Ground-air amphibious dual-rotor unmanned aerial vehicle trajectory tracking control method based on NMPC

Abstract

The invention discloses a ground-air amphibious dual-rotor unmanned aerial vehicle trajectory tracking control method based on NMPC, and the method comprises the steps: building a ground-air dual-mode comprehensive dynamic model comprising a motion mode switching variable through fusing an air flight mode and a ground movement mode; based on differential flat characteristic proof, parameterizing state and control input into finite-order derivatives of flat output (position and yaw angle); according to the method, a ground-air dual-mode predictive controller (AGB)-NMPC) is designed, height information is dynamically identified in rolling horizon optimization so as to switch motion modes, and system dynamics constraints are integrated, so that the optimal reference state output from a planned trajectory is tracked. According to the method, the decision variable dimension is effectively reduced, the calculation efficiency is improved, and high-precision robust tracking of the ground-air trajectory is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle (UAV) control, and in particular relates to a ground-to-air dual-mode trajectory tracking control method suitable for a wheel-wing compound dual-rotor UAV. Background Art

[0002] With the widespread application of drone technology in logistics and distribution, disaster search and rescue, and facility inspection, wheel-wing hybrid drones with ground-to-air capabilities have become a research hotspot due to their cross-domain mobility. These drones must seamlessly switch between aerial flight and ground movement in structured environments, and the accuracy and efficiency of their trajectory tracking control directly impact mission performance. However, existing technologies face the following key bottlenecks:

[0003] (1) Problem of splitting the ground-air dynamics model: Current controllers generally adopt a split-model architecture (such as cascade PID), which causes state jumps when switching models, resulting in trajectory tracking jitter.

[0004] (2) Insufficient ability to handle nonlinear constraints: Traditional control methods (such as PID and LQR) have difficulty explicitly handling multi-mode coupling constraints, have poor adaptability to sudden changes in trajectory curvature, and are prone to overshoot when turning. Although some studies have introduced model predictive control (MPC), due to the high dimensionality of decision variables (needing to optimize both state and input), real-time performance is difficult to guarantee.

[0005] (3) Computational efficiency restricts real-time performance: The existing NMPC method directly processes the full-state dynamics equation. The 12-dimensional state space (position + attitude + velocity + angular velocity) leads to an explosion in the dimensionality of the optimization problem. The online solution is time-consuming and cannot meet the requirements of high-speed maneuvers.

[0006] (4) The system structure characteristics are not fully utilized: the existing controller has not considered the differential flatness characteristics of the dual rotor + differential wheel.

[0007] Therefore, designing a ground-to-air trajectory tracking control method with unified dynamic modeling, dimensionality reduction optimization, and strong real-time performance plays an important role in promoting the development and deployment of wheel-wing composite UAVs and enhancing their application value in actual scenarios. Summary of the Invention

[0008] In order to solve the above technical problems existing in the prior art, the purpose of the present invention is to provide a trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV based on NMPC, and its specific technical solution is as follows:

[0009] A trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV based on NMPC includes the following steps:

[0010] (1) Constructing a ground-air dual-mode integrated dynamic model, through the motion mode switch variable s aerial and sground Distinguishing air modes aerial =1,s ground = 0 and ground mode s aerial =0,s ground =1;

[0011] (2) With flat output Parameterized state and control inputs;

[0012] (3) Design a unified ground-to-air dual-mode predictive controller;

[0013] (4) Forward Euler discretization is used to transform the continuous dynamics into a nonlinear programming problem, and the control sequence is optimized in real time using the CasADi solver.

[0014] Furthermore, step (1) is as follows:

[0015] use and Represents the world inertial system Harmony system Two basic coordinate systems, using Represents the state variables of the machine system, where Indicates the position of the machine's center of mass in the world coordinate system; and They are the velocity and angular velocity in the body coordinate system, and the direction is given by the Euler angle define; adopt As the input of the control system, including the thrust T of the brushless motor and the servo angle δ of the servo motor; the comprehensive dynamic model f(x,u) of the machine is expressed as:

[0016]

[0017] Where m is the total mass of the machine; G = [0, 0, -mg] T ; J is the moment of inertia matrix; The rotation matrix of the machine's rigid body posture from the body coordinate system to the world coordinate system:

[0018]

[0019] When s aerial =1,s ground =0 means the machine is in air mode, at this time the machine is only affected by the thrust vector of the brushless motor and the torque based on thrust

[0020]

[0021]

[0022] When s aerial =0,s ground =1 indicates that the machine is in ground mode, at which point the machine is only subject to ground reaction force. and ground reaction torque μ is the rolling friction coefficient, F s The output force of the servo motor is:

[0023]

[0024] Furthermore, in step (2), for the horizontal twin rotors in the air mode, their state position Directly belongs to σ; inertial system velocity Machine speed in system state

[0025] Rewrite the system input as u=[u1,u2,u3,u4] T

[0026]

[0027] The total thrust of the twin rotors is and total torque It can be expressed as:

[0028]

[0029] Transfer Matrix We can get:

[0030]

[0031] Right now:

[0032]

[0033] Combining the above formulas, we can get:

[0034]

[0035] Since the system state variables There is the following rotation transformation relationship with the Euler angle Θ in:

[0036]

[0037] so:

[0038]

[0039] Combining the above formulas, we can get:

[0040]

[0041] The above equations can be combined to obtain 6 equations, corresponding to the 6 unknown variables {T1, T2, δ1, δ2, φ, θ}. The explicit solution is obtained by numerical calculation. Given a flat output σ = [x, y, z, ψ] T and its finite derivatives uniquely determine the state and input of the system, indicating that the dual-rotor power system satisfies the differential flatness characteristic.

[0042] Furthermore, in step (2), the state of the differential two-wheeled vehicle system in the ground mode is compressed to a two-dimensional plane and simplified to x = [x, y, v x ,ω z ] T , Input T1 = T2 = 0, i.e. u = [0, 0, δ1, δ2] T , the input variable is simplified to u=[δ1,δ2] T ; Introduce the left and right wheel speed v l and v r , it is easy to get the linear velocity and angular velocity of the two-wheeled vehicle respectively:

[0043]

[0044] Vehicle dynamics are partially expressed as:

[0045]

[0046] The above equations can be used to deduce the relationship between a part of the system state, input variables and flat output

[0047]

[0048] F n_l +F n_r =mg, F f_r +F f_l =μmg, solving for:

[0049]

[0050] It can be seen that and are all flattened by σ;

[0051] The system state x and control u are parameterized by the flat output σ and its finite-order derivatives:

[0052]

[0053] Among them, x With Ψ uThe flat transformations corresponding to the system state and control are uniquely determined by the system state equation.

[0054] Furthermore, step (3) is as follows:

[0055] The optimal control input is found by solving the nonlinear optimal control problem (NOCP) in a receding horizon manner. NOCP includes elements such as cost function and constraints and has the following form:

[0056]

[0057] x(t0)=x0

[0058] x min ≤x(t)≤x max

[0059] u min ≤u(t)≤u max

[0060] Among them, J(·) is the optimization target, including the process cost function L(·) and the terminal cost function E(·); t∈[t0,t g ], indicating the time from the current time t0 to the target time t g The limited prediction time horizon is given by the following equation:

[0061] x(t0)=x0

[0062] The process cost function L(·) is designed as the following quadratic form:

[0063]

[0064] in, and The current estimated state x(t) and input u(t) are respectively related to the expected state x d (t) and input u d The error of (t) is calculated. The expected value comes from the planned target trajectory. The current system state and input are flattened to produce the flat output σ = [x, y, z, ψ] T and its finite derivative, Q x and Q u Respectively represent the weight coefficients of various indicators, specifically expressed as:

[0065] Q x =diag(Q p ,Q v ,Q Θ ,Q ω )

[0066] Q u =diag(Q T ,Q δ )

[0067] The terminal cost function E(·) is expressed as:

[0068]

[0069] Define s = [s aerial ,s ground ]and The following two equivalent constraints are introduced to fully consider the different characteristics of the ground mode and the air mode:

[0070] x min ≤x(t)·s≤x max

[0071] u min ≤u(t)·s≤u max

[0072] Among them, the sports mode switch variable s aerial and s ground Assign values ​​to switch different motion modes according to the reference trajectory height state, x max 、x min 、u max 、u min They are the maximum and minimum values ​​of the state quantity and control quantity in the air mode and ground mode respectively:

[0073]

[0074] Furthermore, step (4) is as follows:

[0075] When solving the constructed continuous form NOCP, a simple forward Euler discretization method is chosen to convert the continuous-time dynamic system differential equation into a discrete difference form;

[0076] The discretized system equation is expressed as:

[0077] x k+1 =x k +dt·f(x k ,u k )

[0078] Its expanded form is:

[0079]

[0080] Using a fixed prediction step length dt, the corresponding finite horizon length N = l / dt, where l is the finite prediction time range, l = t g-t0; obtain the optimal control command sequence

[0081]

[0082] stx(k+1)=f(x(k),u(k))

[0083] x(0)=x0

[0084] x min ≤x(k)·s≤x max

[0085] u min ≤u(k)·s≤u max

[0086] Where k is the current prediction step, and U * The first control command is used as the control input of the system and is continuously cycled to achieve online rolling optimization.

[0087] Compared with the prior art, the present invention has at least the following beneficial effects: the present invention constructs a comprehensive dynamics model of a new wheel-wing composite UAV that integrates aerial flight and ground movement, uses motion mode switch variables to realize the inclusion of hybrid dynamics, takes into account the support force and friction force of the horizontal twin-rotor UAV on the ground, proves its differential flatness characteristics, greatly reduces the dimension of decision variables, improves computational efficiency, and enhances the controller's processing capabilities for complex constraints and trajectory planning; based on the proof of the differential flatness characteristics of the proposed control model, a nonlinear model predictive controller AGB-NMPC for trajectory tracking is studied, which naturally includes the dynamic constraints of the new UAV, realizes the restriction of control and state by dynamically identifying the height information in the state variables, and accurately tracks the optimal reference state output from the planned trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] The drawings are only for purposes of illustrating the embodiments and are not to be considered limiting of the invention.

[0089] Figure 1 This is a framework diagram of the trajectory tracking control method of the ground-to-air amphibious dual-rotor UAV based on NMPC of the present invention;

[0090] Figure 2 The ground-air dual-mode integrated dynamics model of the present invention;

[0091] Figure 3 This is the flow chart of the AGB-NMPC trajectory tracking controller of the present invention;

[0092] Figure 4 This is a simplified processing diagram of the differential flatness on the system dynamics constraints of the present invention;

[0093] Figure 5 The land-air split-mode cascade PID controller is used as a comparison for the present invention.

[0094] Figure 6a and Figure 6b The following are the simulation results for the comparison of figure-8 trajectory tracking on the ground and in the air. Specific implementation methods

[0095] like Figure 1 As shown, the NMPC-based ground-to-air amphibious dual-rotor UAV trajectory tracking control method of the present invention includes the following steps:

[0096] (1) Constructing a ground-air dual-mode integrated dynamic model, through the motion mode switch variable s aerial and s ground Distinguish between air modes (s aerial =1,s ground =0) and ground mode (s aerial =0,s ground =1).

[0097] The present invention uses and Represents the world inertial system Harmony system Two basic coordinate systems, such as Figure 2 As shown, the North-East-Down (NED) coordinates are used. The orientation is defined by a rotation matrix with the Euler angles for roll, pitch, and yaw. Follow the ZYX sequence. The differential two-wheel wheelbase is L, the wheel radius is r, and the ground support force F is applied to the ground. n and friction force F f , subscripts l and r correspond to the left and right wheels respectively; the wheelbase of the twin rotors is D, and the thrust vectors of the two brushless motors are constrained to be parallel to The thrust angles δ1 and δ2 are respectively represented by T1 and T2, and the thrust vector The angle between the planes is defined, and the sign is defined by the servo rotation axis.

[0098] For simplicity, the following assumptions are made during modeling: 1) The mass of the brushless motor and the servo dynamics associated with the servo motor can be neglected. 2) The machine reference frame is aligned with the center of mass of the machine. 3) Propeller drag is negligible. 4) The machine is approximated as a symmetric rigid body to simplify the inertia matrix to a diagonal matrix.

[0099] Unified adoption Represents the state variables of the machine system, where Indicates the position of the machine's center of mass in the world coordinate system; and They are the velocity and angular velocity in the body coordinate system, and the direction is given by the Euler angle Define. Unified adoption As the input of the control system, the thrust T of the brushless motor and the servo angle δ of the servo motor are included. Therefore, the comprehensive dynamic model f(x,u) of the machine can be expressed as:

[0100]

[0101] Where m is the total mass of the machine; G = [0, 0, -mg] T ; J is the moment of inertia matrix; The rotation matrix of the machine's rigid body posture from the body coordinate system to the world coordinate system:

[0102]

[0103] When s aerial =1,s ground =0 means the machine is in air mode, at this time the machine is only affected by the thrust vector of the brushless motor and the torque based on thrust

[0104]

[0105] When s aerial =0,s ground =1 indicates that the machine is in ground mode, at which point the machine is only subject to ground reaction force. and ground reaction torque μ is the rolling friction coefficient, F s The output force of the servo motor is:

[0106]

[0107] (2) Prove the system differential flatness characteristics, with flat output Parameterizing states and control inputs, thereby converting complex dynamic problems into algebraic calculations with flat outputs, can significantly reduce the dimensionality of optimization variables and enhance planning efficiency.

[0108] For the horizontal twin rotors in air mode, their status position Directly belongs to σ; inertial system velocity So the machine system speed in the system state

[0109] In this section, the system input is rewritten as u=[u1,u2,u3,u4] T For ease of description:

[0110]

[0111] The total thrust of the twin rotors is and total torque It can be expressed as:

[0112]

[0113] Transfer Matrix We can get:

[0114]

[0115] Right now:

[0116]

[0117] Combining the above formulas, we can get:

[0118]

[0119] Since the system state variables There is the following rotation transformation relationship with the Euler angle Θ in:

[0120]

[0121] so:

[0122]

[0123] Combining the above formulas, we can get:

[0124]

[0125] The above equations can be combined to obtain 6 equations, corresponding to the 6 unknown variables {T1, T2, δ1, δ2, φ, θ}. The explicit solution can be obtained by numerical calculation, so given the flat output σ = [x, y, z, ψ] T and its finite derivatives can uniquely determine the state and input of the system, indicating that the dual-rotor power system satisfies the differential flatness characteristic.

[0126] The state of the differential two-wheeled vehicle system in ground mode can be compressed to a two-dimensional plane and simplified as x = [x, y, v x ,ω z ] T , obviously Since the rotor does not participate in the work, the input T1=T2=0, that is, u=[0,0,δ1,δ2] T , so the system input variables can be simplified to u=[δ1,δ2] T . Introduce the left and right wheel speed v l and v rThese two intermediate variables are used to facilitate process derivation, and the linear velocity and angular velocity of the two-wheeled vehicle are easily obtained as follows:

[0127]

[0128] So the vehicle dynamics can be partially expressed as:

[0129]

[0130] The above equations can be used to deduce the relationship between a part of the system state, input variables and flat output

[0131]

[0132] It is worth noting that only by integrating the above equation can δ be accurately expressed. For servo motors, δ(0) can be obtained through the encoder, and in most cases δ(0) = 0, which makes the solution of δ always unique.

[0133] Easy to get F n_l +F n_r =mg, F f_r +F f_l =μmg, solving for:

[0134]

[0135] As can be seen from the previous article and All of them can be flattened by σ, so the variables described in the above equation can also be flattened. In summary, all state variables and inputs of the differential two-wheeled vehicle can be represented by the flat output σ and its derivative, satisfying the differential flatness characteristic.

[0136] In summary, the novel wheel-wing composite UAV proposed in this invention satisfies the differential flatness characteristic, and its system state x and control u can be parameterized by the flat output σ and its finite-order derivative:

[0137]

[0138] Among them, x With Ψ u The flat transformations corresponding to the system state and control are uniquely determined by the system state equation.

[0139] (3) Design a unified ground-air dual-mode predictive controller AGB-NMPC (Air-Ground Bicopter NonlinearModel Predictive Control), the process is as follows Figure 3 shown.

[0140] The core of the NMPC trajectory tracking controller design is to find the optimal control input by solving the nonlinear optimal control problem (NOCP) with a backward horizon. A typical NOCP includes elements such as a cost function and constraints, and has the following form:

[0141]

[0142] x(t0)=x0

[0143] x min ≤x(t)≤x max

[0144] u min ≤u(t)≤u max

[0145] Among them, J(·) is the optimization target, including the process cost function L(·) and the terminal cost function E(·); t∈[t0,t g ], indicating the time from the current time t0 to the target time t g A finite prediction time horizon; the nonlinear dynamic model used to predict future states and establish equality constraints is described by the following equation:

[0146] x(t0)=x0

[0147] For the trajectory tracking problem of a ground-to-air dual-mode cross-domain rotorcraft, the optimization goal is not only to track the reference trajectory as closely as possible, but also to avoid sudden changes in speed to ensure smooth and stable operation. Therefore, the process cost function L(·) is designed to be in the following quadratic form:

[0148]

[0149] in, and The current estimated state x(t) and input u(t) are respectively related to the expected state x d (t) and input u d The error of (t) is expected to come from the planned target trajectory. As deduced above, the current system state and input can be flattened to produce the flat output σ = [x, y, z, ψ] T and its finite derivatives, so that the originally complex system dynamics constraints can be completely processed in the flat output space, such as Figure 4 As shown; Q x and Q u Respectively represent the weight coefficients of various indicators, specifically expressed as:

[0150] Q x =diag(Q p ,Q v ,QΘ ,Q ω )

[0151] Q u =diag(Q T ,Q δ )

[0152] Consideration Determines the tracking performance of the system for the reference trajectory; the cost term Determines the system input characteristics under continuous sampling time.

[0153] The terminal cost function E(·) is expressed as shown in the following formula to ensure the feasibility of recursion, so that the optimization objective function can achieve gradual convergence to a given path in the rolling optimization:

[0154]

[0155] In order to ensure the dynamic feasibility of the system, it is necessary to constrain the state and input of the system, and define s = [s aerial ,s ground ]and The following two equivalent constraints are introduced to fully consider the different characteristics of the ground mode and the air mode:

[0156] x min ≤x(t)·s≤x max

[0157] u min ≤u(t)·s≤u max

[0158] Among them, the sports mode switch variable s aerial and s ground Assign values ​​to switch different motion modes according to the reference trajectory height state, x max 、x min 、u max 、u min They are the maximum and minimum values ​​of the state quantity and control quantity in the air mode and ground mode respectively:

[0159] x max =[x max_aerial ,x max_ground ]

[0160] x min =[x min_aerial ,x min_ground ]

[0161] u max =[u max_aerial ,u max_ground ]

[0162] u min =[u min_aerial ,u min_ground ]

[0163] (4) Forward Euler discretization is used to transform the continuous dynamics into a nonlinear programming problem, and the control sequence is optimized in real time using the CasADi solver.

[0164] When solving the constructed continuous form NOCP, both direct and indirect methods require a discretization process, thereby converting the continuous problem into a nonlinear programming problem for processing. The present invention chooses to use a simple forward Euler discretization method to convert the continuous-time dynamic system differential equation described in the present invention into a discrete difference form.

[0165] The Euler method uses a first-order linear approximation based on Taylor expansion, adopts uniform step size discretization, and has a fixed distance between adjacent nodes. It is simple to calculate and suitable for real-time or fast solutions. Accuracy can also be guaranteed by setting a reasonable time step size. The discretized system equation is expressed as:

[0166] x k+1 =x k +dt·f(x k ,u k )

[0167] Its expanded form is:

[0168]

[0169] Using a fixed prediction step length dt, the corresponding finite horizon length N = l / dt, where l is the finite prediction time range, l = t g -t0. Therefore, the continuous system dynamics can be transformed into a constrained nonlinear programming problem (Constrained Nonlinear Programming) to solve, thereby obtaining the optimal control command sequence

[0170]

[0171] stx(k+1)=f(x(k),u(k))

[0172] x(0)=x0

[0173] x min ≤x(k)·s≤x max

[0174] u min ≤u(k)·s≤u max

[0175] Where k is the current prediction step, and U* The first control command is used as the control input of the system and continuously looped to achieve online rolling optimization. So far, the unified NMPC trajectory tracking controller of the ground-to-air dual-rotor system can be obtained as follows: Figure 3 As shown, the discretized NMPC trajectory tracking problem is solved using the open source optimization tool CasADi.

[0176] (5) This paper builds a Gazebo and RViz joint simulation platform based on the Robot Operating System (ROS Noetic) on Ubuntu 20.04 to verify the effectiveness of the proposed control algorithm. Gazebo uses the robot URDF model to construct a robot simulation environment including obstacles, gravity field, dynamics, sensors, etc., while RViz is used to display the robot status and sensor information.

[0177] Design as Figure 5 The traditional PID split-mode cascade controller shown is used as a comparison, and the fixed trajectory tracking performance of the proposed controller is verified by testing the air mode and ground mode respectively.

[0178]

[0179] The simulation environment is set up to track the two-dimensional figure-8 trajectory shown in the following equation at a constant speed in an open map, with the maximum speed and acceleration set to 2.0 m / s and 1.5 m / s respectively. 2 , the reference speed is 1.5m / s, and the physical parameter settings of the robot model in the simulation environment are:

[0180]

[0181] The horizon length N and time step dt of the AGB-NMPC controller are set to 20 and 0.1s respectively, and the weight coefficient is set as:

[0182]

[0183] Figure 6a and Figure 6bThe simulation results of the figure-8 trajectory tracking comparison of the two controllers are presented. The comparison shows that the NMPC-based trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV of the present invention has a significant improvement in trajectory tracking accuracy compared to the traditional ground-to-air split-mode cascade PID controller. Under the same conditions, the ground trajectory tracking error of the method proposed by the present invention is reduced by 60.2%, and the air trajectory tracking error is reduced by 62.3%. This is because the rolling optimization framework based on multi-step prediction can proactively solve the trajectory curvature changes in future time steps, and the established cost function including lateral displacement error and heading angle deviation can respond to turns in advance. In comparison, the PID trajectory tracking controller is limited by the single-step feedback control architecture. Its fixed forward-looking distance geometric tracking strategy is difficult to adapt to nonlinear dynamic characteristics, resulting in overshoot of the steering actuator when the path curvature changes.

Claims

1. A trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV based on NMPC, characterized in that The steps include: (1) Constructing a ground-air dual-mode integrated dynamic model, through the motion mode switch variable s aerial and s ground Distinguishing air modes aerial =1,s ground = 0 and ground mode s aerial =0,s ground =1; (2) With flat output Parameterized state and control inputs; (3) Design a unified ground-to-air dual-mode predictive controller; (4) Forward Euler discretization is used to transform the continuous dynamics into a nonlinear programming problem, and the control sequence is optimized in real time using the CasADi solver.

2. The NMPC-based trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV as claimed in claim 1, characterized in that: Step (1) is as follows: use and Represents the world inertial system Harmony system Two basic coordinate systems, using Represents the state variables of the machine system, where Indicates the position of the machine's center of mass in the world coordinate system; and They are the velocity and angular velocity in the body coordinate system, and the direction is given by the Euler angle define; adopt As the input of the control system, including the thrust T of the brushless motor and the servo angle δ of the servo motor; the comprehensive dynamic model f(x,u) of the machine is expressed as: Where m is the total mass of the machine; G = [0, 0, -mg] T ; J is the moment of inertia matrix; The rotation matrix of the machine's rigid body posture from the body coordinate system to the world coordinate system: When s aerial =1,s ground =0 means the machine is in air mode, at this time the machine is only affected by the thrust vector of the brushless motor and the torque based on thrust When s aerial =0,s ground =1 indicates that the machine is in ground mode, at which point the machine is only subject to ground reaction force. and ground reaction torque μ is the rolling friction coefficient, F s The output force of the servo motor is:

3. The NMPC-based trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV as claimed in claim 2, characterized in that: In step (2), for the horizontal twin rotor in the air mode, its state position Directly belongs to σ; inertial system velocity Machine speed in system state Rewrite the system input as u=[u1,u2,u3,u4] T The total thrust of the twin rotors is and total torque It can be expressed as: Transfer Matrix We can get: Right now: Combining the above formulas, we can get: Since the system state variables There is the following rotation transformation relationship with the Euler angle Θ in: so: Combining the above formulas, we can get: The above equations can be combined to obtain 6 equations, corresponding to the 6 unknown variables {T1, T2, δ1, δ2, φ, θ}. The explicit solution is obtained by numerical calculation. Given a flat output σ = [x, y, z, ψ] T and its finite derivatives uniquely determine the state and input of the system, indicating that the dual-rotor power system satisfies the differential flatness characteristic.

4. The NMPC-based trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV as claimed in claim 3, characterized in that: In step (2), the state of the differential two-wheeled vehicle system in the ground mode is compressed to a two-dimensional plane and simplified to x = [x, y, v x ,ω z ] T , Input T1 = T2 = 0, i.e. u = [0, 0, δ1, δ2] T , the input variable is simplified to i=[δ1,δ2] T ; Introduce the left and right wheel speed v l and v r , it is easy to get the linear velocity and angular velocity of the two-wheeled vehicle respectively: Vehicle dynamics are partially expressed as: The above equations can be used to deduce the relationship between a part of the system state, input variables and flat output F n_l +F n_r =mg, F f_r +F f_l =μmg, solving for: It can be seen that and are all flattened by σ; The system state x and control u are parameterized by the flat output σ and its finite-order derivatives: Among them, x With Ψ u The flat transformations corresponding to the system state and control are uniquely determined by the system state equation.

5. The NMPC-based trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV as claimed in claim 4, characterized in that: Step (3) is as follows: The optimal control input is found by solving the nonlinear optimal control problem (NOCP) in a receding horizon manner. NOCP includes elements such as cost function and constraints and has the following form: x(t0)=x0 x min ≤x(t)≤x max u min ≤u(t)≤u max Among them, J(·) is the optimization target, including the process cost function L(·) and the terminal cost function E(·); t∈[t0,t g ], indicating the time from the current time t0 to the target time t g The limited prediction time horizon is given by the following equation: x(t0)=x0 The process cost function L(·) is designed as the following quadratic form: in, and The current estimated state x(t) and input u(t) are respectively related to the expected state x d (t) and input u d The error of (t) is calculated. The expected value comes from the planned target trajectory. The current system state and input are flattened to produce the flat output σ = [x, y, z, ψ] T and its finite derivative, Q x and Q u Respectively represent the weight coefficients of various indicators, specifically expressed as: Q x =diag(Q p ,Q v ,Q Θ ,Q ω ) Q u =diag(Q T ,Q δ ) The terminal cost function E(·) is expressed as: Define s = [s aerial ,s ground ]and The following two equivalent constraints are introduced to fully consider the different characteristics of the ground mode and the air mode: x min ≤x(t)·s≤x max u min ≤u(t)·s≤u max Among them, the sports mode switch variable s aerial and s ground Assign values ​​to switch different motion modes according to the reference trajectory height state, x max 、x min 、u max 、u min They are the maximum and minimum values ​​of the state quantity and control quantity in the air mode and ground mode respectively: x max =[x max_aerial ,x max_ground ] x min =[x min_aerial ,x min_ground ] in max =[in max_aerial ,in max_ground ]。 in min =[in min_aerial ,in min_ground ] 6. The NMPC-based trajectory tracking control method for a ground-to-air amphibious dual-rotor UAV as claimed in claim 5, characterized in that: Step (4) is as follows: When solving the constructed continuous form NOCP, a simple forward Euler discretization method is chosen to convert the continuous-time dynamic system differential equation into a discrete difference form; The discretized system equation is expressed as: x k+1 =x k +dt·f(x k ,u k ) Its expanded form is: Using a fixed prediction step length dt, the corresponding finite horizon length N = l / dt, where l is the finite prediction time range, l = t g -t0; obtain the optimal control command sequence stx(k+1)=f(x(k),u(k)) x(0)=x0 x min ≤x(k)·s≤x max in min ≤u(k)·s≤u max Where k is the current prediction step, and U * The first control command is used as the control input of the system and is continuously cycled to achieve online rolling optimization.

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