A method for tracking the takeoff path of a flying car based on model predictive control

Abstract

This invention discloses a method for tracking the takeoff path of a flying car based on model predictive control, comprising the following steps: S1: Obtaining a reference path corresponding to the quadrotor flying vehicle; S2: Establishing an airborne model and a ground model of the quadrotor flying vehicle based on its dynamic model and the vehicle's dynamic model, and establishing a connection between the two; S3: Obtaining the state and control variables at the current moment, establishing an MPC prediction model based on the airborne model and the ground model, inputting the reference path, the state and control variables at the current moment into the MPC prediction model to obtain the control increment at the current moment, and predicting the state variables at the next moment; using an objective function for real-time optimization to minimize the error between the reference path and the actual path of the quadrotor flying vehicle; S4: Applying the control increment at the current moment to the quadrotor flying vehicle to ensure that the quadrotor flying vehicle can accurately track the reference path.

Description

Technical Field

[0001] This invention relates to the field of aircraft control technology, and in particular to a method for tracking the takeoff path of a flying car based on model predictive control. Background Technology

[0002] Quadcopter flying vehicles, commonly known as quadcopters or quadcopters, are multi-rotor aircraft with four rotors. They are powered by four electric motors driving propellers to achieve vertical takeoff and landing and flight control. They belong to the category of vertical takeoff and landing unmanned aerial vehicles (UAVs) and are widely used in both civilian and military fields due to their ease of operation, high maneuverability, and good stability.

[0003] Quadrone flying vehicles control their attitude and position by adjusting the rotational speeds of their four motors to change the rotor speed. Specifically, when vertical ascent is needed, the output power of all four motors is increased, increasing the rotor speed and total thrust. When the total thrust is sufficient to overcome the weight of the entire aircraft, it lifts off the ground and ascends vertically. Conversely, decreasing the output power of the four motors causes the aircraft to descend vertically. Furthermore, by adjusting the differences in the rotational speeds of the different motors, pitch, roll, and yaw movements can be achieved, thus enabling comprehensive control of the aircraft.

[0004] For quadcopter vehicles, taking off while in motion increases their maneuverability. Path tracking is a crucial factor for their normal and safe operation, and prediction error is an effective way to improve path tracking. Currently, quadcopter vehicles take off by vertically ascending via their rotors after the vehicle has come to a complete stop. This means that a quadcopter needs to be stationary on a stable ground or platform before increasing rotor speed to generate sufficient lift, allowing the vehicle to ascend vertically. This stationary takeoff method limits the quadcopter's maneuverability and rapid response capabilities. Quadrotors taking off while in motion offer better maneuverability, but existing quadcopters using this method have discrepancies between their actual flight path and the reference path, resulting in poor path tracking. Summary of the Invention

[0005] In view of the above-mentioned prior art, the present invention provides a method for tracking the takeoff path of a flying car based on model predictive control, which mainly solves the technical problems existing in the background art.

[0006] To achieve the above objectives, the technical solution of this invention is implemented as follows:

[0007] A method for tracking the takeoff path of a flying car based on model predictive control includes the following steps:

[0008] S1: Obtain the reference path corresponding to the quadcopter flying vehicle;

[0009] S2: Based on the dynamic model of the quadcopter, establish an aerial model of the quadcopter; based on the vehicle's dynamic model, establish a ground model of the quadcopter; and establish a connection between the aerial model and the ground model.

[0010] S3: Obtain the state and control variables at the current moment, establish an MPC prediction model based on the air model and the ground model, input the reference path, the state and control variables at the current moment into the MPC prediction model, obtain the control increment at the current moment, and predict the state variables at the next moment; use the objective function to optimize in real time and minimize the error between the reference path and the actual path of the quadcopter.

[0011] S4: Apply the control increment of the next moment to the quadcopter vehicle to enable the quadcopter vehicle to track the reference path.

[0012] Optionally, the aerial model is:

[0013]

[0014] in, Let X represent the velocity along the X, Y, and Z axes in a coordinate system with Earth as the reference point. Let X be the acceleration along the X, Y, and Z axes in a coordinate system with Earth as the reference point. The velocity of the attitude angle of the quadcopter. K is the acceleration of the attitude angle of the quadcopter. ftx ,K fty ,K ftz These are the drag coefficients (K) of the quadcopter on the X, Y, and Z axes. fax ,K fay ,K faz The coefficient of air resistance friction along the X, Y, and Z axes, I x ,I y ,I z This represents the moment of inertia of the UAV body about its coordinate system.

[0015]

[0016] Where ω1, ω2, ω3, and ω4 are the rotational speeds of each rotor, and K p It is the lift coefficient, K d It is the air drag coefficient, U i(i = 1, 2, 3, 4) represents the actual control inputs of the quadcopter drone. U1 controls the vertical motion of the quadcopter drone, U2 controls the roll motion of the quadcopter drone, U3 controls the pitch motion of the quadcopter drone, and U4 controls the yaw motion of the quadcopter drone.

[0017] Optionally, the ground model is:

[0018]

[0019] in, These represent the positions of the vehicle's center of mass in the world coordinate system. Let ω be the vehicle's heading angle. c v is the yaw rate about the Z-axis, δ is the front wheel steering angle, and v x Let v be the velocity of the vehicle along the x-axis at its center of mass. y Let F be the velocity of the vehicle in the y-axis direction at its center of mass. D C is the longitudinal force acting on the center of mass. w C is the air drag coefficient. f For rolling resistance, F i,y (i = f, r, representing the front and rear wheels) represents the lateral force of the tires, m is the total mass of the vehicle, and l f l is the distance from the vehicle's center of gravity to the front axle. r I is the distance from the vehicle's center of gravity to the rear axle. z Moment of inertia about the Z-axis;

[0020] The formula for calculating tire lateral force is as follows:

[0021]

[0022] Among them, F y Let α be the tire lateral force, α be the slip angle, B be the stiffness factor, C be the curve shape factor, E be the curvature factor, and S be the lateral force. v For horizontal deformation, S h For vertical deformation;

[0023] The vehicle load distribution can be derived using a formula:

[0024]

[0025] Among them, F zf For the front wheel load, F zr For the rear wheel load, f z Let m be the lift generated by the rotor, m be the mass of the quadcopter, and g be gravity.

[0026] Rotor lift expression:

[0027]

[0028] Where ω1, ω2, ω3, and ω4 are the rotational speeds of each rotor, and K p It is the lift coefficient.

[0029] Optionally, establishing a connection between the aerial model and the ground model includes:

[0030] By altering the rotor lift of the quadcopter flying vehicle, the vertical load of the vehicle is changed, thereby establishing a connection between the aerial model and the ground model. Constraints are set when f... z >mg G D =0.

[0031] Optionally, the step of inputting the reference path, the current state variable, and the control variable into the MPC prediction model to obtain the control increment at the current moment, predicting the state variable at the next moment, and using an objective function for real-time optimization to minimize the error between the reference path and the actual path of the quadcopter vehicle includes:

[0032] S31: Convert the MPC prediction model into a state-space representation. The state equation expression is as follows:

[0033]

[0034] u=[ω1,ω2,ω3,ω4,F D ,δ] T

[0035] Where f(,) is the state transition matrix, ξ(t) is the state variable, u(t) is the control variable, η(t) is the output variable, and C is the output matrix;

[0036] S32: Convert the control quantity into the control increment, and construct new state quantities and new state equations;

[0037] New state variables:

[0038]

[0039] New equation of state:

[0040]

[0041] Δu(k)=u(k)-u(k-1)

[0042] S33: The state quantity at the next moment is predicted by the reference path, the state quantity at the current moment, and the control increment at the current moment;

[0043] S34: Optimize the objective function, change the control increment at the current moment, thereby changing the state quantity at the next moment, reducing the error between the reference path and the actual path of the quadcopter, and apply the control increment at the current moment to the quadcopter.

[0044] S35: Repeat steps S33-S34 until multiple predictions within the prediction time domain are completed.

[0045] Optionally, the objective function is:

[0046]

[0047] Where Q, R, and ρ are the weight matrices for the corresponding terms, and N is the weight matrix for the term. p N c These represent the prediction time domain and the control time domain, respectively; ε is the relaxation factor.

[0048] Optionally, the real-time optimization process using the objective function further includes constraining the state variables, control increments, and output variables of the MPC prediction model, with the following constraints:

[0049]

[0050] Where, Δu min Δu is the minimum value of the output control increment. max To output the maximum value of the control increment, u min u is the minimum value of the input control increment. max η is the maximum value of the input control increment. min η max This represents the hard constraint boundary of the system output.

[0051] Optionally, the output expression in the prediction time domain is:

[0052] Y(k)=Ψ k ξ(k|k)+Θ k ΔU(k)+Φ k D(k)

[0053]

[0054] The beneficial effects of this invention are as follows: Based on the established ground model and air model, an MPC prediction model is constructed. The reference path, the current state variable, and the control variable are input into the MPC prediction model, and the state variable at the next moment is predicted through the MPC prediction model. The objective function is used for real-time optimization to solve for the control increment at the current moment, and the control increment at the current moment is applied to the quadcopter vehicle. Through this method, the quadcopter vehicle can take off while in motion, and the objective function is used to optimize and minimize the error between the reference path and the actual path, so as to ensure that the quadcopter vehicle can accurately track the reference path. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of a model predictive control-based takeoff path tracking method for flying cars provided in an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the aerial model provided in an embodiment of the present invention;

[0057] Figure 3 This is a schematic diagram of the ground model provided in an embodiment of the present invention. Detailed Implementation

[0058] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. In the following description, the expression "some embodiments" refers to a subset of all possible embodiments; however, it should be understood that "some embodiments" can be the same subset or different subsets of all possible embodiments and can be combined with each other without conflict.

[0059] In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention can be practiced without one or more of these details. In other instances, certain technical features well-known in the art have not been described in order to avoid obscuring the invention.

[0060] It should be understood that the present invention can be embodied in various forms and should not be construed as being limited to the embodiments set forth herein. Rather, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Furthermore, the terminology used herein is intended only to describe particular embodiments and is not intended to limit the invention. When used herein, the singular forms “a,” “an,” and “the” are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the terms “compose” and / or “comprising,” when used in this specification, identify the presence of the stated features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups. When used herein, the term “and / or” includes any and all combinations of the associated listed items.

[0061] It should also be noted that when an element is referred to as being "fixed to" another element, it can be directly attached to the other element or there may be an intervening element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or there may be an intervening element. The terms "vertical," "horizontal," "inner," "outer," "left," "right," and similar expressions used herein are for illustrative purposes only and do not represent the only possible implementation.

[0062] To fully understand this invention, a detailed structure will be presented in the following description to illustrate the technical solution proposed by this invention. Optional embodiments of the invention are described in detail below; however, in addition to these detailed descriptions, the invention may have other embodiments.

[0063] Example

[0064] The reference path provides a clear target trajectory for the quadcopter flying vehicle, which needs to fly along this path. However, the quadcopter flying vehicle may be affected by the external environment during actual flight, causing its actual flight path to deviate from the reference path. Therefore, it is very important to dynamically adjust the actual path in real time to track the reference path. Based on this, this invention proposes a flying car take-off path tracking method based on model predictive control.

[0065] Please refer to the attached document. Figure 1 This invention provides a method for tracking the takeoff path of a flying car based on model predictive control, comprising the following steps:

[0066] S1: Obtain the reference path corresponding to the quadcopter flying vehicle;

[0067] S2: Based on the dynamic model of the quadcopter, establish an aerial model of the quadcopter; based on the vehicle's dynamic model, establish a ground model of the quadcopter; and establish a connection between the aerial model and the ground model.

[0068] Specifically, there are two takeoff methods for quadcopter flying vehicles: takeoff from a stationary position and takeoff while in motion. Takeoff from a stationary position means that the quadcopter flying vehicle rises vertically from a stationary state without needing to taxi or move on the ground. Takeoff while in motion, on the other hand, involves the quadcopter flying vehicle taxiing or moving a certain distance on the ground before accelerating and lifting off. Therefore, compared to takeoff from a stationary position, takeoff while in motion reduces takeoff time, is more flexible, and has better adaptability.

[0069] The quadcopter vehicle of this invention takes off while in motion. However, takeoff while in motion has two stages. The first stage is the flight stage when the quadcopter is gliding on the ground and has not yet left the ground. In this stage, the quadcopter is mainly affected by ground friction and gravity. At this time, the acceleration, deceleration and steering of the quadcopter are mainly determined by the contact force between the tires and the ground. Therefore, it is necessary to establish a ground model of the quadcopter based on the vehicle's dynamic model to describe its motion state on the ground. The second stage is the flight stage after the quadcopter leaves the ground. In this stage, after the quadcopter is lifted by the rotor, it is no longer limited by ground friction, but is mainly affected by gravity, rotor lift and air resistance. Therefore, it is necessary to establish an aerial model based on the quadcopter's dynamic model to describe its motion state in the air. The purpose of establishing a connection between the aerial model and the ground model is to better describe the dynamic characteristics of the quadcopter transitioning from the ground to the air and from the air to the ground, thereby describing its behavior at different stages during takeoff and landing and improving the accuracy of flight control.

[0070] S3: Obtain the state and control variables at the current moment, establish an MPC prediction model based on the air model and the ground model, input the reference path, the state and control variables at the current moment into the MPC prediction model, obtain the control increment at the current moment, and predict the state variables at the next moment; use the objective function to optimize in real time and minimize the error between the reference path and the actual path of the quadcopter.

[0071] Specifically, the constructed MPC prediction model can predict the state variables at the next time step. The state variables at the next time step serve as the control input of the MPC prediction model. The objective function is used to optimize the control increment at the current time step. Only the first control increment in the optimized control sequence is applied to the quadcopter vehicle. Then, the MPC prediction model adjusts the state variables (i.e., adjusts the control input) according to the control increment and recalculates the new control increment in the next control cycle. The new control increment is then applied to the quadcopter vehicle again.

[0072] S4: Apply the control increment at the current moment to the quadcopter to enable the quadcopter to track the reference path;

[0073] Specifically, the control increment at the current moment is applied to the quadcopter, thereby adjusting the motor speed of the quadcopter, which in turn changes the thrust and attitude of the quadcopter, enabling the adjustment and tracking of the flight path, until all cycles of prediction are completed, so as to achieve path tracking of the quadcopter.

[0074] As an optional implementation method, please refer to the appendix. Figure 2 The aerial model is as follows:

[0075]

[0076] in, Let X represent the velocity along the X, Y, and Z axes in a coordinate system with Earth as the reference point. Let X be the acceleration along the X, Y, and Z axes in a coordinate system with Earth as the reference point. The velocity of the attitude angle of the quadcopter. K is the acceleration of the attitude angle of the quadcopter. ftx ,K fty ,K ftz These are the drag coefficients (K) of the quadcopter on the X, Y, and Z axes. fax ,K fay ,K faz The coefficient of air resistance friction along the X, Y, and Z axes, I x ,I y ,I z This represents the moment of inertia of the UAV body about its coordinate system.

[0077]

[0078] Where ω1, ω2, ω3, and ω4 are the rotational speeds of each rotor, and K p It is the lift coefficient, K d It is the air drag coefficient, U i(i = 1, 2, 3, 4) represents the actual control inputs of the quadcopter drone. U1 controls the vertical motion of the quadcopter drone, U2 controls the roll motion of the quadcopter drone, U3 controls the pitch motion of the quadcopter drone, and U4 controls the yaw motion of the quadcopter drone.

[0079] In the kinematic equations of the aerial model

[0080]

[0081] v x v y v z These represent the velocities of the flying vehicle in the x, y, and z degrees of freedom, respectively. When taking off from the ground, the drag can be calculated by combining the current ground velocity with the aerodynamic formulas to help the flying vehicle take off more easily. Since the vehicle takes off while in motion, the vehicle's speed in the x and y directions on the ground is also the speed at which it takes off while in motion. These speeds can be used to calculate the drag in each direction during takeoff. Then, by substituting the drag in each direction into the expression of the aerial model, the acceleration in the x, y, and z directions and the acceleration of the attitude angle can be calculated.

[0082] As an optional implementation method, please refer to the appendix. Figure 3 The ground model is as follows:

[0083]

[0084] in, These represent the positions of the vehicle's center of mass in the world coordinate system. Let ω be the vehicle's heading angle. c v is the yaw rate about the Z-axis, δ is the front wheel steering angle, and v x Let v be the velocity of the vehicle along the x-axis at its center of mass. y Let F be the velocity of the vehicle in the y-axis direction at its center of mass. D C is the longitudinal force acting on the center of mass. w C is the air drag coefficient. f For rolling resistance, F i,y (i = f, r, representing the front and rear wheels) represents the lateral force of the tires, m is the total mass of the vehicle, and l f l is the distance from the vehicle's center of gravity to the front axle. r I is the distance from the vehicle's center of gravity to the rear axle. z Moment of inertia about the Z-axis;

[0085] The formula for calculating tire lateral force is as follows:

[0086]

[0087] Among them, Fy Let α be the tire lateral force, α be the slip angle, B be the stiffness factor, C be the curve shape factor, E be the curvature factor, and S be the lateral force. v For horizontal deformation, S h For vertical deformation;

[0088] The vehicle load distribution can be derived using a formula:

[0089]

[0090] Among them, F zf For the front wheel load, F zr For the rear wheel load, f z Let m be the lift generated by the rotor, m be the mass of the quadcopter, and g be gravity.

[0091] Rotor lift expression:

[0092]

[0093] Where ω1, ω2, ω3, and ω4 are the rotational speeds of each rotor, and K p It is the lift coefficient.

[0094] As an optional implementation, the step of establishing a connection between the aerial model and the ground model includes:

[0095] By altering the rotor lift of the quadcopter flying vehicle, the vertical load of the vehicle is changed, thereby establishing a connection between the aerial model and the ground model. Constraints are set when f... z >mg F D =0;

[0096] Specifically, as the rotor lift gradually increases, the vertical load of the quadcopter gradually decreases, causing it to accelerate upwards. When the rotor lift reaches its maximum value, if the weight of the quadcopter is completely offset by the lift, the vertical load of the quadcopter is zero, and the quadcopter will maintain a constant speed of ascent or hover. When the rotor lift decreases, the vertical load of the quadcopter increases, causing it to decelerate and descend or fall. The constraint set here is that when the lift generated by the rotor is sufficient to overcome gravity and provide additional lift, the longitudinal force (force along the flight direction) of the quadcopter is set to zero. This constraint defines the critical point for the quadcopter to transition from the ground model (in contact with the ground) to the air model (in flight), thus establishing a connection between the air model and the ground model.

[0097] As an optional implementation, the step of inputting the reference path, the current state variables, and the control variables into the MPC prediction model to obtain the control increment at the current moment, predicting the state variables at the next moment, and using an objective function for real-time optimization to minimize the error between the reference path and the actual path of the quadcopter vehicle includes:

[0098] S31: Convert the MPC prediction model into a state-space representation. The state equation expression is as follows:

[0099]

[0100] u=[ω1,ω2,ω3,ω4,F D ,δ] T

[0101] Where f(,) is the state transition matrix, ξ(t) is the state variable, u(t) is the control variable, η(t) is the output variable, and C is the output matrix;

[0102] By constructing aerial and ground models, select Let u = [ω1, v2, ω3, ω4, F] be the state variable. D ,δ] T To control the quantity;

[0103] Since the state-space equations are nonlinear, and nonlinear model predictive control (NMPC) cannot meet the real-time requirements of control algorithms, linearization is necessary. Currently, linearization mainly includes two methods: approximate exact linearization and approximate linearization. Exact linearization is complex and highly accurate, but has poor applicability; approximate linearization is simple, has low accuracy, but is widely adaptable. In this invention, approximate linearization is used for linearization, and subsequent optimization is performed using the objective function to reduce errors.

[0104] Specifically, the system operating point is obtained by using a zero-order system hold. Performing a second-order Taylor expansion at the reference point, and ignoring higher-order terms, yields:

[0105]

[0106] In the formula:

[0107]

[0108] Discretization using the forward Euler method yields:

[0109] ξ(k+1)=Aξ(k)+Bu(k)+d(k)

[0110] In the formula:

[0111]

[0112] S32: Convert the control quantity into the control increment, and construct new state quantities and new state equations;

[0113] New state variables:

[0114]

[0115] New equation of state:

[0116]

[0117] Δu(k)=u(k)-u(k-1)

[0118] The control increment is the difference between the control input at the current moment and the control input at the previous moment. Its purpose is to make the control of the underlying actuator smoother. Therefore, the control quantity is converted into the control increment. In the path tracking process of the quadcopter flying vehicle, it is desirable for the control increment to be as small as possible, preferably 0 (that is, the expected state can be achieved by keeping the current control quantity unchanged).

[0119] S33: The state quantity at the next moment is predicted by the reference path, the state quantity at the current moment, and the control increment at the current moment;

[0120] S34: Optimize the objective function, change the control increment at the current moment, thereby changing the state quantity at the next moment, reducing the error between the reference path and the actual path of the quadcopter, and apply the control increment at the current moment to the quadcopter.

[0121] S35: Repeat steps S33-S34 until multiple predictions within the prediction time domain are completed.

[0122] Specifically, the prediction time domain length (the prediction time domain refers to the number of future time steps considered by the MPC prediction model in the optimization problem; the length of the prediction time domain affects how far into the future the MPC prediction model can predict) is set to N. p The control time domain length (referring to the number of control inputs actually applied to the MPC prediction model after each optimization solution) is N. c And N c ≤N p As can be seen from the state equation analysis, if the state variables and control increments at the current time are known, the state variables at the next time can be derived, and thus the state variables in the prediction time domain can be derived. The specific derivation process is as follows:

[0123] Assuming the current time is k, and since the prediction time domain is relatively short, we can assume that in N... pIn the time domain, the system's state matrix With control matrix It remains consistent with time k, that is:

[0124]

[0125] Time k+1:

[0126]

[0127] k+2 time:

[0128]

[0129] k+3 time:

[0130]

[0131] k+N c time:

[0132]

[0133] k+N p time:

[0134]

[0135] The output quantity in the prediction time domain can be derived from the output quantity equation in the state equation:

[0136] Y(k)=Ψ k ξ(k|k)+Θ k ΔU(k)+Φ k D(k)

[0137] In the formula:

[0138]

[0139] As an optional implementation, the objective function is:

[0140]

[0141] Where Q, R, and ρ are the weight matrices for the corresponding terms, and N is the weight matrix for the term. p N c These represent the prediction time domain and the control time domain, respectively; ε is the relaxation factor.

[0142] Accurate and stable following of the desired path are two important indicators of path tracking control. On the one hand, accuracy is reflected in the accumulation of errors between the actual position and the reference position during vehicle operation. Therefore, the first term of the objective function is the future predicted state variable minus the future reference state variable, reflecting the quadcopter controller's ability to follow the desired path, making the quadcopter's posture as close as possible to the reference path to achieve the tracking purpose. On the other hand, stability is closely related to the rate and magnitude of change of the front wheel steering angle. Frequent steering will lead to a decrease in the vehicle's lateral stability. Therefore, the second term of the objective function consists of the input increment that needs to be increased, reflecting the vehicle's driving stability during the tracking process. The third term is the addition of a relaxation factor to ensure that a feasible solution can be found in each control cycle.

[0143] Since the objective function is a quadratic optimization problem with multiple constraints, it can be transformed into a standard quadratic programming problem to find the minimum value of the objective function and thus reduce errors. The specific form of quadratic programming (QuadProg, QP) is as follows:

[0144]

[0145] Where H is the Hessian matrix, G is the gradient matrix, and x is the variable to be solved;

[0146] Therefore, the MPC prediction model calculates the required control increment based on the current state of the quadcopter and the reference path, and then applies this increment to the current state variable to predict and generate the state variable at the next moment. This process is repeated, and the objective function is used for optimization. The control increment is fed back in real time to adjust the state variable at the next moment, reduce the deviation between the reference path and the actual path, and at the same time apply the control increment at the current moment to the quadcopter to control the speed of the quadcopter motor and adjust the flight attitude of the quadcopter.

[0147] As an optional implementation, the real-time optimization process using the objective function further includes constraining the state variables, control increments, and output variables of the MPC prediction model. The constraint conditions are as follows:

[0148]

[0149] Where, Δu min Δu is the minimum value of the output control increment. max To output the maximum value of the control increment, u min u is the minimum value of the input control increment. max η is the maximum value of the input control increment. min η max The hard constraint boundary for the system output;

[0150] By setting constraints, the range of changes in control increments and state variables can be limited, reducing control deviations caused by uncertainties in the MPC prediction model or external disturbances, and ensuring that the system operates within a safe range.

[0151] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for tracking the takeoff path of a flying car based on model predictive control, characterized in that, Includes the following steps: S1: Obtain the reference path corresponding to the quadcopter flying vehicle; S2: Based on the dynamic model of the quadcopter, establish an aerial model of the quadcopter; based on the vehicle's dynamic model, establish a ground model of the quadcopter; and establish a connection between the aerial model and the ground model. The ground model is as follows: in, These represent the positions of the vehicle's center of mass in the world coordinate system. Let ω be the vehicle's heading angle. c v is the yaw rate about the Z-axis, δ is the front wheel steering angle, and v x Let v be the velocity of the vehicle along the x-axis at its center of mass. y Let F be the velocity of the vehicle in the y-axis direction at its center of mass. D C is the longitudinal force acting on the center of mass. w C is the air drag coefficient. f For rolling resistance, F i,y (i = f, r, representing the front and rear wheels) represents the lateral force of the tires, m is the total mass of the vehicle, and l f l is the distance from the vehicle's center of gravity to the front axle. r I is the distance from the vehicle's center of gravity to the rear axle. z Moment of inertia about the Z-axis; The formula for calculating tire lateral force is as follows: Among them, F y Let α be the tire lateral force, α be the slip angle, B be the stiffness factor, C be the curve shape factor, E be the curvature factor, and S be the lateral force. v For horizontal deformation, S h For vertical deformation; The vehicle load distribution can be derived using a formula: Among them, F zf For the front wheel load, F zr For the rear wheel load, f z Let m be the lift generated by the rotor, m be the mass of the quadcopter, and g be gravity. Rotor lift expression: Where ω1, ω2, ω3, and ω4 are the rotational speeds of each rotor, and K p It is the lift coefficient; The process of establishing a connection between the aerial model and the ground model includes: By altering the rotor lift of the quadcopter flying vehicle, the vertical load of the vehicle is changed, thereby establishing a connection between the aerial model and the ground model. Constraints are set when f... z >mg F D =0; S3: Obtain the state and control variables at the current moment, establish an MPC prediction model based on the air model and the ground model, input the reference path, the state and control variables at the current moment into the MPC prediction model, obtain the control increment at the current moment, and predict the state variables at the next moment; use the objective function to optimize in real time and minimize the error between the reference path and the actual path of the quadcopter. S4: Apply the control increment at the current moment to the quadcopter to enable the quadcopter to track the reference path.

2. The method for tracking the takeoff path of a flying car based on model predictive control according to claim 1, characterized in that, The aerial model is: in, Let X represent the velocity along the X, Y, and Z axes in a coordinate system with Earth as the reference point. Let X be the acceleration along the X, Y, and Z axes in a coordinate system with Earth as the reference point. The velocity of the attitude angle of the quadcopter. Let K be the acceleration of the quadcopter's attitude angle, and K be the drag coefficients of the quadcopter along the X, Y, and Z axes. fax ,K fay ,K faz The coefficient of air resistance friction along the X, Y, and Z axes, I x ,I y ,I z This represents the moment of inertia of the UAV body about its coordinate system. Where ω1, ω2, ω3, and ω4 are the rotational speeds of each rotor, and K p It is the lift coefficient, K d It is the air drag coefficient, U i (i = 1, 2, 3, 4) represents the actual control inputs of the quadcopter drone. U1 controls the vertical motion of the quadcopter drone, U2 controls the roll motion of the quadcopter drone, U3 controls the pitch motion of the quadcopter drone, and U4 controls the yaw motion of the quadcopter drone.

3. The method for tracking the takeoff path of a flying car based on model predictive control according to claim 1, characterized in that, The process involves inputting the reference path, the current state variables, and the control variables into the MPC prediction model to obtain the control increment at the current moment, predicting the state variables at the next moment, and using an objective function for real-time optimization to minimize the error between the reference path and the actual path of the quadcopter vehicle; including: S31: Convert the MPC prediction model into a state-space representation. The state equation expression is as follows: u=[ω1,ω2,ω3,ω4,F D ,d] T Where f(,) is the state transition matrix, ξ(t) is the state variable, u(t) is the control variable, η(t) is the output variable, and C is the output matrix; S32: Convert the control quantity into the control increment, and construct new state quantities and new state equations; New state variables: New equation of state: Δu(k)=u(k)-u(k-1) S33: The state quantity at the next moment is predicted by the reference path, the state quantity at the current moment, and the control increment at the current moment; S34: Optimize the objective function, change the control increment at the current moment, thereby changing the state quantity at the next moment, reducing the error between the reference path and the actual path of the quadcopter, and apply the control increment at the current moment to the quadcopter. S35: Repeat steps S33-S34 until multiple predictions within the prediction time domain are completed.

4. The method for tracking the takeoff path of a flying car based on model predictive control according to claim 3, characterized in that, The objective function is: Where Q, R, and ρ are the weight matrices for the corresponding terms, and N is the weight matrix for the term. p N c These represent the prediction time domain and the control time domain, respectively; ε is the relaxation factor.

5. The method for tracking the takeoff path of a flying car based on model predictive control according to claim 4, characterized in that, The real-time optimization process using the objective function also includes constraining the state variables, control increments, and output variables of the MPC prediction model. The constraints are as follows: Where, Δu min Δu is the minimum value of the output control increment. max To output the maximum value of the control increment, u min u is the minimum value of the input control increment. max η is the maximum value of the input control increment. min η max This represents the hard constraint boundary of the system output.

6. The method for tracking the takeoff path of a flying car based on model predictive control according to claim 5, characterized in that, The output expression in the prediction time domain is: Y(k)=Ψ k ξ(k|k)+Θ k ΔU(k)+Φ k D(k)

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