A control method for a columnar unmanned helicopter cooperative hoisting system

Abstract

The application relates to a control method of a longitudinal unmanned helicopter cooperative hoisting system, which introduces a virtual point in a dynamic model of the longitudinal unmanned helicopter cooperative hoisting system, designs a controller based on a backstepping method, realizes trajectory tracking control of the virtual point, reduces the complexity of controller design of the multi-machine cooperative hoisting system, and realizes configuration control of a cable, wherein the longitudinal unmanned helicopter cooperative hoisting system comprises multiple longitudinal unmanned helicopters connected with a load through flexible cables, state variables of the system movement include the position and speed of the point mass load, the speed and angular speed of each unmanned helicopter, and the direction and angular speed of each connecting cable, the input is the thrust of the unmanned helicopter and the angular speed of the unmanned helicopter, and the direction of the thrust is limited to the direction perpendicular to the fuselage. Compared with the prior art, the application considers the dynamic characteristics of the load, realizes cooperative control of multiple longitudinal unmanned helicopters when transporting large heavy loads, and guarantees the stability of the control.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to a control method for a tandem unmanned helicopter collaborative hoisting system. Background Technology

[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 connect the load via cables, featuring simple structure and high flexibility. However, the complex dynamic characteristics of the lifting system, especially in multi-helicopter collaborative lifting scenarios, significantly increase the control difficulty due to the dynamic coupling between the UAV and the load. Designing an effective controller to achieve high-precision trajectory tracking of the load and system stability has become a key research focus.

[0003] Existing research on controller design methods for UAV lifting systems mainly focuses on trajectory tracking and sway suppression. To address these issues, researchers have proposed various approaches, such as introducing disturbance observers to monitor and compensate for external disturbances in real time, or combining adaptive estimators to handle unknown parameters in the system, thereby improving the robustness and applicability of the controller. In multi-UAV cooperative lifting scenarios, the challenge in controller design lies in coordinating the movements of multiple UAVs to ensure they work together on the load and achieve the desired trajectory tracking. CN116300466A discloses a robust control method for the collaborative lifting of point mass loads by a swarm of rotary-wing UAVs, comprising the following steps: establishing a dynamic model of a quadrotor UAV swarm collaborative lifting system containing disturbances based on Lagrange mechanics and Hamilton's principle; constructing a robust controller for the collaborative lifting of point mass loads using a backstepping method based on the dynamic model, sequentially controlling the load position, cable direction, and UAV attitude; simultaneously, introducing a saturation function to ensure that the thrust of the rotary-wing UAV is bounded relative to the load position and velocity errors; introducing a disturbance estimate and embedding it into the control input of each rotary-wing UAV; and determining the update method for the disturbance estimate through a projection function to obtain the desired thrust and UAV angular velocity, thereby controlling the stable motion of the point mass load under the presence of disturbances. However, this method is overly complex, with high controller computational overhead and difficult controller analysis, making it unsuitable for deployment on low-level computing hardware.

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

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

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A control method for a tandem unmanned helicopter collaborative lifting system is disclosed. This method introduces virtual points into the dynamic model of the tandem unmanned helicopter collaborative lifting system and designs a controller based on the backstepping method to achieve trajectory tracking control of the virtual points. This reduces the complexity of the controller design for the multi-helicopter collaborative lifting system and enables configuration control of the cables. The tandem unmanned helicopter collaborative lifting system includes multiple tandem unmanned helicopters, each of which is considered a six-degree-of-freedom rigid body driven by thrust and torque and connected to the load via flexible cables. The motion state variables 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 unmanned helicopter, and the direction and angular velocity of each connecting cable. The system inputs are the thrust and angular velocity of the unmanned helicopters, and the direction of the thrust is restricted to a direction perpendicular to the fuselage.

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

[0009] Assuming the connection point between the cable and the drone is located at the center of mass of the fuselage and is always kept taut, determine the relationship between the position of the drone and the position of the load;

[0010] The first set of dynamic equations for the tandem unmanned helicopter collaborative hoisting system is determined 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 Lagrange method;

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

[0013] Let the distance between the i-th UAV and the payload be l. i If the flexible ropes are connected, then the position x of the i-th aircraft... i With respect to the position x of the load L The relationship between them is represented as follows:

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

[0015] The first set of dynamic equations for the tandem unmanned helicopter collaborative lifting system includes two parts: translation and rotation, specifically:

[0016]

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

[0018] The second set of dynamic equations is as follows:

[0019]

[0020] in, P ni =n i n i T I is the identity matrix, k is the number of drones, and m L and m i Let u represent the load and the mass of the i-th drone, respectively. i Generate a thrust vector for the rotor, denoted as u. i =-U i R i e3, U i For the magnitude of 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 inputs for the tandem unmanned helicopter collaborative lifting system are determined to be the thrust magnitude and angular velocity of each UAV. Based on the system's dynamic model, the effect of the UAV thrust on the system dynamics is restricted to the direction parallel to the cable. Considering a virtual point on the cable, the controller takes the virtual point as the controlled object, solves the dynamic equation of the virtual point, and defines the first Lyapunov function based on the position and velocity error between the virtual point and the desired trajectory to control the virtual point to stably track its desired trajectory, thereby achieving position control of the virtual point. 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 UAV's angular velocity.

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

[0024]

[0025] in, Let δ be the linear velocity of the virtual point. i It is a constant representing the distance of the selected virtual point from the load.

[0026]

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

[0028] For each virtual point, its expected trajectory is given. The position error and velocity error of trajectory tracking are defined as follows:

[0029]

[0030] in, Let i be the position of the i-th virtual point. For a constant term, it is specified in the following way: k i ,k d Adjustable gain;

[0031] Based on the position error and velocity error, the definition of the i-th term in the first Lyapunov function is given as follows:

[0032]

[0033] The first Lyapunov function is defined as:

[0034]

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

[0036] Considering all k UAVs, the position error, velocity error, and desired thrust of all UAVs are combined into a 3k×1 vector, represented as: Let i be the expected value of the i-th input thrust;

[0037] Differentiating the first Lyapunov function V1, we get:

[0038]

[0039] in, As a positive definite term, k2 is an adjustable gain. The coefficients of thrust in the velocity error derivative of the above equation can be written in matrix form:

[0040]

[0041] Define intermediate quantity ξ i for: And set the desired thrust as: u d =M -1 ξ, eliminating the Lyapunov function One step simplifies the derivative of the first Lyapunov function to:

[0042]

[0043] Where u is the thrust vector of the UAV.

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

[0045] Let the actual thrust direction of the i-th UAV be... The desired thrust direction is The error in the thrust direction, i.e., the error in the z-axis direction, is defined as:

[0046] Introducing thrust direction errors for all UAVs The vector formed Establish a second Lyapunov function:

[0047]

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

[0049]

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

[0051] The control law for the thrust magnitude of the i-th UAV is:

[0052] To control the UAV's z-axis to tend towards its desired direction, the angular velocity control law for the i-th aircraft is:

[0053]

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

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

[0056]

[0057] Where, x d For the desired load trajectory, δ i It is a constant representing the distance t from the selected virtual point to the load. f This is the end time.

[0058] The method includes the following steps:

[0059] Determine the desired trajectory of the load;

[0060] The expected motion trajectory based on the load determines the expected cable direction during the load operation, and the expected motion trajectory of each virtual point is determined according to the expected cable direction.

[0061] The desired motion trajectory of each virtual point is input into the controller, and the controller parameters are set. Based on the controller, the drone thrust and drone angular velocity are determined 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 hoisting task is completed.

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

[0064] This invention relates to a control method for a tandem unmanned helicopter collaborative lifting system, aiming to solve the problems of collaborative control, load dynamic characteristics, and system stability when multiple tandem unmanned aerial vehicles (UAVs) are transporting heavy loads. First, based on Newton's laws of kinematics and the positional relationship between the load and the UAVs, a dynamic model of the tandem UAV lifting system is established, incorporating the system's underactuated and highly nonlinear characteristics. For this multi-tandem UAV collaborative lifting system, a nonlinear controller based on the backstepping method is designed. By setting virtual points, the controller is simplified and the order of the reference trajectory is reduced. The cable direction is decoupled, thereby achieving control of the cable configuration. This simplifies the controller design, enables efficient and high-precision system control, and the controller has been verified to be stable. This invention can be widely applied in logistics transportation, disaster relief, and other fields, providing theoretical support and technical assistance for the design and optimization of tandem UAV collaborative lifting systems. Attached Figure Description

[0065] Figure 1 A schematic diagram showing the positional relationship of various parts of a tandem unmanned helicopter lifting system;

[0066] Figure 2 This is a schematic diagram of the controller construction process of the present invention;

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

[0068] Figure 4 This is a flowchart of the control method of the present invention. Detailed Implementation

[0069] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0070] This embodiment provides a control method for a tandem unmanned helicopter collaborative hoisting system. By introducing virtual points into the dynamic model of the tandem unmanned helicopter collaborative hoisting 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 controller design for the multi-robot collaborative hoisting system and realizing cable configuration control.

[0071] like Figure 1 As shown, the multi-tandem unmanned helicopter collaborative lifting system considers a total of k unmanned helicopters. Each tandem unmanned helicopter is regarded as a six-degree-of-freedom rigid body driven by thrust and torque, connected to the load by flexible cables. The system model is established based on this, including an inertial coordinate system and k body coordinate systems. The i-th body coordinate system fixed to the helicopter body is denoted as {B}.i The origin of its coordinate system is located at the centroid of the i-th UAV; the inertial coordinate system is denoted as {I}, and the square matrix is ​​R. i For the purpose of {B i The rotation matrix from {I} to {I}. The state variables of the multi-column unmanned helicopter collaborative lifting system include the position and velocity of the point mass load, the velocity and angular velocity of each UAV, and the direction and angular velocity of each connecting cable. The system input is the UAV thrust u. i and the angular velocity Ω of the drone i For i = 1, 2, ..., k, the direction of the thrust is restricted to be perpendicular to the fuselage. The rotor generates a thrust of magnitude U. i The thrust vector is represented as u i =-U i R i e3,R i Let e3 be the rotation matrix for the i-th UAV, where 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 the connection point between the cable and the drone is located at the center of mass of the drone and is always kept taut. Determine the relationship between the position of the drone and the position of the load.

[0074] Let the distance between the i-th UAV and the payload be l. i The flexible cable is connected to the drone, and the connection point between the cable and the drone is located at the center of mass of the fuselage, and it is always kept under tension. Then the position x of the i-th aircraft is... i With respect to the position x of the load L The relationship between them is represented as follows:

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

[0076] A2, the first set of dynamic equations for the tandem unmanned helicopter collaborative hoisting system is determined based on the relationship between the position of the UAV and the position of the load.

[0077] The first set of dynamic equations for the tandem unmanned helicopter collaborative lifting system includes two parts: translation and rotation, specifically:

[0078]

[0079] Where, n i Let v be the direction vector of the i-th rope. L v is the linear velocity of the load. iLet ω be the linear velocity of the i-th drone. i Let Ω be the angular velocity of the i-th rope. i R is the angular velocity of the drone. i Let S be the rotation matrix of the i-th UAV, and the superscript · denotes 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 rotate one of the three-dimensional vectors belonging to the i-th UAV. vector mapping to P n and Π n Let P represent two projection operators that are perpendicular to each other. n =nn T , Π n =I-nn T =-S(n) 2 .

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

[0081] A31, establish the Lagrange equation for a tandem unmanned helicopter collaborative lifting system.

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

[0083]

[0084] Where, m L and m i Let represent the load and the mass of the i-th drone, 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] The Lagrangian function is determined based on the system's total kinetic energy and total gravitational potential energy. A32, Calculate the partial derivatives of the Lagrangian function with respect to each state of motion:

[0089]

[0090] A33, Calculate the variation of action integral and virtual work.

[0091]

[0092] Where, η i For an infinitesimal quantity, according to Lagrange-Lombell's 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 equations are obtained through integration by parts.

[0096]

[0097] Differentiating equations (8) and (10), and then from and Substituting the derivative into equation (13), we obtain the second set of dynamic equations for 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 collaborative hoisting system is constructed.

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

[0102] The control inputs for the tandem unmanned helicopter collaborative lifting system are determined to be the thrust magnitude and angular velocity of each UAV. Based on the system's dynamic model, the effect of the UAV thrust on the system dynamics is limited to the direction parallel to the cable. To address this issue, simplify the controller design process, and reduce the smoothness order requirement for the desired trajectory, this invention considers a virtual point on the cable. The controller uses this virtual point as the controlled 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, ensuring the positive definiteness of the second Lyapunov function and the negative definiteness of its derivative, thus obtaining the control law for the UAV's angular velocity. The specific analysis process is as follows:

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

[0104]

[0105] in, Let δ be the position of the i-th virtual point.i It is a constant representing the distance of the selected virtual point from the load, δ i Satisfying 0 < δ i <l i .

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

[0107]

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

[0109]

[0110] in,

[0111] As can be seen from equation (23), after controlling the position of the virtual point to replace the load position, the thrust contribution of the i-th UAV in the resulting dynamic equation is: The introduction of a component perpendicular to the cable makes the thrust action no longer limited to the direction of the cable, which simplifies the subsequent controller design.

[0112] For each virtual point, its expected trajectory is given. (Requires at least third-order continuous derivatives), this invention designs a controller that can drive each virtual point to track its desired trajectory. The position error and velocity error of the trajectory tracking are defined as follows:

[0113]

[0114] In formulas (24) and (25) For a constant term, it is specified in the following way: The introduction of the cable integral term (0) ensures convergence when all outputs of the system reach 0, suppressing unwanted oscillations in the system. i ,k d It is an adjustable gain.

[0115] Based on the definitions of the two error terms, the definition of the i-th term in the first Lyapunov function is given as follows:

[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] Considering all k UAVs, the system variables are represented as a 3k×1 vector, which is: Let be the expected value of the i-th input thrust.

[0121] Differentiating with respect to V1, we get:

[0122]

[0123] in k1 is a positive definite term, and k2 is an adjustable gain. The coefficients of thrust in the velocity error derivative of the above equation can be written in matrix form:

[0124]

[0125] By making reasonable selection of δ i l i m i The value of can avoid the problem of the invertibility of M. This invention only considers the case where M is invertible. To eliminate the Lyapunov function... One term, defining the intermediate quantity ξ i for:

[0126]

[0127] The desired thrust is set as follows:

[0128] u d =M -1 ξ (30)

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

[0130]

[0131] Where u is the thrust vector of the UAV.

[0132] To align the thrust direction with the desired thrust direction, a control law for the UAV's angular velocity needs to be further designed. 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 all UAV z-axis direction errors The vector formed Establish a second Lyapunov function:

[0135]

[0136] Among them, h r It is an adjustable control gain, set as a constant greater than 0, thus V2 is also positive definite. Take the derivative of V2, and add or subtract a term. get

[0137]

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

[0139] Since the direction of the UAV's thrust is restricted to being perpendicular to the fuselage and cannot be arbitrarily specified, this embodiment provides a control law for the thrust magnitude, the specific expression of which is:

[0140]

[0141] To control the UAV's z-axis to tend towards its desired direction, the angular velocity control law for the i-th aircraft is given as follows:

[0142]

[0143] in, M ji Let be a block matrix in 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] It is a semi-negative definite function. When E x E v and E r When both are 0, In 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, the system trajectory tracking error always converges, thus achieving the purpose of trajectory tracking control.

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

[0147]

[0148] in, For virtual point position error, This represents the initial position error of the virtual point.

[0149] From the above formula, it can be deduced that as time approaches infinity, To achieve the goal of making the virtual point move along its desired trajectory, it is necessary to make Therefore, constant The setup method is as follows:

[0150]

[0151] n i (t f The value of is related to the generation of the virtual point's trajectory. When each virtual point reaches the desired position, the position of the load (k≥3) can be uniquely determined through the positional constraints of the triangle, and correspondingly, the direction of each cable can also be uniquely determined. When the parameter takes certain values, two spatially symmetrical solutions may appear, but based on the actual system characteristics, the case 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] Where, x d For the desired load trajectory, δ i It is a constant representing the distance t from the selected virtual point to the load. f This is the end time.

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

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

[0156] S2, based on the expected motion trajectory of the load, determine the expected cable direction of each point during the load operation, and determine the expected motion trajectory of each virtual point according to the expected cable direction.

[0157] S3, input the desired motion trajectory of each virtual point into the controller, set the controller parameters, and determine 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 explanation. The expected trajectory of the load is as follows:

[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 The value of ) varies depending on the range of 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 respectively and In the system parameters, the masses of the three UAVs, m1, m2, and m3, are all 0.3 kg, and the payload mass m L The weight 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 / s². 2 In the initial 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 attitude matrices R1(0), R2(0), and R3(0) are [1,0,0; 0,0,1; 0,-1,0], respectively. Furthermore, the values ​​of the initial position vectors n1(0), n2(0), and n3(0) are respectively... and In the control parameter section, 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 follows: δ1=0.6, δ2=0.5, δ3=0.4. When appropriate parameters are selected, the controller designed in this invention can control all virtual points and the load to converge to the desired trajectory within 5 seconds, while making the cable reach the desired configuration.

[0162] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A control method for a tandem unmanned helicopter collaborative hoisting system, characterized in that, This method introduces virtual points into the dynamic model of a tandem unmanned helicopter collaborative lifting system and designs a controller based on backstepping to achieve trajectory tracking control of the virtual points. This reduces the complexity of controller design for multi-robot collaborative lifting systems and enables configuration control of the cables. The tandem unmanned helicopter collaborative lifting system includes multiple tandem unmanned helicopters, each of which is considered a six-degree-of-freedom rigid body driven by thrust and torque and connected to the load via flexible cables. The motion state variables 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 unmanned helicopter, and the direction and angular velocity of each connecting cable. The system inputs are the thrust and angular velocity of the unmanned helicopters, with the direction of the thrust restricted to be perpendicular to the fuselage.

2. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 1, characterized in that, The dynamic model construction process of the tandem unmanned helicopter cooperative hoisting system is as follows: Assuming the connection point between the cable and the drone is located at the center of mass of the fuselage and is always kept taut, determine the relationship between the position of the drone and the position of the load; The first set of dynamic equations for the tandem unmanned helicopter collaborative hoisting system is determined 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 Lagrange method; A dynamic model of a tandem unmanned helicopter collaborative hoisting system is constructed based on the first and second sets of dynamic equations.

3. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 2, characterized in that, Let the distance between the i-th UAV and the payload be l. i If the flexible ropes are connected, then the position x of the i-th aircraft... i With respect to the load position x L The relationship between them is represented as follows: x i =x L -l i n i The first set of dynamic equations for the tandem unmanned helicopter collaborative lifting system includes two parts: translation and rotation, specifically: Where, n i Let v be the direction vector of the i-th rope. L v is the linear velocity of the load. i Let ω be the linear velocity of the i-th drone. i Let Ω be the angular velocity of the i-th rope. i R is the angular velocity of the drone. i Let S be the rotation matrix of the i-th UAV, with the superscript · indicating the derivative, and the symbol S(·) being an operator. For two three-dimensional vectors m and n, S(m)n = m × n.

4. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 3, characterized in that, The second set of dynamic equations is as follows: in, P ni =n i n i T I is the identity matrix, k is the number of drones, and m L and m i Let u represent the load and the mass of the i-th drone, respectively. i Generate a thrust vector for the rotor, denoted as u. i =-U i R i e3, U i For the magnitude of the thrust, e3 = [0 0 1] T g is the acceleration due to gravity.

5. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 4, characterized in that, The design of the controller includes the following steps: The control inputs for the tandem unmanned helicopter collaborative lifting system are determined to be the thrust magnitude and angular velocity of each UAV. Based on the system's dynamic model, the effect of the UAV thrust on the system dynamics is restricted to the direction parallel to the cable. Considering a virtual point on the cable, the controller takes the virtual point as the controlled object, solves the dynamic equation of the virtual point, and defines the first Lyapunov function based on the position and velocity error between the virtual point and the desired trajectory to control the virtual point to stably track its desired trajectory, thereby achieving position control of the virtual point. 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 UAV's angular velocity.

6. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 5, characterized in that, The dynamic equation of the virtual point is: in, Let δ be the linear velocity of the virtual point. i It is a constant representing the distance of the selected virtual point from the load.

7. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 6, characterized in that, The position control of the virtual point is specifically as follows: For each virtual point, its expected trajectory is given. The position error and velocity error of trajectory tracking are defined as follows: in, Let i be the position of the i-th virtual point. For a constant term, the way it is specified is as follows k i ,k d Adjustable gain; Based on the position error and velocity error, the definition of the i-th term in the first Lyapunov function is given as follows: The first Lyapunov function is defined as: Where k1 is the position error gain and β is the joint gain; Considering all k UAVs, the position error, velocity error, and desired thrust of all UAVs are combined into a 3k×1 vector, represented as: Let i be the expected value of the i-th input thrust; Differentiating the first Lyapunov function V1, we get: in, As a positive definite term, k2 is an adjustable gain. The coefficients of thrust in the velocity error derivative of the above equation can be written in matrix form: Define intermediate quantity ξ i for: And set the desired thrust as: u d =M -1 ξ, eliminating the Lyapunov function One step simplifies the derivative of the first Lyapunov function to: Where u is the thrust vector of the UAV.

8. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 7, characterized in that, The method for determining the control law of the UAV's angular velocity is as follows: Let the actual thrust direction of the i-th UAV be... The desired thrust direction is The error in the thrust direction, i.e., the error in the z-axis direction, is defined as: Introducing thrust direction errors for all UAVs The vector formed Establish a second Lyapunov function: Among them, h r It is an adjustable control gain, set as a constant greater than 0; taking the derivative of the second Lyapunov function V2, we get: in, k r Adjustable control gain; The control law for the thrust magnitude of the i-th UAV is: To control the UAV's z-axis to tend towards its desired direction, the angular velocity control law for the i-th aircraft is: Among them, Ω i Let be the angular velocity of the i-th drone. M ji Let be a block matrix in matrix M.

9. A control method for a tandem unmanned helicopter collaborative hoisting system according to claim 5, characterized in that, The desired trajectory of the virtual point is determined based on the desired cable direction: Where, x d For the desired load trajectory, δ i It is a constant representing the distance t from the selected virtual point to the load. f This is the end time.

10. The control method for a tandem unmanned helicopter collaborative hoisting system according to claim 1, characterized in that, The method includes the following steps: Determine the desired trajectory of the load; The expected motion trajectory based on the load determines the expected cable direction during the load operation, and the expected motion trajectory of each virtual point is determined according to the expected cable direction. The desired motion trajectory of each virtual point is input into the controller, and the controller parameters are set. Based on the controller, the drone thrust and drone angular velocity are determined 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 hoisting task is completed.

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