under flight conditions, sliding mode controller design, and RBF neural network approximation.

[0042] Furthermore, step 2 includes the following sub-steps:

[0043] Step 2.1, describe the vehicle system in flight mode:

[0044] The flight altitude of a flying car is expressed as:

[0045]

[0046] in, Indicates flight altitude. Indicates time, Indicates control gain. Indicates control input, Indicates the system status. For external interference and , The critical value representing external disturbance;

[0047] Define function , The expression for the flight altitude of the flying car described above can be expressed in state-space form as follows:

[0048]

[0049] in , Indicates the vertical speed of the flying car;

[0050] Ideal tracking height ,make The tracking error is defined as:

[0051]

[0052] The sliding surface is designed as follows: , It is a general sliding surface coefficient and Then the derivative of the sliding surface is:

[0053]

[0054] Step 2.2, approximation based on RBF neural network Sliding mode control of functions:

[0055] The RBF neural network algorithm is as follows:

[0056]

[0057] in For network input, Indicates the first The center point vector value of each hidden layer neuron The width of the Gaussian function representing the hidden layer neurons. This is the output of the Gaussian function. For the ideal weights of the network, For the approximation error of the network, and , It is a small positive number;

[0058] Network input The neural network output is:

[0059]

[0060] in, For RBF neural networks, use the Gaussian function.

[0061] Therefore, the control input formula is designed as follows:

[0062]

[0063] in, For switching item gain;

[0064] The adaptive law is designed as follows:

[0065]

[0066] in, It is a positive integer;

[0067] The saturation function sat(s) is used instead of the sign function, i.e.

[0068]

[0069] Where s is the sliding surface. This represents the boundary layer thickness.

[0070] Furthermore, in step 3, the front wheel steering angle is calculated by solving a constrained quadratic programming problem based on the linear model predictive control algorithm.

[0071] Furthermore, step 3 includes the following sub-steps:

[0072] Step 3.1: Establish a kinematic model for vehicle trajectory tracking.

[0073] A trajectory tracking model is established to represent the relationship between the vehicle and the reference trajectory, wherein, This indicates the preview point from the vehicle's center of gravity to the reference trajectory. lateral distance, Indicates the closest point from the vehicle's center of gravity to the reference trajectory. distance, It is the vehicle's actual heading angle. It is the expected heading angle. Indicates the preview distance; ,in It is the aiming time, defined as , and These represent the lower and upper limits of the aiming distance, respectively; It is the predictive range of the controller. It is the time step;

[0074] Based on the relative positional relationship between the vehicle and the reference trajectory, the trajectory tracking model based on single-point preview is as follows:

[0075]

[0076] in, It is a lateral error. It is a heading error. The road curvature represents the reference trajectory. This indicates the yaw rate of the vehicle. , These represent the vehicle's longitudinal and lateral speeds, respectively.

[0077] The longitudinal velocity tracking model is as follows:

[0078]

[0079] in, This refers to the longitudinal force of the car tire. Indicates the mass of the flying car. and These represent the ideal longitudinal velocity and acceleration, respectively.

[0080] Therefore, the state vector of the system is defined as The control vector is The interference vector is And the output vector is defined as The state-space equation of the tracking model is expressed as follows:

[0081]

[0082] in, Indicates the centroid sideslip angle. Indicates the front wheel steering angle. and These represent the lateral stiffness of the front and rear wheels, respectively. and These represent the distances from the center of gravity to the front and rear axles, respectively.

[0083] ,

[0084] ,

[0085] ;

[0086] Step 3.2, Design the trajectory tracking controller

[0087] The trajectory tracking controller is designed using MPC theory, and the vehicle tracking model equations are discretized as follows:

[0088]

[0089] Among them, time from Time's up time, , , ;

[0090] By using discrete state vectors With control vector Combine and expand the state vector It is expressed as:

[0091]

[0092] Combining the above two equations, we obtain the expanded state-space equations:

[0093]

[0094] in, , , ,

[0095] , ;

[0096] The output vector in the prediction time domain is represented as:

[0097]

[0098] in, ,

[0099] ,

[0100] ,

[0101] ,

[0102] ,

[0103] ;

[0104] The objective function of MPC control is defined as:

[0105]

[0106] in, and These are the weight matrices for the system output and control input, respectively. Let be the relaxation factor, and its weight coefficients be... ;

[0107] Considering the feasibility of the actuator, the dynamic constraints are set as follows:

[0108]

[0109] The optimal solution for the MPC-based trajectory tracking controller is transformed into a quadratic programming problem:

[0110]

[0111] in, ,

[0112] ,

[0113] ;

[0114] Solving the transformed quadratic programming problem yields the ideal front wheel steering angle at the corresponding moment.

[0115] The beneficial effects of this invention are as follows:

[0116] 1. An adaptive RBF neural network is used to approximate unknown aerodynamics and parameter perturbations online and is integrated with sliding mode control. A weight update law is designed under the Lyapunov framework to make the height tracking error globally consistent and eventually bounded. Furthermore, chattering is suppressed through a saturation function to reduce actuator wear.

[0117] 2. Using a single-point pre-aiming kinematic model as the core, the air-to-ground state variables are incorporated into the same augmented state space. After discretization, linear MPC is used to solve the constrained quadratic programming in the prediction time domain to achieve the optimal sequence of front wheel steering angles, ensuring that the lateral error of the transition segment converges and meets the hard constraints of the control quantity.

[0118] 3. Establish a coupled dynamic model of motor-propeller-vehicle body, introduce a weighted penalty of energy consumption and control amplitude into the MPC objective function, and use rolling optimization to ensure that the motor operating point is always in the high-efficiency zone, while limiting the transient peak values ​​of speed and torque, and extending the fault-free operation cycle of the system. Attached Figure Description

[0119] Figure 1 This is a flowchart of the method of the present invention;

[0120] Figure 2 Force analysis diagram for a flying car;

[0121] Figure 3 This is a diagram of the kinematic model for trajectory tracking. Detailed Implementation

[0122] The invention will now be further explained with reference to the accompanying drawings.

[0123] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0124] like Figure 1 The diagram shown is an overall framework diagram of sliding mode dynamic height control and linear model predictive control trajectory tracking based on adaptive RBF neural network in an embodiment of the present invention, which includes the following three steps:

[0125] Step 1: In flight mode, establish a quadcopter flying car dynamics model that includes a flying car structure model, a motor model, and a propeller model;

[0126] Step 1 includes the following sub-steps:

[0127] Step 1.1, establish the flying car structural model:

[0128] In the force analysis of flying cars, Indicates the geodetic coordinate system. The vehicle body coordinate system is represented; the relationship between these two systems is expressed as:

[0129]

[0130] in, , , , , , , Indicates the position within the system. Indicates the position in the geodetic coordinate system. Represents the transfer matrix. , and Representing the coordinates in the geodetic coordinate system , and The included angle of the axis;

[0131] definition ,in, , and These represent the flying car orbiting in the vehicle's fixed coordinate system. , and The angular velocity vector of the axis; by express:

[0132]

[0133] The lift of a propeller is expressed as:

[0134]

[0135] in, This indicates the distance between the propeller and its main body. This represents the lift of the four propellers. ;

[0136] The torque of a force is expressed as:

[0137]

[0138] In the formula, Indicates the motor speed. , Indicates the reaction torque coefficient. , and These represent the aerodynamic drag coefficients in the three directions of the geodetic coordinate system. Indicates lift torque. Indicates the propeller reaction torque. Indicates air resistance torque;

[0139] The control input of the flying car is determined by the lift generated by the propeller, and is expressed as... , These inputs are represented as:

[0140]

[0141] in, , and Representing the coordinate system of the flying car around its body , and Moment of inertia of the shaft;

[0142] By combining the above equations, the translational motion of the flying car can be expressed as:

[0143]

[0144] The rotation of a flying car is written as:

[0145]

[0146] in, , and These represent the lift interference from the flying car in three directions. , and These represent the disturbances to the rotational torque in three directions of the flying car;

[0147] Step 1.2, establish the motor model:

[0148] The flying car involved in this invention is electrically powered, therefore employing a brushless DC motor, the motion equation of which is expressed as:

[0149]

[0150] Among them, subscript The variable representing armature voltage, subscript The variable representing the excitation voltage. , , and These represent resistance, inductance, current, and voltage, respectively. Represents the electromotive force coefficient. Indicates magnetic flux. This indicates the motor's rotational speed (in r / min). This represents the moment of inertia of the motor. It represents the electromagnetic torque of the motor, used to accurately calculate the thrust of the propeller;

[0151] Step 1.3, Create a propeller model:

[0152] The propeller thrust is obtained by varying the rotational speed:

[0153]

[0154] in, Indicates air density, Indicates the propeller coefficient. Indicates the propeller diameter. This represents the thrust coefficient.

[0155] Step 2: Based on the quadcopter flying car dynamics model established in Step 1, design an altitude controller based on adaptive RBF neural network sliding mode control, and control the flight altitude by dynamically adjusting the motor speed.

[0156] Among them, an altitude controller based on adaptive RBF neural network sliding mode control is designed, including system description under flight conditions, sliding mode controller design and RBF neural network approximation;

[0157] Step 2 includes the following sub-steps:

[0158] Step 2.1, describe the vehicle system in flight mode:

[0159] Based on the preceding analysis, the flight altitude of the flying car can be expressed as:

[0160]

[0161] in, Indicates flight altitude. Indicates time, Indicates control gain. Indicates control input, Indicates the system status. For external interference and , The critical value representing external disturbance;

[0162] Define function , The expression for the flight altitude of the flying car described above can be expressed in state-space form as follows:

[0163]

[0164] in , Indicates the vertical speed of the flying car;

[0165] Ideal tracking height ,make The tracking error is defined as:

[0166]

[0167] The sliding surface is designed as follows: , It is a general sliding surface coefficient and Then the derivative of the sliding surface is:

[0168]

[0169] Step 2.2, approximation based on RBF neural network Sliding mode control of functions:

[0170] The RBF neural network algorithm is as follows:

[0171]

[0172] in For network input, Indicates the first The center point vector value of each hidden layer neuron The width of the Gaussian function representing the hidden layer neurons. This is the output of the Gaussian function. For the ideal weights of the network, For the approximation error of the network, and , It is a small positive number;

[0173] Network input The neural network output is:

[0174]

[0175] in, For RBF neural networks, use the Gaussian function.

[0176] Therefore, the control input formula is designed as follows:

[0177]

[0178] in, For switching item gain;

[0179] The adaptive law is designed as follows:

[0180]

[0181] in, It is a positive integer;

[0182] Due to modeling uncertainties and significant interference, a large switching term gain is required. This leads to significant chattering. To prevent chattering, a saturation function `sat(s)` can be used instead of the sign function, i.e.

[0183]

[0184] Where s is the sliding surface. This represents the boundary layer thickness.

[0185] Step 3: Under ground driving conditions, establish a vehicle trajectory tracking model, and calculate the front wheel steering angle by solving a constrained quadratic programming problem based on the linear model predictive control algorithm to achieve trajectory tracking control;

[0186] Step 3 includes the following sub-steps:

[0187] Step 3.1: Establish a kinematic model for vehicle trajectory tracking.

[0188] To express the relationship between the vehicle and the reference trajectory, a trajectory tracking model was established, such as... Figure 2 As shown. Among them, This indicates the preview point from the vehicle's center of gravity to the reference trajectory. lateral distance, Indicates the closest point from the vehicle's center of gravity to the reference trajectory. distance, It is the vehicle's actual heading angle. It is the expected heading angle. Indicates the preview distance; ,in It is the aiming time, defined as , and These represent the lower and upper limits of the aiming distance, respectively; It is the predictive range of the controller. It is the time step;

[0189] Based on the relative positional relationship between the vehicle and the reference trajectory, the trajectory tracking model based on single-point preview is as follows:

[0190]

[0191] in, It is a lateral error. It is a heading error. The road curvature represents the reference trajectory. This indicates the yaw rate of the vehicle. , These represent the vehicle's longitudinal and lateral speeds, respectively.

[0192] The longitudinal velocity tracking model is as follows:

[0193]

[0194] in, This refers to the longitudinal force of the car tire. Indicates the mass of the flying car. and These represent the ideal longitudinal velocity and acceleration, respectively.

[0195] Therefore, the state vector of the system is defined as The control vector is The interference vector is And the output vector is defined as The state-space equation of the tracking model is expressed as follows:

[0196]

[0197] in, Indicates the centroid sideslip angle. Indicates the front wheel steering angle. and These represent the lateral stiffness of the front and rear wheels, respectively. and These represent the distances from the center of gravity to the front and rear axles, respectively.

[0198] ,

[0199] ,

[0200] ;

[0201] Step 3.2, Design the trajectory tracking controller

[0202] The trajectory tracking controller is designed using MPC theory, and the vehicle tracking model equations are discretized as follows:

[0203]

[0204] Among them, time from Time's up time, , , ;

[0205] By using discrete state vectors With control vector Combine and expand the state vector It is expressed as:

[0206]

[0207] Combining the discretized expression of the vehicle tracking model equations and the extended state vector The expression yields the expanded state-space equation:

[0208]

[0209] in, , , ,

[0210] , ;

[0211] The output vector in the prediction time domain is represented as:

[0212]

[0213] in, ,

[0214] ,

[0215] ,

[0216] ,

[0217] ,

[0218] ;

[0219] The objective function of MPC control is defined as:

[0220]

[0221] in, and These are the weight matrices for the system output and control input, respectively. Let be the relaxation factor, and its weight coefficients be... ;

[0222] Considering the feasibility of the actuator, the dynamic constraints are set as follows:

[0223]

[0224] The optimal solution for the MPC-based trajectory tracking controller is transformed into a quadratic programming problem:

[0225]

[0226] in, ,

[0227] ,

[0228] ;

[0229] Solving the transformed quadratic programming problem yields the ideal front wheel steering angle at the corresponding moment.

[0230] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for flight height control and trajectory tracking in air-land dual mode of a flying car, characterized in that: The method comprises the following steps: Step 1, in the flight state, a quad-rotor flying car dynamics model is established; Step 2, according to the quad-rotor flying car dynamics model established in step 1, a height controller based on adaptive RBF neural network sliding mode control is designed, and the flight height is controlled by dynamically adjusting the rotating speed of the motor; Step 3, in the ground driving state, a vehicle trajectory tracking model is established, a linear model predictive control algorithm is designed, and the required front wheel steering angle is output to realize trajectory tracking control.

2. The method of claim 1, wherein: In step 1, the quad-rotor flying car dynamics model comprises a flying car structure model, a motor model and a propeller model.

3. The method according to claim 1 or 2, characterized in that: Step 1 comprises the following sub-steps: Step 1.1, the flying car structure model is established: In the force analysis of the flying car, denotes the earth coordinate system, denotes the vehicle body coordinate system; the relationship between the two systems is represented as: wherein , , , , , , denotes the position in the system, denotes the position in the geodetic coordinate system, denotes the transfer matrix, , and denote the angle to the axes , and of the geodetic coordinate system, respectively; Definitions wherein, , and denote the angular velocity vectors of the flying car around the body-fixed coordinate system's , and axes; is denoted by . The lift of the propeller is represented as: wherein, represents the distance between the propeller and its body, represents the lift of the four propellers, ; The moment of force is represented as: wherein represents the motor speed, , represents the reaction torque coefficient, , and respectively represent the aerodynamic drag coefficients in three directions of the earth coordinate system, represents the lift moment, represents the propeller reaction torque, represents the air resistance moment; The control inputs of the flying car are determined by the lift generated by the propellers and are expressed as , ; these inputs are expressed as: wherein, , and denote the moments of inertia of the flying car about the body coordinate system , and axes, respectively. By combining the above equations, the translational motion of the flying car is represented as: The rotation of the flying car is written as: wherein, , and represent the interference of the lift in three directions of the flying car, respectively, , and represent the interference of the rotational moment in three directions of the flying car, respectively; Step 1.2, the motor model is established: The flying car adopts a brushless direct current motor, and the motion equation of the motor is represented as: wherein the subscript represents a variable of the armature voltage, the subscript represents a variable of the excitation voltage, , , and represent resistance, inductance, current and voltage, respectively; represents an electromotive force coefficient, represents a magnetic flux, represents a rotational speed of the motor, represents a moment of inertia of the motor, represents an electromagnetic torque of the motor, for accurately calculating the thrust of the propeller; Step 1.3, the propeller model is established: Through the rotating speed, the thrust of the propeller is obtained as: wherein, represents the air density, represents the propeller coefficient, represents the propeller diameter, represents the thrust coefficient.

4. The method of claim 1, wherein: In step 2, the height controller based on adaptive RBF neural network sliding mode control is designed, comprising system description in the flight state, sliding mode controller design and RBF neural network approximation.

5. The method according to claim 1 or 4, characterized in that: Step 2 comprises the following sub-steps: Step 2.1, the system of the flying car in the flight state is described: The flight height of the flying car is represented as: wherein denotes the flight altitude, denotes the time, denotes the control gain, denotes the control input, denotes the system state, is an external disturbance and , denotes a threshold value for the external disturbance; Definition of functions , The flight altitude expression of the above-described air car is converted into a state space expression form, which is represented as wherein , represents the vertical velocity of the flying car; Ideal tracking height , let , define the tracking error as: The sliding surface is designed as , is a general sliding surface coefficient and The derivative of the sliding surface is then Step 2.2, RBF neural network approximation based Function-based sliding mode control: The RBF neural network algorithm is: wherein is the input to the network, represents the center point vector value of the th hidden layer neuron, represents the width of the Gaussian function of the hidden layer neuron, is the output of the Gaussian function, is the ideal weight of the network, is the approximation error of the network, and , is a positive number; The input to the network is The neural network output is then: wherein, Gaussian function of RBF neural network; Therefore, the design control input is: wherein, is the switching term gain; The adaptive law is designed as: wherein is a constant; The saturation function sat(s) is used instead of the sign function, that is where s is the sliding surface, is the boundary layer thickness.

6. The method of claim 1, wherein: In step 3, based on the linear model predictive control algorithm, the front wheel steering angle is calculated by solving a quadratic programming problem with constraints.

7. The method of claim 1 or 6, wherein: Step 3 comprises the following sub-steps: Step 3.1, a vehicle trajectory tracking kinematics model is established A trajectory tracking model is established to express the relationship between the vehicle and the reference trajectory, where, represents the lateral distance from the vehicle's center of mass to the preview point on the reference trajectory, represents the distance from the vehicle's center of mass to the nearest point on the reference trajectory, is the actual heading angle of the vehicle, is the desired heading angle, represents the preview distance; where is the preview time, defined as , and represent the lower and upper limits of the preview distance, respectively; is the prediction range of the controller, is the time step.​​ According to the relative position relationship between the vehicle and the reference trajectory, the trajectory tracking model based on single-point preview is: wherein is a lateral error, is a heading error, denotes a road curvature of the reference trajectory, denotes a yaw rate of the vehicle, , denote a longitudinal and lateral velocity of the vehicle, respectively; The longitudinal velocity tracking model is: wherein, is the longitudinal force of the car tire, denotes the mass of the flying car, and denote the ideal longitudinal velocity and acceleration, respectively; The state vector of the system is therefore defined as the control vector as the disturbance vector as and the output vector as The state-space equation of the tracking model is therefore expressed as wherein, denotes the side slip angle of the center of mass, denotes the front wheel steering angle, and denote the front and rear wheel side slip stiffness, respectively, and denote the distance of the center of mass to the front and rear axle, respectively, ， ， ； Step 3.2, a trajectory tracking controller is designed The trajectory tracking controller is designed by using the MPC theory, and the vehicle tracking model equation is discretized as: wherein the time is from to , , , ; By combining the discrete state vector with the control vector the extended state vector is expressed as: Combining the above two formulas, the extended state space equation is obtained: wherein , , , ， ； The output vector in the prediction time domain is represented as: wherein , ， ， ， ， ; The objective function of the MPC control is defined as: wherein, and are weight matrices for system outputs and control inputs, respectively, is a relaxation factor with weight coefficient ; Considering the feasibility of the actuator, the dynamic constraint is set as: The optimal solution of the trajectory tracking controller based on MPC is converted into a quadratic programming problem: wherein , ， ； The quadratic programming problem after conversion is solved, and the ideal front wheel steering angle at the corresponding time is obtained.

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