A model predictive control based quadrotor autonomous landing method

Abstract

The application discloses a kind of model predictive control-based quadrotor autonomous landing methods, and the landing process of quadrotor aircraft is divided into first stage and second stage, the distance of aircraft and landing platform in first stage is longer than in second stage, trajectory of aircraft is planned using model predictive control method in first stage and second stage, and the objective function in model predictive control method is different in first stage and second stage.The model predictive control-based quadrotor autonomous landing method disclosed by the application has low computational complexity, stable landing and strong anti-interference capability.

Description

TECHNICAL FIELD

[0001] The application relates to a model predictive control-based four-rotor autonomous landing method and belongs to the technical field of aircraft control. BACKGROUND

[0002] To solve the endurance capability constraint of a four-rotor aircraft, a vehicle or a ship is often used as a landing platform in practical applications to expand the use range and application scenarios of the four-rotor aircraft, which requires the aircraft to have the capability of autonomous landing, especially the capability of autonomous landing of the four-rotor aircraft on a moving platform.

[0003] The existing aircraft autonomous landing methods include a backstepping method, a dynamic control surface method and a model predictive control method.

[0004] The backstepping method and the dynamic control surface method can realize accurate landing of the unmanned aerial vehicle, but there is a fly-around tracking in the early stage, causing unnecessary energy and time consumption of the aircraft; the model predictive control method plans a trajectory by setting a fixed sampling time, comprehensively considers various soft and hard constraints, can realize limited time domain rolling optimization and is widely applied to solve the path planning and tracking problems of the four-rotor aircraft.

[0005] However, the model predictive control method has a large amount of calculation and needs to be matched with visual detection, which causes great limitation on the onboard computer.

[0006] In addition, the fixed sampling time in the model predictive control method cannot plan a variable target function, which causes the model predictive control method to be unable to well meet the performance requirements in different stages of the landing process, for example, the aircraft detects a target speed slowly in the early landing stage and cannot cope with environmental disturbances in the landing stage, causing large fluctuation of landing stability.

[0007] Therefore, it is necessary to further study the model predictive control-based four-rotor autonomous landing to improve the landing stability of the aircraft. SUMMARY

[0008] To overcome the above problems, the present application has been made through deep research, and a model predictive control-based four-rotor autonomous landing method is provided, which divides the landing process of the four-rotor aircraft into a first stage and a second stage, the distance between the aircraft and the landing platform in the first stage is greater than that in the second stage,

[0009] The model predictive control method is used to plan the trajectory of the aircraft in the first stage and the second stage, and the target functions in the model predictive control method in the first stage and the second stage are different.

[0010] In a preferred embodiment, in the model predictive control method in the first stage and the second stage, the dynamic equation of the model is expressed as:

[0011]

[0012]

[0013] where k denotes different time instants, x(k) is the state vector, representing the state of the aerial vehicle at time k, y(k) is the output vector, representing the output state of the aerial vehicle at time k under the action of the control variable; A d is the discretized system matrix, B d is the discretized input matrix, T s is the sampling period; A is the system matrix in state space, B is the control matrix in state space, C is the output matrix in state space, s is the complex variable in discrete process, and u(k) is the control variable at time k.

[0014] In a preferred embodiment, in the first stage, the objective function of the model predictive control method is:

[0015]

[0016] x A (i) = P r (i)

[0017] where i denotes different time instants, N is the prediction horizon, x A (i) represents the relative position of the aerial vehicle and the landing platform at time i, T represents transposition, P r is the relative position of the aerial vehicle to the landing platform, T A is the estimation of the time required for the aerial vehicle to land, and matrices and are weight matrices, represent the real number set.

[0018] In a preferred embodiment, in the first stage, the estimation of the time required for the aerial vehicle to land T A is:

[0019]

[0020] where ||P r || is the relative distance of the quadcopter aerial vehicle and the landing platform, V r is the relative speed of the quadcopter aerial vehicle and the landing platform, e r represents the direction of the line connecting the quadcopter aerial vehicle and the landing platform.

[0021] In a preferred embodiment, in the second stage, the objective function of the model predictive control method is:

[0022]

[0023] where i denotes different time instants, N is the prediction horizon, x L (i) = [P r (i), V r (i)] T , P r (i) is the relative position of the quadrotor to the landing pad at time i, V r is the relative velocity of the quadrotor and the landing pad; u(i) = [j x (i), j y (i), j z (i)] T is the jerk of the quadrotor, i.e., the control of the quadrotor;

[0024] a L = [a x , a y ] T is the acceleration of the quadrotor in the horizontal plane, and the weight matrix and are constant matrices.

[0025] In a preferred embodiment, in the model predictive control method, when the position and velocity information of the landing pad is estimated and updated, the entire trajectory is re-planned, and each planning solves the following optimization problem:

[0026]

[0027] s.t.x(k+1) = A d x(k) + B d u(k)

[0028] x(0) = x0, x(N) = x f z(k+1) > h p

[0029] |a d (k+1)| < a d,max , |u d (k)| < u d,max c = x, y, z

[0030] k = 0, 1,..., N-1

[0031] where h p is the height of the landing pad, z represents the height position of the quadrotor, x0 represents the initial height of the quadrotor, a d,max represents the acceleration upper limit of the quadrotor, u d,max represents the jerk upper limit of the quadrotor, and d = x, y, z represents different directions.

[0032] In a preferred embodiment, in the model predictive control method of the first and second stages, the prediction horizon is a fixed value and the sampling time is a variable value,

[0033] Sampling time T s is expressed as:

[0034]

[0035] where T A is an estimation of the time required for the aircraft to land, N is the prediction horizon, and a is a constant coefficient.

[0036] In a preferred embodiment, the aircraft is controlled to track the planned trajectory using a cascade incremental dynamic inversion method, in which,

[0037] The controller of the outer loop is set as:

[0038]

[0039] where u t is the control variable of the outer loop, u f is the control variable u t filtered value, is the filtered acceleration, G1 is the control matrix of the outer loop, m represents the mass of the aircraft, T0 is the total thrust generated by the motor at the current time, Θ0 represents the attitude angle at the current time, v t is the virtual control variable of the outer loop;

[0040] The controller of the inner loop is set as:

[0041]

[0042] where u r is the control variable, ω f is the filtered control variable, G2 is the control matrix of the outer loop, is the filtered angular acceleration, v r is the virtual control variable of the inner loop, represents the increment of the motor thrust.

[0043] In a preferred embodiment, in the cascade incremental dynamic inversion method, the dynamics equation of the aircraft is set as:

[0044]

[0045]

[0046] G = [0, 0, mg] T

[0047] Ω = [p, q, r]T

[0048] wherein V is the speed of the aircraft, F c is the thrust generated by the motor, F d is the disturbance force, I q = diag{I x , I y , I z} is the moment of inertia matrix, M c is the moment generated by the motor, M r is the gyroscopic moment, M d is the disturbance moment, Ω is the angular velocity of the aircraft in the body coordinate system, p represents the roll angular velocity in the body coordinate system, q represents the pitch angular velocity, and r represents the yaw angular velocity.

[0049] In a preferred embodiment, the inner loop virtual control quantity v r is obtained by PD control on the position deviation, and is represented as:

[0050]

[0051] wherein P d is the desired position, obtained from the planned trajectory, K p and K d are gain matrices, and P represents the position at the current time;

[0052] The inner loop virtual control quantity v r is obtained by PD control on the attitude deviation, and is represented as:

[0053]

[0054] wherein Θ d is the desired attitude angle, K p ' and K d ' are gain matrices, and Θ represents the attitude angle at the current time.

[0055] The present application has the beneficial effects including:

[0056] (1) According to the actual four-rotor landing process, the landing platform is locked as a node to divide the landing stage, and the objective function is designed respectively, the previous stage focuses on time optimization, which ensures the rapid locking of the landing platform, and the latter stage focuses on stability, which ensures the smooth landing of the aircraft at the end, and meets the speed and attitude requirements during landing;

[0057] (2) The variable sampling time ensures that the sampling frequency of the previous stage is low, which reduces the operation pressure of the onboard computer, facilitates the wide-range search of the landing platform with the sensor information such as vision, and the sampling frequency of the latter stage is high, which fully releases the computing capacity, facilitates multiple planning, corrects the landing trajectory, and ensures the landing accuracy;

[0058] (3) The designed cascade incremental dynamic inverse control method improves the anti-interference ability of the landing system, and the quadrotor aircraft can still stably track the planned trajectory and realize accurate and smooth landing under the influence of external interference. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 A flowchart of a model predictive control-based quadrotor autonomous landing method according to a preferred embodiment of the present application is shown;

[0060] Figure 2 A three-dimensional diagram of the landing process of the quadrotor aircraft in Example 1 is shown;

[0061] Figure 3 Position curves of the quadrotor aircraft and the mobile platform during the landing process in Example 1 are shown;

[0062] Figure 4 Velocity curves of the quadrotor aircraft and the mobile platform during the landing process in Example 1 are shown;

[0063] Figure 5 Attitude curves of the quadrotor aircraft during the landing process in Example 1 are shown;

[0064] Figure 6 Acceleration curves of the quadrotor aircraft during the landing process in Example 1 are shown;

[0065] Figure 7 Sampling times of the model predictive control during the landing process in Example 1 are shown;

[0066] Figure 8 Trajectory points of the model predictive planning during the landing process in Example 1 are shown. DETAILED DESCRIPTION

[0067] The present application will be further described in detail by the accompanying drawings and examples. Through these descriptions, the features and advantages of the present application will become more apparent.

[0068] The special word "exemplary" here means "serving as an example, embodiment or illustration". Any embodiment described as "exemplary" here is not necessarily interpreted as superior or better than other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless specifically indicated.

[0069] The present application provides a model predictive control-based quadrotor autonomous landing method, which divides the landing process of the quadrotor aircraft into a first stage and a second stage, and the model predictive control method is used to plan the trajectory of the aircraft in both the first stage and the second stage, and the objective functions in the model predictive control method are different in the first stage and the second stage.

[0070] Model predictive control (MPC) is one of modern control modes, which is widely used in aerospace, guidance and other fields. In the present application, the model predictive control is used to plan the landing trajectory of the aircraft, and the aircraft realizes autonomous landing by tracking the flight trajectory.

[0071] Further, in the conventional model predictive control based four-rotor autonomous landing method, the whole process is regarded as a complete stage, and a short sampling time is required to improve the accuracy of the aircraft landing. However, this method requires a high requirement for the on-board computer of the aircraft, and the landing time is also long.

[0072] In the present application, a two-stage model predictive control method is provided, and by selecting appropriate target functions in different landing stages, the four-rotor aircraft can be accurately and smoothly landed, and the landing time is shortened.

[0073] In a preferred embodiment, in the model predictive control method of the first stage and the second stage, the dynamic equation of the model is represented as:

[0074]

[0075]

[0076] wherein k represents the discretized time, x(k) is a state vector, representing the state quantity of the aircraft at k time, y(k) is an output vector, representing the output state of the aircraft under the action of the control quantity at k time; A d represents the discretized system matrix, B d represents the discretized control matrix, T s is the sampling period; A represents the system matrix of the original state space of the dynamic equation, B represents the control matrix of the original state space, C represents the output matrix of the original state space, s represents the complex variable of the discrete process, and u(k) represents the control quantity at k time.

[0077] Unlike the prediction model in the conventional model predictive control four-rotor aircraft landing method, the model provided in the present application only considers the position of the four-rotor aircraft, ignores the influence of disturbance, and simplifies it to a three-order integrator model, so as to simplify the model, improve the calculation speed of prediction, and reduce the requirement for the on-board computer. In addition, the cascade incremental dynamic inverse method is used, and a unique controller is set to compensate for the ignored disturbance, so as to ensure the accuracy of landing.

[0078] According to the present application, the distance between the first stage aircraft and the landing platform is farther than the second stage, and preferably, when the relative distance ‖P r ‖ between the four-rotor aircraft and the landing platform is greater than a threshold value When the first stage, less than the threshold value When the second stage, threshold value The specific numerical value can be determined by experience or multiple experiments by those skilled in the art, and the actual visual locking distance is usually 30-50 m during the landing process.

[0079] According to a preferred embodiment of the present application, in the first stage, the objective function of the model predictive control method is:

[0080]

[0081] x A (i) = P r (i)

[0082] Wherein, i represents different time, N is the prediction time domain, x A (i) represents the relative position of the aircraft to the landing platform at i time, the superscript T represents transposition, P r is the relative position of the aircraft to the landing platform, T A is the estimation of the time required for the aircraft to land, and matrices and are weight matrices and positive definite, represents the real number set.

[0083] According to the present application, the matrix Q A influences the speed of the quadcopter approaching the platform, W A is related to the time required for the entire landing process.

[0084] The inventors found that Q A and W A have weak correlation, that is, the faster the aircraft speed, the shorter the time required, and accordingly a dynamic parameter γ is designed for Q A and W A adjustment, that is:

[0085]

[0086] Wherein, ‖P r ‖ is the relative distance between the quadcopter and the landing platform, η is a normalization coefficient, usually taking a value of 10-20, and ensuring that γ ∈ (0, 1).

[0087] Further, the inventors also found that the larger the relative distance ‖P r ‖, the smaller the γ, the larger the speed required, and the time required is as small as possible, according to this rule, those skilled in the art can set the above parameters according to actual needs.

[0088] Preferably, Q A and WA Examples of general values of γ are I:

[0089]

[0090] W A = γ * I

[0091] More preferably, in the first phase, the estimate T A of the time required for the aircraft to land is:

[0092]

[0093] where ||P r || is the relative distance of the quadcopter and the landing platform, V r is the relative speed of the quadcopter and the landing platform, and e r represents the direction of the line connecting the quadcopter and the landing platform.

[0094] According to the present application, in the first phase, the quadcopter is far away from the landing platform, and the above settings enable the aircraft to spend less time approaching and detecting the landing mark. Specifically, the relative position P r and the relative speed V r can be obtained by detecting the landing platform and estimating the state, thereby simplifying the parameters involved in the design of the predictive control. Although the curve flight trajectory of the aircraft causes errors in this estimation method and reduces the accuracy of the trajectory, the rapid re-planning of the model predictive control compensates for this error to some extent, and the quadcopter is far away from the landing platform, so the trajectory accuracy obtained in the first phase enables the aircraft to quickly approach the landing platform. Moreover, as the aircraft approaches the landing platform, the estimate of T A becomes more and more accurate, and the obtained trajectory becomes more and more accurate, fully meeting the accuracy required for the aircraft to approach the landing platform.

[0095] According to the present application, in the second phase, the objective function of the model predictive control method is:

[0096]

[0097] where i represents different time points, N is the prediction time domain, x L (i) = [P r (i), V r (i)] T , P r (i) is the relative position of the aircraft from the landing platform at time i, V r (i) is the relative speed of the quadcopter and the landing platform at time i; u(i) = [j x (i), j y (i), jz (i)] T is the jerk of the quadrotor at time i, i.e. the control variable of the quadrotor;

[0098] a L = [a x , a y ] T is the acceleration of the quadrotor in the horizontal plane, the weight matrix and are constant matrices, where Q L is positive semi-definite.

[0099] In the second stage, the above objective function mainly considers the smoothness of the trajectory and the terminal attitude, so that the generated trajectory is as smooth as possible, preventing the maneuver from being too large to cause the loss of the landing platform target; at the same time, the attitude angle of the quadrotor at the terminal is as small as possible to avoid the quadrotor from tipping over when it meets the landing platform,

[0100] Specifically, Q L determines the landing accuracy, and R L is adjusted to make the generated trajectory as smooth as possible; by adjusting the weight W L of the terminal horizontal acceleration, the attitude angle of the quadrotor when meeting is reduced, thereby ensuring the final smooth landing.

[0101] In a preferred embodiment, Q L is positive semi-definite, and I is taken as an example,

[0102]

[0103] The diagonal main elements of Q L correspond to P L (i) of x r (i), i.e. the control relative position; R L and W L are positive definite matrices, and the parameters of the main diagonal elements thereof need to be adjusted according to actual conditions; λ is generally relatively small, and the value range is 0-1, R L the main diagonal element takes a value of 5-15, and W L the main diagonal element takes a value range of 1-5.

[0104] According to a preferred embodiment of the present application, in the model predictive control method, when the position and speed information of the landing platform are estimated and updated, the entire trajectory is re-planned, and each time the following optimization problem is solved:

[0105]

[0106] s.t.x(k+1)=A d x(k)+Bd u(k)

[0107] x(0)=x0,x(N)=x f z(k+1)>h p

[0108] |a d (k+1)|≤a d,max ,|u d (k)|≤u d,max ,d=x,y,z

[0109] k = 0, 1, ..., N-1

[0110] Among them, h p Let z represent the altitude of the landing platform, z represent the altitude position of the aircraft, x0 represent the initial altitude of the aircraft, and a represent the altitude of the landing platform. d,max u represents the upper limit of the aircraft's acceleration. d,max This represents the upper limit of the aircraft's jerk, where d = x, y, z represent different directions.

[0111] Specifically, the state and control constraints of the rotorcraft can be obtained through differential flatness theory, which will not be elaborated upon in this invention. When the pitch angle is zero, the horizontal acceleration is a. x =gθ, a y =gφ, where g represents gravitational acceleration, θ represents pitch angle, and φ represents roll angle. The maximum attitude angle φ of the quadcopter... max and θ max We can obtain the upper bound of horizontal acceleration by using the same method, and we can also obtain the upper bound of horizontal jerk.

[0112] In this invention, the specific solution process will not be described in detail. Preferably, the CVXGEN toolbox can be used to solve the problem, reducing the pressure of real-time calculation and obtaining the planned trajectory.

[0113] Unlike traditional model predictive control methods for autonomous landing of aircraft, in this invention, the prediction time domain is a fixed value while the sampling time is a variable value in the first and second stages of the model predictive control method.

[0114] Sampling time T s Represented as:

[0115]

[0116] Among them, T A This is an estimate of the time required for the aircraft to land, where N is the prediction time domain and α is a constant coefficient, typically 0-1.

[0117] The sampling time gradually decreases as the quadrotor approaches the landing platform, so that the planned trajectory is constantly corrected to meet the landing accuracy requirements. When the relative distance is large, the landing accuracy requirement is relatively low, and the use of a longer sampling time can greatly reduce the calculation amount.

[0118] In a preferred embodiment, the planned trajectory is also linearly interpolated. Since the control period of the first stage controller is much smaller than the sampling time, the linear interpolation setting can improve the control performance. Specifically, the linear interpolation can be expressed as:

[0119]

[0120] where k = 0, 1,..., N-1, k represents different sampling points, t(k) represents the time of the k sampling point, t(c) represents the inserted sampling point, and x(k) represents the value collected at the k sampling point.

[0121] The sampling interval in linear interpolation is determined by the control period of the controller.

[0122] According to a preferred embodiment of the present application, the Incremental Nonlinear Dynamic Inversion (INDI) method is used to control the aircraft to track the planned trajectory. The INDI method is a method for designing flight control laws, which has been widely proven to be a control method that can be easily applied and has strong robustness and fault tolerance performance. The INDI control method designed based on sensor measurement information can reduce the dependence on the model, enhancing the robustness of the system. Moreover, INDI does not need to design complex neural networks or real-time identification to estimate the aircraft model, and it is easy to implement in open source flight control.

[0123] Further, in the present application, in the Incremental Nonlinear Dynamic Inversion method, the controller of the outer loop is set as:

[0124]

[0125] where u t is the control quantity of the outer loop, u f is the control quantity u t is the filtered value, is the filtered acceleration, which can be obtained by the measurement value of the accelerometer, G1 is the control matrix of the outer loop, which can be obtained by the Taylor expansion formula of the dynamics equation, m represents the mass of the aircraft, T0 is the total thrust generated by the motor at the current time, Θ0 represents the attitude angle, v t is the virtual control quantity of the outer loop; and u t = [φ d , θ d , Td T d d d are the calculated desired roll angle, pitch angle and desired thrust respectively.

[0126] Further, different from the traditional cascade controller, in the present application, the controller of the inner loop is set as:

[0127]

[0128] wherein u r is the control quantity, ω f is the filtered control quantity, G2 is the control matrix of the outer loop, is the filtered angular acceleration, v r is the virtual control quantity of the inner loop, represents the increment of the motor thrust.

[0129] Further, the increment of the motor thrust T d is the desired thrust calculated by the outer loop, T f is the current filtered thrust.

[0130] Further, in the cascade increment dynamic inversion method, the dynamics equation of the aircraft is set as:

[0131]

[0132]

[0133] G = [0, 0, mg] T

[0134] Ω = [p, q, r] T

[0135] wherein V is the speed of the aircraft, F c is the thrust generated by the motor, F d is the disturbance force, I q = diag{I x , I y , I z} is the moment of inertia matrix, M c is the motor generated torque, M r is the gyroscopic torque, M d is the disturbance torque, Ω is the angular velocity of the aircraft in the body coordinate system, p represents the angular velocity around the x-axis of the body system, q represents the angular velocity around the y-axis of the body system, and r represents the angular velocity around the z-axis of the body system.

[0136] Further, the virtual control quantity v r ​​​​The position deviation is obtained by PD control, and is expressed as:

[0137]

[0138] P is the desired position, K d P is obtained from the planned trajectory, K p and K d are gain matrices, P represents the position at the current time; K p , K d both need to be debugged according to the control situation, and generally take a value range of 0-1.

[0139] The inner loop virtual control quantity v r is obtained by PD control on the attitude deviation, and is expressed as:

[0140]

[0141] K p ′, K d ′ generally take a value range of 0-1.

[0142] Embodiment

[0143] Embodiment 1

[0144] A simulation experiment is set, in which the landing platform moves linearly, the quadrotor aircraft has a mass of 0.96 kg, and the moment of inertia matrix is I q = diag{0.039, 0.034, 0.071} kg·m 2 , the distance l of each motor to the center along the x and y axes of the body coordinate system is 0.16 m; in the model predictive control, the prediction time domain N = 20, the acceleration constraint of the aircraft during the entire landing process is a min,i = -5 m / s 2 , a max,i = 5 m / s 2 , the jerk constraint is j min,d = -10 m / s 3 , j max,d = 10 m / s 3 , and d = x, y, z. At the same time, the disturbance torque M a = I q [1+sin(5t), 1+cos(5t), 0.5(1+sin(5t)+cos(5t))] T N·m.

[0145] The initial position of the quadrotor aircraft is [0, -20, 20] T m, and the initial speed is [2, 0, 0] T m / s. The initial position of the moving platform is [50, 7, 2]T m, and moves along the x-axis at a speed of 3m / s.

[0146] In the experiment, the landing process of the quadrotor is divided into a first stage and a second stage, and the model predictive control method is used to plan the trajectory of the aircraft in the first stage and the second stage. In the model predictive control method in the first stage and the second stage, the dynamic equation of the model is expressed as:

[0147]

[0148] In the first stage, the objective function of the model predictive control method is:

[0149]

[0150] The matrix and W A are set as:

[0151]

[0152] W A = 0.9

[0153] The estimation T of the time required for the aircraft to land is: A

[0154]

[0155] In the second stage, the objective function of the model predictive control method is:

[0156]

[0157] The weight matrix and are set as:

[0158]

[0159]

[0160]

[0161] In the model predictive control method, when the position and velocity information of the landing platform are estimated and updated, the entire trajectory is re-planned, and each planning solves the following optimization problem:

[0162]

[0163] s.t.x(k+1)=A d x(k)+B d u(k)

[0164] x(0)=x0,x(N)=x​f z(k+1) > h p

[0165] |a i (k+1)|≤a i,max ,|u i (k)|≤u i,max ,i=x,y,z

[0166] k=0,1,…,N-1

[0167] In the model predictive control method of the first stage and the second stage, the prediction time domain is a fixed value, and the sampling time is a variable value,

[0168] The sampling time T s is expressed as:

[0169]

[0170] Alpha is 0.25.

[0171] The aircraft tracks the planning trajectory flight by using the cascade incremental dynamic inverse method control, in the cascade incremental dynamic inverse method,

[0172] The controller of the outer ring is set as:

[0173]

[0174] The controller of the inner ring is set as:

[0175]

[0176] In the cascade incremental dynamic inverse method, the dynamic equation of the aircraft is set as:

[0177]

[0178]

[0179] The finally obtained simulation results are shown in Figures 2 to 8 .

[0180] Wherein, Figure 2 The three-dimensional diagram of the landing process of the quad-rotor aircraft is shown, it can be seen that the landing accuracy of the trajectory gradually improves as the aircraft approaches the mobile platform, and under the influence of external interference, the quad-rotor aircraft can accurately track the reference trajectory and complete landing.

[0181] Figure 3 And Figure 4The position and velocity curves of the quadcopter and the mobile platform during the landing process are given separately. As can be seen from the figures, the quadcopter completes its landing in approximately 25 seconds. When the quadcopter lands on the mobile platform, the positions and velocities of both are equal, satisfying the set terminal constraints. Figure 5 As can be seen, during the landing process, once the aircraft's position and speed in the y-direction are aligned with the moving platform, it approaches the landing platform in the other two directions without needing to track the platform for a certain distance, thus reducing the landing time.

[0182] Figure 5 and Figure 6 The attitude and acceleration curves of the quadcopter during landing are shown separately. Figure 5 It can be seen that when the quadcopter rendezvous with the mobile platform, both the pitch and roll angles are less than 6°. Therefore, the defined objective function can ensure that the aircraft achieves a smooth landing and will not overturn due to excessive attitude angles. From Figure 7 It can be seen that the aircraft's acceleration satisfies the constraints given in the model predictive control throughout the entire landing process.

[0183] Figure 7 The sampling time of the model predictive control during the landing process is shown. It can be seen that the sampling time gradually decreases. When the relative distance is large, the landing accuracy requirement of the planned trajectory is low, and using a longer time is beneficial to reduce the computational cost of solving the optimization problem. As the relative distance decreases, the sampling time shortens, thereby continuously improving the planned trajectory and improving the landing accuracy. This method not only optimizes the entire landing trajectory, but also takes into account both computational cost and landing accuracy.

[0184] This is Figure 8 This can also be reflected in the text. Figure 8 The diagram shows the trajectory points predicted and planned by the model during the landing process. The dashed lines in the diagram represent the times when the state information is updated, and the short lines represent the planned trajectory points. Each time the platform state information is updated, a new trajectory will be planned. In the initial stage, the time interval between trajectory points is relatively long. As the distance between the aircraft and the mobile platform decreases, the new trajectory points obtained within the same time interval gradually become denser, so as to correct the trajectory.

[0185] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship in the working state of this invention, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0186] In the description of the application, it should be noted that unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting" should be understood in a broad sense, for example, it can be fixed connection, or detachable connection, or integral connection; it can be mechanical connection, or electrical connection; it can be direct connection, or indirect connection through intermediate medium; it can be internal communication of two elements. For those skilled in the art, the specific meaning of the above terms in the application can be understood according to the specific circumstances.

[0187] The above describes the application in combination with the preferred embodiments, but these embodiments are only exemplary and serve only to illustrate. On this basis, various substitutions and improvements can be made to the application, which all fall within the protection scope of the application.

Claims

1. A model predictive control based quadrotor autonomous landing method, characterized in that, The landing process of the quadrotor is divided into a first stage and a second stage, the distance between the quadrotor and the landing platform in the first stage is farther than that in the second stage, The model predictive control method is used to plan the trajectory of the quadrotor in the first stage and the second stage, the objective functions in the model predictive control method in the first stage and the second stage are different; In the model predictive control method in the first stage and the second stage, the dynamic equation of the model is expressed as: where k represents different time, x(k) is a state vector, representing the state quantity of the aircraft at k time, y(k) is an output vector, representing the output state of the aircraft under the action of the control quantity at k time;A d represents the discretized system matrix, B d represents the discretized input matrix, T s is a sampling period;A represents the system matrix of the state space, B represents the control matrix of the state space, C represents the output matrix of the state space, s represents a complex variable in a discrete process, and u(k) represents a control quantity at k time; In the first stage, the objective function of the model predictive control method is: x A (i) = P r (i) where i denotes different time instants, N is the prediction horizon, x A (i) denotes the relative position of the aircraft and the landing platform at time i, T denotes the transpose, P r is the relative position of the aircraft from the landing platform, T A is the estimate of the time needed for the aircraft to land, the matrix and are weight matrices, denotes the set of real numbers; In the second stage, the objective function of the model predictive control method is: where i represents different time, N is the prediction horizon, x L (i) = [P r (i), V r (i)] T , P r (i) is the relative position of the quadrotor to the landing platform at time i, V r is the relative velocity of the quadrotor and the landing platform; u(i) = [j x (i), j y (i), j z (i)] T is the jerk of the quadrotor, i.e., the control variable of the quadrotor; a L = [a x ,a y ] T is the acceleration of the aircraft in the horizontal plane, the weight matrix and are constant matrices.

2. The model predictive control based quadrotor autonomous landing method according to claim 1, characterized in that, First phase, estimation of the time T required for the aircraft to land A is: wherein ||P r is the relative distance between the quadcopter and the landing platform, V r is the relative velocity between the quadcopter and the landing platform, e r denotes the direction of the line connecting the quadcopter and the landing platform.

3. The model predictive control based quadrotor autonomous landing method according to claim 1, characterized in that, In the model predictive control method, when the position and velocity information of the landing platform are estimated and updated, the whole trajectory is re-planned, and each planning solves the following optimization problem: s.t. x(k+1) = A d x(k) + B d u(k) x(0) = x0, x(N) = x f z(k + 1) > h p |a d (k+1)|≤a d,max ,|u d (k)|≤u d,max ,d=x,y,z k=0,1,…,N-1 where h p is the height of the landing platform, z denotes the height position of the aircraft, xo denotes the state vector at the initial time, a d,max denotes the upper limit of the acceleration of the aircraft, u d,max denotes the upper limit of the jerk of the aircraft, d = x, y, z denotes different directions.

4. The model predictive control based quadrotor autonomous landing method according to claim 1, characterized in that, In the model predictive control method in the first stage and the second stage, the prediction horizon is a fixed value, and the sampling time is a variable value, Sampling time T s is represented as: where T A is an estimate of the time required for the aircraft to land, N is the prediction horizon, and a is a constant factor.

5. The model predictive control based quadrotor autonomous landing method according to claim 1, characterized in that, The cascade incremental dynamic inversion method is used to control the quadrotor to track and fly along the planned trajectory, in the cascade incremental dynamic inversion method, The controller of the outer loop is set as: wherein u t is the control quantity of the outer loop, u f is the control quantity u t is the filtered value, is the filtered acceleration, G1is the control matrix of the outer loop, m represents the mass of the aircraft, T0is the total thrust generated by the motor at the current time, Θ0represents the attitude angle at the current time, v t is the virtual control quantity of the outer loop; The controller of the inner loop is set as: wherein u r is a control quantity, represents the rotational speed of the motor, ω f is a filtered control quantity, G2 is a control matrix of the outer loop, is a filtered angular acceleration, v r is an inner loop virtual control quantity, represents an increment of the motor thrust.

6. The model predictive control based quadrotor autonomous landing method according to claim 5, characterized in that, In the cascade incremental dynamic inversion method, the dynamic equation of the quadrotor is set as: G = [0, 0, mg] T Ω = [p, q, r] T where V is the velocity of the aircraft, F c is the thrust generated by the motor, F d is the disturbance force, I q = diag{I x , I y , I z} is the moment of inertia matrix, M c is the moment generated by the motor, M r is the gyroscopic moment, M d is the disturbance moment, and Ω is the angular velocity of the aircraft in the body frame, p represents the roll angular velocity in the body frame, q represents the pitch angular velocity, and r represents the yaw angular velocity.

7. The model predictive control based quadrotor autonomous landing method according to claim 5, characterized in that, inner loop virtual control variable v r is obtained by PD control of the position deviation, and is expressed as: where P d is the desired position, obtained from the planned trajectory, K p and K d are gain matrices, and P represents the current position; inner loop virtual control variable v r is obtained by PD control of the attitude deviation and is expressed as where Θ d is the desired attitude angle, K p ′ and K d ′ is the gain matrix, and Θ represents the attitude angle at the current time.

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