An adaptive adjustment control method for a quad-rotor unmanned aerial vehicle considering error constraints and unknown disturbances

Abstract

The application discloses a kind of adaptive adjustment control method of quadrotor unmanned aerial vehicle considering error constraint and unknown interference, comprising: the position dynamics model and attitude dynamics model of quadrotor unmanned aerial vehicle are established, consider external interference in the modeling process, the unification of quadrotor unmanned aerial vehicle dynamics system expression is realized by introducing coordinate transformation and symbol substitution;The non-zero equilibrium point of quadrotor unmanned aerial vehicle is transferred to the origin by coordinate transformation, the controller of quadrotor unmanned aerial vehicle and adaptive rate are designed, and the stability of quadrotor unmanned aerial vehicle system with external disturbance is analyzed by selecting Lyapunov function, and the logarithmic barrier Lyapunov function is introduced to realize the scheduled performance control, to ensure that tracking error remains within the preset boundary;Robust control simulation experiment of quadrotor unmanned aerial vehicle system with disturbance is given.The application can effectively improve the safety and reliability of the system, ensure the stability of quadrotor unmanned aerial vehicle flight.

Description

Technical Field

[0001] This invention belongs to the field of automatic control technology for quadrotor unmanned aerial vehicles (UAVs), and relates to an adaptive adjustment control method for quadrotor UAVs that considers error constraints and unknown interference. Background Technology

[0002] A quadrotor unmanned aerial vehicle (UAV) is an underactuated, nonlinear, strongly coupled system with six degrees of freedom of motion but only four control inputs, exhibiting highly complex dynamic characteristics. Ensuring the strong robustness, adaptability, and tracking accuracy of a quadrotor UAV during operation is crucial. During control, the quadrotor UAV is also affected by parametric and nonparametric uncertainties in the model, measurement noise, and external disturbances. These requirements and factors make the modeling and control design research of quadrotor UAVs extremely scientific and challenging. Meanwhile, quadrotor UAVs, due to their simple structure, stable flight, flexible operation, strong environmental adaptability, low cost, and high safety, as well as their ability to take off vertically, hover freely, and fly in any direction, are widely used in military reconnaissance, information gathering, mapping, emergency search and rescue, pesticide spraying, and logistics transportation, among other military and civilian fields, demonstrating a very broad range of applications and research value.

[0003] In practical applications, quadrotor drones inevitably encounter external interferences such as airflow, wind, electromagnetic interference, and center-of-gravity shift during daily flight. If these interferences are not properly addressed, they can affect the flight stability and accuracy of the quadrotor drone, and even lead to flight accidents. Therefore, designing an effective anti-interference controller is essential for improving the flight stability and accuracy of quadrotor drones. Current research has shown that tracking errors of quadrotor drones under external interference can be narrowed to a small neighborhood. However, to improve the robustness and tracking accuracy of quadrotor drones, it is crucial to develop an adaptive control method that brings the tracking error towards zero. Simultaneously, the transient performance of the quadrotor drone system cannot be ignored. Good transient performance makes the quadrotor drone more stable during flight, which is of great significance for a range of cargo-carrying quadrotor drones. Therefore, considering the error constraints of the quadrotor drone system and ensuring that the system simultaneously achieves both transient and steady-state performance is a critical issue. Due to the complex structure of quadrotor drones, controller design is often also complex. Making the quadrotor drone control design process clearer and simpler is also a problem that needs to be addressed. Therefore, standardizing the control design steps for quadrotor UAVs and developing adaptive control technology for quadrotor UAVs that considers error constraints and unknown interferences, in order to promote the development of a new generation of anti-interference automatic control technology for quadrotor UAVs with more stable performance, are urgent problems to be solved. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide an adaptive adjustment and control method for quadcopter drones that considers error constraints and unknown interference. This method can not only effectively overcome the influence of external interference, but also take into account the transient and steady-state performance of quadcopter drones, improve the safety and reliability of quadcopter drones, and ensure the stability of operation during operation.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution.

[0006] An adaptive adjustment control method for a quadcopter unmanned aerial vehicle (UAV) considering error constraints and unknown disturbances includes the following steps:

[0007] Step 1: Assumptions and variable definitions are given for modeling the quadrotor UAV; position dynamics and attitude dynamics models of the quadrotor UAV are established using Newton's second law and Euler's equations, respectively, and external disturbances are considered in the modeling process; using the dual-closed-loop control concept, the control is divided into attitude control and position control, and the quadrotor UAV system is decoupled by introducing a virtual controller; the expression of the quadrotor UAV dynamics system is unified by introducing coordinate transformation and symbol substitution, which improves the clarity and simplicity of controller design.

[0008] Step 2: Transfer the non-zero equilibrium point of the quadcopter UAV to the origin through coordinate transformation. After designing the position controller and adaptive rate, the position controller of the quadcopter UAV is completed. The Lyapunov function is selected to perform stability analysis on the quadcopter UAV system with external disturbances. The Lyapunov function with obstacles is introduced to achieve the predetermined performance control and ensure that the tracking error is kept within the preset boundary.

[0009] Step 3: Obtain the control target trajectory of the attitude using the inverse kinematics method. Transfer the non-zero equilibrium point of the quadrotor UAV to the origin through coordinate transformation. After designing the attitude controller and adaptive rate, complete the design of the quadrotor UAV attitude controller. Select the Lyapunov function to perform stability analysis on the quadrotor UAV system with external disturbances. In this process, the obstacle Lyapunov function is introduced to achieve the predetermined performance control, ensuring that all signals of the closed-loop system are globally bounded, and the system's state variables are globally asymptotically adjusted to the non-zero equilibrium point.

[0010] Step 4: Using actual DJI quadcopter drone parameters, simulation experiments were conducted to achieve fixed-point hovering and trajectory tracking experiments of the quadcopter drone. The results were compared with existing PID methods and interference observer-based methods to complete comparative experiments and verify the superiority of the proposed method.

[0011] The definitions of the assumptions and variables required for modeling a quadcopter UAV include:

[0012] Assumption 1: The structure of a quadcopter drone is rigid and strictly symmetrical;

[0013] Assumption 2: The geometric center of the quadcopter drone coincides with its center of gravity;

[0014] Assumption 3: The rotational inertia and mass of the quadcopter drone remain constant, and the mass of the quadcopter is uniformly distributed;

[0015] Assumption 4: The flight state of the quadcopter drone is very stable, with very little change in various angles;

[0016] Assumption 5: Unknown disturbance d i (t) is bounded, |d i (t)|≤D i Where i = 1, ..., 6, D i For unknown positive constants;

[0017] Definition: Earth-centered coordinate system E = [O e x e y e , z e The body coordinate system B = [O] of the quadcopter UAV. b x b y b , z b By representing the position and velocity of the quadcopter in the Earth-centric coordinate system E, the operator can more directly understand the position and velocity of the quadcopter; while representing the thrust and torque of the quadcopter in the body coordinate system B is more intuitive; therefore, establishing two coordinate systems is necessary for modeling; we define x(t), y(t), z(t) to represent the absolute position of the quadcopter UAV in the geocentric coordinate system E, and φ(t), θ(t), ψ(t) to represent the roll angle (φ(t), θ(t), ψ(t)) of the quadcopter UAV in the geocentric coordinate system E, respectively. e x e Rotation), pitch angle (θ(t), around O e y e (rotation) and yaw angle (ψ(t), around O) e z e (rotation); V(t) = [v x (t), v y (t), v z (t)] T This indicates that the quadcopter UAV is in the geocentric coordinate system E. e x e O e y e O e z eLinear velocity on the axis; angular velocity in quadcopter body coordinate system B is represented by Ω(t) = [p(t), q(t), r(t)]. T The symbols represent the directions along O. b x b O b y b O b z b Angular velocity of the axis.

[0018] Further, in step 1, the position dynamics model and attitude dynamics model of the quadrotor UAV are established respectively using Newton's second law and Euler's equations, and external disturbances are considered in the modeling process; using the dual-closed-loop control concept, the control is divided into attitude control and position control, and the quadrotor UAV system is decoupled by introducing a virtual controller; the quadrotor UAV dynamics system expression is unified by introducing coordinate transformation and symbol substitution, improving the clarity and simplicity of controller design; including:

[0019] Step 1-1: Establish a position dynamics model of the quadcopter UAV using Newton's second law, considering the influence of external disturbances; the relationship between the total external force and the velocity of the quadcopter can be derived from Newton's second law:

[0020]

[0021] Where m is the mass of the quadcopter drone; g is the acceleration due to gravity; Fg = [0 0 -mg] T F f f(t) = [0 0 f(t)] T f(t) is the propeller thrust. ω i (t) represents the rotational speed of each rotor, and b is the thrust factor; n(t) = [n1(t) n2(t) n3(t)] T It is the sum of air resistance and unknown external disturbances, and satisfies... The rotation matrix R(t) is:

[0022]

[0023] In (2), sin(·) and cos(·) are abbreviated as S(·) and C(·);

[0024] The positional dynamics model of the quadcopter UAV is as follows:

[0025]

[0026] Steps 1-2: Establish the attitude dynamics model of the quadcopter UAV using Euler's equations, considering the influence of external disturbances; from Euler's equations, we can obtain:

[0027]

[0028] Inertia matrix J and matrix Defined as:

[0029]

[0030] Where I x I y and I z These are the inertial moments in the roll, pitch, and yaw directions, respectively; the torque τ(t) generated by the propeller on the crankshaft is τ = [τ x (t) τ y (t) τ z (t)] T , l is the distance between the quadrotor's center of mass and its rotation axis, a is the drag coefficient; s(t) = [s1(t) s2(t) s3(t)] T It is the sum of air resistance and unknown external disturbances, and satisfies... Furthermore, the relationship between attitude angular velocity and angular rate is expressed as:

[0031]

[0032] Assumption 4 ensures that the quadcopter UAV uses a small attitude angle to change its flight state, thereby ensuring flight safety; therefore, the attitude angular velocity can be approximately equivalent to the rotational angular velocity of the quadcopter, i.e., θ(t)→0, φ(t)→0. Then, the attitude dynamics model of the quadcopter UAV is:

[0033]

[0034] Steps 1-3: Through coordinate transformation, symbol substitution, and the dual-closed-loop control concept, the position dynamics model and attitude dynamics model of the quadcopter UAV are unified respectively:

[0035] Introduce U1(t) = f(t) and U2(t) = τ x (t) / l,U3(t=τ y (t) / l,U4(t=τ z (t), d1(t)=n1 / m, d2(t)=n2 / m, d3(t)=n3 / m, d4(t)=s1 / I x d5(t)=s2 / I y d6(t)=s3 / Iz ,get:

[0036]

[0037] Introduction And state variables and virtual controllers:

[0038]

[0039] The unified dynamic model expression for the quadcopter UAV is obtained as follows:

[0040]

[0041] Steps 1-4: Decompose the unified quadcopter UAV dynamics model expression into a unified position dynamics model and attitude dynamics model:

[0042] Step 1-4-1, Dynamic model of the quadrotor position subsystem obtained from equation (12):

[0043]

[0044] Therefore, the positional dynamics model of the quadcopter UAV can be expressed as:

[0045]

[0046] When i = 1, 2, and 3, they correspond to χ = x, y, and z, respectively.

[0047] Step 1-4-2, Dynamic model of the quadrotor position subsystem obtained from equation (12):

[0048]

[0049] The attitude dynamics model of a quadcopter UAV can be expressed as:

[0050]

[0051] in When i = 4, 5, 6, they correspond to Λ = φ, θ, ψ, respectively.

[0052] Further, in step 2, the non-zero equilibrium point of the quadcopter UAV is transferred to the origin through coordinate transformation. After designing the position controller and adaptive rate, the design of the quadcopter UAV position controller is completed. The Lyapunov function is selected to perform stability analysis on the quadcopter UAV system with external disturbances. An obstacle is introduced into the Lyapunov function to achieve predetermined performance control, ensuring that the tracking error remains within a preset boundary. This includes:

[0053] Step 2-1, Controller Design: Given any signal x whose first and second derivatives are bounded for all t≥0. d (t), y d (t), z d (t), serving as the reference signal for the quadrotor; the non-zero equilibrium point is transformed into the origin by defining the following coordinate transformation:

[0054]

[0055] Where i = 1, 2, 3, when i is 1, χ takes the value x; when i is 2, χ takes the value y; when i is 3, χ takes the value z. d (t) is a given target value. It is a virtual control law that needs to be designed;

[0056] Step 2-1-1: First, in order to ensure |z χ1 (t)|<k χ k χ >0 is a design parameter; the logarithmic barrier Lyapunov function is selected as follows:

[0057]

[0058] Differentiating the barrier Lyapunov function yields:

[0059]

[0060] Select virtual control signal:

[0061]

[0062] Among them, c χ1 >0 is a design parameter;

[0063] Therefore, the derivative of the Lyapunov function is:

[0064]

[0065] Step 2-1-2: Select the Lyapunov function:

[0066]

[0067] in, It is an unknown parameter D i The estimate, γ i >0 is a design parameter;

[0068] Taking the derivative of the Lyapunov function, we get:

[0069]

[0070] From the inequality available:

[0071]

[0072]

[0073] Substituting the above equation into the formula for the derivative of the Lyapunov function, we get:

[0074]

[0075] The continuous adaptive controller is now designed as follows:

[0076]

[0077] Among them, c χ2 If >0 is a design parameter, then the formula for the derivative of the Lyapunov function can be written as:

[0078]

[0079] Step 2-2, Stability Analysis: First, choose ε(t) = e -t Integrating both sides of the above equation from 0 to t, it is not difficult to obtain

[0080]

[0081] Therefore, it can be deduced that:

[0082]

[0083]

[0084] That is, z χ1 (t)∈L ∞ , z χ2 (t)∈L ∞ ,

[0085] On the other hand, integrating both sides of (18) from 0 to ∞, we get:

[0086]

[0087]

[0088] Then we can obtain z χ1 (t)∈L2, z χ2 (t)∈L2; furthermore, it can be deduced that:

[0089]

[0090]

[0091] Therefore, we can obtain: u χ (t)∈L ∞ but:

[0092]

[0093]

[0094] Finally, according to Barbalet's lemma, we have:

[0095] lim t→∞ z χ1 (t)=0,lim t→∞ z χ2 (t)=0 (31)

[0096] This completes the control design and stability verification of the position subsystem.

[0097] Steps 2-3: Use the known intermediate control u x (t),u y (t),u z (t), the tracking signal φ is obtained by inverse kinematics. d (t) and θ d (t):

[0098]

[0099] Given an arbitrary signal ψ d (t) yields all the reference signals required for the attitude subsystem control design.

[0100] Further, in step 3, the inverse kinematics method is used to obtain the control target trajectory of the attitude. Coordinate transformation is used to transfer the non-zero equilibrium point of the quadrotor UAV to the origin. After designing the attitude controller and adaptive rate, the design of the quadrotor UAV attitude controller is completed. The Lyapunov function is selected to perform stability analysis on the quadrotor UAV system with external disturbances. An obstacle Lyapunov function is introduced to achieve predetermined performance control, ensuring that all signals of the closed-loop system are globally bounded, and that the system's state variables are globally asymptotically adjusted to the non-zero equilibrium point. This includes:

[0101] Step 3-1, Controller Design: Given a bounded signal φ d (t), θ d (t) and a given arbitrary signal ψ d (t), ψ d(t) For all t≥0, the first and second derivatives are bounded. The non-zero equilibrium point can be transformed into the origin by the following coordinate transformation:

[0102]

[0103] Step 3-1-1: First, to ensure |z Λ1 (t)|<k Λ Choosing a logarithmic barrier Lyapunov function:

[0104]

[0105] Differentiating the barrier Lyapunov function yields:

[0106]

[0107] Select the virtual control signal as follows:

[0108]

[0109] Where c Λ1 If the design parameters are positive, then:

[0110]

[0111] Step 3-1-2: Select the Lyapunov function:

[0112]

[0113] in, It is an unknown parameter D i The estimate, γ i >0 represents the design parameter; taking the derivative of the Lyapunov function for this parameter yields:

[0114]

[0115] From the inequality It can be known that:

[0116]

[0117] available:

[0118]

[0119] Therefore, we can obtain:

[0120]

[0121] The adaptive controller is designed as follows:

[0122]

[0123] Then we have:

[0124] Choose ε(t) = e -t Integrating both sides of the above equation from 0 to t, we get:

[0125]

[0126] Therefore, it can be deduced that:

[0127]

[0128]

[0129] That is, z Λ1 (t)∈L ∞ , z Λ2 (t)∈L ∞ ,

[0130] Integrating both sides of (18) from 0 to ∞, we get:

[0131]

[0132]

[0133] Then we can obtain z Λ1 (t)∈L2, z Λ2 (t)∈L2; furthermore, it can be deduced that:

[0134]

[0135]

[0136] Therefore, we can obtain: u Λ (t)∈L ∞ ,but:

[0137]

[0138]

[0139] Finally, according to Barbalet's lemma, we have:

[0140] lim t→∞ z Λ1 (t)=0,lim t→∞ z Λ2 (t)=0 (48)

[0141] This completes the control design and stability verification of the attitude subsystem.

[0142] Furthermore, in step 4, during the adaptive control design process, the design parameters are selected as γ1=γ2=γ3=γ4=γ5=γ6=2, k x =k y =k φ =k ψ =k θ =2,k z =7,c x1 =12, c x2 =9,c y1 =5,c y2 =8, c z1 =2,c z2 =1,c φ1 =1,c φ2 =8, c θ1 =5,c θ2 =5,c ψ1 =1,c ψ2 =8.

[0143] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0144] 1. This invention, considering external interference to a quadrotor UAV, establishes a dynamic model of the quadrotor UAV under interference using Newton's second law and Euler's equations. Furthermore, through coordinate transformation, symbol substitution, and a dual-closed-loop control approach, it unifies the position dynamics model and attitude dynamics model of the quadrotor UAV, respectively; and thus provides a unified controller design process for position and attitude tracking.

[0145] 2. This invention eliminates the assumptions about the upper bound of disturbances in existing technologies. Instead, it introduces an exponentially decaying term to achieve asymptotic tracking of quadcopter UAVs under external disturbances. This not only improves the robustness of quadcopter UAVs but also enhances their versatility in resisting various disturbances. Furthermore, in this invention, the tracking error converges to zero under external disturbances, rather than being compactly set, thereby improving the tracking accuracy of quadcopter UAVs.

[0146] 3. This invention introduces a logarithmic barrier Lyapunov function to ensure that the tracking error remains within a preset boundary, eliminates the overshoot of the quadcopter system, and takes into account both the transient and steady-state performance of the quadcopter UAV system. Furthermore, by introducing a time-varying decreasing function, the oscillation of the system is eliminated, thereby improving the flight stability of the quadcopter UAV.

[0147] 4. This invention proposes a novel adaptive control method that enables asymptotic tracking of a given position reference signal by a quadrotor UAV while ensuring tracking error constraints. This method effectively controls unknown disturbances and tracking error constraints, greatly improving the applicability and robustness of the quadrotor UAV control algorithm, thereby ensuring the global stability of the closed-loop system. Attached Figure Description

[0148] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0149] Figure 2 This is a block diagram illustrating the overall control flow design of one embodiment of the present invention.

[0150] Figures 3a-3c These are, respectively, the fixed-point tracking curves for a target of 1.5m in the x-axis direction, a target of 1m in the y-axis direction, and a target of 6m in the height direction, according to an embodiment of the present invention.

[0151] Figure 4 This is a three-dimensional curve diagram of a fixed-point tracking experiment according to an embodiment of the present invention.

[0152] Figures 5a-5c These are the trajectory tracking curves for the x-axis tracking trajectory sin(0.2πt), the y-axis tracking trajectory cos(0.2πt), and the height tracking trajectory t, respectively, according to an embodiment of the present invention.

[0153] Figure 6 This is a three-dimensional curve diagram of a trajectory tracking experiment according to an embodiment of the present invention.

[0154] Figures 7a-7c These are schematic diagrams comparing the tracking error response curves under three control methods. The same target was tracked using the three control methods: the x-axis tracking trajectory sin(0.2πt), the y-axis tracking trajectory cos(0.2πt), and the target at a fixed altitude of 3m. The solid line represents the result obtained by the control method proposed in this invention; the dashed line represents the result obtained by the PID-based control method; and the dotted dashed line represents the result obtained by the state observer-based control method. Detailed Implementation

[0155] This invention presents an adaptive adjustment and control method for a quadrotor unmanned aerial vehicle (UAV) considering error constraints and unknown disturbances. This method is applicable to handling a series of external disturbances encountered by the quadrotor UAV during operation, including airflow, wind, electromagnetic interference, and center-of-mass shift, thereby improving the transient and steady-state performance of the quadrotor UAV and achieving stable tracking operation. This invention employs physical modeling to establish the position and attitude dynamics models of the quadrotor UAV. It solves the decoupling problem of the quadrotor UAV model by introducing virtual control variables, and unifies the dynamic model of the quadrotor UAV by introducing coordinate transformation and symbol substitution. The non-zero equilibrium point of the quadrotor UAV is transferred to the origin through coordinate transformation. The nominal controller is designed by designing virtual and actual control signals, and the Lyapunov function is selected to perform stability analysis on the quadrotor UAV model system. The method described above remains effective for other flight phases of the quadrotor UAV. Therefore, an adaptive control strategy is proposed for a quadrotor UAV system with disturbances to address external disturbances in the system, thereby improving the robustness of the adaptive controller under disturbance conditions. Finally, the proposed adaptive control strategy was simulated to verify the effectiveness of the control algorithm, providing a control theory basis and design reference for the safe flight of quadcopter UAVs.

[0156] The present invention will now be described in further detail with reference to the accompanying drawings.

[0157] An adaptive adjustment control method for a quadcopter unmanned aerial vehicle (UAV) considering error constraints and unknown disturbances, according to the present invention, includes the following steps:

[0158] Step 1: Assumptions and variable definitions are given for modeling the quadrotor UAV; position dynamics and attitude dynamics models of the quadrotor UAV are established using Newton's second law and Euler's equations, respectively, and external disturbances are considered in the modeling process; using the dual-closed-loop control concept, the control is divided into attitude control and position control, and the quadrotor UAV system is decoupled by introducing a virtual controller; the expression of the quadrotor UAV dynamics system is unified by introducing coordinate transformation and symbol substitution, which improves the clarity and simplicity of controller design.

[0159] Specifically, step 1 includes the following process:

[0160] Step 1-1: The purpose of establishing a mathematical model of the quadrotor is to analyze the influence of external forces and torques on the position and attitude of the quadrotor. To facilitate the nonlinear modeling of the quadrotor, the following assumptions are made first:

[0161] Assumption 1: The structure of the quadcopter drone is rigid and strictly symmetrical.

[0162] Assumption 2: The geometric center of the quadcopter drone coincides with its center of gravity.

[0163] Assumption 3: The rotational inertia and mass of the quadcopter drone remain constant, and the mass of the quadcopter is uniformly distributed.

[0164] Assumption 4: The flight state of the quadcopter drone is very stable, with very little change in any angle.

[0165] Assumption 5: Unknown disturbance d i (t) is bounded, |d i (t)|≤D i Where i = 1, ..., 6, D i It is an unknown positive number.

[0166] Then, define the Earth-centered coordinate system E = [O e x e y e , z e The body coordinate system B = [O] of the quadcopter UAV. b x b y b , z b By representing the position and velocity of the quadcopter in the Earth-centric coordinate system E, the operator can more directly understand the quadcopter's position and velocity. Representing the quadcopter's thrust and torque in the body coordinate system B is even more intuitive. Therefore, establishing two coordinate systems is necessary for modeling. We define x(t), y(t), z(t) to represent the absolute position of the quadcopter UAV in the Earth-centric coordinate system E, and φ(t), θ(t), ψ(t) to represent the roll angle (φ(t), θ(t), ψ(t)) of the quadcopter UAV in the Earth-centric coordinate system E, respectively. e x e Rotation), pitch angle (θ(t), around O e y e (rotation) and yaw angle (ψ(t), around O) e z e Rotation). V(t) = [v x (t), v y (t), v z (t)] T This indicates that the quadcopter UAV is in the geocentric coordinate system E. e x e O e y e O e z e Linear velocity along the axis. Angular velocity in the quadrotor's body coordinate system B is represented by Ω(t) = [p(t), q(t), r(t)]. T The symbols represent the directions along O. b x b O b yb O e z b Angular velocity of the axis.

[0167] Steps 1-2: Establish a positional dynamics model of the quadcopter UAV using Newton's second law, considering the effects of external disturbances. The relationship between the total external force and the quadcopter's velocity can be derived from Newton's second law, as shown below:

[0168]

[0169] Where m is the mass of the quadcopter drone; g is the acceleration due to gravity; Fg = [0 0 -mg] T F f f(t) = [0 0 f(t)] T f(t) is the propeller thrust. ω i (t) represents the rotational speed of each rotor, and b is the thrust factor; n(t) = [n1(t) n2(t) n3(t)] T It is the sum of air resistance and unknown external disturbances, and satisfies... The rotation matrix R(t) is:

[0170]

[0171] In (2), sin(·) and cos(·) are abbreviated as S(·) and C(·).

[0172] The positional dynamics model of the quadcopter UAV is as follows:

[0173]

[0174] Steps 1-3: Establish the attitude dynamics model of the quadcopter UAV using Euler's equations, considering the effects of external disturbances. From Euler's equations, we can obtain:

[0175]

[0176] Inertia matrix J and matrix Defined as:

[0177]

[0178] Where I x I y and I z These are the inertial moments in the roll, pitch, and yaw directions, respectively; the torque τ(t) generated by the propeller on the crankshaft is τ = [τ x (t) τ y (t) τ z (t)]T , l is the distance between the quadrotor's center of mass and its rotation axis, a is the drag coefficient; s(t) = [s1(t) s2(t) s3(t)] T It is the sum of air resistance and unknown external disturbances, and satisfies... Furthermore, the relationship between attitude angular velocity and angular rate is expressed as:

[0179]

[0180] Assumption 4 ensures that the quadcopter UAV uses a small attitude angle to change its flight state, thus guaranteeing flight safety. Therefore, the attitude angular velocity can be approximately equivalent to the rotational angular velocity of the quadcopter, i.e., θ(t)→0, φ(t)→0. The attitude dynamics model of the quadcopter UAV is then:

[0181]

[0182] Steps 1-4: Through coordinate transformation, symbol substitution, and the dual-closed-loop control concept, the position dynamics model and attitude dynamics model of the quadcopter UAV are unified respectively.

[0183] Introduce U1(t) = f(t) and U2(t) = τ x (t) / l,U3(t=τ y (t) / l,U4(t=τ z (t), d1(t)=n1 / m, d2(t)=n2 / m, d3(t)=n3 / m, d4(t)=s1 / I x d5(t)=s2 / I y d6(t)=s3 / I z ,get:

[0184]

[0185] Introduction And state variables and virtual controllers:

[0186]

[0187] The unified dynamic model expression for the quadcopter UAV is obtained as follows:

[0188]

[0189] This dynamic model forms the basis for the subsequent design of the quadcopter UAV controller. We obtain expressions for the position subsystem model and attitude subsystem model with a unified structure. The structure presented in this invention simplifies the controller design process.

[0190] Steps 1-5: Decompose the unified quadcopter UAV dynamics model expression into a unified position dynamics model and attitude dynamics model:

[0191] Step 1-5-1: The dynamic model of the quadrotor position subsystem obtained from equation (12) is as follows:

[0192]

[0193] Therefore, the positional dynamics model of the quadcopter UAV can be expressed as:

[0194]

[0195] When i = 1, 2, 3, they correspond to χ = x, y, z, respectively.

[0196] Step 1-5-2, the dynamic model of the quadrotor position subsystem obtained from equation (12) is as follows:

[0197]

[0198] The attitude dynamics model of a quadcopter UAV can be expressed as:

[0199]

[0200] in When i = 4, 5, 6, they correspond to Λ = φ, θ, ψ, respectively.

[0201] Step 2: Transfer the non-zero equilibrium point of the quadcopter UAV to the origin through coordinate transformation. After designing the position controller and adaptive rate, the position controller of the quadcopter UAV is completed. The Lyapunov function is selected to perform stability analysis on the quadcopter UAV system with external disturbances. The Lyapunov function with obstacles is introduced to achieve the predetermined performance control and ensure that the tracking error is kept within the preset boundary.

[0202] Specifically, step 2 includes the following process:

[0203] Step 2-1, Controller Design: Given any signal x whose first and second derivatives are bounded for all t≥0. d (t),y d (t),z d (t), serving as the reference signal for the quadrotor. The non-zero equilibrium point is transformed into the origin using the following coordinate transformation:

[0204]

[0205] Where i = 1, 2, 3, when i is 1, χ takes the value x; when i is 2, χ takes the value y; when i is 3, χ takes the value z. d (t) is a given target value. It is a virtual control law that needs to be designed.

[0206] Step 2-1-1: First, to ensure |z χ1 (t)| <k χ k χ >0 is a design parameter; the logarithmic barrier Lyapunov function is selected as follows:

[0207]

[0208] Differentiating the barrier Lyapunov function yields:

[0209]

[0210] Select virtual control signal:

[0211]

[0212] Among them, c χ1 >0 is a design parameter.

[0213] Therefore, the derivative of the Lyapunov function is:

[0214]

[0215] Step 2-1-2: Select the Lyapunov function:

[0216]

[0217] in It is an unknown parameter D i The estimate, γ i >0 is a design parameter.

[0218] Taking the derivative of the Lyapunov function, we get:

[0219]

[0220] From the inequality We can obtain:

[0221]

[0222]

[0223] Substituting the above equation into the formula for the derivative of the Lyapunov function, we get:

[0224]

[0225] The continuous adaptive controller is now designed as follows:

[0226]

[0227] in, These are design parameters. Therefore, the formula for the derivative of the Lyapunov function can be written as:

[0228]

[0229] Step 2-2, Stability Analysis: First, choose ε(t) = e -t Integrating both sides of the above equation from 0 to t, it is not difficult to obtain:

[0230]

[0231] Therefore, it can be deduced that:

[0232]

[0233]

[0234] That is, z χ1 (t)∈L ∞ , z χ2 (t)∈L ∞ ,

[0235] On the other hand, integrating both sides of (18) from 0 to ∞, we get:

[0236]

[0237]

[0238] Then we can obtain z χ1 (t)∈L2, z χ2 (t)∈L2. Furthermore, it can be inferred that:

[0239]

[0240]

[0241] Therefore, we can obtain: u χ (t)∈L ∞ ,but:

[0242]

[0243]

[0244] Finally, according to Barbalet's lemma, we have:

[0245] lim t→∞ z χ1 (t)=0,lim t→∞ z χ2 (t)=0 (31)

[0246] At this point, the control design and stability verification of the position subsystem have been completed.

[0247] Steps 2-3: Next, we can use the known intermediate control u x (t),u y (t),u z (t), the tracking signal φ is obtained by inverse kinematics. d (t) and θ d (t):

[0248]

[0249] Given an arbitrary signal ψ d (t) yields all the reference signals required for the attitude subsystem control design.

[0250] Step 3: Obtain the control target trajectory of the attitude using the inverse kinematics method. Transfer the non-zero equilibrium point of the quadrotor UAV to the origin through coordinate transformation. After designing the attitude controller and adaptive rate, complete the design of the quadrotor UAV attitude controller. Select the Lyapunov function to perform stability analysis on the quadrotor UAV system with external disturbances. In this process, the obstacle Lyapunov function is introduced to achieve the predetermined performance control, ensuring that all signals of the closed-loop system are globally bounded, and the system's state variables are globally asymptotically adjusted to the non-zero equilibrium point.

[0251] Specifically, step 3 includes the following process:

[0252] Step 3-1, Controller Design: Given a bounded signal φ d (t), θ d (t) and a given arbitrary signal ψ d (t), ψ d (t) For all t≥0, the first and second derivatives are bounded. The non-zero equilibrium point can be transformed into the origin by the following coordinate transformation:

[0253]

[0254] Step 3-1-1: First, to ensure |z Λ1 (t)| <k Λ Choosing a logarithmic barrier Lyapunov function:

[0255]

[0256] Differentiating the barrier Lyapunov function yields:

[0257]

[0258]

[0259] Select the virtual control signal as follows:

[0260]

[0261] Where c Λ1 The design parameters are positive. Therefore:

[0262]

[0263] Step 3-1-2: Next, select the Lyapunov function:

[0264]

[0265] in It is an unknown parameter D i The estimate, γ i >0 is a design parameter. Taking the derivative of the Lyapunov function for this parameter yields:

[0266]

[0267] From the inequality It can be known that:

[0268]

[0269] We can get:

[0270]

[0271] Therefore, we can obtain:

[0272]

[0273] The adaptive controller is designed as follows:

[0274]

[0275] Then we have:

[0276] We choose ε(t) = e -t Integrating both sides of the above equation from 0 to t, it is not difficult to obtain:

[0277]

[0278] Therefore, it can be deduced that:

[0279]

[0280]

[0281] That is, z Λ1 (t)∈L ∞ z Λ2 (t)∈L ∞ ,

[0282] On the other hand, integrating both sides of (18) from 0 to ∞, we get:

[0283]

[0284]

[0285] Then we can obtain z Λ1 (t)∈L2, z Λ2 (t)∈L2. Furthermore, it can be inferred that:

[0286]

[0287]

[0288] Therefore, we can obtain: u Λ (t)∈L ∞ ,but:

[0289]

[0290]

[0291] Finally, according to Barbalet's lemma, we have:

[0292] lim t→∞ z Λ1 (t)=0,lim t→∞ z Λ2 (t)=0 (48)

[0293] At this point, the control design and stability verification of the attitude subsystem have been completed.

[0294] In the above text, the design process of the adaptive controller for the anti-interference quadrotor UAV system was completed by using the improved adaptive inversion control strategy, and the stability analysis of the system was given. The main conclusions are as follows: For the quadrotor UAV system (8) that satisfies the assumptions, the designed adaptive controller guarantees the global boundedness of all closed-loop signals and realizes the global adaptive adjustment of the non-zero equilibrium point. The following are all the designed coordinate transformations, controllers and adaptive rates:

[0295]

[0296]

[0297]

[0298]

[0299]

[0300]

[0301]

[0302]

[0303] It should be noted that the actual control input U1(t) is obtained by the following inverse equation:

[0304]

[0305] Step 4: Using actual DJI quadcopter drone parameters, simulation experiments were conducted. Based on the above design method, fixed-point hovering and trajectory tracking experiments of the quadcopter drone were implemented respectively. The results were compared with existing PID methods and interference observer-based methods to complete comparative experiments and verify the superiority of the proposed method.

[0306] Furthermore, the specific process of step 4 is as follows:

[0307] Step 4-1: System Model with Disturbance. In practical engineering applications, control systems often experience noise and disturbances, which affect system stability. Therefore, studying the noise and disturbances present in quadrotor UAV systems is of great significance. A typical quadrotor UAV system model with external disturbances is as follows:

[0308]

[0309] Among them, d(t)=[d1(t), d2(t), d3(t), d4(t), d5(t), d6(t)] T ∈R 6For unknown disturbance vectors, such as turbulence, wind disturbances, and electromagnetic disturbances existing in the atmosphere, the adaptive control strategy proposed in this invention is adopted to address external disturbances in quadcopter UAV systems, thereby improving the robustness of the controller.

[0310] Step 4-2: This invention uses parameters from the DJI quadcopter drone as an example for simulation verification:

[0311] Step 4-2-1, DJI quadcopter drone system model parameters are as follows: m = 0.9 kg, l = 0.175 m, I x =0.008276 kg·m 2 I y =0.008276 kg·m 2 I z =0.01612 kg·m 2 And g = 9.81 m / s 2 After multiple debugging sessions, the system design parameters were set as follows: γ1=γ2=γ3=γ4=γ5=γ6=2, k x =k y =k φ =k ψ =k θ =2,k z =7,c x1 =12, c x2 =9,c y1 =5,c y2 =8,c z1 =2, C z2 =1,c φ1 =1,c φ2 =8, C θ1 =5,c θ2 =5,c ψ1 =1,c ψ2 =8.

[0312] Step 4-2-2: Design control signals U1, U2, U3, and U4, and an adaptive law for interference, using the method described in this invention. The simulation experiment was conducted using a DJI quadcopter drone system model, including the following process:

[0313] Step F1, Fixed-point tracking: Select the initial conditions for the position subsystem and attitude subsystem of the quadcopter UAV as [x1(0), x2(0), x3(0), x4(0), x5(0), x6(0)]. T = [0, 0, 0, 0.1, 0.1, 0.1] T Next, we design the total external disturbance as [d1(t), d2(t), d3(t), d4(t), d5(t), d6(t)].T =[sin(t),sin(t),sin(t),sin(t),sin(t),sin(t)] T The experiment is set with the fixed target as [x]. d y d , z d , ψ d ] T =[1.5, 1, 6, 2] T The fixed-point tracking curves for the x-axis, y-axis, and height are as follows: Figure 3a As shown in --3c, the three-dimensional curve of the fixed-point tracking experiment is as follows: Figure 4 As shown in the tracking curve, the quadcopter UAV can quickly and accurately reach the preset target, complete the fixed-point tracking task, and the aircraft's state variables are asymptotically adjusted to a non-zero equilibrium point.

[0314] Step F2, Trajectory Tracking: Select the initial conditions for the position subsystem and attitude subsystem of the quadcopter UAV as [x1(0), x2(0), x3(0), x4(0), x5(0), x6(0)]. T = [0, 0, 0, 0.1, 0.1, 0.1] T Next, we design the total external disturbance as [d1(t), d2(t), d3(t), d4(t), d5(t), d6(t)]. T =[sin(t),sin(t),sin(t),sin(t),sin(t),sin(t)] T Set the tracking target to [x d y d , z d , ψ d ] T =[sin(0.2πt), cos(0.2πt), t, 2] T The fixed-point tracking curves for the x-axis, y-axis, and height are as follows: Figure 5a As shown in Figure 5c, the three-dimensional curve of the trajectory tracking experiment of the quadcopter UAV is shown in Figure 5. The tracking curve shows that the quadcopter UAV can quickly and accurately reach the preset target, complete the trajectory tracking task, and the aircraft's state variables asymptotically adjust to a non-zero equilibrium point.

[0315] Step F3: Comparative simulation with existing methods: Select the same initial conditions [x1(0), x2(0), x3(0), x4(0), x5(0), x6(0)] in the comparative experiment. T = [0, 0, 0, 0.1, 0.1, 0.1] TThe total external disturbances are designed as [d1(t), d2(t), d3(t), d4(t), d5(t), d6(t)]. T =[sin(t),sin(t),sin(t),sin(t),sin(t),sin(t)] T Set the tracking target to [x d y d , z d , ψ d ] T =[sin(0.2πt), cos(0.2πt), 3, 2] T The simulation results curves for trajectory tracking along the x-axis, y-axis, and height are shown below. Figure 7a As shown in Figure 7c, the simulation curves of the system state error variable demonstrate that, under the same system parameters, equilibrium point, external disturbances, and initial conditions, the method proposed in this invention outperforms both PID-based and state observer-based control methods.

Claims

1. An adaptive adjustment and control method for a quadcopter unmanned aerial vehicle considering error constraints and unknown disturbances, characterized in that, Includes the following steps: Step 1: State the assumptions required for modeling the quadcopter UAV, and define the variables; The position dynamics model and attitude dynamics model of the quadrotor UAV are established by Newton's second law and Euler's equation, respectively, and external disturbances are taken into account in the modeling process. Using the dual closed-loop control concept, the control of the quadrotor UAV is divided into attitude control and position control. By introducing a virtual controller, the decoupling of the quadrotor UAV system is achieved. The expression of the quadrotor UAV dynamics system is unified by introducing coordinate transformation and symbol substitution. Step 2: Transfer the non-zero equilibrium point of the quadcopter UAV to the origin through coordinate transformation. After designing the position controller and adaptive law, the position controller of the quadcopter UAV is designed. The Lyapunov function is selected to perform stability analysis on the quadcopter UAV system with external disturbances. The Lyapunov function with obstacles is introduced to achieve the predetermined performance control and ensure that the tracking error is kept within the preset boundary. Step 3: Obtain the control target trajectory of the attitude using the inverse kinematics method. Transfer the non-zero equilibrium point of the quadrotor UAV to the origin through coordinate transformation. After designing the attitude controller and adaptive law, complete the design of the quadrotor UAV attitude controller. Select the Lyapunov function to perform stability analysis on the quadrotor UAV system with external disturbances. In this process, the obstacle Lyapunov function is introduced to achieve the predetermined performance control, ensuring that all signals of the closed-loop system are globally bounded, and the system's state variables are globally asymptotically adjusted to the non-zero equilibrium point. Step 4: Using actual DJI quadcopter drone parameters, simulation experiments were conducted to achieve fixed-point hovering and trajectory tracking experiments of the quadcopter drone. The results were compared with existing PID methods and interference observer-based methods to complete comparative experiments and verify the superiority of the proposed method. The definitions of the assumptions and variables required for modeling a quadcopter UAV include: Assumption 1: The structure of a quadcopter drone is rigid and strictly symmetrical; Assumption 2: The geometric center of the quadcopter drone coincides with its center of gravity; Assumption 3: The rotational inertia and mass of the quadcopter drone remain constant, and the mass of the quadcopter is uniformly distributed; Assumption 4: The flight state of the quadcopter drone is very stable, and the changes in various angles are very small; Assumption 5: Unknown disturbance Bounded, ,in For unknown positive constants; Definition: Earth-centered coordinate system The body coordinate system of a quadcopter drone It's more intuitive to represent the quadrotor's position and velocity in the Earth's central coordinate system E, and its thrust and torque in the body coordinate system B. Therefore, establishing two coordinate systems is necessary for modeling. Indicate the absolute position of the quadcopter UAV in the geocentric coordinate system E: These represent the orbital movements of the quadcopter UAV in the geocentric coordinate system E. Roll angle of rotation , around Pitch angle of rotation and around Yaw angle of rotation ; This indicates that the quadcopter UAV is in the geocentric coordinate system E. Linear velocity on the axis; angular velocity in quadrotor body coordinate system B is... Indicates, respectively, along Angular velocity of the axis; The specific process of step 2 includes: Step 2-1, Controller Design: Given any signal whose first and second derivatives are bounded for all t≥0 , serving as the reference signal for the quadcopter; the non-zero equilibrium point is transformed into the origin of the coordinate system by defining the following coordinate transformation: ； in, When taking 1 Pick ; When taking 2 Pick ; Take 3 Pick , It is a given target value. It is a virtual control law that needs to be designed; Step 2-1-1: First, in order to ensure , The design parameters are as follows, and the logarithmic barrier Lyapunov function is selected: ； Differentiating the barrier Lyapunov function yields: （17）； Select virtual control signal: ； in, These are design parameters; Therefore, the derivative of the Lyapunov function is: ； Step 2-1-2: Select the Lyapunov function: ； in, , It is an unknown parameter The estimate, These are design parameters; Taking the derivative of the Lyapunov function, we get: （21）； From the inequality ,available: ； ； Substituting the above equation into the formula for the derivative of the Lyapunov function, we get: ； The continuous adaptive controller is now designed as follows: ； in, If these are design parameters, then the formula for the derivative of the Lyapunov function can be written as: ； Step 2-2, Stability Analysis: First, select... Integrating both sides of the above equation from 0 to t, it is not difficult to obtain: ; Therefore, it can be deduced that: （28）； Right now, , ; On the other hand, integrating both sides of (18) from 0 to ∞, we get: ； ； Then we can get , Furthermore, it can be inferred that: ； ； Therefore, we can obtain: , ,but: ； ； Finally, according to Barbalet's lemma, we have: ; This completes the control design and stability verification of the position subsystem. Steps 2-3: Use known intermediate controls The tracking signal is obtained through inverse kinematics. and : ； Given an arbitrary signal This allows us to obtain all the reference signals required for the attitude subsystem control design. The specific process of step 3 includes: Step 3-1, Controller Design: Given a bounded signal , and given any signal For all t≥0, the first and second derivatives are bounded. The non-zero equilibrium point can be transformed into the origin by defining the following coordinate transformation: ； Step 3-1-1: First, to ensure Choosing a logarithmic barrier Lyapunov function: ； Differentiating the barrier Lyapunov function yields: （35）； Select the virtual control signal as follows: ； in If the design parameters are positive, then: ； Step 3-1-2: Select the Lyapunov function: ； in , It is an unknown parameter The estimate, These are design parameters; taking the derivative of the Lyapunov function for this, we get: （39）； From the inequality Therefore, we can conclude that: ； available: ； Therefore, we can obtain: ； The adaptive controller is designed as follows: ； Then we have: ; choose Integrating both sides of the above equation from 0 to t, we get: ; Therefore, it can be deduced that: ， ； Right now, , ; Integrating both sides of (18) from 0 to ∞, we get: ； ； Then we can get , Furthermore, it can be inferred that: ， ； Therefore, we can obtain: , ,but: ， ； Finally, according to Barbalet's lemma, we have: ； This completes the control design and stability verification of the attitude subsystem.

2. The adaptive adjustment and control method for a quadcopter UAV considering error constraints and unknown disturbances according to claim 1, characterized in that, In step 1, the position dynamics model and attitude dynamics model of the quadrotor UAV are established respectively using Newton's second law and Euler's equation, and external disturbances are taken into account during the modeling process; using the dual closed-loop control concept, the control of the UAV is divided into attitude control and position control, and the decoupling of the quadrotor UAV system is achieved by introducing a virtual controller; the unified expression of the quadrotor UAV dynamics system is achieved by introducing coordinate transformation and symbol substitution. include: Step 1-1: Establish a position dynamics model of the quadcopter UAV using Newton's second law, considering the influence of external disturbances; the relationship between the total external force and the velocity of the quadcopter can be derived from Newton's second law: ； Where m is the mass of the quadcopter drone; g is the acceleration due to gravity; , It is the propeller thrust. , The rotational speed of each rotor, It is the thrust factor; It is the sum of air resistance and unknown external disturbances, and satisfies... Rotation matrix for: ； in and In (2), it is abbreviated as and ; The positional dynamics model of the quadcopter UAV is as follows: ； Steps 1-2: Establish the attitude dynamics model of the quadcopter UAV using Euler's equations, considering the influence of external disturbances; from Euler's equations, we can obtain: （4）； Inertia matrix J and matrix Defined as: , ； in , and These are the inertial moments in the roll, pitch, and yaw directions, respectively; and the torque generated by the propeller on the crankshaft. , This is the distance between the center of mass of the quadrotor and the axis of rotation of the quadrotor. This is the drag coefficient; It is the sum of air resistance and unknown external disturbances, and satisfies... Furthermore, the relationship between attitude angular velocity and angular rate is expressed as: ； Assumption 4 ensures that the quadcopter UAV uses a small attitude angle to change its flight state, thereby guaranteeing flight safety; therefore, the attitude angular velocity can be approximately equivalent to the rotational angular velocity of the quadcopter, i.e. The attitude dynamics model of the quadcopter UAV is as follows: ； Steps 1-3: Through coordinate transformation, symbol substitution, and the dual-closed-loop control concept, the position dynamics model and attitude dynamics model of the quadcopter UAV are unified respectively: Let U1(t) = f(t), U2(t) = τ x (t) / l, U3(t) = τ y (t) / l, U4(t) =τ z (t), d1(t) = n1 / m, d2(t) = n2 / m, d3(t) = n3 / m, d4(t) = s1 / I x , d5(t) = s2 / I y , d6(t) = s3 / I z , we obtain: ； Introduction , as well as state variables and virtual controllers: ； The unified dynamic model expression for the quadcopter UAV is obtained as follows: (10)； Steps 1-4: Decompose the unified quadcopter UAV dynamics model expression into a unified position dynamics model and attitude dynamics model: Step 1-4-1, Dynamic model of the quadrotor position subsystem obtained from equation (12): ； Therefore, the positional dynamics model of the quadcopter UAV can be expressed as: ； in The time corresponds to ; Step 1-4-2, Dynamic model of the quadrotor position subsystem obtained from equation (12): ； The attitude dynamics model of a quadcopter UAV can be expressed as: ； in when Corresponding to = , , .

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