Quad-rotor unmanned aerial vehicle trajectory tracking control method, quad-rotor unmanned aerial vehicle and storage medium

Abstract

The invention discloses a quadrotor unmanned aerial vehicle trajectory tracking control method, a quadrotor unmanned aerial vehicle and a storage medium, and relates to the technical field of unmanned aerial vehicle control. The method is technically characterized by comprising the following steps: firstly, providing a fast terminal sliding mode disturbance observer for unknown disturbance of a system so as to realize accurate estimation of the disturbance within preset time; then designing a preset time fast terminal sliding mode controller based on disturbance estimation information, and further weakening a buffeting phenomenon of the system by using a saturation function; finally, based on a Lyapunov function method, it is proved that the system can achieve global predetermined time stability; according to the method, predefined time convergence of the trajectory tracking error of the quad-rotor unmanned aerial vehicle under unknown disturbance can be realized, the upper bound of the stabilization time can be randomly preset in a physical limitation range, the rapidity of the system is ensured, buffeting is eliminated, and the stability of the system is improved.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to a method for trajectory tracking and control of a quadcopter UAV, a quadcopter UAV, and a storage medium. Background Technology

[0002] In recent years, quadcopter drones have attracted widespread attention in both military and civilian fields due to their simple structure, vertical takeoff and landing capabilities, and high maneuverability. Attitude and position control of quadcopter drones is the core of achieving tasks such as trajectory tracking, attitude stabilization, and position stabilization, and is of great significance for meeting the requirements of high-performance missions. However, the design of attitude and position control for quadcopter drones faces several challenges. First, it is an underactuated, nonlinear, and strongly coupled system. Second, unknown disturbances such as external wind, electromagnetic interference, and model uncertainties can seriously affect control performance and threaten flight safety. Therefore, drones must be equipped with fast and robust controllers that can effectively cope with time-varying disturbances under harsh flight conditions. Summary of the Invention

[0003] The main objective of this invention is to propose a UAV trajectory tracking control method, a quadcopter UAV, and a storage medium. A predetermined time sliding mode observer is designed, which can quickly and accurately estimate unknown disturbances. Based on this estimation information, a predetermined time fast terminal sliding mode controller is designed, which can achieve global predetermined time stability of the system, effectively reduce chattering, and ensure the speed and robustness of the system.

[0004] To achieve the above objectives, in a first aspect, the present invention proposes a method for tracking and controlling the trajectory of an unmanned aerial vehicle (UAV), comprising:

[0005] S1: Assuming the quadcopter UAV is a symmetrical rigid body structure, starting from the kinematics of the rigid body and based on the Newton-Euler-Lagrange method, we establish the disturbed dynamic equations of the quadcopter UAV in the Earth coordinate system.

[0006] S2: The torques acting on the three axes of the fuselage position ring are decoupled in three channels to obtain the corresponding three-channel virtual control quantities; and based on these virtual torques, the desired roll angle and pitch angle signals are solved in reverse, thus establishing a dynamic model of the tracking error of the quadcopter UAV.

[0007] S3: For the tracking error system in S2, based on the predetermined time stability theory and combined with the sliding mode control method, a disturbance observer is designed to achieve accurate estimation and compensation of unknown disturbances within a predetermined time.

[0008] S4: Based on the disturbance estimation information in S3, design a fast terminal sliding mode controller with a predetermined time to realize the position and attitude control of the quadcopter UAV and ensure the rapid convergence of tracking error;

[0009] S5: Design a Lyapunov function based on Lyapunov stability theory and prove the stability of the invented method.

[0010] In one embodiment, the disturbed dynamics model of the quadcopter UAV in S1 is as follows:

[0011]

[0012] Equation (1) is the position loop dynamic equation, and equation (2) is the attitude loop dynamic equation; where x, y, z are the positions of the center of mass of the quadcopter UAV in the Earth coordinate system, φ, θ, ψ are the roll angle, pitch angle, and yaw angle of the UAV in the Earth coordinate system, respectively; m is the mass of the quadcopter UAV, g is the gravitational acceleration; k p and k a I represents the drag coefficients of the position and attitude systems, respectively; x ,I y and I z Representing the x-axis around the body coordinate axis respectively b axis, y b axis and z b Moment of inertia of the shaft; d x ,d y ,d z and d φ ,d θ ,d ψ Let u be the external disturbances in the position system and attitude system, respectively, and assume that the disturbances are bounded; φ ,u θ ,u ψ For the three-axis control torque of the UAV attitude loop; u x ,u y ,u z This is a virtual control variable for the position loop.

[0013] In one embodiment, the establishment of the dynamic model of the quadcopter UAV tracking error in S2 specifically includes the following steps:

[0014] The virtual control quantity of the position loop and the UAV along z b The relationship between the total lift u of the shaft is decoupled as follows:

[0015]

[0016] In the above formula: S (·) C (·) These represent the abbreviations for the trigonometric functions sin(·) and cos(·), respectively. Based on equation (3), the virtual control quantity u for generating the position loop is... x ,u y ,u zRequired total lift u and desired attitude angle φ d ,θ d They are respectively

[0017]

[0018] For ease of description, the quadcopter unmanned aerial vehicle systems (1) and (2) can be represented as follows:

[0019]

[0020] Where i = x, y, z, φ, θ, ψ; |d i |≤D i D i ≥0.

[0021] Define the system tracking error e i =ii d The UAV tracking error system can then be written as:

[0022]

[0023] In one embodiment, the predetermined time sliding mode perturbation observer designed in S3 is as follows:

[0024]

[0025] in λ>0, μ>0, k≥D i , Then the disturbance observation error Achieve convergence within the predetermined time, i.e., convergence time T 0i satisfy:

[0026]

[0027] In one embodiment, the predetermined time fast terminal sliding mode controller designed in S4 is as follows:

[0028]

[0029] Where 0 < ι < 1, X > 0, If e is a natural constant, then the tracking error system achieves convergence within a predetermined time, i.e., the convergence time satisfies:

[0030]

[0031] In one embodiment, the system stability proof in S5 includes the following steps:

[0032] S5-1: Introduce relevant lemmas and theorems;

[0033] Lemma 1: If there exists a positive definite Lyapunov function V satisfying...

[0034]

[0035] in 0<α≤1, λ>0, μ>0, T c If the value is greater than 0, then the system is globally time-stable, meaning the settling time satisfies T(x0) ≤ T. c .

[0036] Theorem 1: If there exists a positive definite Lyapunov function V satisfying:

[0037]

[0038] Where 0 < ι < 1, X > 0, T c If the value is greater than 0, the system achieves global time-stability, meaning the stable time satisfies T(x0) ≤ T. c .

[0039] Prove that integrating equation (12) yields the following:

[0040]

[0041] Therefore

[0042]

[0043] Q.E.D.

[0044] Theorem 2: If there exists a positive definite Lyapunov function V satisfying:

[0045]

[0046] Where 0 < X ​​< 1, T c If e > 0 and e is a natural constant, then the system achieves global predetermined time stability, i.e., the stability time satisfies T(x0) ≤ T. c .

[0047] Prove that integrating equation (13) yields the following:

[0048]

[0049] Therefore

[0050]

[0051] Let function It can be calculated by the software MATLAB. The steady-state time then satisfies

[0052]

[0053] Q.E.D.

[0054] S5-2: Proof of stability of sliding mode disturbance observer at predetermined time;

[0055] S5-3: Proof of stability of the scheduled time fast terminal sliding mode controller.

[0056] In one embodiment, S5-2 includes:

[0057] For s in equation (7) i0 =e i0 +e i1 Differentiating both sides, we get

[0058]

[0059] Define Lyapunov functions but

[0060]

[0061] From Lemma 1, we can obtain the sliding mode variable s i0 The scheduled time converges, and the arrival time satisfies the condition.

[0062]

[0063] When the state reaches the sliding surface, i.e., s i0 =0, there is e i0 =-e i1 Differentiating, we get

[0064]

[0065] Define Lyapunov functions but

[0066]

[0067] By Lemma 1, we obtain the variable e i0 The convergence occurs within the predetermined time, and the convergence time satisfies the following conditions:

[0068]

[0069] at the same time Convergence, that is The convergence occurred within the predetermined time; Q.E.D.

[0070] In one embodiment, S5-3 includes:

[0071] Define Lyapunov functions but

[0072]

[0073] According to Theorem 2, the sliding mode variable s i It converges at the scheduled time; the system converges at the scheduled time. The system reaches the sliding surface. Once the system state reaches the sliding surface, i.e., s... i =0, there is

[0074]

[0075] Define Lyapunov functions but

[0076]

[0077] According to Theorem 1, the error variable e i It converges within a predetermined time; after the system reaches the sliding surface, the error is within the predetermined time. Converging inwards; Q.E.D.

[0078] Secondly, embodiments of the present invention provide a quadcopter drone, comprising:

[0079] processor;

[0080] A memory, coupled to the processor, stores program instructions for implementing the quadcopter UAV trajectory tracking control method as described in the above embodiments;

[0081] The processor is used to execute the program instructions stored in the memory to control the flight trajectory of the quadcopter drone.

[0082] Thirdly, embodiments of the present invention provide a storage medium, including: a processor;

[0083] The memory stores a computer program that can run on the processor, and when executed by the processor, the computer program is a program file that implements the quadcopter UAV trajectory tracking control method as described in the above embodiments.

[0084] This invention first proposes a fast terminal sliding mode disturbance observer to accurately estimate the disturbance within a predetermined time, addressing the unknown disturbances in the system. Then, based on the disturbance estimation information, a predetermined-time fast terminal sliding mode controller is designed, and a saturation function is further used to reduce the system's chattering phenomenon. Finally, based on the Lyapunov function method, it is proved that the system can achieve global predetermined-time stability. This invention can achieve predefined-time convergence of the trajectory tracking error of a quadcopter UAV under unknown disturbances. The upper bound of the stability time can be arbitrarily preset within physical constraints, ensuring the system's speed, eliminating chattering, and improving system stability. The invention also explores the control problem of a quadcopter UAV with unknown disturbances achieving trajectory tracking within a predetermined time. This method ensures that the system's tracking error converges to near zero within the predetermined time. Facing unknown disturbances, this method demonstrates good adaptability, ensuring stable flight of the UAV in complex environments. Furthermore, the upper limits of the convergence time for attitude and position can be arbitrarily preset within physical constraints. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0086] Figure 1 This is a schematic diagram of the trajectory tracking and control method for a quadcopter UAV according to the present invention;

[0087] Figure 2 This is a graph showing the sliding mode variable changes of the sliding mode disturbance observer at a predetermined time in the trajectory tracking and control method for quadcopter unmanned aerial vehicles of the present invention.

[0088] Figure 3 This is a real-time estimation diagram of the unknown disturbance in the position loop of a quadrotor UAV, which is the trajectory tracking and control method of the quadrotor UAV of the present invention.

[0089] Figure 4 This is a real-time estimation diagram of unknown disturbances in the attitude loop of a quadrotor UAV, which is the trajectory tracking and control method of the quadrotor UAV of the present invention.

[0090] Figure 5 This is a graph showing the sliding mode variable changes of the sliding mode controller in the predetermined time fast terminal sliding mode controller of the quadcopter UAV trajectory tracking control method of the present invention;

[0091] Figure 6 The diagram shows the position and attitude tracking error curves of the quadrotor UAV, which is part of the trajectory tracking control method for quadrotor UAVs of the present invention.

[0092] Figure 7This is a trend diagram of the three-axis velocity variation of the quadrotor UAV position loop in the trajectory tracking control method of the present invention.

[0093] Figure 8 This is a graph showing the trend of attitude angular velocity variation of a quadrotor UAV, which is part of the trajectory tracking and control method for quadrotor UAVs of the present invention.

[0094] Figure 9 This is a curve of the virtual control quantity of the quadrotor UAV position in the trajectory tracking and control method of the present invention.

[0095] Figure 10 This invention provides a three-axis control torque diagram for the attitude loop of a quadrotor UAV, illustrating the trajectory tracking and control method for quadrotor UAVs.

[0096] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0097] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0098] It should be noted that if the embodiments of the present invention involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative positional relationship and movement of the components in a specific posture. If the specific posture changes, the directional indications will also change accordingly.

[0099] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the use of "and / or" or "and / or" throughout the text includes three parallel solutions. For example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0100] In recent years, quadcopter unmanned aerial vehicles (UAVs) have attracted widespread attention in both military and civilian fields due to their simple structure, vertical takeoff and landing capabilities, and high maneuverability. Attitude and position control of quadcopter UAVs is crucial for achieving tasks such as trajectory tracking, attitude stabilization, and position stabilization, and is of great significance for meeting high-performance mission requirements. However, the design of attitude and position control for quadcopter UAVs faces several challenges. First, it is an underactuated, nonlinear, and strongly coupled system; second, unknown disturbances such as external wind, electromagnetic interference, and model uncertainties can severely affect control performance and threaten flight safety. Therefore, UAVs must be equipped with fast and robust controllers capable of effectively responding to time-varying disturbances under harsh flight conditions.

[0101] Unmanned aerial vehicle (UAV) control faces numerous limitations and challenges. To address these, the academic community has proposed various control strategies aimed at optimizing system performance and ensuring stability. Examples include the classic PID controller, the linear quadratic regulator (LQR), and the nonlinear model predictive control (NMPC) method. However, none of these controllers possess finite-time stability. Among these control strategies, sliding mode control (SMC) has been widely used in UAV trajectory tracking control due to its strong robustness to system parameter and model uncertainties and external disturbances, and its ability to effectively guarantee stability. Based on different stability characteristics, SMC can generally be classified into four categories: (1) asymptotic stability; (2) finite-time stability; (3) fixed-time stability; and (4) predefined-time stability.

[0102] Traditional sliding mode control typically employs a linear sliding surface to achieve asymptotic convergence of tracking errors. However, asymptotically convergent controllers cannot set a clear upper bound on the convergence time. Therefore, finite-time stability is studied to determine this upper bound. Some researchers have proposed fractional-order fast terminal sliding surfaces and integral terminal sliding surfaces, achieving finite-time convergence with both speed and robustness. However, it's important to note that the convergence time of a finite-time stable system depends on the initial conditions; when the initial system state is far from the origin, the convergence time may approach infinity. Therefore, fixed-time stability is studied, ensuring that the upper bound of the convergence time depends only on the control parameters and is unaffected by initial conditions. To achieve fixed-time stability, a sliding function is constructed using a power function, but this introduces the singularity problem inherent in fixed-time controllers. To address this, some researchers have introduced an auxiliary polynomial function, effectively avoiding singularities and ensuring convergence accuracy, but this also introduces chattering. To address this, Rui-Qi Dong et al. proposed a sliding mode function based on a cosine function to ensure the fixed-time stability of the closed-loop system without singularities, and solved the chatter problem by slightly modifying the proposed controller. Furthermore, Sanchez-Torres et al. introduced the concept of predefined time stability, a special case of fixed-time stability. The upper bound of the convergence time of predefined time control can be directly determined by a specific parameter. Some scholars, by combining the concept of predefined time stability, have proposed a jitter-free, robust predefined-time sliding mode control scheme to solve the trajectory tracking control problem of remotely operated underwater vehicles.

[0103] Existing technologies propose a novel predetermined-time sliding mode control strategy for achieving predetermined-time synchronization of chaotic systems. Simulations show that this scheme has a shorter synchronization time advantage compared to previous finite-time and fixed-time control schemes. Furthermore, researchers have summarized a general Lyapunov condition for achieving predetermined-time stability and designed a robust controller. Some scholars have further extended the aforementioned general Lyapunov characteristic, providing a unified approach to achieve predefined-time stability of dynamic systems, and based on this, designed a predefined-time sliding mode controller.

[0104] This invention designs a controller based on a predefined stability theory to obtain a clear upper bound on the stable time, achieving predetermined time stability and ensuring the system's speed and robustness. Although sliding mode control (SMC) is widely used due to its simplicity and strong robustness, it requires a high switching control gain to handle disturbances and uncertainties, leading to chattering. In practical flight applications, chattering significantly impacts the stability and robustness of actuator systems and is therefore considered a negative effect of sliding mode control. An effective solution is to use a disturbance observer to accurately estimate the system's external disturbances and uncertainties, allowing for the design of real-time compensation strategies to reduce chattering amplitude and improve control accuracy and robustness. Recent research has proposed a robust controller based on a disturbance observer, highlighting the importance of this control scheme and its potential applications. For example, existing technologies have proposed control methods combining nonlinear disturbance observers, nonlinear finite-time disturbance observers, finite-time extended state observers, and nonsingular terminal sliding mode, achieving finite-time stability of quadcopter UAVs under external disturbances and parameter uncertainties. To further improve control performance, this invention combines predefined time stability theory and fast terminal sliding mode design to create a predetermined time sliding mode observer, which can accurately estimate unknown disturbances within a predetermined time, reduce chattering, and ensure the robustness of the system.

[0105] This invention addresses the rapid trajectory tracking control of a quadcopter UAV under unknown disturbances, proposing a global predetermined-time sliding mode control method to ensure that the system tracking error converges to near zero within a predetermined time. First, for the unknown disturbances of the system, a fast terminal sliding mode disturbance observer is proposed to achieve accurate estimation of the disturbance within a predetermined time. Then, based on the disturbance estimation information, a predetermined-time fast terminal sliding mode controller is designed, and the global predetermined-time stability of the system is proved based on the Lyapunov function method. Finally, simulation experiments verify the effectiveness of the proposed control method. The specific steps include:

[0106] S1: Assuming the quadcopter UAV is a symmetrical rigid body structure, starting from the kinematics of the rigid body and based on the Newton-Euler Lagrange method, we establish the disturbed dynamic equations of the quadcopter UAV in the Earth coordinate system.

[0107] S2: The torques acting on the three axes (X-axis, Y-axis, and Z-axis) of the fuselage position ring are decoupled in three channels to obtain the corresponding three-channel virtual control quantities. Based on these virtual torques, the desired roll angle and pitch angle signals are solved inversely, thus establishing a dynamic model of the tracking error of the quadcopter UAV.

[0108] S3: For the tracking error system in S2, based on the predetermined time stability theory and combined with the sliding mode control method, a disturbance observer is designed to achieve accurate estimation and compensation of unknown disturbances within a predetermined time.

[0109] S4: Based on the disturbance estimation information in S3, a fast terminal sliding mode controller with a predetermined time is designed to realize the position and attitude control of the quadcopter UAV and ensure the rapid convergence of tracking error.

[0110] S5: Design a Lyapunov function based on Lyapunov stability theory and prove the stability of the invented method.

[0111] S6: Simulation experiments were conducted using MATLAB software to verify that the tracking error system can converge within a predetermined time.

[0112] In one embodiment of this application, the disturbed dynamics model of the quadcopter UAV in S1 is as follows:

[0113]

[0114]

[0115] Equation (1) is the position loop dynamics equation, and equation (2) is the attitude loop dynamics equation. In the equations: x, y, z are the positions of the quadcopter UAV's center of mass in the Earth coordinate system; φ, θ, ψ are the roll angle, pitch angle, and yaw angle of the UAV in the Earth coordinate system, respectively; m is the mass of the quadcopter UAV; g is the acceleration due to gravity; k p and k a I represents the drag coefficients of the position and attitude systems, respectively; x ,I y and I z Representing the x-axis around the body coordinate axis respectively b axis, y b axis and z b Moment of inertia of the shaft; d x ,d y ,d z and d φ ,d θ ,d ψ Let u be the external disturbances in the position system and attitude system, respectively, and assume that the disturbances are bounded; φ ,u θ ,u ψ For the three-axis control torque of the UAV attitude loop; u x ,u y ,u z This is a virtual control variable for the position loop.

[0116] In this scheme, the "." above a letter represents the derivative of the meaning expressed by that letter. When there is a "." above a letter, it represents the first derivative of the meaning expressed by that letter; when there is a ".." above a letter, it represents the second derivative of the meaning expressed by that letter.

[0117] In one embodiment of this application, S2 specifically includes: the virtual control quantity of the position loop and the UAV along z-axis. b The relationship between the total lift u of the shaft is decoupled as follows:

[0118]

[0119] In the above formula: S (·) C (·) These represent the abbreviations for the trigonometric functions sin(·) and cos(·), respectively; according to equation (3), the virtual control quantity u of the position loop is generated. x ,u y ,u z Required total lift u and desired attitude angle φ d ,θ d They are respectively

[0120]

[0121] For ease of description, the quadcopter unmanned aerial vehicle systems (1) and (2) can be represented as follows:

[0122]

[0123] Where i = x, y, z, φ, θ, ψ; |d i |≤D i D i ≥0.

[0124] Define the system tracking error e i =ii d The UAV tracking error system can then be written as:

[0125]

[0126] In one embodiment of this application, the predetermined time sliding mode perturbation observer designed in S3 is as follows:

[0127]

[0128] in 0<α≤1, λ>0, μ>0, k≥D i , Then the disturbance observation error Achieve convergence within the predetermined time, i.e., convergence time T 0i satisfy

[0129]

[0130] In one embodiment of this application, the predetermined time fast terminal sliding mode controller designed in S4 is as follows:

[0131]

[0132] Where 0 < ι < 1, X > 0, If e is a natural constant, then the tracking error system achieves convergence within a predetermined time, i.e., the convergence time satisfies...

[0133]

[0134] In one embodiment of this application, the system stability proof in S5 includes the following steps:

[0135] 1) Relevant Lemmas and Theorems

[0136] Lemma 1: If there exists a positive definite Lyapunov function V satisfying...

[0137]

[0138] in 0<α≤1, λ>0, μ>0, T c If the value is greater than 0, then the system is globally time-stable, meaning the settling time satisfies T(x0) ≤ T. c .

[0139] Theorem 1: If there exists a positive definite Lyapunov function V satisfying...

[0140]

[0141] Where 0 < ι < 1, X > 0, T c If the value is greater than 0, the system achieves global time stability, meaning the stable time satisfies T(x0) ≤ T. c .

[0142] Prove that integrating equation (12) yields:

[0143]

[0144] Therefore

[0145]

[0146] Q.E.D.

[0147] Theorem 2: If there exists a positive definite Lyapunov function V satisfying...

[0148]

[0149] Where 0 < X ​​< 1, T c If e > 0 and e is a natural constant, then the system achieves global predetermined time stability, i.e., the stability time satisfies T(x0) ≤ T. c .

[0150] Prove that integrating equation (13) yields the following:

[0151]

[0152] Therefore

[0153]

[0154] Let function It can be calculated by the software MATLAB. The steady-state time then satisfies:

[0155]

[0156] Q.E.D.

[0157] 2) Proof of stability of the sliding mode perturbation observer at the predetermined time

[0158] For s in equation (7) i0 =e i0 +e i1 Differentiating both sides, we get

[0159]

[0160] Define Lyapunov functions but

[0161]

[0162] From Lemma 1, we can obtain the sliding mode variable s i0 The scheduled time converges, and the arrival time satisfies the condition.

[0163]

[0164] When the state reaches the sliding surface, i.e., s i0 =0, there is e i0 =-e i1 Differentiating, we get

[0165]

[0166] Define Lyapunov functions but

[0167]

[0168] By Lemma 1, we obtain the variable e i0 The convergence occurs within the predetermined time, and the convergence time satisfies the following conditions:

[0169]

[0170] at the same time Convergence, that is The convergence occurred within the predetermined time; Q.E.D.

[0171] 3) Proof of stability of the scheduled time rapid terminal sliding mode controller

[0172] Define Lyapunov functions but

[0173]

[0174] According to Theorem 2, the sliding mode variable s i It converges at the scheduled time; the system converges at the scheduled time. The system reaches the sliding surface. Once the system state reaches the sliding surface, i.e., s... i =0, there is

[0175]

[0176] Define Lyapunov functions but

[0177]

[0178] According to Theorem 1, the error variable e i It converges within a predetermined time; after the system reaches the sliding surface, the error is within the predetermined time. Converging inwards; Q.E.D.

[0179] In one embodiment of this application, the MATLAB-based simulation experiment in step S6 includes the following steps:

[0180] To verify the performance of the proposed method, this section simulates the position and attitude tracking control of a quadcopter UAV using MATLAB / Simulink.

[0181] 1) Parameter settings

[0182] The values ​​of the fuselage parameters of the quadcopter UAV are shown in Table 1;

[0183] Table 1. Parameter values ​​of the quadcopter UAV model

[0184] parameter numerical values parameter numerical values parameter numerical values <![CDATA[I x / (kg·m 2 )]]> 0.082 <![CDATA[I y / (kg·m 2 )]]> 0.082 <![CDATA[I z / (kg·m 2 )]]> 0.149 m / kg 2 <![CDATA[g / (m·s -2 )]]> 9.8 <![CDATA[k p ,k a ]]> 0.6

[0185] The drone reference trajectory is set to [x] d ,y d ,zd ] = [sin(t),cos(t),t], with the expected heading angle being ψ d =πsin(t), and the external disturbances are respectively set as:

[0186]

[0187] The initial state of the drone is set as follows:

[0188]

[0189] The observer parameter values ​​are shown in Table 2;

[0190] Table 2 Observer parameter values

[0191]

[0192] The controller parameter values ​​are shown in Table 3;

[0193] Table 3 Controller Parameter Values

[0194]

[0195] Note: To further mitigate chattering in the system, this paper replaces the sign function `sign(·)` in the observer and controller design with the saturation function `sat(·)`. The introduction of the saturation function effectively reduces chattering while maintaining the sliding mode characteristics of the system, thereby improving the system's dynamic performance and practical feasibility. The expression for the saturation function is as follows:

[0196]

[0197] in, δ0 is a very small positive number, and the value of this invention is 0.05.

[0198] 2) Simulation Result Analysis

[0199] Based on the above parameter settings, simulation was performed using Matlab R2023a, and the results are as follows. Figure 1-9 As shown.

[0200] The sliding mode variable changes of the pre-defined time disturbance observer are as follows: Figure 1 As shown; its estimation of the position and attitude perturbations of the quadcopter UAV is as follows. Figure 2 , 3 As shown. From Figure 1 It can be seen that the observer sliding mode variable converges to within 0.05 within 0.5s and converges within the predetermined time of 3s; from Figure 2 , 3 It can be seen that the sliding mode disturbance observer achieved an accurate estimate of the unknown disturbance within 0.6s, which is less than the predetermined time of 2s.

[0201] Sliding mode variables of the predetermined time controller, such as Figure 4 As shown, the sliding mode variable achieves convergence within the predetermined time. Figure 5 The figure shows the position tracking error and attitude tracking error. As can be seen from the figure, the UAV can bring the tracking error to a very small neighborhood near zero within a predetermined time, ensuring the speed and robustness of the UAV system. Figure 6 and Figure 7 It demonstrates the velocity variation trends of each of the six degrees of freedom of a quadcopter drone during flight.

[0202] Under unknown disturbances, the control input of the quadcopter drone is as follows Figure 8 and Figure 9 As shown in the figure, each control input is a finite value, which is consistent with the input characteristics of a real quadcopter UAV system. In addition, under the sliding mode control strategy of this invention, no obvious chattering phenomenon is observed in each control input, showing strong potential for practical application.

[0203] Secondly, the present invention also provides a quadcopter drone, the quadcopter drone including a processor and a memory coupled to the processor; the memory stores program instructions for implementing the quadcopter drone trajectory tracking control method described in any of the above embodiments.

[0204] In this embodiment, the processor is used to execute program instructions stored in the memory to control the flight trajectory of the quadcopter drone; the processor may also be called a CPU (Central Processing Unit); the processor may be an integrated circuit chip with signal processing capabilities; it is understood that the processor may also be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components; the general-purpose processor may be a microprocessor or any conventional processor, etc.

[0205] Thirdly, the present invention also provides a storage device. This embodiment provides a storage device storing program files capable of implementing all the above methods. The program files can be stored in the storage device in the form of a software product, including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage device includes various media capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, or terminal devices such as computers, servers, mobile phones, and tablets.

[0206] The above description is merely an exemplary embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention specification and drawings under the technical concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A trajectory tracking and control method for a quadcopter unmanned aerial vehicle (UAV), characterized in that, include: S1: Assuming the quadcopter UAV is a symmetrical rigid body structure, starting from the kinematics of the rigid body and based on the Newton-Euler-Lagrange method, we establish the disturbed dynamic equations of the quadcopter UAV in the Earth coordinate system. S2: Perform three-channel decoupling on the torques acting on the three axes of the fuselage position ring to obtain the corresponding three-channel virtual control quantities; Based on this virtual torque, the desired roll angle and pitch angle signals were solved in reverse, thus establishing a dynamic model of the tracking error of the quadcopter UAV. S3: For the tracking error system in S2, based on the predetermined time stability theory and combined with the sliding mode control method, a disturbance observer is designed to achieve accurate estimation and compensation of unknown disturbances within a predetermined time. S4: Based on the disturbance estimation information in S3, design a fast terminal sliding mode controller with a predetermined time to realize the position and attitude control of the quadcopter UAV and ensure the rapid convergence of tracking error; S5: Design a Lyapunov function based on Lyapunov stability theory and prove the stability of the invented method.

2. The quadcopter UAV trajectory tracking and control method as described in claim 1, characterized in that, The disturbed dynamics model of the quadcopter UAV in S1 is as follows: Equation (1) is the position loop dynamic equation, and equation (2) is the attitude loop dynamic equation; where x, y, z are the positions of the center of mass of the quadcopter UAV in the Earth coordinate system, φ, θ, ψ are the roll angle, pitch angle, and yaw angle of the UAV in the Earth coordinate system, respectively; m is the mass of the quadcopter UAV, g is the gravitational acceleration; k p and k a I represents the drag coefficients of the position and attitude systems, respectively; x ,I y and I z Representing the x-axis around the body coordinate axis respectively b axis, y b axis and z b Moment of inertia of the shaft; d x ,d y ,d z and d φ ,d θ ,d ψ Let u be the external disturbances in the position system and attitude system, respectively, and assume that the disturbances are bounded; φ ,u θ ,u ψ For the three-axis control torque of the UAV attitude loop; u x ,u y ,u z This is a virtual control variable for the position loop.

3. The quadcopter UAV trajectory tracking and control method as described in claim 2, characterized in that, The establishment of the dynamic model for the tracking error of the quadcopter UAV in S2 is detailed below. Includes the following steps: The virtual control quantity of the position loop and the UAV along z b The relationship between the total lift u of the shaft is decoupled as follows: In the above formula: S (·) C (·) Let sin(·) and cos(·) be the abbreviations for the trigonometric functions respectively. According to equation (3), the virtual control quantity u of the position loop is generated. x ,u y ,u z Required total lift u and desired attitude angle φ d ,θ d They are respectively: For ease of description, the quadcopter unmanned aerial vehicle systems (1) and (2) can be represented as follows: where i=x,y,z,φ,θ,ψ; |d i |≤D i ,D i ≥0。 Define the system tracking error e i =ii d The UAV tracking error system can then be written as:

4. The quadcopter UAV trajectory tracking and control method as described in claim 3, characterized in that, The predetermined time sliding mode perturbation observer designed in S3 is as follows: in, 0<α≤1, λ>0, μ>0, k≥D i , Then the disturbance observation error Achieve convergence within the predetermined time, i.e., convergence time T 0i satisfy:

5. The quadcopter UAV trajectory tracking and control method as described in claim 4, characterized in that, The predetermined time fast terminal sliding mode controller designed in S4 is as follows: Where 0 < ι < 1, X > 0, If e is a natural constant, then the tracking error system achieves convergence within a predetermined time, i.e., the convergence time satisfies:

6. The quadcopter UAV trajectory tracking control method as described in claim 5, characterized in that, The system stability proof in S5 includes the following steps: S5-1: Introduce relevant lemmas and theorems; Lemma 1: If there exists a positive definite Lyapunov function V satisfying: in 0<α≤1, λ>0, μ>0, T c If the value is greater than 0, then the system is globally time-stable, meaning the settling time satisfies T(x0) ≤ T. c . Theorem 1: If there exists a positive definite Lyapunov function V satisfying: Where 0 < ι < 1, X > 0, T c If the value is greater than 0, the system achieves global time-stability, meaning the stable time satisfies T(x0) ≤ T. c . Proof: Integrating equation (12) yields: Therefore Theorem 2: If there exists a positive definite Lyapunov function V satisfying: Where 0 < X ​​< 1, T c If e > 0 and e is a natural constant, then the system achieves global predetermined time stability, i.e., the stability time satisfies T(x0) ≤ T. c . Proof: Integrating equation (13) yields: Therefore Let function It can be calculated by the software MATLAB. The steady-state time then satisfies: S5-2: Proof of stability of sliding mode disturbance observer at predetermined time; S5-3: Proof of stability of the scheduled time fast terminal sliding mode controller.

7. The quadcopter UAV trajectory tracking and control method as described in claim 6, characterized in that, S5-2 includes: For s in equation (7) i0 =e i0 +e i1 Differentiating both sides, we get: Define Lyapunov functions but From Lemma 1, we can obtain the sliding mode variable s i0 The scheduled times converge, and the arrival times satisfy the following: When the state reaches the sliding surface, i.e., s i0 =0, there is e i0 =-e i1 Differentiating, we get: Define Lyapunov functions but By Lemma 1, we obtain the variable e i0 The convergence occurs within the predetermined time, and the convergence time satisfies the following conditions: at the same time Convergence, i.e. The scheduled convergence time has been reached.

8. The quadcopter UAV trajectory tracking control method as described in claim 6, characterized in that, S5-3 includes: Define Lyapunov functions but According to Theorem 2, the sliding mode variable s i It converges at the scheduled time; the system converges at the scheduled time. The system reaches the sliding surface; when the system state reaches the sliding surface, i.e., s i =0, there is Define Lyapunov functions but According to Theorem 1, the error variable e i It converges within a predetermined time; after the system reaches the sliding surface, the error is within the predetermined time. Convergence.

9. A quadcopter drone, characterized in that, include: processor; A memory, coupled to the processor, stores program instructions for implementing the trajectory tracking control method for a quadcopter unmanned aerial vehicle as described in any one of claims 1-8; The processor is used to execute the program instructions stored in the memory to control the flight trajectory of the quadcopter drone.

10. A storage medium, characterized in that, include: processor; The memory stores a computer program that can run on the processor, and when executed by the processor, the computer program implements a program file of the quadcopter unmanned aerial vehicle trajectory tracking control method as described in any one of claims 1-8.

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