Four-rotor hanging transportation control method based on double time-varying interference estimators

Abstract

The invention discloses a four-rotor hanging transportation control method based on double time-varying interference estimators. The method comprises the following steps: S1, establishing a kinetic model of a four-rotor unmanned aerial vehicle and a hanging load; s2, simplifying the model by using a feedback linearization technology, and decoupling a nonlinear coupling system into an anti-swing subsystem and a trajectory tracking subsystem; s3, constructing a time-varying uncertainty and interference estimator in the anti-swing controller according to the swing model of the lifted cargo, and dynamically aggregating time-varying interference to eliminate swing of the heavy object; s4, constructing a time-varying uncertainty and interference estimator in a trajectory tracking controller according to the four-rotor kinematics model, and realizing accurate trajectory tracking of the four-rotor unmanned aerial vehicle; s5, proving the stability of an estimation error system by using a linear time-varying system theory, and optimizing the interference estimation performance by adjusting auxiliary parameters; and S6, the stability of the anti-swing subsystem and the trajectory tracking subsystem is proved, and the interference estimation performance is optimized by adjusting auxiliary parameters.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft automatic control, and in particular relates to a quadrotor suspension transportation control method based on a dual time-varying interference estimator. Background Art

[0002] In recent years, quadcopters have been widely used in many fields due to their low cost, high maneuverability and excellent hovering ability, and have successfully completed aerial operations such as aerial photography, formation performances, and remote sensing detection. As an emerging mode of transportation, quadcopters are also used in the field of air transportation. For example, when natural disasters such as earthquakes and mudslides occur, quadcopters are entrusted with the task of delivering emergency rescue supplies such as water, food, and medicine to trapped people because they can take off and land vertically and hover regardless of the terrain, so that trapped people can save themselves, especially in areas without suitable landing areas, such as mountains, jungles, islands, etc.

[0003] The payload of a quadcopter drone faces complex interferences caused by gusts, air resistance, and waypoint changes. These time-varying interferences often exacerbate the load swing. If not eliminated, they may seriously affect the stability of the drone or even cause it to lose control. Similarly, these time-varying interferences and the resulting load swings will also pose a great challenge to the drone's precise trajectory tracking, especially when the external environment has strict constraints on the drone's flight trajectory. If the trajectory tracking is not controlled against time-varying interference, it may lead to collisions and crashes, causing great danger and loss. Therefore, it is of great significance to eliminate swings and track interference during transportation. Summary of the invention

[0004] The purpose of the present invention is to solve the above problems and provide a control framework based on dual time-varying uncertainty and disturbance estimator (TVUDE) to solve the time-varying multi-interference problem of the suspended load of a quadrotor UAV in different flight phases, so as to realize the efficient transportation of the load; coordinate the anti-swing control and trajectory tracking control, and realize the quadrotor suspension transportation control method of the two at the same time.

[0005] In order to solve the above technical problems, the technical solution of the present invention is: a quadrotor suspension transportation control method based on a dual time-varying interference estimator, comprising the following steps:

[0006] S1. Establish the dynamic model of the quadrotor UAV and the suspended load, including the transformation relationship among the world coordinate system, the body coordinate system, the suspension coordinate system and the load coordinate system;

[0007] S2. Use feedback linearization technology to simplify the model and decouple the nonlinear coupled system into two subsystems: anti-swing and trajectory tracking.

[0008] S3. Based on the sway model of the hoisted cargo, a time-varying uncertainty and disturbance estimator (TVUDE) is constructed in the sway elimination controller to dynamically aggregate the time-varying disturbance to eliminate the sway of the heavy object.

[0009] S4. Based on the kinematic model of the quadrotor, a time-varying uncertainty and disturbance estimator (TVUDE) is constructed in the trajectory tracking controller to achieve accurate trajectory tracking of the quadrotor UAV.

[0010] S5. Use the linear time-varying system theory to prove the stability of the estimation error system and optimize the interference estimation performance by adjusting the auxiliary parameters;

[0011] S6. Prove the stability of the anti-sway subsystem and trajectory tracking subsystem, and optimize the interference estimation performance by adjusting auxiliary parameters.

[0012] Furthermore, the rotation matrix of the quadrotor in S1 is given by the following formula:

[0013]

[0014] The symbols C(·) and S(·) represent the sin(·) and cos(·) trigonometric functions respectively; θ, φ, ψ represent the Euler angles of the quadrotor in the inertial system; B refers to the aircraft system, W refers to the world system, P refers to the load system, and S refers to the suspension system; is the rotation matrix from the machine system to the world system; other rotation matrices are defined in the same way.

[0015] Furthermore, the dynamic model of the hanging load in S1 includes a model of cargo swaying, and the model of cargo swaying is expressed as:

[0016]

[0017] where λ x ,λ y It is expressed as two swing angles of the cargo; L is the length of the rope used to lift the cargo; m p It is the quality of the goods; Indicates the acceleration vector of the quadrotor drone in three axes. The symbol "T" in the upper right corner represents the transpose of the vector or matrix; F pd =[F pdx ,F pdy ,F pdz ] T is the air resistance vector acting on the cargo; g is the acceleration due to gravity.

[0018] Furthermore, based on the cargo sway model, a comprehensive model of quadrotor load is established, and the quadrotor linear motion dynamics formula in the world coordinate system is given by the following formula:

[0019]

[0020] Where m q is the mass of the quadrotor; F qt =[0,0,F qt ] T is the quadrotor thrust command vector in the body coordinate system; is the rope tension vector on the quadrotor in the drone world coordinate system; F qd is the interference signal vector of the quadrotor position loop. The interference signal includes model uncertainty, wind interference and load swing interference. The derivatives of the disturbance are all bounded. g = [0, 0, g] T is the acceleration due to gravity.

[0021] Furthermore, in step S2, the model is simplified by using feedback linearization technology, and the simplified swing angle model is:

[0022]

[0023] where λ = [λ x ,λ y ] T is the swing angle of the quadrotor, u λ =[u λx ,u λy ] T is a virtual control input, and has:

[0024]

[0025] f λ =[f λx ,f λy ] T is the lumped interference, and:

[0026]

[0027] In order to prevent the quadrotor from making aggressive vertical maneuvers that could cause a collision, the system input It comes down to the interference term f λ middle.

[0028] Furthermore, after using the feedback linearization technology, the quadrotor load comprehensive model (3) is simplified to:

[0029]

[0030] where u p is a virtual input:

[0031]

[0032] f p is the aggregate interference:

[0033]

[0034] At this point, the model has been simplified to facilitate subsequent control design.

[0035] Furthermore, the swing angle in S3 converges quickly and actively resists interference during swinging. The interference is the uncertainty of the model and external interference. An outer loop and an inner loop are set. The outer loop is a control loop and the inner loop is a posture loop. The first component of the outer loop is designed: the swing elimination controller. The simplified swing angle model (4) is rewritten as a state space expression:

[0036]

[0037] Where x1 and x2 represent the swing angle and angular velocity of the quadrotor, respectively, assuming that the required state is generated by the following reference model:

[0038]

[0039] The robust control algorithm based on uncertainty and disturbance estimator designed for the model of formula (10) is expressed as:

[0040]

[0041] u λ0 is a nominal controller, designed to:

[0042]

[0043] where u λd is the feedforward term, which can be considered as zero in this robust stabilization problem, kp = diag{kpx, kpy} and k d =diag{k dx ,k dy} is the feedback gain, is the quadrotor angle tracking error, is the angular velocity tracking error, and in this problem, the pendulum angle x 1d and x 2d The expected value of can also be regarded as zero; Substituting formula (13) into formula (12), we get:

[0044]

[0045] is the interference estimation signal generated by TVUDE, which is designed in the time domain as:

[0046]

[0047] Where T λ(t) = diag{T λx (t),T λy (t)} is a time-varying parameter matrix designed artificially. Combining formula (4) and formula (12), we get

[0048] Furthermore, the trajectory tracking controller of the TVUDE in S4 is the second component of the outer loop. The simplified trajectory tracking model is expressed by formula (7), and its state space expression is:

[0049]

[0050] in and Represent the position and speed of the quadrotor respectively.

[0051] Furthermore, in S5, the stability of the estimation error system is proved by using the linear time-varying system theory, and the interference estimation performance is optimized by adjusting the auxiliary parameters, taking into account the swing interference estimator. and trajectory tracking disturbance estimator It is consistent in form. When proving, we only need to prove that one of the estimated error systems is stable. Therefore, all subscripts in the system are removed in the subsequent proof. The estimated error is defined as:

[0052]

[0053] Integrate both sides of formula (25) with respect to time t, and then substitute it into formula (15) to obtain the estimated error subsystem:

[0054]

[0055] According to linear system theory, we know that the state transfer matrix of the linear time-varying system (26) is:

[0056]

[0057] The solution of system (26) is:

[0058]

[0059] Time-varying parameter T = diag{T x (t),T y (t),T z (t)} is an artificially set and bounded positive number. For the x-axis, set 0<T xmin ≤T x (t)≤T xmax , and there is From formula (28), we know that the solution of this system consists of two components: zero input response and zero state response. When t→∞, the zero input response Then scaling the zero-state response yields:

[0060]

[0061] in When t→∞, The zero-state response can be simplified to:

[0062]

[0063] In the same way, we can prove and It is also convergent; when t→∞, we have:

[0064]

[0065] in T m =diag{T xmax ,T ymax ,T zmax};make The advantage of this is that the time-varying parameter matrix T can be changed by adjusting the size of the scalar ζ. m The size of each component, so far, it can be proved that when the external disturbance f is bounded, the output is also bounded, which proves that system (26) is stable.

[0066] Furthermore, when the stability of the anti-sway subsystem and the trajectory tracking subsystem is proved in S6, and the interference estimation performance is optimized by adjusting the auxiliary parameters, it is also observed that the anti-sway subsystem (10) and the trajectory tracking subsystem (19) have the same state space expression, so only one of them is proved; the swing angle error and angular velocity error are defined as:

[0067]

[0068] Combining formula (10), formula (11), formula (12), formula (13) and formula (25), we get the swing error system:

[0069]

[0070] If the swing angle error and angular velocity error Bounded convergence, system (33) must satisfy:

[0071] The matrix A is the Hurwitz matrix, that is, the gain k p >0,kd >0; Estimated error Bounded convergence; the solution of the swing error system is:

[0072]

[0073] When t→∞, the zero input response e At →0, substituting formula (31) into the zero state response, we get:

[0074]

[0075]

[0076] Obviously, when t→∞, (||I||2-||e At ||2)→||I||2, and when ζ→0, ε(ζ)→0, so it is proved that the swing error system satisfies: So far, it can be proved that the swing elimination system and trajectory tracking system are exponentially stable, and the performance of disturbance estimation can be improved by reducing the auxiliary parameter ζ.

[0077] The beneficial effects of the present invention are:

[0078] 1. The present invention provides a quadrotor suspension transport control method based on a dual time-varying interference estimator. By introducing a dual time-varying uncertainty and interference estimator (TVUDE), the present invention significantly improves the anti-interference ability of the quadrotor UAV in a time-varying multi-interference environment. TVUDE can dynamically estimate and compensate for time-varying interference caused by wind disturbance, load swing, etc., thereby reducing the impact of these interferences on the flight stability of the UAV. The present invention achieves high-precision tracking of a predetermined trajectory by integrating TVUDE in a trajectory tracking controller. TVUDE helps to correct trajectory deviations caused by external interference in real time, ensuring that the UAV can fly stably and accurately along the predetermined trajectory. There is a contradiction between transient response and steady-state performance in traditional interference estimators. The present invention optimizes the interference estimation bandwidth by introducing time-varying parameters, effectively resolving this contradiction. The introduction of time-varying parameters enables TVUDE to achieve a better trade-off between transient response and steady-state performance, thereby improving the overall control performance.

[0079] 2. The present invention has the following advantages: the present invention can adapt to the diversity of interference and effectively improve the anti-interference performance of the system by introducing time-varying parameters; the dual-loop TVUDE control framework of the present invention has significant advantages in simultaneously improving the sway elimination and trajectory tracking performance compared to the single estimator framework; the present invention sets corresponding control schemes and controller parameters for the scenarios of sway elimination and trajectory tracking of quad-rotor load lifting.

[0080] 3. The present invention adopts payload suspension technology, that is, the payload is connected to the center of gravity of the quadrotor through a cable. Compared with the rigid connection equipped with a mechanical arm, the payload suspension technology effectively retains the agility of the quadrotor itself because there is no direct introduction of inertia. In order to complete the rescue mission safely and efficiently, the present invention considers the anti-interference problem of the quadrotor load lifting system. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a coordinate system model diagram of a quadrotor dispatching system targeted by a quadrotor suspension transportation control method based on a dual time-varying interference estimator of the present invention;

[0082] Figure 2 It is a control framework diagram of the present invention;

[0083] Figure 3 A top view of the simulated flight result of the present invention;

[0084] Figure 4 This is a simulation result diagram of the swing elimination control of the present invention;

[0085] Figure 5 This is a diagram of the trajectory tracking control simulation results of the present invention. DETAILED DESCRIPTION

[0086] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments:

[0087] like Figures 1 to 5 As shown, the present invention provides a quadrotor suspension transportation control method based on a dual time-varying interference estimator, comprising the following steps:

[0088] S1. Establish the dynamic model of the quadrotor UAV and the suspended load, including the transformation relationship among the world coordinate system, the body coordinate system, the suspension coordinate system and the load coordinate system.

[0089] In order to achieve robust control of the quadrotor position loop, it is first necessary to establish a position loop model of the quadrotor drone and an interference model for load swing. Figure 1 As shown, the rotation matrix of the quadrotor is given by:

[0090]

[0091] The symbols C(·) and S(·) represent the sin(·) and cos(·) trigonometric functions respectively; θ, φ, ψ represent the Euler angles of the quadrotor in the inertial system; B refers to the aircraft system, W refers to the world system, P refers to the load system, and S refers to the suspension system; is the rotation matrix from the machine system to the world system; other rotation matrices are defined in the same way.

[0092] In order to achieve cargo sway control, it is necessary to first model the cargo sway. The dynamic model of the hanging load in S1 includes the cargo sway model, which is expressed as:

[0093]

[0094] where λ x ,λ y It is expressed as two swing angles of the cargo; L is the length of the rope used to lift the cargo; m p It is the quality of the goods; Indicates the acceleration vector of the quadrotor drone in three axes. The symbol "T" in the upper right corner represents the transpose of the vector or matrix; F pd =[F pdx ,F pdy ,F pdz ] T is the air resistance vector acting on the cargo; g is the acceleration due to gravity.

[0095] Based on the cargo sway model, a comprehensive quadrotor load model is established, and the quadrotor linear motion dynamics formula in the world coordinate system is given by the following formula:

[0096]

[0097] Where m q is the mass of the quadrotor; F qt =[0,0,F qt ] T is the quadrotor thrust command vector in the body coordinate system; is the rope tension vector on the quadrotor in the drone world coordinate system; F qd is the interference signal vector of the quadrotor position loop. The interference signal includes model uncertainty, wind interference and load swing interference. The derivatives of the disturbance are all bounded. g = [0, 0, g] T is the acceleration due to gravity.

[0098] S2. Use feedback linearization technology to simplify the model and decouple the nonlinear coupled system into two subsystems: anti-swing and trajectory tracking.

[0099] After obtaining the above models, the quadrotor swing angle model and the quadrotor kinematic model are nonlinear and strongly coupled, making it difficult to design their control. Therefore, feedback linearization technology is first applied to simplify the swing angle model and the kinematic model.

[0100] First, the swing angle model (2) is simplified. In S2, the feedback linearization technology is used to simplify the model. The simplified swing angle model is:

[0101]

[0102] where λ = [λ x ,λ y ] T is the swing angle of the quadrotor, u λ =[u λx ,u λy ] T is a virtual control input, and has:

[0103]

[0104] f λ =[f λx ,f λy ] T is the lumped interference, and:

[0105]

[0106] In order to prevent the quadrotor from making aggressive vertical maneuvers that could cause a collision, the system input It comes down to the interference term f λ In this embodiment, model (2) refers to the model corresponding to formula (2).

[0107] The quadrotor load comprehensive model (3) refers to the model corresponding to formula (3). After using the feedback linearization technology, the quadrotor load comprehensive model (3) is simplified as follows:

[0108]

[0109] where u p is a virtual input:

[0110]

[0111] f p is the aggregate interference:

[0112]

[0113] At this point, the model is simplified to facilitate the subsequent control design. Model (3) refers to the model corresponding to formula (3).

[0114] S3. Based on the sway model of hoisted cargo, a time-varying uncertainty and disturbance estimator (TVUDE) is constructed in the sway elimination controller to dynamically aggregate time-varying disturbances to eliminate the sway of heavy objects.

[0115] The overall control framework of the present invention is as follows Figure 2As shown, in order to ensure the rapid convergence of the swing angle during the swing in S3 and actively resist interference, the interference is the uncertainty of the model and the external interference. An outer loop and an inner loop are set. The outer loop is the control loop and the inner loop is the attitude loop. The first component of the outer loop is designed: the anti-swing controller. The simplified swing angle model (4) is rewritten as a state space expression:

[0116]

[0117] Where x1 and x2 represent the swing angle and angular velocity of the quadrotor, respectively. The swing angle model (4) refers to the model corresponding to formula (4). It is assumed that the required state is generated by the following reference model:

[0118]

[0119] The robust control algorithm based on uncertainty and disturbance estimator designed for the model of formula (10) is expressed as:

[0120]

[0121] u λ0 is a nominal controller, designed to:

[0122]

[0123] where u λd is the feedforward term, which can be considered as zero in this robust stabilization problem, kp = diag{kpx, kpy} and k d =diag{k dx ,k dy} is the feedback gain, is the quadrotor angle tracking error, is the angular velocity tracking error, and in this problem, the pendulum angle x 1d and x 2d The expected value of can also be regarded as zero; Substituting formula (13) into formula (12), we get:

[0124]

[0125] is the interference estimation signal generated by TVUDE, which is designed in the time domain as:

[0126]

[0127] Where T λ (t) = diag{T λx (t),T λy (t)} is a time-varying parameter matrix designed artificially. Combining formula (4) and formula (12), we get In formula (15), use Replace and multiply both sides of formula (15) by the matrix Get the derivative of the interference estimation signal:

[0128]

[0129] By integrating both sides of formula (16) simultaneously and applying partial integration, the interference estimation signal of the anti-sway controller is obtained:

[0130]

[0131]

[0132] After completing the anti-sway control design, we can inversely solve formula (5) to get and By setting the anti-sway acceleration on the Z axis to zero, we can get the anti-sway acceleration commands on the three axes:

[0133]

[0134] S4. Based on the kinematic model of the quadrotor, a time-varying uncertainty and disturbance estimator (TVUDE) is constructed in the trajectory tracking controller to achieve accurate trajectory tracking of the quadrotor UAV.

[0135] In order to balance the contradiction between swing elimination and trajectory tracking control, the trajectory tracking controller of TVUDE in S4 is used as the second component of the outer loop. The simplified trajectory tracking model is expressed by formula (7), and its state space expression is:

[0136]

[0137] in and Respectively represent the position and speed of the quadrotor. Next, we will design the quadrotor trajectory tracking controller:

[0138]

[0139] Where u pd Feedforward term, k pp =diag{k ppx ,k ppy} and k pd =diag{k pdx ,k pdy} is the feedback gain, e p =x 3d -x3 is defined as the trajectory tracking error, x 3d is the desired position signal of the quadrotor. The trajectory tracking TVUDE is designed as:

[0140]

[0141] Similarly, we multiply both sides of formula (21) by the matrix T p (t) and convert and x4=u p +f p Substitutions are:

[0142]

[0143] By integrating both sides of formula (22) and applying partial integration, the trajectory tracking controller disturbance estimation signal is obtained:

[0144]

[0145] So far, all designs of the swing elimination and trajectory tracking controllers have been completed. The outer loop control can be expressed as the sum of these two controllers:

[0146]

[0147] S5. Use the linear time-varying system theory to prove the stability of the estimation error system, and optimize the interference estimation performance by adjusting auxiliary parameters.

[0148] After completing the control design, the stability of the estimation error system is proved by using the linear time-varying system theory, and the interference estimation performance is optimized by adjusting the auxiliary parameters, taking into account the swing interference estimator. and trajectory tracking disturbance estimator It is consistent in form. When proving, we only need to prove that one of the estimated error systems is stable. Therefore, all subscripts in the system are removed in the subsequent proof. The estimated error is defined as:

[0149]

[0150] Integrate both sides of formula (25) with respect to time t, and then substitute it into formula (15) to obtain the estimated error subsystem:

[0151]

[0152] According to linear system theory, we know that the state transfer matrix of the linear time-varying system (26) is:

[0153]

[0154] The solution of system (26) is:

[0155]

[0156] Time-varying parameter T = diag{T x (t),T y (t),T z (t)} is an artificially set and bounded positive number. For the x-axis, set 0<T xmin ≤T x (t)≤T xmax , and there is From formula (28), we know that the solution of this system consists of two components: zero input response and zero state response. When t→∞, the zero input response Then scaling the zero-state response yields:

[0157]

[0158] in When t→∞, The zero-state response can be simplified to:

[0159]

[0160] In the same way, we can prove and It is also convergent; when t→∞, we have:

[0161]

[0162] in T m =diag{T xmax ,T ymax ,T zmax};make The advantage of this is that the time-varying parameter matrix T can be changed by adjusting the size of the scalar ζ. m The size of each component, so far, it can be proved that when the external disturbance f is bounded, the output is also bounded, which proves that system (26) is stable.

[0163] S6. Prove the stability of the anti-sway subsystem and trajectory tracking subsystem, and optimize the interference estimation performance by adjusting auxiliary parameters.

[0164] In S6, when proving the stability of the swing elimination subsystem and the trajectory tracking subsystem and optimizing the interference estimation performance by adjusting the auxiliary parameters, it is also observed that the swing elimination subsystem (10) and the trajectory tracking subsystem (19) have the same state space expression, so only one of them is proved; the swing angle error and angular velocity error are defined as:

[0165]

[0166] Combining formula (10), formula (11), formula (12), formula (13) and formula (25), we get the swing error system:

[0167]

[0168] If the swing angle error and angular velocity error Bounded convergence, system (33) must satisfy:

[0169] (1) Matrix A is the Hurwitz matrix, i.e., the gain k p >0,k d >0;

[0170] (2) Estimation error Bounded convergence; the solution of the swing error system is:

[0171]

[0172] When t→∞, the zero input response e At →0, substituting formula (31) into the zero state response, we get:

[0173]

[0174] Obviously, when t→∞, (||I||2-||e At ||2)→||I||2, and when ζ→0, ε(ζ)→0, so it is proved that the swing error system satisfies: So far, it can be proved that the swing elimination system and trajectory tracking system are exponentially stable, and the performance of disturbance estimation can be improved by reducing the auxiliary parameter ζ.

[0175] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A quadrotor suspension transportation control method based on dual time-varying disturbance estimator, characterized in that: The following steps are involved: S1. Establish the dynamic model of the quadrotor UAV and the suspended load, including the transformation relationship among the world coordinate system, the body coordinate system, the suspension coordinate system and the load coordinate system; S2. Use feedback linearization technology to simplify the model and decouple the nonlinear coupled system into two subsystems: anti-swing and trajectory tracking. S3. Based on the sway model of the hoisted cargo, a time-varying uncertainty and disturbance estimator (TVUDE) is constructed in the sway elimination controller to dynamically aggregate the time-varying disturbance to eliminate the sway of the heavy object. S4. Based on the kinematic model of the quadrotor, a time-varying uncertainty and disturbance estimator (TVUDE) is constructed in the trajectory tracking controller to achieve accurate trajectory tracking of the quadrotor UAV. S5. Use the linear time-varying system theory to prove the stability of the estimation error system and optimize the interference estimation performance by adjusting the auxiliary parameters; S6. Prove the stability of the anti-sway subsystem and trajectory tracking subsystem, and optimize the interference estimation performance by adjusting auxiliary parameters.

2. A quadrotor suspension transportation control method based on a dual time-varying disturbance estimator according to claim 1, characterized in that: The rotation matrix of the quadrotor in S1 is given by the following formula: The symbols C(·) and S(·) represent the sin(·) and cos(·) trigonometric functions respectively; θ, φ, ψ represent the Euler angles of the quadrotor in the inertial system; B refers to the aircraft system, W refers to the world system, P refers to the load system, and S refers to the suspension system; is the rotation matrix from the machine system to the world system; The other rotation matrices are defined in the same way.

3. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1 is characterized in that: The dynamic model of the hanging load in S1 includes a cargo swaying model, which is expressed as: where λ x ,λ y It is expressed as two swing angles of the cargo; L is the length of the rope used to lift the cargo; m p It is the quality of the goods; Indicates the acceleration vector of the quadrotor drone in three axes. The symbol "T" in the upper right corner represents the transpose of the vector or matrix; F pd =[F pdx ,F pdy ,F pdz ] T is the air resistance vector acting on the cargo; g is the acceleration due to gravity.

4. A quadrotor suspension transportation control method based on a dual time-varying disturbance estimator according to claim 3, characterized in that: Based on the cargo sloshing model, a comprehensive model of quadrotor load is established, and the quadrotor linear motion dynamics formula in the world coordinate system is given by the following formula: Where m q is the mass of the quadrotor; F qt =[0,0,F qt ] T is the quadrotor thrust command vector in the body coordinate system; is the rope tension vector on the quadrotor in the drone world coordinate system; F qd is the interference signal vector of the quadrotor position loop. The interference signal includes model uncertainty, wind interference and load swing interference. The derivatives of the disturbance are all bounded. g = [0, 0, g] T is the acceleration due to gravity.

5. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1 is characterized in that: In step S2, the model is simplified by using feedback linearization technology, and the simplified swing angle model is: where λ = [λ x ,λ y ] T is the swing angle of the quadrotor, u λ =[u λx ,u λy ] T is a virtual control input, and has: f λ =[f λx ,f λy ] T is the lumped interference, and: In order to prevent the quadrotor from making aggressive vertical maneuvers that could cause a collision, the system input It comes down to the interference term f λ middle.

6. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1 is characterized in that: The quadrotor load comprehensive model (3) is simplified to the following model after using feedback linearization technology: where u p is a virtual input: f p is the aggregate interference: At this point, the model has been simplified to facilitate subsequent control design.

7. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1 is characterized in that: The swing angle in S3 converges quickly and actively resists interference during swinging. The interference is the uncertainty of the model and external interference. An outer loop and an inner loop are set. The outer loop is a control loop and the inner loop is a posture loop. The first component of the outer loop is designed: the anti-swing controller. The simplified swing angle model (4) is rewritten as a state space expression: Where x1 and x2 represent the swing angle and angular velocity of the quadrotor, respectively, assuming that the required state is generated by the following reference model: The robust control algorithm based on uncertainty and disturbance estimator designed for the model of formula (10) is expressed as: u λ0 is a nominal controller, designed to: where u λd is the feedforward term, which can be considered as zero in this robust stabilization problem, kp = diag{kpx, kpy} and k d =diag{k dx ,k dy } is the feedback gain, is the quadrotor angle tracking error, is the angular velocity tracking error, and in this problem, the pendulum angle x 1d and x 2d The expected value of can also be regarded as zero; Substituting formula (13) into formula (12), we get: is the interference estimation signal generated by TVUDE, which is designed in the time domain as: Where T λ (t) = diag{T λx (t),T λy (t)} is a time-varying parameter matrix designed artificially. Combining formula (4) and formula (12), we get 8. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1 is characterized in that: The trajectory tracking controller of the TVUDE in S4 is the second component of the outer loop. The simplified trajectory tracking model is expressed by formula (7), and its state space expression is: in and Represent the position and speed of the quadrotor respectively.

9. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1, characterized in that: In S5, the stability of the estimation error system is proved by using the linear time-varying system theory, and the interference estimation performance is optimized by adjusting the auxiliary parameters. and trajectory tracking disturbance estimator It is consistent in form. When proving, we only need to prove that one of the estimated error systems is stable. Therefore, all subscripts in the system are removed in the subsequent proof. The estimated error is defined as: Integrate both sides of formula (25) with respect to time t, and then substitute it into formula (15) to obtain the estimated error subsystem: According to linear system theory, we know that the state transfer matrix of the linear time-varying system (26) is: The solution of system (26) is: Time-varying parameter T = diag{T x (t),T y (t),T z (t)} is an artificially set and bounded positive number. For the x-axis, set 0<T xmin ≤T x (t)≤T xmax , and there is From formula (28), we know that the solution of this system consists of two components: zero input response and zero state response. When t→∞, the zero input response Then scaling the zero-state response yields: in When t→∞, The zero-state response can be simplified to: In the same way, we can prove and It is also convergent; when t→∞, we have: in T m =diag{T xmax ,T ymax ,T zmax };make The advantage of this is that the time-varying parameter matrix T can be changed by adjusting the size of the scalar ζ. m The size of each component, so far, it can be proved that when the external disturbance f is bounded, the output is also bounded, which proves that system (26) is stable.

10. The quadrotor suspension transportation control method based on dual time-varying disturbance estimator according to claim 1, characterized in that: In S6, when proving the stability of the sway elimination subsystem and the trajectory tracking subsystem and optimizing the interference estimation performance by adjusting the auxiliary parameters, it is also observed that the sway elimination subsystem (10) and the trajectory tracking subsystem (19) have the same state space expression, so only one of them is proved; The swing angle error and angular velocity error are defined as: Combining formula (10), formula (11), formula (12), formula (13) and formula (25), we get the swing error system: If the swing angle error and angular velocity error Bounded convergence, system (33) must satisfy: The matrix A is the Hurwitz matrix, that is, the gain k p >0,k d >0; Estimated error Bounded convergence; the solution of the swing error system is: When t→∞, the zero input response e At →0, substituting formula (31) into the zero state response, we get: Obviously, when t→∞, (||I||2-||e At ||2)→||I||2, and when ζ→0, ε(ζ)→0, so it is proved that the swing error system satisfies: So far, it can be proved that the swing elimination system and trajectory tracking system are exponentially stable, and the performance of disturbance estimation can be improved by reducing the auxiliary parameter ζ.

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