Posture control method for multi-uav tethered load airlift system

Abstract

The present application belongs to the field of flight control of multi-unmanned aerial vehicle tethered load air transport system, and is used for realizing online estimation of unknown parameters under the condition that the rigid body inertia matrix and air damping coefficient matrix exist uncertainties, simultaneously accurately tracking expected attitude, effectively compensating the influence of unknown parameters and better restraining external interference, and accurately controlling the position of the load. The attitude control method of the multi-unmanned aerial vehicle tethered load air transport system is based on the Lagrange modeling method, and the dynamic model of the multi-unmanned aerial vehicle tethered load air transport system is established. The control moment is designed, the adaptive updating law of the inertia matrix and the air damping coefficient matrix is designed, and the consistent boundedness of the tracking error and the estimation error is determined. The present application is mainly applied to the occasion of multi-unmanned aerial vehicle formation flight control.

Description

Technical Field

[0001] This invention belongs to the field of flight control for multi-UAV tethered load air transport systems. To address the requirements of UAVs tracking targets with desired attitudes and suppressing external disturbances during load transport, a novel robust adaptive control method is proposed. Background Technology

[0002] Quadcopter drones, with their vertical takeoff and landing capabilities, superior hovering performance, and high flexibility, are widely used in emergency rescue, power line inspection, agricultural protection, and cargo transportation. (Journal: IEEE Access ;Author: Jeongeun Kim , Seungwon Kim , Chanyoung Ju , HyoungIl Son Publication date: 2019; Article title: Unmanned Aerial Vehicles in Agriculture: A Review of Perspective of Platform, Control, and Applications; Pages: 105-100–105-115; (Journal: IEEETransactions onIndustrial Electronics ;Author: Bo Zhao , Bin Xian , Yao Zhan g, Xu Zhan g; Publication Date: 2014; Article Title: Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology; Pages: 2891–2902). With the continuous advancement of UAV research technology, UAVs are increasingly being applied to tasks with higher complexity and greater uncertainty. Especially in the field of air logistics, a single UAV needs to be both lightweight and small, but logistics transportation tasks require UAVs to have greater carrying capacity. Therefore, to resolve this contradiction, the working method of UAVs has begun to shift from independent operation by a single UAV to collaborative operation by multiple UAVs. (Journal: Aerospace Science and Technology; Author: Behzad Shirani , Majdeddin Najafi and Iman Izadi Publication date: 2019; Article title: Cooperative load transportation using multiple UAVs; Pages: 158–169.

[0003] Currently in the field of UAV control and single UAV suspension transportation, many researchers focus on the system's maneuvering flight capability (Journal: IEEE TransactionsonControl Systems Technolo gy; Authors: Ezra Tal , Sertac Karaman ; Publication Year: 2021; Article Title: Accurate Tracking of Aggressive Quadrotor Trajectories Using Incremental Nonlinear Dynamic Inversion and Differential Flatness; Page: 1203-1218). A UAV system with strong maneuvering flight capability can fly quickly in complex environmental conditions, and even pass through narrow gaps with a size similar to its own. Although the maneuverability of the single UAV suspension system is weakened, it can also achieve fast flight of the system by planning a reasonable motion trajectory and selecting a suitable controller. Inspired by this, this paper aims to improve the efficient transportation capability of the multi-UAV suspension system by establishing an accurate system model and designing a controller that is more conducive to achieving maneuvering flight. At the same time, by enhancing the robustness of the system, external disturbances can be effectively suppressed, thereby ensuring safe and stable completion of the transportation task.

[0004] In the multi-UAV suspension load transportation system, the position control and attitude tracking of the load depend on the traction force exerted on the load by the four-rotor UAV through the rope, and the attitude tracking speed and tracking accuracy of the UAV itself directly affect whether the multi-UAV suspension system can better complete the transportation task. Therefore, the design of the attitude control law for each four-rotor UAV in the multi-UAV suspension system is a crucial link.

[0005] In recent years, some good results have been achieved in the study of multi-UAV suspension transportation systems, but there are still some limitations: 1) When modeling the system dynamics, the UAV is usually modeled as a point mass, and its attitude loop control is not considered. 2) For the control problem of the UAV, most studies usually ignore the aerodynamic effect or consider it as an unknown disturbance. This can achieve good control effect when the system is close to hovering conditions, but as the speed increases, the pose tracking accuracy will gradually decrease. 3) Most studies usually assume that the inertia matrix of the UAV is known, but it is difficult to accurately measure it in actual situations. SUMMARY

[0006] In order to overcome the defects of the prior art, the adaptive robust control algorithm based on geometric control is proposed, in the case that the inertia matrix of the rigid body and the air damping coefficient matrix exist uncertainty, the online estimation of unknown parameters is realized, the expected attitude can be accurately tracked, the influence of unknown parameters can be effectively compensated and the external interference can be well inhibited, and the accurate control of the load attitude is realized.

[0007] Firstly, an inertia coordinate system is defined And four body coordinate systems The center of the 0th body coordinate system is established at the center of mass of the rigid load, the centers of the 1st, 2nd and 3rd body coordinate systems are respectively established at the centers of mass of the three unmanned aerial vehicles, and the three unmanned aerial vehicles are collectively hung through three ropes with equal length.

[0008] Assuming that the ropes are always tensioned, in the inertia coordinate system, the position of the load and the position of the ith unmanned aerial vehicle have the following relationship: p i =p L +R L η i -l i ξ i . Wherein, represents a vector from the center of mass of the load to the connecting point of the ith rope on the load, represents a vector space composed of three-dimensional real vectors, represents the length of the rope, represents a real number set, and i (t)∈S 2 is a unit vector from the center of mass of the ith unmanned aerial vehicle to the connecting point of the ith rope on the load, and the subscript i represents the ith unmanned aerial vehicle and the ith rope, and S 2 represents a two-dimensional spherical surface.

[0009] Based on the Lagrange modeling method, the dynamic model of the multi-unmanned aerial vehicle tethered load air transportation system is obtained:

[0010]

[0011] The definitions of the variables in the dynamic equation are as follows: and are the mass and inertia matrix of the load respectively, Ω L ∈TSO(3) are the position, linear velocity and angular velocity of the center of mass of the load in the inertia coordinate system respectively, g is the gravity acceleration, z=[0,0,1] T , R L ∈SO(3) is the attitude rotation matrix of the load in the body coordinate system, and SO(3) represents the orthogonal rotation group; Ωi ∈TSO(3) are the position, linear velocity and angular velocity of the i-th UAV in the inertial frame, R i ∈SO(3) is the attitude rotation matrix of the i-th UAV in the body frame, is the angular velocity of the i-th tether, are the mass and inertia matrix of the UAV, denotes the air damping coefficient matrix of the i-th UAV, the diagonal elements are the air damping coefficients of the quadrotor UAV body around the three axes of the body frame, respectively;

[0012] In equation (1), is the virtual control input of the payload, △ p (t) and are the unknown external disturbances in the payload position and attitude models, respectively, is the unknown external disturbance in the i-th UAV attitude model, is the acceleration of the i-th connection point, expressed as the control input of the i-th UAV the parallel component along the corresponding tether direction vector has the following relationship with v i (t):

[0013]

[0014] In the above model, S(·) represents the skew-symmetric matrix formed by the vector, that is, for the vector ω(t) = [ω φ (t) ω θ (t) ω ψ (t)] T The expression of S(ω) is

[0015]

[0016] Define the attitude error function of the i-th UAV as is

[0017]

[0018] By taking the derivative of the attitude error function , the attitude tracking error of the i-th UAV is obtained The expression of the angular velocity tracking error is

[0019]

[0020]

[0021] where the desired rotation matrix representing the load, the desired rotation matrix representing the load, the desired angular velocity representing the load attitude. For the derivative is taken to obtain

[0022]

[0023] the derivative is taken to obtain

[0024]

[0025] When the given attitude command is not fixed, the attitude tracking control system needs to obtain the accurate information of the inertia matrix, however, it is difficult to accurately measure the value of the inertia matrix of the quadrotor UAV, thus an estimation error is usually generated, the expressions of the estimation errors of the inertia matrix and the air damping coefficient matrix are respectively represented as:

[0026]

[0027] wherein, and respectively represent the true values of the inertia matrix and the air damping coefficient matrix, and represent the corresponding measured values, and the above matrices are all symmetric matrices;

[0028] an augmented error vector is defined as the expression is as follows:

[0029]

[0030] the control moment is designed as

[0031]

[0032] wherein,

[0033]

[0034]

[0035] the adaptive update law of the inertia matrix and the air damping coefficient matrix is designed as

[0036]

[0037]

[0038] for the given desired attitude and the positive control gain and ​If the control moment expressed by formula (11) and the adaptive update law expressed by formula (14) and (15) satisfy the following conditions:

[0039]

[0040] Then when sigma i The tracking error and the estimation error can be uniformly bounded when sigma is small enough.

[0041] The system error vector can be uniformly bounded by combining the Lyapunov analysis method.

[0042] The characteristics and beneficial effects of the present application are:

[0043] 1. The present application studies the attitude control problem of each unmanned aerial vehicle in the multi-unmanned aerial vehicle suspension system. When modeling, the influence of air resistance on the system with the increase of the speed of the unmanned aerial vehicle is considered, and unknown external disturbances that may exist are also considered.

[0044] 2. The present application considers the problem that the inertia matrix and the air resistance coefficient in the model are difficult to accurately measure in practice, and designs an adaptive robust control algorithm based on geometric control;

[0045] 3. The present application provides a complete stability analysis for the unmanned aerial vehicle attitude part in the multi-unmanned aerial vehicle suspension system based on the Lyapunov analysis method, and proves the stability of the closed-loop system and the uniform boundedness of the system state error.

[0046] 4. The present application verifies the control method proposed by numerical simulation, and compares it with the PD control method, and the simulation results show that the control method designed in the present application can estimate unknown parameters online, and has good performance in disturbance suppression. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is the air damping coefficient matrix estimation curve;

[0048] Figure 2 is the inertia matrix estimation curve;

[0049] Figure 3 is the attitude angle (roll) tracking comparison curve in comparative simulation 1;

[0050] Figure 4 is the attitude angle (pitch) tracking comparison curve in comparative simulation 1;

[0051] Figure 5 is the attitude angle (yaw) tracking comparison curve in comparative simulation 1;

[0052] Figure 6 is the attitude angle (roll) tracking comparison curve in comparative simulation 2;

[0053] Figure 7 is the pitch tracking comparison curve in simulation 2;

[0054] Figure 8 is the yaw tracking comparison curve in simulation 2;

[0055] Figure 9 is the control flow chart of the patent. DETAILED DESCRIPTION

[0056] In view of the problems and difficulties existing in the prior art, the present application proposes an adaptive robust control algorithm based on geometric control. In the case of uncertainty of the inertia matrix of the rigid body and the air damping coefficient matrix, the proposed controller can realize online estimation of unknown parameters, while accurately tracking the expected attitude. Considering that the multi-aircraft hanging system will be disturbed by external interference during flight, the ordinary adaptive controller may cause the tracking effect to be poor in the presence of interference, therefore, the present application further improves the adaptive controller by adding a sliding mode term.

[0057] The present application aims to meet the needs of tracking trajectory and resisting external interference during the process of hanging load transportation, and proposes a new nonlinear robust control method. On the basis of considering unknown external disturbance and system internal state coupling, the present application designs a nonlinear robust control strategy based on error sign function integral (RISE) and geometric control method, which is used to compensate the influence of unknown external disturbance and realize accurate control of the load pose.

[0058] The present application aims to propose a new robust adaptive control method. The method realizes accurate tracking of the attitude part of the unmanned aerial vehicle in the multi-unmanned aerial vehicle hanging system, and can effectively compensate the influence of unknown parameters and better suppress external interference. The technical scheme adopted by the present application is as follows: on the basis of considering unknown external disturbance and the model with unknown parameters, a robust adaptive control strategy based on geometric control is designed, and the specific steps are as follows:

[0059] Firstly, an inertial coordinate system is defined and four body coordinate systems The center of the 0th body coordinate system is established at the center of mass of the rigid load, and the centers of the 1st, 2nd and 3rd body coordinate systems are respectively established at the centers of mass of the three unmanned aerial vehicles, and the three unmanned aerial vehicles are collectively hanging a rigid load through three ropes with equal length;

[0060] Assuming that the ropes are always tensioned, in the inertial coordinate system, the positions of the load and the ith unmanned aerial vehicle have the following relationship: p i =p L +R L ηi -l i ξ i .in, This represents the vector pointing from the load's centroid to the connection point of the i-th rope on the load. Represents a vector space consisting of three-dimensional real vectors. Indicates the length of the rope. Denotes the set of real numbers, ξ i (t)∈S 2 The unit vector from the centroid of the i-th UAV to the point where the i-th rope connects to the load, where the subscript i represents the i-th UAV and the i-th rope. 2 Represents a two-dimensional sphere;

[0061] Based on the Lagrange modeling method, a dynamic model of a multi-UAV tethered load air transport system can be obtained:

[0062]

[0063] The variables in the dynamic equations are defined as follows: These are the load mass and the inertia matrix, respectively. Ω L ∈TSO(3) represent the position, linear velocity, and angular velocity of the load's center of mass in the inertial coordinate system, respectively, where g is the acceleration due to gravity, and z = [0, 0, 1]. T R L SO(3) is the attitude rotation matrix of the load in the body coordinate system, and SO(3) represents the orthogonal rotation group. Ω i ∈TSO(3) represent the position, linear velocity, and angular velocity of the center of mass of the i-th UAV in the inertial coordinate system, respectively. i ∈SO(3) is the attitude rotation matrix of the i-th UAV in the volume coordinate system. Let be the angular velocity of the i-th rope. These are the mass and inertial matrices of the UAV, respectively. Let represent the air damping coefficient matrix of the i-th UAV, with the diagonal elements representing the air damping coefficients of the three axes of the quadrotor UAV's body around the body coordinate system.

[0064] In equation (1), For the virtual control input of the load, △ p (t) and These are the unknown external disturbances in the load position and attitude models, respectively. Let be the unknown external disturbance in the attitude model of the i-th UAV. Let be the acceleration of the i-th connection point, expressed as: Control input of the i-th UAV Parallel component along the corresponding rope direction vector With v i (t) has the following relationship:

[0065]

[0066] In the above model, S(·) represents an anti-symmetric matrix spanned by the vector, that is, for the vector ω(t) = [ω φ (t) ω θ (t) ω ψ (t)] T The expression of S(ω) is

[0067]

[0068] Define the attitude error function of the i-th UAV is

[0069]

[0070] By taking the derivative of the attitude error function The expression of the attitude tracking error of the i-th UAV The angular velocity tracking error is

[0071]

[0072]

[0073] Wherein represents the expected rotation matrix of the load, represents a three-order real number matrix, represents the expected angular velocity of the load attitude. By taking the derivative of , we can get

[0074]

[0075] By taking the derivative of , we can get

[0076]

[0077] When the given attitude command is not fixed, the attitude tracking control system needs to obtain the accurate information of the inertia matrix, however, it is very difficult to accurately measure the value of the inertia matrix of the quadrotor UAV, so an estimation error is usually generated. The expressions of the estimation errors of the inertia matrix and the air damping coefficient matrix are respectively represented as

[0078]

[0079] Wherein, and These represent the true values ​​of the inertia matrix and the air damping coefficient matrix, respectively. and This represents the corresponding measured value, and all of the above matrices are symmetric matrices.

[0080] Define an enhancement error vector The expression is as follows:

[0081]

[0082] The control torque is designed as follows:

[0083]

[0084] in,

[0085]

[0086]

[0087] The adaptive update law for the inertia matrix and air damping coefficient matrix is ​​designed as follows:

[0088]

[0089]

[0090] For a given desired pose and positive control gain and If the control torque represented by equation (11) and the adaptive update law represented by equations (14) and (15) satisfy the following conditions:

[0091]

[0092] Then when σ i When the error is sufficiently small, the tracking error and the estimation error can be uniformly bounded. The specific verification steps are as follows: using Lyapunov analysis, it can be proven that the system error vector can be uniformly bounded.

[0093] The present invention will be described in detail below with reference to specific examples and accompanying drawings.

[0094] I. Introduction to Simulation Verification

[0095] To verify the effectiveness of the proposed adaptive attitude controller, numerical simulations were performed using MATLAB / Simulink software. The relevant parameters of the model are: m Q =0.755kg, m L =1.5kg, l=1m, g=9.81m / s2 and J L = diag([0.0850, 0.1300, 0.2050]) kgm 2 , the inertia matrix and the air damping coefficient matrix are respectively set as

[0096] J i = diag([0.0820, 0.0845, 0.1377]) kg·m 2 ,

[0097] B i = diag([0.1, 0.1, 0.1]).

[0098] The application sets the expected motion trajectory of the load and the corresponding expected attitude rotation matrix as follows:

[0099] ω ref = 2π / T rad / s

[0100]

[0101]

[0102] According to the expected position and the expected attitude of the load, the expected control force u of each UAV can be calculated i = -f i R i z, wherein R i z corresponds to the direction of the third body coordinate axis of the UAV. Therefore, the direction of the third body coordinate axis of the expected attitude of the UAV can be selected as

[0103]

[0104] The expected attitude rotation matrix of the UAV can be set as

[0105]

[0106] wherein, is a smoothing function.

[0107] II. Simulation verification analysis

[0108] To verify the control effect of the controller proposed in the application and the proportional differential (PD) controller, the application completes comparative simulation in the presence of disturbance. In the first group of simulation, the disturbance is added at the initial moment and is set as

[0109]

[0110] In the second set of simulations, the perturbation was increased and the perturbation generation time was set to the 10th second. The perturbation settings are as follows:

[0111]

[0112] (1) Parameter selection

[0113] The control gain of the PD controller was selected through multiple simulations as follows:

[0114]

[0115] The relevant gain of the controller proposed in this invention is selected as follows:

[0116]

[0117]

[0118]

[0119] (2) Results Analysis

[0120] During the simulation, a steady state is defined as the system entering when the error vector remains within a specified error band (5% of the target position). In the first set of simulations, Figures 3 to 5 The attitude angle tracking curves under two different controllers are shown, where the solid line represents the desired attitude angle curve, the dashed line represents the attitude angle curve under the method of this invention, and the dotted line represents the attitude angle curve under the PD controller.

[0121] Figure 3 The image shows a comparison curve of Euler angle (roll) tracking. It can be seen that the method of this invention has a certain deviation in the initial stage, approximately ±4.2°, which then quickly stabilizes, generally consistent with the trend of the desired Euler angle. Comparing the tracking curve under the PD controller, the oscillation amplitude is smaller in the initial stage, and the overall tracking result leads the desired curve, with larger tracking errors at the peaks and troughs. Throughout the attitude tracking process, the maximum steady-state error under the method of this invention is ±0.49°, while the maximum steady-state error under the PD controller reaches ±1.71°.

[0122] Figure 4 and Figure 5The comparative tracking curves of Euler angle (pitch) and Euler angle (yaw) under two controllers are respectively shown. Among them, the overall tracking result of the pitch angle is good, whether under the robust adaptive controller proposed in the application or under the PD controller, the change trend and change size of the two are basically consistent with the expected attitude angle curve. In the initial transient stage, both of them can also track the expected attitude curve well. After entering the steady state, the tracking curve of the PD controller lags slightly from the 5th second to the 14th second, and the lag problem is not obvious in the remaining stage. While the method of the application realizes fast tracking in the whole 30 seconds, especially the advantage is more obvious at the peak and valley.

[0123] Table 1: Comparative simulation 1: comparison of attitude angle error after adding small disturbance at initial time

[0124]

[0125] By observing the yaw angle tracking curve in Figure 5 , it can be seen that the expected attitude angle curve produces a large fluctuation in the first 2 seconds. Both controllers have a large tracking error in the transient stage. Compared with the tracking effect of the PD controller, the tracking effect of the method of the application is more stable, and the tracking effect of the PD controller is more affected by the disturbance. The overall tracking curve around the expected curve has a certain degree of oscillation, and the maximum error in the steady state reaches ±2.87°. In Table 1, the attitude angle error data of the two controllers in this simulation is sorted, and it can be seen that under the condition of adding small disturbance at the initial time, the anti-disturbance effect of the controller proposed in the application is better than that of the PD control.

[0126] The simulation results of the second group of simulations are shown in Figures 6 to 8 , which respectively represent the attitude angle tracking curves of the unmanned aerial vehicle under two kinds of controllers. At the initial time, when the disturbance is set to 0, it can be seen that after entering the steady state, both controllers can track the expected attitude angle curve well. However, after adding disturbance at the 10th second, the three attitude angle curves under the PD controller all appear different degrees of deviation. The three attitude angles under the controller proposed in the application are less affected by the disturbance, and can accurately track the expected curve when the disturbance exists.

[0127] Table 2: Comparative simulation 2: comparison of attitude angle error after adding large disturbance at the 10th second

[0128]

[0129] The simulation of the present group verifies the anti-interference effect of the method from the angle of the attitude angle tracking curve, and the attitude angle error related data is arranged in Table 2. It can be seen that the steady-state mean square error and the steady-state maximum error of the three attitude angles under the controller proposed in the present application are far less than the attitude angle error under the PD controller. By comparing with the data in Table 1, it can be found that after the disturbance is increased, the attitude angle error under the PD controller increases greatly, and the attitude angle error under the controller proposed in the present application changes little, which further verifies the anti-interference performance of the proposed controller.

[0130] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any change or replacement easily thought of by those skilled in the art within the technical range disclosed in the present application should be covered within the protection scope of the present application.

Claims

1. An attitude control method for a multi-UAV tethered load air transport system, characterized in that, First, define an inertial coordinate system. and 4 body coordinate systems The center of the 0th individual coordinate system is established at the center of mass of the rigid body load, and the centers of the 1st, 2nd and 3rd individual coordinate systems are established at the centers of mass of the three drones respectively. The three drones are suspended by a rigid body load by three ropes of equal length. Assuming the rope is always taut, in the inertial coordinate system, the load position and the first... The location of the drone has the following relationship: ,in, Indicates the direction from the load centroid to the first The vector of the connection point of the rope on the load. Represents a vector space consisting of three-dimensional real vectors. Indicates the length of the rope. Represents the set of real numbers. By the The center of mass of the drone points to the first The unit vector in the direction of the point where the rope connects to the load, with subscript [value]. Characterizing the first drones and the first A rope, Represents a two-dimensional sphere; Based on the Lagrange modeling method, a dynamic model of the multi-UAV tethered load air transport system is obtained: The variables in the dynamic equations are defined as follows: These are the load mass and the inertia matrix, respectively. These represent the position, linear velocity, and angular velocity of the load's center of mass in the inertial coordinate system, respectively. It is the acceleration due to gravity. , Let be the attitude rotation matrix of the load in volume coordinates. Represents the orthogonal rotation group; The first The position, linear velocity, and angular velocity of the UAV's center of mass in the inertial coordinate system. For the first The attitude rotation matrix of the UAV in volume coordinates. For the first The angular velocity of the rope, These are the mass and inertial matrices of the UAV, respectively. Indicates the first The air damping coefficient matrix of the quadcopter unmanned aerial vehicle, with the diagonal elements representing the air damping coefficients of the three axes of the body coordinate system around the quadcopter unmanned aerial vehicle. In equation (1), For virtual control input of the load, These are the unknown external disturbances in the load position and attitude models, respectively. For the first Unknown external disturbances in the attitude model of a drone. For the first The acceleration of each connection point is expressed as: , No. Control input for drones Parallel component of the corresponding rope direction vector and It has the following relationship: In the above model, Let represent the antisymmetric matrix spanned by vectors, i.e., for vectors . , The expression is Definition of the first Attitude error function of a drone for By analyzing the attitude error function Differentiation yields the first... Attitude tracking error of a drone Angular velocity tracking error The expressions are respectively right Taking the derivative, we get: right Taking the derivative, we get: When the given attitude command is not fixed, the attitude tracking control system needs to obtain accurate information about the inertial matrix. However, accurately measuring the value of the inertial matrix of a quadcopter UAV is difficult, thus introducing an estimation error. The expressions for the estimation errors of the inertial matrix and the air damping coefficient matrix are respectively: in, These represent the true values ​​of the inertia matrix and the air damping coefficient matrix, respectively. This represents the corresponding measured value, and all of the above matrices are symmetric matrices; Define an enhancement error vector The expression is as follows: The control torque is designed as follows: in, The adaptive update law for the inertia matrix and air damping coefficient matrix is ​​designed as follows: For a given desired pose and positive control gain If the control torque represented by equation (11) and the adaptive update law represented by equations (14) and (15) satisfy the following conditions: So when When the error is sufficiently small, the tracking error and the estimation error become uniformly bounded.

2. The attitude control method for a multi-UAV tethered load airlift system as described in claim 1, characterized in that, We prove, using Lyapunov analysis, that the system error vector can achieve uniform boundedness.

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