Control method for cooperative hoisting system of tandem unmanned helicopters

Abstract

The invention relates to a tandem unmanned helicopter cooperative hoisting system control method, which is characterized in that virtual points are introduced into a kinetic model of a tandem unmanned helicopter cooperative hoisting system, a controller based on a backstepping method is designed, and trajectory tracking control of the virtual points is realized. The tandem type unmanned helicopter cooperative hoisting system comprises a plurality of tandem type unmanned helicopters which are connected with a load through flexible cables, and the state quantity of movement of the system comprises the position and the speed of a point mass load, the position and the speed of the point mass load, the position and the speed of the point mass load and the position and the speed of the point mass load. The speed and the angular speed of each unmanned aerial vehicle and the direction and the angular speed of each connecting cable are input into the unmanned aerial vehicle thrust and the unmanned aerial vehicle angular speed, and the direction of the thrust is limited to be the direction perpendicular to the fuselage. Compared with the prior art, the method has the advantages that the dynamic characteristics of the load are considered, cooperative control of the multiple tandem unmanned aerial vehicles during transportation of the large-weight load is realized, and the control stability is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle control, and in particular to a control method for a tandem unmanned helicopter collaborative lifting system. Background Art

[0002] In recent years, tandem unmanned helicopters have been widely used in cargo transportation, disaster relief, and other fields due to their flexibility and high maneuverability. Tandem unmanned helicopter lifting systems, which connect loads via cables, offer a simple structure and high flexibility. However, the complex dynamics of the lifting system, particularly in multi-machine collaborative lifting scenarios, significantly increase the control complexity due to the dynamic coupling between the drones and the load. Designing effective controllers to achieve high-precision trajectory tracking and system stability for the load has become a key research focus.

[0003] Existing research on controller design for UAV lifting systems primarily focuses on trajectory tracking and sway suppression. To this end, researchers have proposed various approaches, such as introducing disturbance observers to monitor and compensate for external disturbances in real time, or incorporating adaptive estimators to handle unknown system parameters, thereby improving the robustness and applicability of controllers. In multi-machine collaborative lifting scenarios, the difficulty of controller design lies in coordinating the motion of multiple UAVs so that they act together on the load and achieve the desired trajectory tracking. CN116300466A discloses a robust control method for the coordinated lifting of mass loads by a cluster of rotorcraft drones, comprising the following steps: establishing a dynamic model of a four-rotor drone cluster coordinated lifting system including disturbances based on Lagrangian mechanics and the Hamilton principle; constructing a robust controller for the coordinated lifting mass loads using the backstepping method based on the dynamic model, sequentially controlling the load position, cable direction, and drone attitude; introducing a saturation function to ensure that the rotorcraft thrust is bounded relative to the load position error and velocity error; introducing a disturbance estimator and embedding it into the control input of each rotorcraft; and determining an update method for the disturbance estimator using a projection function to obtain the desired thrust and drone angular velocity, thereby controlling the point mass load to maintain stable motion in the presence of disturbances. However, this method is overly complex, has high controller computational overhead, and is difficult to analyze, making it unsuitable for deployment on underlying computing hardware.

[0004] Therefore, how to design a simple controller that can achieve high-precision trajectory tracking, strong stability and is suitable for multi-machine collaborative lifting scenarios to cope with complex dynamic coupling relationships remains a difficult problem that needs to be solved urgently. Summary of the Invention

[0005] The purpose of the present invention is to optimize the control effect of the unmanned helicopter lifting system in a real environment, provide a control method for a tandem unmanned helicopter collaborative lifting system, and design a controller based on the backstepping method. This virtual point-based control strategy decomposes the complex multi-machine collaborative problem into multiple single-machine control problems by defining the virtual control point of the load. By designing the control law of the thrust and angular velocity of each aircraft, it ensures that each drone can accurately track the desired trajectory of the virtual point, thereby indirectly achieving control of the load.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A control method for a tandem unmanned helicopter collaborative lifting system is disclosed. The method introduces virtual points into the dynamic model of the tandem unmanned helicopter collaborative lifting system, designs a controller based on the backstepping method, and realizes trajectory tracking control of the virtual points, thereby reducing the complexity of the controller design of the multi-machine collaborative lifting system and realizing the configuration control of the cable. The tandem unmanned helicopter collaborative lifting system includes multiple tandem unmanned helicopters, each of which is regarded as a six-degree-of-freedom rigid body driven by thrust and torque and connected to the load through flexible cables. The state quantities of the motion of the multi-tandem unmanned helicopter collaborative lifting system include the position and velocity of the point mass load, the velocity and angular velocity of each drone, and the direction and angular velocity of each connecting cable. The input of the system is the drone thrust and drone angular velocity, and the direction of the thrust is limited to the direction perpendicular to the fuselage.

[0008] The dynamic model construction process of the tandem unmanned helicopter collaborative lifting system is as follows:

[0009] Assume that the connection point between the cable and the drone is located at the center of mass of the fuselage and is always kept in a tensioned state. Determine the relationship between the position of the drone and the position of the payload.

[0010] Determine the first dynamic equations of the tandem unmanned helicopter cooperative lifting system based on the relationship between the position of the UAV and the position of the load;

[0011] The second set of dynamic equations is derived based on the Lagrangian method;

[0012] A dynamic model of a tandem unmanned helicopter cooperative lifting system is constructed based on the first and second dynamic equations.

[0013] Assume that the distance between the i-th UAV and the payload is l i The position x of the i-th aircraft is connected to the flexible rope. i With the load position x L The relationship between them is expressed as:

[0014] x i=x L -l i n i

[0015] The first dynamic equations of the tandem unmanned helicopter cooperative lifting system include two parts: translation and rotation, specifically:

[0016]

[0017] Among them, n i is the direction vector of the i-th rope, v L is the load linear velocity, v i is the linear velocity of the i-th UAV, ω i is the angular velocity of the i-th rope, Ω i is the angular velocity of the drone, R i is the rotation matrix of the i-th UAV, the superscript · represents the derivative, and the symbol S(·) is an operator. For two three-dimensional vectors m and n, S(m)n=m×n.

[0018] The second set of dynamic equations is specifically:

[0019]

[0020] in, P ni =n i n i T , I is the identity matrix, k is the number of drones, m L and m i denote the load and mass of the i-th UAV, u i Generates thrust vector for the rotor, denoted as u i =-U i R i e3, U i is the thrust, e3=[0 0 1] T , g is the acceleration due to gravity.

[0021] The design of the controller includes the following steps:

[0022] The control input of the tandem unmanned helicopter cooperative lifting system is determined to be the thrust and angular velocity of each UAV; based on the system's dynamic model, the effect of the UAV's thrust on the system dynamics is limited to a direction parallel to the cable. Considering a virtual point on the cable, the controller takes the virtual point as the control object, solves the dynamic equation of the virtual point, and defines the first Lyapunov function through the position and velocity errors between the virtual point and the desired trajectory to control the virtual point to stably track its desired trajectory and realize the position control of the virtual point; based on the desired thrust, a second Lyapunov function is defined, and the positivity of the second Lyapunov function and the negative definiteness of its derivative are ensured to obtain the control law of the UAV's angular velocity.

[0023] The dynamic equation of the virtual point is:

[0024]

[0025] in, is the linear velocity of the virtual point, δ i is a constant that represents the distance between the selected virtual point and the load.

[0026]

[0027] The position control of the virtual point is specifically as follows:

[0028] For each virtual point, give its expected motion trajectory The position error and velocity error of trajectory tracking are defined as:

[0029]

[0030] in, is the position of the i-th virtual point, is a constant term, which is specified as k i ,k d is adjustable gain;

[0031] According to the position error and velocity error, the definition of the i-th term in the first Lyapunov function is given:

[0032]

[0033] The first Lyapunov function is defined as:

[0034]

[0035] Where k1 is the position error gain, β is the joint gain;

[0036] Consider all k drones, and form a 3k×1 vector of position errors, velocity errors, and expected thrusts for all drones, expressed as is the expected value of the i-th input thrust;

[0037] Taking the derivative of the first Lyapunov function V1, we get:

[0038]

[0039] in, is a positive definite term, k2 is an adjustable gain, and the coefficient of thrust in the velocity error derivative in the above formula is written in matrix form:

[0040]

[0041] Define the intermediate quantity ξ i for: And set the expected thrust to: u d =M -1 ξ, eliminates the Lyapunov function One term, simplifying the derivative of the first Lyapunov function to:

[0042]

[0043] Where u is the UAV thrust vector.

[0044] The method for determining the control law of the angular velocity of the UAV is:

[0045] Assume that the actual thrust direction of the i-th UAV is The desired thrust direction is The error in the thrust direction, that is, the error in the z-axis direction, is defined as:

[0046] Introducing thrust direction errors for all drones The vector Create a second Lyapunov function:

[0047]

[0048] Among them, h r is an adjustable control gain, set to a constant greater than 0; taking the derivative of the second Lyapunov function V2, we get:

[0049]

[0050] in, k r is an adjustable control gain;

[0051] Then the control law of the thrust of the i-th UAV is:

[0052] In order to control the z-axis of the drone to its desired direction, the angular velocity control law of the i-th aircraft is:

[0053]

[0054] Among them, Ω i is the angular velocity of the i-th UAV, M ji is a block matrix in the matrix M.

[0055] The desired motion trajectory of the virtual point is determined based on the desired cable direction:

[0056]

[0057] Among them, x d is the expected load trajectory, δ i is a constant that represents the distance between the selected virtual point and the load, t f The end time.

[0058] The method comprises the following steps:

[0059] Determine the desired motion trajectory of the load;

[0060] Determining the desired cable directions during the operation of the load based on the desired motion trajectory of the load, and determining the desired motion trajectory of each virtual point based on the desired cable directions;

[0061] Inputting the desired motion trajectory of each virtual point into a controller and setting controller parameters, and determining the drone thrust and drone angular velocity based on the controller to control the drone;

[0062] During the control process, sensors are used to feed back the real-time motion status of the drone and the load to the controller, and the control law is updated in real time until the load lifting task is completed.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention relates to a control method for a tandem unmanned helicopter cooperative lifting system, aiming to solve the problems of cooperative control, load dynamic characteristics and system stability of multiple tandem unmanned aerial vehicles when transporting heavy loads. The present invention first establishes a dynamic model of the tandem unmanned helicopter lifting system based on Newton's laws of kinematics and the positional relationship between the load and the unmanned aerial vehicle, and the model includes the under-actuation and high nonlinear characteristics of the system. For the multiple tandem unmanned helicopter cooperative lifting system, a nonlinear controller based on the backstepping method is designed. The controller is simplified and the reference trajectory is reduced in order by setting virtual points, and the cable direction is decoupled to achieve control of the cable configuration, simplifying the controller design, and achieving efficient and high-precision system control. It has been verified that the controller is stable. The present invention can be widely used in logistics, transportation, disaster relief and other fields, and provides theoretical and technical support for the design and optimization of the tandem unmanned helicopter cooperative lifting system. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a schematic diagram of the positional relationship of various parts of a multiple-tandem unmanned helicopter lifting system;

[0066] Figure 2 A schematic diagram of the controller construction process of the present invention;

[0067] Figure 3 Schematic diagram of the control problem of multiple tandem unmanned helicopter lifting systems;

[0068] Figure 4 This is a flow chart of the control method of the present invention. DETAILED DESCRIPTION

[0069] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0070] This embodiment provides a control method for a tandem unmanned helicopter collaborative lifting system. By introducing virtual points into the dynamic model of the tandem unmanned helicopter collaborative lifting system, a controller based on the backstepping method is designed to achieve trajectory tracking control of the virtual points, thereby reducing the complexity of the multi-machine collaborative lifting system controller design and realizing cable configuration control.

[0071] like Figure 1 As shown in the figure, the multi-tandem unmanned helicopter cooperative lifting system considers a total of k unmanned aerial vehicles. Each tandem unmanned helicopter is regarded as a rigid body with six degrees of freedom driven by thrust and torque, connected to the load through a flexible cable. The system model is established, including an inertial coordinate system and k individual coordinate systems. The i-th body coordinate system fixed to the body is denoted as {Bi}, the origin of its coordinate system is located at the center of mass of the i-th UAV; the inertial coordinate system is recorded as {I}, and the matrix R i For {B i The state quantities of the multi-column unmanned helicopter cooperative lifting system include the position and velocity of the point mass load, the velocity and angular velocity of each drone, and the direction and angular velocity of each connecting cable. The input of the system is the drone thrust u i and the drone's angular velocity Ω i , i=1,2,…,k, the thrust direction is limited to the direction perpendicular to the fuselage. The thrust generated by the rotor is U i , the thrust vector is represented by u i =-U i R i e3, R i is the rotation matrix of the i-th UAV, e3=[0 0 1] T .

[0072] The process of constructing the dynamic model of the tandem unmanned helicopter collaborative lifting system is as follows:

[0073] A1. Assume that the connection point between the cable and the UAV is located at the center of mass of the fuselage and is always kept in a tensioned state. Determine the relationship between the position of the UAV and the position of the payload.

[0074] Assume that the distance between the i-th UAV and the payload is l i The connection point between the cable and the UAV is located at the center of mass of the fuselage and is always kept in a tensioned state. Then the position x of the i-th aircraft is i With the load position x L The relationship between them is expressed as:

[0075] x i =x L -l i n i (1)

[0076] A2, based on the relationship between the position of the UAV and the position of the load, the first dynamic equation group of the tandem unmanned helicopter cooperative lifting system is determined.

[0077] The first dynamic equations of the tandem unmanned helicopter cooperative lifting system include two parts: translation and rotation, specifically:

[0078]

[0079] Among them, n i is the direction vector of the i-th rope, v L is the load linear velocity, v iis the linear velocity of the i-th UAV, ω i is the angular velocity of the i-th rope, Ω i is the angular velocity of the drone, R i is the rotation matrix of the i-th UAV, and the superscript · represents the derivative. The symbol S(·) is an operator. For two three-dimensional vectors m and n, S(m)n=m×n; the result of this operation is to transform a vector belonging to The vector is mapped to P n and Π n Represents two projection operators, which are perpendicular to each other, P n =nn T , Π n =I-nn T =-S(n) 2 .

[0080] A3, the second set of dynamic equations is derived based on the Lagrangian method.

[0081] A31. Establish the Lagrangian equations for the coordinated lifting system of a tandem unmanned helicopter.

[0082] Determine the sum of the kinetic energies of the parts of the system:

[0083]

[0084] Among them, m L and m i denote the payload and the mass of the i-th UAV respectively.

[0085] Determine the total gravitational potential energy of the payload and all drones:

[0086]

[0087] Where, e3 = [0 0 1] T , g is the acceleration due to gravity.

[0088] Determine the Lagrangian function based on the total kinetic energy and total gravitational potential energy of the system A32, calculate the partial derivatives of the Lagrangian function with respect to each motion state quantity:

[0089]

[0090] A33, Computing the Variation of Action Integrals and Virtual Work

[0091]

[0092] Among them, η i is an infinitesimal quantity. According to the Lagrange-Lambert principle, we have:

[0093]

[0094] Where W represents the virtual work done by the non-conservative force.

[0095] A34, according to equations (8)-(13), the following Euler-Lagrange equation is obtained through partial integration transformation:

[0096]

[0097] Derivatives of equations (8) and (10) yield and Substituting the derivative result into equation (13), we can obtain the second set of dynamic equations of the system:

[0098]

[0099] in, P ni =n i n i T .

[0100] A4. Based on the first set of dynamic equations, equations (2)-(5), and the second set of dynamic equations, equations (17)-(18), a dynamic model of the tandem unmanned helicopter cooperative lifting system is constructed.

[0101] In this embodiment, Figure 2 As shown, the controller design includes the following steps:

[0102] The control input of the tandem unmanned helicopter collaborative lifting system is determined to be the thrust and angular velocity of each drone. Based on the system's dynamic model, the effect of the drone's thrust on the system's dynamics is limited to a direction parallel to the cable. To solve this problem, simplify the controller design steps, and reduce the smoothness order requirements for the desired trajectory, the present invention considers a virtual point on the cable. The controller uses the virtual point as the control object, solves the dynamic equation of the virtual point, and defines a first Lyapunov function based on the position and velocity error between the virtual point and the desired trajectory to control the virtual point to track its desired trajectory. Based on the desired thrust, a second Lyapunov function is defined, and the positive definiteness of the second Lyapunov function and the negative definiteness of its derivative are ensured to obtain the control law for the drone's angular velocity. The specific analysis process is as follows:

[0103] like Figure 3 As shown in Figure 2, the positional relationship between the virtual point on the i-th cable and the load is:

[0104]

[0105] in, is the position of the i-th virtual point, δi is a constant that represents the distance between the selected virtual point and the load, δ i Satisfying 0<δ i <l i .

[0106] To simplify the expression, some known quantities are expressed as:

[0107]

[0108] By taking the second-order derivative of Equation (19), we can obtain the dynamic equation of the virtual point, which is specifically expressed as:

[0109]

[0110] in,

[0111] It can be seen from Equation (23) that after replacing the load position by controlling the position of the virtual point, the thrust contribution of the i-th UAV in the generated dynamic equation is The introduction of the component perpendicular to the cable means that the thrust is no longer limited to the direction of the cable, which simplifies the subsequent controller design.

[0112] For each virtual point, give its expected motion trajectory (requires at least third-order continuous derivatives). The present invention designs a controller that can achieve the goal of driving each virtual point to track its desired trajectory. The position error and velocity error of trajectory tracking are defined as:

[0113]

[0114] In formulas (24) and (25), is a constant term, which is specified as The introduction of (0) as the cable integral term ensures the convergence of the system output when it reaches 0, thus suppressing the undesirable oscillation in the system. i ,k d For adjustable gain.

[0115] According to the definition of the two error terms, the definition of the i-th term in the first Lyapunov function is given:

[0116]

[0117] The first Lyapunov function is defined as:

[0118]

[0119] Where k1 is the position error gain and β is the joint gain.

[0120] Consider all k drones and group the system variables into 3k×1 vectors, expressed as is the expected value of the i-th input thrust.

[0121] Taking the derivative of V1, we get:

[0122]

[0123] in is a positive term, and k2 is an adjustable gain. The coefficient of thrust in the velocity error derivative in the above formula is written as a matrix:

[0124]

[0125] By reasonably choosing δ i 、l i 、m i The value of can avoid the irreversibility problem of M. In this invention, only the case where M is reversible is considered. To eliminate the Lyapunov function One, define the intermediate quantity ξ i for:

[0126]

[0127] Set the desired thrust to:

[0128] u d =M -1 ξ (30)

[0129] Then the derivative of the first Lyapunov function can be simplified to:

[0130]

[0131] Where u is the UAV thrust vector.

[0132] In order to make the thrust direction tend to the desired thrust direction, it is necessary to further design the control law of the angular velocity of the UAV. The actual thrust direction of the i-th aircraft is The desired thrust direction is The error in the thrust direction (z-axis direction) is defined as:

[0133]

[0134] Introducing z-axis errors for all drones The vector Create a second Lyapunov function:

[0135]

[0136] Among them, h r Is an adjustable control gain, set to a constant greater than 0, so that V2 is also positive. Take the derivative of V2 and add or subtract one term get

[0137]

[0138] in, k r is an adjustable control gain.

[0139] Since the thrust direction of the drone is limited to being perpendicular to the fuselage and cannot be arbitrarily specified, this embodiment provides a control law for the thrust magnitude. The specific expression is:

[0140]

[0141] In order to control the z-axis of the drone to its desired direction, the angular velocity control law of the i-th aircraft is given as:

[0142]

[0143] in, M ji is a block matrix in the matrix M. When the input thrust and angular velocity are set according to equations (35) and (36), respectively, the derivative of the Lyapunov function can be simplified to

[0144]

[0145] is a semi-negative definite function. x 、E v and E r When both are 0, For other cases, Therefore, the Lyapunov function V2 is bounded, and its upper bound is its initial value V2(E x (0),E v (0),E r (0)), according to Lyapunov stability theory, it can be obtained that the system trajectory tracking error always converges, achieving the purpose of trajectory tracking control.

[0146] Based on the above controller design process, cable direction control is performed.

[0147]

[0148] in, is the virtual point position error, is the position error of the virtual point at the initial moment.

[0149] From the above formula, we can infer that when time tends to infinity, In order to achieve the goal that the virtual point can finally move along its desired trajectory, it is necessary to Therefore, the constant The setting method is:

[0150]

[0151] n i (t f ) is related to the trajectory generation of the virtual point. When each virtual point reaches the desired position, the position of the load can be uniquely determined (k ≥ 3) through the positional relationship constraints of the triangle, and accordingly, the direction of each cable can also be uniquely determined. When the parameters take certain values, two solutions may appear that are symmetrical in space, but according to the actual system characteristics, the situation where the load is above the drone can be eliminated. Therefore, the desired trajectory of the virtual point can be determined by the desired cable direction:

[0152]

[0153] Among them, x d is the expected load trajectory, δ i is a constant that represents the distance between the selected virtual point and the load, t f The end time.

[0154] In one embodiment, Figure 4 As shown, the control method includes the following steps:

[0155] S1, determine the desired motion trajectory of the load;

[0156] S2, determining the desired cable directions during the operation of the load based on the desired motion trajectory of the load, and determining the desired motion trajectory of each virtual point according to the desired cable directions;

[0157] S3, inputting the desired motion trajectory of each virtual point into the controller, setting the controller parameters, and determining the UAV thrust and UAV angular velocity based on the controller to control the UAV;

[0158] S4, during the control process, uses sensors to feed back the real-time motion status of the drone and the load to the controller, and updates the control law in real time until the load lifting task is completed.

[0159] To verify the effectiveness of the above control method, this embodiment provides actual simulation data for detailed description. The expected trajectory of the load is:

[0160]

[0161] The parameter settings in the simulation specifically include system parameters, initial value parameters and control parameters. The terminal position vector n1(t f )、n2(t f ) and n3(t f ) varies with the time t. When t<15, When 15≤t<30, When t>30, the values of the initial position vectors n1(0), n2(0) and n3(0) are and In the system parameters, the mass of the three drones m1, m2, and m3 are all 0.3 kg, and the load mass m L The weight of the suspension cable is 0.05 kg, the lengths of the suspension cables l1, l2, and l3 are 0.5 m, 0.8 m, and 1 m respectively, and the acceleration due to gravity g is 9.8 m / s 2 In the initial value parameters, the initial position x of the UAV is L (0) is [0,0,1]m, initial velocity v L (0) and angular velocity ω L (0) are all [0,0,0]. The initial posture matrices R1(0), R2(0), and R3(0) are [1,0,0; 0,0,1; 0,-1,0]. In addition, the values of the initial position vectors n1(0), n2(0), and n3(0) are respectively and Control parameter part, k x =4,k v =4,k r =100,k i =10,k d =0.1,h r = 10, β = 2. The virtual point position parameters are selected as: δ1 = 0.6, δ2 = 0.5, and δ3 = 0.4. When appropriate parameters are selected, the controller designed in this invention can control all virtual points and loads to converge to the desired trajectory within 5 seconds, while also achieving the desired cable configuration.

[0162] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A control method for a tandem unmanned helicopter collaborative lifting system, characterized in that: The method introduces virtual points into the dynamic model of the multi-machine collaborative lifting system, designs a controller based on the backstepping method, and realizes the trajectory tracking control of the virtual points, thereby reducing the complexity of the controller design of the multi-machine collaborative lifting system and realizing the configuration control of the cable. The multi-machine collaborative lifting system includes multiple longitudinal unmanned helicopters, each of which is regarded as a six-degree-of-freedom rigid body driven by thrust and torque, and is connected to the load through a flexible cable. The state quantities of the motion of the multi-longitudinal unmanned helicopter collaborative lifting system include the position and velocity of the point mass load, the velocity and angular velocity of each drone, and the direction and angular velocity of each connecting cable. The input of the system is the drone thrust and drone angular velocity, and the direction of the thrust is limited to the direction perpendicular to the fuselage.

2. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 1, characterized in that: The dynamic model construction process of the tandem unmanned helicopter collaborative lifting system is as follows: Assume that the connection point between the cable and the drone is located at the center of mass of the fuselage and is always kept in a tensioned state. Determine the relationship between the position of the drone and the position of the payload. Determine the first dynamic equations of the tandem unmanned helicopter cooperative lifting system based on the relationship between the position of the UAV and the position of the load; The second set of dynamic equations is derived based on the Lagrangian method; A dynamic model of a tandem unmanned helicopter cooperative lifting system is constructed based on the first and second dynamic equations.

3. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 2, characterized in that: Assume that the distance between the i-th UAV and the payload is l i The position x of the i-th aircraft is connected to the flexible rope. i With the load position x L The relationship between them is expressed as: x i =x L -l i n i The first dynamic equations of the tandem unmanned helicopter cooperative lifting system include two parts: translation and rotation, specifically: Among them, n i is the direction vector of the i-th rope, v L is the load linear velocity, v i is the linear velocity of the i-th UAV, ω i is the angular velocity of the i-th rope, Ω i is the angular velocity of the drone, R i is the rotation matrix of the i-th UAV, the superscript · represents the derivative, and the symbol S(·) is an operator. For two three-dimensional vectors m and n, S(m)n=m×n.

4. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 3, characterized in that: The second set of dynamic equations is specifically: in, P ni =n i n i T , I is the identity matrix, k is the number of drones, m L and m i denote the load and mass of the i-th UAV, u i Generates thrust vector for the rotor, denoted as u i =-U i R i e3, U i is the thrust, e3=[0 0 1] T , g is the acceleration due to gravity.

5. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 4, characterized in that: The design of the controller includes the following steps: The control input of the tandem unmanned helicopter cooperative lifting system is determined to be the thrust and angular velocity of each UAV; based on the system's dynamic model, the effect of the UAV's thrust on the system dynamics is limited to a direction parallel to the cable. Considering a virtual point on the cable, the controller takes the virtual point as the control object, solves the dynamic equation of the virtual point, and defines the first Lyapunov function through the position and velocity errors between the virtual point and the desired trajectory to control the virtual point to stably track its desired trajectory and realize the position control of the virtual point; based on the desired thrust, a second Lyapunov function is defined, and the positivity of the second Lyapunov function and the negative definiteness of its derivative are ensured to obtain the control law of the UAV's angular velocity.

6. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 5, characterized in that: The dynamic equation of the virtual point is: in, is the linear velocity of the virtual point, δ i is a constant that represents the distance between the selected virtual point and the load.

7. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 6, characterized in that: The position control of the virtual point is specifically as follows: For each virtual point, give its expected motion trajectory The position error and velocity error of trajectory tracking are defined as: in, is the position of the i-th virtual point, is a constant term, which is specified as k i ,k d is adjustable gain; According to the position error and velocity error, the definition of the i-th term in the first Lyapunov function is given: The first Lyapunov function is defined as: Where k1 is the position error gain, β is the joint gain; Consider all k drones, and form a 3k×1 vector of position errors, velocity errors, and expected thrusts for all drones, expressed as is the expected value of the i-th input thrust; Taking the derivative of the first Lyapunov function V1, we get: in, is a positive definite term, k2 is an adjustable gain, and the coefficient of thrust in the velocity error derivative in the above formula is written in matrix form: Define the intermediate quantity ξ i for: And set the expected thrust to: u d =M -1 ξ, eliminates the Lyapunov function One term, simplifying the derivative of the first Lyapunov function to: Where u is the UAV thrust vector.

8. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 7, characterized in that: The method for determining the control law of the angular velocity of the UAV is: Assume that the actual thrust direction of the i-th UAV is The desired thrust direction is The error in the thrust direction, that is, the error in the z-axis direction, is defined as: Introducing thrust direction errors for all drones The vector Create a second Lyapunov function: Among them, h r is an adjustable control gain, set to a constant greater than 0; taking the derivative of the second Lyapunov function V2, we get: in, k r is an adjustable control gain; Then the control law of the thrust of the i-th UAV is: In order to control the z-axis of the drone to its desired direction, the angular velocity control law of the i-th aircraft is: Among them, Ω i is the angular velocity of the i-th UAV, M ji is a block matrix in the matrix M.

9. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 5, characterized in that: The desired motion trajectory of the virtual point is determined based on the desired cable direction: Among them, x d is the expected load trajectory, δ i is a constant that represents the distance between the selected virtual point and the load, t f The end time.

10. The control method of a tandem unmanned helicopter cooperative lifting system according to claim 1, characterized in that: The method comprises the following steps: Determine the desired motion trajectory of the load; Determining the desired cable directions during the operation of the load based on the desired motion trajectory of the load, and determining the desired motion trajectory of each virtual point based on the desired cable directions; Inputting the desired motion trajectory of each virtual point into a controller and setting controller parameters, and determining the drone thrust and drone angular velocity based on the controller to control the drone; During the control process, sensors are used to feed back the real-time motion status of the drone and the load to the controller, and the control law is updated in real time until the load lifting task is completed.

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