Lifting wing multi-rotor fault tolerance method based on nonlinear model predictive control

Abstract

The invention provides a lifting wing multi-rotor fault-tolerant method based on nonlinear model predictive control. The method comprises the following steps: step 1, establishing a dynamic model of a lifting wing multi-rotor aircraft; 2, deducing a relaxation hovering solution of the multiple rotors of the lift wing; 3, designing an attitude controller based on the NMPC; 4, designing a speed controller; and 5, designing an EKF-based disturbance observer. The method is used for solving the stability problem under rotor wing faults and complex pneumatic conditions. According to the invention, fault-tolerant control is expanded to a scene in a multi-fault and complex environment, and the overall flight stability and control precision are improved. According to the method, the disturbance observation technology based on the extended Kalman filter (EKF) is introduced, the relaxation hovering solution of the lift wing multi-rotor aircraft considering the aerodynamic effect is deduced in combination with phi-thory, and the problem of aerodynamic complexity of the lift wing multi-rotor aircraft in high-speed flight is effectively solved.

Description

Technical Field

[0001] The present invention relates to a key technology applicable to fault-tolerant control of a lift-wing multi-rotor aircraft, in particular to a non-linear model predictive control (NMPC) method for a lift-wing multi-rotor aircraft. The invention covers technical fields such as non-linear dynamic modeling, extended Kalman filter (EKF), fault-tolerant control, and attitude stabilization control. By introducing a fault-tolerant control method based on a disturbance observer and a non-linear model predictive control strategy, it is possible to maintain the attitude stability of the lift-wing multi-rotor in the case of rotor failure or system disturbance, and improve the reliability and autonomous flight ability of the lift-wing multi-rotor in a complex flight environment. Background Art

[0002] In recent years, with the rapid development of unmanned aerial vehicle technology, especially lift-wing multi-rotor aircraft have been widely used in many fields due to their vertical takeoff and landing capabilities, long endurance, and efficient forward flight performance. They have played an important role in search and rescue, military reconnaissance, cargo transportation, environmental monitoring, etc. However, with the increasing demand for these applications, the complex aerodynamic characteristics of lift-wing multi-rotor aircraft and potential fault problems of the multi-rotor system have become key technical challenges that must be overcome. When the aircraft is flying at high speed or hovering vertically, it not only faces different aerodynamic disturbances, but may also encounter sensor noise, rotor failure or other emergencies, seriously affecting flight stability and mission execution effectiveness.

[0003] Traditional control technologies for multi-rotor aircraft cannot effectively cope with these highly non-linear dynamic changes. Especially in the case of partial rotor failure, it is often difficult to maintain the attitude and trajectory of the aircraft. Therefore, the application of fault-tolerant control (FTC) technology in flight control systems has become increasingly important in recent years. FTC can maintain the stability and mission execution ability of the aircraft through an adaptive control strategy in the case of rotor failure, sensor noise or external disturbance, thereby improving the reliability and safety of multi-rotor aircraft. In this context, as an advanced control strategy, NMPC, with its predictive ability based on the non-linear model of the system, can optimize control commands in real time to ensure that the aircraft still maintains an efficient and stable flight attitude in a changing environment. The NMPC method predicts the system state over a period of time in the future, and combines the current control input and state feedback to optimize the output control signal to maintain the steady-state operation of the system. This makes the method particularly suitable for lift-wing multi-rotor aircraft, and it can still perform efficient attitude control and fault recovery in the face of complex aerodynamic disturbances.

[0004] The present invention proposes a fault-tolerant method for lift-wing multi-rotors based on non-linear model predictive control, which can effectively address the control challenges of lift-wing multi-rotor aircraft under different rotor failure conditions. Through the EKF technology, the system can quickly adjust the control strategy in the face of external disturbances or sensor errors, ensuring the stability of the aircraft's attitude and trajectory. This fault-tolerant control system has been verified not only in the simulation environment but also through actual flight tests, demonstrating its excellent stability and robustness in the event of single or multiple rotor failures. The application of this technology not only enhances the safety and reliability of lift-wing multi-rotor aircraft during mission execution but also provides a new solution for the wide application of unmanned aerial vehicles in complex environments. Summary of the Invention

[0005] The present invention proposes a fault-tolerant method for lift-wing multi-rotors based on non-linear model predictive control, designed specifically for lift-wing multi-rotor aircraft to address their stability issues under rotor failures and complex aerodynamic conditions. Different from traditional single fault-tolerant control schemes, the present invention extends fault-tolerant control to scenarios of multiple faults and complex environments, improving the overall flight stability and control accuracy. The present invention introduces disturbance observation technology based on the Extended Kalman Filter (EKF) and derives a relaxed hover solution for lift-wing multi-rotor aircraft considering aerodynamic effects in combination with Φ-theory, effectively solving the aerodynamic complexity problem of lift-wing multi-rotors during high-speed flight.

[0006] A fault-tolerant method for lift-wing multi-rotors based on non-linear model predictive control according to the present invention includes the following steps:

[0007] Step 1: Establish the dynamic model of the lift-wing multi-rotor aircraft

[0008] In this step, the dynamic model of the lift-wing multi-rotor aircraft is established to accurately describe its dynamic characteristics under high-speed rotation and aerodynamic influence, providing a basis for fault-tolerant control design.

[0009] According to the model of the lift-wing multi-rotor and the corresponding aerodynamic influence, the dynamic model of the lift-wing multi-rotor is expressed as follows:

[0010]

[0011] Wherein, e p, e v and b ω respectively represent the position, velocity, and angular velocity of the lift-wing multi-rotor. 1 f a , 1 τ a respectively represent the aerodynamic force and moment of the lift-wing multi-rotor. b f r = [0 0 -f tT Represents the thrust generated by the motor rotor. i = 1, 2, 3, 4, f i Represents the lift force generated by the i-th rotor; g = [0 0g] T , where g is the acceleration due to gravity, m is the mass of the multi-rotor with lift wings, and J is the inertia matrix of the multi-rotor helicopter with lift wings; b τ r is the moment generated by the rotor, 1 τ a represents the aerodynamic moment acting on the lift wing. is the rotation matrix from the Earth-fixed coordinate system, and its internal elements are composed of the Euler angles Φ, θ, and ψ. is the rotation matrix from the lift wing coordinate system to the multi-rotor coordinate system, determined by the installation angle κ:

[0012]

[0013] Since the multi-rotor with lift wings is in a high-speed rotation state after rotor failure, the traditional aerodynamic model cannot accurately characterize the aerodynamic forces and moments generated by the lift wing. The present invention uses Φ-theory to express a continuous and singularity-free aerodynamic model. The description of the aerodynamic forces and moments is as follows:

[0014]

[0015] Where, l v and l ω are the velocity and angular velocity in the lift wing coordinate system; S represents the wing surface area of the lift wing; ρ is the air density; μ ∈ R + is a variable parameter, c is the chord length of the lift wing; C = diag(1, 1, 1, b, c, b), b is the wingspan of the lift wing; the matrix Φ is expressed as:

[0016]

[0017] Where,

[0018]

[0019] In the Φ matrix, are aerodynamic coefficients. Where, Δr is the distance from the aerodynamic center of the aircraft to the center of mass, and when the aerodynamic center is in front of the center of mass, Δr is positive. These four matrices respectively reflect the relationships between aerodynamic forces, moments, velocity, and angular velocity.

[0020] Step 2: Calculate the relaxed hover solution of the multi-rotor with lift wings

[0021] ​In this step, a dynamic model of the lifting-wing multi-rotor under rotor failure and external disturbances is established by assuming a relaxed hover solution with constant speed and angular velocity, ensuring that the aircraft satisfies the constraint conditions of zero acceleration or desired acceleration within one rotation period.

[0022] During the rotation of the lifting-wing multi-rotor, the aerodynamic forces and moments generated by the lifting wing depend on the speed b v and the angular velocity b ω. Therefore, during the solution process, it is necessary to assume in advance that the lifting-wing multi-rotor satisfying the relaxed hover solution maintains a constant angular velocity and speed in the multi-rotor coordinate system, that is

[0023]

[0024] In the case of rotor failure, it cannot be guaranteed that the lifting-wing multi-rotor is simultaneously in force balance and moment balance. Therefore, adopting a relaxed hover scheme can ensure that the lifting-wing multi-rotor maintains zero acceleration within one rotation period:

[0025]

[0026] where T hvr = 2π / || b ω|| represents one rotation period.

[0027] During the time interval from t 0 to t, the rotation vector of the aircraft is expressed as where θ represents the magnitude of the rotation angle, and the unit vector represents the direction of the rotation axis. The rotation matrix at time t is expressed as:

[0028]

[0029] where,

[0030]

[0031] where, represents the transformation of the rotation matrix from time t 0 to time t, and I 3 is the three-dimensional identity matrix. Since zero acceleration is required within one rotation period, it can be obtained that

[0032]

[0033] Therefore, it can be inferred that initially, the angular velocity in the fixed-earth coordinate system is parallel to the direction of gravity, that is,

[0034]

[0035] Among them, sgn(·) is the sgn function that returns the sign of its argument. When the above conditions are met, it is obvious that at any given moment, the angular velocity will be parallel to the gravity.

[0036] By applying the Euclidean norm to both sides of the equation, another constraint for the relaxed hover solution is obtained as:

[0037]

[0038] Due to the constraint of equation (6), the velocity in the multi-rotor coordinate system is constant. Therefore,

[0039]

[0040] The above expression can be transformed into:

[0041]

[0042] Among them, represents the direction of gravity in the multi-rotor coordinate system. Since the relaxed hover solution must satisfy equation (11), n 3 can be expressed as:

[0043]

[0044] In a real environment, due to model inaccuracies and wind disturbances, the lift-wing multi-rotor UAV is subject to disturbing forces b f d and torques b τ d The dynamic model is as follows:

[0045]

[0046] To achieve velocity control, the average acceleration within one rotation period needs to be aligned with the desired acceleration e a d Equation (7) is rewritten as:

[0047]

[0048] The final constraint conditions that the UAV needs to satisfy for hovering are:

[0049]

[0050] The first term in the above equation represents aligning the rotation axis with the desired average thrust direction, while the second term represents achieving force balance in the desired rotation axis direction, which means the lift-wing multi-rotor aircraft will obtain acceleration in this direction.

[0051] Step 3: Design an attitude controller based on NMPC

[0052] This step calculates the output of each rotor by introducing the average thrust direction and the state vector, and combines the NMPC optimization method to achieve efficient attitude control and energy consumption optimization of the multi-rotor.

[0053] Due to the high angular velocity of the multi-rotor, the traditional attitude representation is insufficient for control, and the concept of the average thrust direction needs to be introduced, which is defined as:

[0054]

[0055] For the multi-rotor model of the present invention, the desired average thrust direction is:

[0056]

[0057] For the convenience of subsequent expression, the desired state vector ξ d and the state vector ξ are respectively defined as:

[0058]

[0059] Then, the output of each rotor of the lifting-wing multi-rotor is solved through the optimal control problem:

[0060]

[0061] s.t.u min ≤u≤u max

[0062]

[0063] In the formula, e ξ (t)=ξ d -ξ;u=[f 1 f 2 f 3 f 4 T is the control input of the lifting-wing multi-rotor; Q, R ∈ R 4×4 are diagonal positive definite matrices representing weights. When setting the weights, the first three elements of the Q matrix can be understood as the weights related to the alignment of the rotation axis of the lifting-wing multi-rotor helicopter and the desired rotation axis. The last element of the Q matrix represents the ability of the lifting-wing multi-rotor helicopter to quickly track the required speed. The elements of the R matrix represent the trade-off between energy consumption in the optimization problem. In the present invention, the optimal control problem formula (15) is discretized and solved by numerical methods.

[0064] Step Four: Design the speed controller

[0065] This step constructs the speed controller part of the lifting-wing multi-rotor.

[0066] The speed controller takes the desired speed​e v d is used as the input and then processed by a PI controller to obtain the desired acceleration e a d . The desired acceleration can be calculated by the following formula:

[0067]

[0068] where is a diagonal positive definite matrix

[0069] Step Five: Design an EKF-based disturbance observer

[0070] This step estimates the disturbance force and torque through the Extended Kalman Filter (EKF), combines the system state and the observation vector, and improves the fault-tolerant control ability

[0071] First, define the system state vector of the lift-wing multi-rotor aircraft as x, which includes the position e p, velocity e v, quaternion e q, angular velocity e ω, disturbance force b f d and disturbance torque. The observation vector z consists of the position e p, velocity e v, quaternion e q and the angular velocity e ω obtained from the sensor. The system input u = [f 1 f 2 f 3 f 4 T is the thrust generated by the four rotors

[0072]

[0073] The derivatives of the position e p, velocity e v, attitude and angular velocity b ω are expressed by formula (16). To flexibly apply the disturbance observer, the dynamics of the disturbance force and torque are modeled as a Gaussian random walk, and the discrete form is as follows:

[0074]

[0075] where, w f (k - 1) and w τ (k - 1) are zero-mean Gaussian white noise b f d (k - 1) and b τ d ​(k - 1) represent the disturbing force and disturbing moment at time k - 1 respectively. Then, the standard EKF equations can be used to estimate the disturbing force and moment.

[0076] The advantages and beneficial effects of the present invention are as follows: The core of the present invention is an attitude controller based on NMPC, where the objective function of NMPC is designed based on the relaxed hover solution of the lifting - wing multi - rotor derived from the theory of the present invention. The existence of the relaxed hover solution indicates that even if complex aerodynamic forces and moments are introduced to the lifting wing, stable attitude control can still be achieved by sacrificing yaw. In addition, the present invention combines an EKF - based disturbance observer to ensure that the lifting - wing multi - rotor can maintain fault - tolerant control even in the presence of model errors, sensor noise, and actuator response delays. Brief Description of the Drawings

[0077] Figure 1 is the control block diagram of the controller of the present invention.

[0078] Figure 2 is the experimental result of software - in - the - loop simulation.

[0079] Figure 3 is the schematic diagram of the hardware platform for actual flight experiments.

[0080] Figure 4 is the experimental result of the actual flight experiment with a single - rotor failure.

[0081] Figure 5 is the experimental result of the actual flight experiment with a two - rotor failure. Detailed Embodiment

[0082] The technical solution of the present invention will be further described below in conjunction with the drawings, simulation examples, and actual flight examples to verify in the simulation and actual flight environments that the fault - tolerant control method of the present invention can ensure the safety of the lifting - wing multi - rotor during rotor failure.

[0083] Simulation Example: The simulation and calculation process is carried out on MATLAB R2022b under the Win10 operating system on a computer with a main frequency of 3.70Ghz and a memory of 32.0GB. The specific implementation plan is as follows.

[0084] Step 1: Establish the dynamic model of the lifting - wing multi - rotor aircraft

[0085] In the simulation example, according to the parameters of the lifting - wing multi - rotor in the actual flight example, the present invention sets the parameters of the lifting - wing multi - rotor to the values in Table 1. According to Step 1 of the invention content, substitute them into the dynamic model (16) considering model inaccuracies and wind disturbances to obtain the dynamic model of the lifting - wing multi - rotor aircraft for the simulation experiment.

[0086] Parameter Value κ (°) 34 m (kg) 1.125 b (m) 0.9 c (m) 0.15 <![CDATA[J(kg·m 2 )]]> diag(0.0133,0.0045,0.0162) <![CDATA[u max (N)]]> 8.5 <![CDATA[C d0 > 0.1 <![CDATA[C y0 > 0.1 <![CDATA[C Lα > 2.4 <![CDATA[C lp > 0.4 <![CDATA[C mq > 0.2 <![CDATA[C nr > 0.1 Δr -0.05

[0087] Table 1

[0088] Step 2: Build an attitude controller based on NMPC

[0089] Build the attitude controller according to Step 3 of the invention content. Set the weights of the NMPC cost function to the values in Table 2, and then use an open-source solver to solve (22) to obtain the outputs of each rotor of the lift-wing multi-rotor:

[0090]

[0091] Table 2

[0092] Step 3: Build a speed controller

[0093] Set the parameters of the speed controller in equation (23) and to the values in Table 2 to obtain the speed controller of the lift-wing multi-rotor aircraft for the simulation experiment.

[0094] Step 4: Build a disturbance observer

[0095] Build the disturbance observer for the simulation experiment with reference to Step 6 of the invention content. The control block diagram of the final lift-wing multi-rotor fault-tolerant controller is as Figure 1 shown.

[0096] Step 5: Simulation experiment

[0097] The present invention conducts a software-in-the-loop simulation experiment to evaluate the feasibility of implementing the FTC strategy on a lift-wing multi-rotor. The simulation uses a prediction horizon of 0.8 s, which is discretized into 5 steps. To compare the effectiveness of the controller of the present invention, a benchmark controller is also set for comparison, where the benchmark controller does not consider the influence of lift-wing aerodynamics, and the other settings are the same as those of the controller of the present invention. The controller, lift-wing multi-rotor model, sensor model, and state estimator are all developed in MATLAB / Simulink, and the simulation results are as Figure 2 shown. The initial setting of the aircraft hover height for each experiment is 5 meters, and after 5 seconds, the corresponding rotor fails completely. The expected speed of the aircraft is set to e v d = [0 0 0] T。The simulation results show that the controller proposed in the present invention can effectively achieve FTC control of the lifting-wing multi-rotor in the case of single-rotor failure or double-rotor failure. The benchmark controller successfully stabilized the altitude of the lifting-wing multi-rotor within the first few seconds after the rotor failure. However, as the angular velocity gradually increased, the lifting-wing multi-rotor eventually lost control and crashed to the ground. This is mainly due to the aerodynamic forces and moments generated. At low angular velocities, the aerodynamic forces and moments are also small, allowing compensation through the disturbance observer. At this point, the behavior of the lifting-wing multi-rotor is similar to that of a multi-rotor aircraft, and the benchmark controller can keep it stable. However, as the angular velocity increases, the aerodynamic effects become obvious, making it impossible for the benchmark controller to effectively achieve FTC, resulting in failure.

[0098] Actual flight example: In this experiment, a lifting-wing multi-rotor with a special installation angle (the same installation angle as in the simulation example) was used, as shown in the figure. The power system includes a four-cell lithium polymer battery with a capacity of 2200 mAh, EMAX RS2205s 2600 kV brushless DC motors and HQ5045 BN propellers, as well as 45A electronic speed controllers. The RflyPilot flight controller is rigidly installed at the center of the multi-rotor frame, equipped with an inertial measurement unit, a barometer, and an SD card for flight data recording. The core of this flight control hardware is a Raspberry Pi CM4 computing module, which provides greater computing power compared to traditional microcontroller unit (MCU)-based flight controllers. This enhanced functionality allows the execution of computationally demanding control methods such as NMPC. An independent NEOM8N-based GPS module and a magnetometer are used to read the positioning and heading. The proposed controller was developed in Matlab / Simulink. After verification through MIL simulation, c++ code was automatically generated and uploaded to the RflyPilot. In the actual experiment, the working frequency of the controller was 400 Hz.

[0099] Experiment on Rotor 3 Failure without Speed Control

[0100] As Figure 4 shown, in the first 10 seconds of the experiment, the lifting-wing multi-rotor was in a normal flight state. It can be observed that when the lifting-wing multi-rotor had a certain initial velocity, Rotor 3 failed at 10 seconds. At this time, the fault-tolerant controller abandoned the yaw control and allowed the lifting-wing multi-rotor helicopter to quickly recover and achieve a stable attitude. In the experiment, the required acceleration command header was manually input without any speed control, and the required acceleration was set to [0 0 0]. T 。Therefore, after a short transition, the velocity of the lifting-wing multi-rotor helicopter remained almost unchanged.

[0101] Experiment on Rotor 3 and Rotor 4 Failures with Speed Control

[0102] As Figure 5As shown, within the first 10 seconds, this lifting multi-rotor helicopter was in a normal flight state. At 10 seconds, the No. 3 and No. 4 rotors failed simultaneously. At this time, the fault-tolerant controller abandoned yaw control, allowing the lifting multi-rotor helicopter to quickly recover and achieve a stable attitude. Since speed control was introduced in this experiment, the desired speed was set to e v d = [0 0 0] T . Therefore, the desired acceleration value output by the speed controller changed continuously, resulting in a corresponding adjustment of the average thrust direction. To track this direction, both the angular velocity and the attitude fluctuated. In addition, due to the inaccuracy of the aerodynamic modeling, the significance of sensor noise in the actual experiment, and the influence of outdoor wind, there was a certain delay and error in the disturbance observation of the EKF, further exacerbating the instability of the angular velocity and the attitude.

Claims

1. A fault-tolerant method for a lift wing multi-rotor based on nonlinear model predictive control, characterized in that: The steps include: Step 1: Establish a dynamic model of the lift-wing multi-rotor aircraft; accurately describe its dynamic characteristics under high-speed rotation and aerodynamic influence, and provide a basis for fault-tolerant control design; Step 2: Calculate the relaxed hovering solution of the lift wing multi-rotor; by setting the relaxed hovering solution of constant speed and angular velocity, establish the dynamic model of the lift wing multi-rotor under rotor failure and external interference, and ensure that the aircraft meets the constraint conditions of zero acceleration or expected acceleration within one rotation cycle; Step 3: Design an attitude controller based on NMPC; by introducing the average thrust direction and state vector, combined with the NMPC optimization method, calculate the output of each rotor, and achieve efficient attitude control and energy consumption optimization of the multi-rotor; Step 4: Design the speed controller; build the speed controller part of the lift wing multi-rotor; Step 5: Design a disturbance observer based on EKF; The disturbance force and disturbance torque are estimated by extending the Kalman filter (EKF), and the fault-tolerant control capability is improved by combining the system state and observation vector.

2. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 1, characterized in that: In step 1, according to the model of the lift wing multi-rotor and the corresponding aerodynamic effects, the dynamic model of the lift wing multi-rotor is expressed as follows: in, e p, e v and b ω represents the position, velocity and angular velocity of the lift wing multirotor respectively; 1 f a , 1 τ a They represent the aerodynamic force and moment of the lift-wing multirotor, respectively; b f r =[0 0 -f t ] T Represents the thrust generated by the motor rotor; i=1,2,3,4,f i represents the thrust generated by the i-th rotor; g = [0 0 g] T , g is the acceleration of gravity, m is the mass of the lift wing multirotor, and J is the inertia matrix of the lift wing multirotor helicopter; b τ r is the torque generated by the rotor, 1 τ a represents the aerodynamic moment acting on the lift wing; is the rotation matrix from the earth-fixed coordinate system, whose internal elements consist of the Euler angles Φ, θ and ψ; is the rotation matrix from the lift wing coordinate system to the multirotor coordinate system, which is determined by the installation angle κ:

3. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 1 or 2, characterized in that: The Φ-theory is used to express a continuous aerodynamic model without singularities; the aerodynamic forces and moments are described as follows: in, l v and l ω is the velocity and angular velocity in the lift wing coordinate system; S is the wing surface area of ​​the lift wing; ρ is the air density; μ∈R + is a variable parameter, c is the lift chord length; C = diag (1, 1, 1, b, c, b), b is the lift span length; the matrix Φ is expressed as:

4. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 3, characterized in that: The expressions of the parameters in formula (4) are: In the Φ matrix, is the aerodynamic coefficient; where Δr is the distance from the aerodynamic center of the aircraft to the center of mass. When the aerodynamic center is in front of the center of mass, Δr is a positive value; these four matrices respectively reflect the relationship between aerodynamic force, torque, velocity and angular velocity.

5. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 1, characterized in that: In step 2, it is assumed that the lifting wing multirotor that satisfies the relaxed hovering solution maintains a constant angular velocity and speed in the multirotor coordinate system, that is, In the event of a rotor failure, the force and torque balance of the lift wing multi-rotor cannot be guaranteed at the same time. Therefore, a relaxed hovering scheme is used to ensure that the lift wing multi-rotor maintains zero acceleration within a rotation cycle: Among them, T hvr =2π / || b ω|| represents a rotation period; In the time interval from t0 to t, the rotation vector of the aircraft is expressed as Among them, θ represents the size of the rotation angle, and the unit vector Represents the direction of the rotation axis; the rotation matrix at time t is expressed as: in, in, represents the transformation of the rotation matrix from time t0 to time t, and I3 is the three-dimensional unit matrix; since the acceleration is required to be zero within a rotation cycle, we get, 6. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 5, characterized in that: Initially, the angular velocity in the ground coordinate system is Parallel to the direction of gravity, that is, where sgn(·) is the sgn function that returns the sign of its argument; when the above conditions are met, at any given moment, the angular velocity will be parallel to gravity; By applying the Euclidean norm on both sides of the equation, another constraint on the relaxed hovering solution is obtained: The speed in the multirotor coordinate system is constant, so, Convert the above expression to: in, represents the direction of gravity in the multirotor coordinate system. Since the relaxed hovering solution must satisfy equation (11), n3 is expressed as:

7. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 6, characterized in that: In real environments, due to the inaccuracy of the model and the interference of wind, the multi-rotor UAV is subject to interference forces during flight. b f d and torque b τ d The kinetic model is as follows: To achieve speed control, the average acceleration within a rotation period needs to be the same as the desired acceleration. e a d Align, and get: The constraints that the drone needs to meet in the final hovering are:

8. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 1, characterized in that: In step 3, the concept of mean thrust direction is introduced, which is defined as: For a multi-rotor model, the expected average thrust direction is: To facilitate subsequent expression, the expected state vector ξ d and the state vector ξ are defined as: Then the output of each rotor of the lift wing multi-rotor is solved through the optimal control problem: In the formula, e ξ (t) = ξ d -ξ;u=[f1 f2 f3 f4] T is the lift wing multirotor control input; Q,R∈R 4×4 It is a diagonal positive definite matrix representing weights; when setting weights, the first three elements of the Q matrix are understood as weights related to the alignment of the lift-wing multirotor helicopter's rotation axis with the desired rotation axis; the last element of the Q matrix represents the ability of the lift-wing multirotor helicopter to quickly track the required speed; the elements of the R matrix represent the trade-off between energy consumption in the optimization problem.

9. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 1, characterized in that: In step 4, the speed controller sets the desired speed e v d As input, it is then processed by a PI controller to obtain the desired acceleration e a d ; The expected acceleration is calculated by: In the formula, is a diagonally positive definite matrix.

10. The method for fault-tolerant lift wing multi-rotor based on nonlinear model predictive control according to claim 1, characterized in that: In step 5, define the system state vector of the lift-wing multirotor aircraft as x, which contains the position e p. Speed e v. Quaternion e q, angular velocity e ω, disturbance force b f d and disturbance torque; the observation vector z is determined by the position of the UAV e p. Speed e v. Quaternion e q and the angular velocity obtained from the sensor e ω composition; system input u=[f1 f2 f3 f4] T The thrust generated by the four rotors; The dynamics of the perturbation force and perturbation torque are modeled as Gaussian random walks, and the discretized form is as follows: Among them, w f (k-1) and w τ (k-1) is zero-mean Gaussian white noise, b f d (k-1) and b τ d (k-1) represents the disturbance force and disturbance moment at time k-1 respectively; the standard EKF equation is used to estimate the disturbance force and moment.

Images