Quadrotor double pendulum finite time swing elimination method based on full drive mapping and active disturbance rejection

Abstract

The application belongs to the field of automatic control technology of aircraft, and proposes a quadrotor double pendulum finite time swing elimination method based on full drive mapping and active anti-disturbance, which is applied to a quadrotor unmanned aerial vehicle double pendulum hoisting system. The method adopts a hierarchical control structure composed of an outer ring position and swing elimination control module and an inner ring bottom layer flight control module. The method comprises the following steps: establishing a quadrotor double pendulum horizontal plane block matrix dynamics model; full drive state mapping and dynamic reconstruction facing the controller; Y-axis full drive space isomorphic expansion; UDE-based finite time control law design; closed loop system stability and finite time convergence analysis based on Lyapunov theorem. The application can improve the waypoint tracking accuracy, swing angle suppression effect and robust flight capability of the quadrotor double pendulum hoisting system under the working condition that discrete waypoints are switched and external wind disturbance exists simultaneously.

Description

Technical Field

[0001] This invention relates to the field of aircraft automatic control technology, and in particular to a finite-time oscillation elimination method for quadrotor dual-pendulum based on all-drive mapping and active disturbance rejection. Background Technology

[0002] In recent years, quadcopter drones have been increasingly used in logistics transportation, disaster relief, material delivery, and lifting operations in complex environments due to their simple structure, high maneuverability, and flexible deployment. In these operations, drones typically suspend loads using flexible ropes or rigging. When the slinging system contains multiple connecting structures such as hooks, connecting cables, and end loads, the suspended load is prone to double-pendulum motion, causing the quadcopter drone lifting system to exhibit strong coupling, high nonlinearity, and underactuated dynamic characteristics. In actual discrete waypoint flight missions, quadcopter drones need to switch positions according to preset waypoints. Since waypoint commands usually have step-change characteristics, the instantaneous switching of waypoints can easily cause sudden changes in acceleration and control input, thereby triggering a double-pendulum swing of the hook and load, leading to increased residual load oscillations, which can severely affect the drone's attitude stability and flight safety. Simultaneously, outdoor lifting operations are also affected by factors such as gusts of wind, unmodeled aerodynamic drag, parameter perturbations, and double-pendulum nonlinear coupling, further reducing the fuselage position tracking accuracy and load anti-pendulum performance.

[0003] Existing quadcopter hoisting control methods are often designed primarily for single-pendulum load models, making them difficult to directly apply to dual-pendulum hoisting systems where the hook and load swing simultaneously. Other control methods for dual-pendulum systems rely on precise system parameters or complex nonlinear control designs, and their waypoint tracking, swing angle suppression, and robustness still have room for improvement when discrete waypoint switching, external wind disturbances, and unmodeled coupling coexist. Therefore, how to simultaneously reduce waypoint switching excitation, suppress dual swing angle oscillations, and improve robustness to external disturbances in quadcopter dual-pendulum hoisting systems is a pressing technical problem that needs to be solved in this field. Summary of the Invention

[0004] The purpose of this invention is to provide a finite-time sway elimination method for quadrotor dual-pendulum systems based on all-drive mapping and active disturbance rejection, which can solve the problems of accurate positioning and rapid sway elimination in underactuated dual-pendulum systems under discrete waypoint switching and external disturbances.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows:

[0006] A quadrotor dual-pendulum finite-time sway elimination method based on full-drive mapping and active disturbance rejection is applied to a quadrotor UAV dual-pendulum lifting system. The method adopts a hierarchical control structure consisting of an outer-loop position and sway elimination control module and an inner-loop bottom-level flight control module. The outer-loop position and sway elimination control module is used to complete the full-drive equivalent mapping, waypoint reference smooth reconstruction, finite-time waypoint tracking, dual-pendulum sway elimination, and horizontal channel active disturbance rejection compensation of the quadrotor dual-pendulum system. The inner-loop bottom-level flight control module is used to realize the attitude stabilization, angular velocity adjustment, and motor mixed control execution of the quadrotor UAV according to the desired attitude angle and thrust command output by the outer loop.

[0007] The method includes the following steps:

[0008] Establish a block matrix dynamic model of a quadrotor double pendulum in the horizontal plane;

[0009] Full-drive state mapping and dynamic reconfiguration for controllers;

[0010] Y-axis all-drive spatial isomorphic unfolding;

[0011] Finite-time control law design based on UDE;

[0012] Stability and finite-time convergence analysis of closed-loop systems based on Lyapunov's theorem.

[0013] In some embodiments, the outer ring position and anti-sway control module specifically includes the following units:

[0014] All-drive mapping unit: This unit takes the target discrete waypoints, the actual position and velocity of the quadrotor, the swing angle and angular velocity of the hook and load, the mass parameters of the quadrotor, hook and load, and the sling length parameters as inputs. It is used to mathematically reconstruct the original underactuated horizontal channel into a virtual all-drive subsystem that is convenient for controller design. First, under the condition that the altitude channel is stable and meets the approximate constant altitude condition, the unit establishes a block matrix dynamic model of the horizontal channel of the quadrotor dual-swing system. At the same time, it performs second-order continuous smooth reconstruction of waypoint commands and introduces swing suppression dynamic auxiliary variables to construct an all-drive mapping state variable that integrates position error, swing angle coupling amount and auxiliary variables, thus transforming the original underactuated dual-swing horizontal channel into a second-order virtual all-drive subsystem.

[0015] Finite-time control unit: This unit takes the all-drive mapping state variables and their dynamic information as input to generate virtual control quantities that meet the requirements of waypoint tracking and double-swing angle suppression. This unit designs a finite-time control law with non-smooth feedback characteristics on the basis of the all-drive subsystem and performs closed-loop adjustment of the all-drive mapping state.

[0016] Active Disturbance Rejection Unit: This unit takes the horizontal channel all-drive mapped state variables, the virtual control quantity output by the finite-time control unit, and the system response information as inputs to perform online estimation and active compensation for the equivalent lumped disturbances entering the all-drive subsystem. The equivalent lumped disturbances include external gusts, unmodeled aerodynamic drag, model parameter perturbations, and disturbances caused by the nonlinear coupling of the double pendulum. This unit constructs an uncertainty and disturbance estimator based on a low-pass filter structure, and treats external disturbances and internal uncertainties as lumped disturbances in the horizontal channel for compensation.

[0017] In some embodiments, the inner-loop bottom-level flight control module is used to realize attitude stabilization, angular velocity adjustment, and motor hybrid control execution of the quadcopter UAV based on the desired attitude angle and thrust commands output by the outer loop.

[0018] The inner ring bottom flight control module receives the desired roll angle, desired pitch angle and total thrust commands output by the outer ring, and generates actual aerodynamic forces and control torques through attitude control, angular velocity control and motor hybrid control, so that the quadcopter UAV moves according to the outer ring control commands.

[0019] In some embodiments, establishing the horizontal plane block matrix dynamic model of the quadrotor double pendulum includes: constructing a set of dynamic equations for the three-dimensional space double pendulum with disturbances and designing a robust control design for the height channel and an anti-disturbance model for the X-axis.

[0020] In some embodiments, constructing the three-dimensional spatial dynamic equations of the double pendulum system with disturbances refers to: based on the Lagrange dynamics method, comprehensively considering external lumped wind disturbances and unmodeled damping, the simplified 7-DOF nonlinear coupled dynamic equations of the quadrotor double pendulum system in three-dimensional space are expressed as follows:

[0021] ;

[0022] in, Let be the position vector of the quadcopter UAV in the inertial coordinate system. In this system, These represent the masses of the quadcopter, the hook, and the load, respectively. It is the length of the cable connecting the quadcopter and the hook. It is the length of the cable connecting the hook and the load. Represent the swing angles of the hook and load in three-dimensional space, respectively, and define the control inputs. , This represents the rotation matrix of the quadrotor UAV from its fixed coordinate system to its inertial coordinate system. For total thrust, It is the unit vector of the z-channel, defined , , , , , Where g is the total mass of the system, and g is the acceleration due to gravity. This is the three-axis equivalent control input acting on the translational channel of the machine body. This refers to the external physical disturbance force acting on the translational channel of the machine body. Here are the angular damping coefficients of the hook and load in the X and Y axes. This is the vertical nonlinear coupling term caused by the oscillation of the double pendulum.

[0023] In some embodiments, the robust control design for the height channel and the disturbance rejection model design for the X-axis adopt a hierarchical decoupling strategy: a finite-time height controller is designed first for the Z-axis, and the double pendulum nonlinear coupling of the height axis is performed. With lumped interference Treating the bounded lumped disturbance of the height channel as a standard finite-time control law, the following standard finite-time control law is designed:

[0024] ;

[0025] in, , For the feedback gain of the height channel, the non-smooth function is defined as follows: And the finite-time parameters satisfy ;

[0026] Under this closed-loop control, the system enters a constant-altitude level flight or hovering state, at which point it is assumed that the vertical acceleration satisfies... Due to the decoupling characteristics defined by the spatial projection angle, the X-axis dynamics composed of the first three equations in the 7-DOF nonlinear coupled dynamics equation set and the Y-axis dynamics composed of the fourth to sixth equations exhibit orthogonal symmetric isomorphism.

[0027] The extracted X-axis dynamic equations are reconstructed into a structure separating "driven" and "underdriven" states, where the X-axis translational displacement is defined as the driving state variable. Define the double-projection swing angle as an underactuated state variable. Based on the above definition, the dynamics of the quadrotor double pendulum system can be rewritten in a standard compact block matrix form:

[0028] ;

[0029] in , , , , ; , , , ; , .

[0030] In some embodiments, the controller-oriented full-drive state mapping and dynamic reconstruction includes: reconstruction of the X-axis disturbed dynamic equation and coupled variables, and de-swaying state reconstruction by introducing dynamic auxiliary filtering.

[0031] In some embodiments, when reconstructing the X-axis disturbed dynamic equations and coupled variables, the X-axis controlled translation degree of freedom equations are written as:

[0032] ;

[0033] Based on the rewritten equations above, the following total drive mapping relationship is obtained:

[0034] ;

[0035] During the sway-reconstruction process involving the introduction of dynamic auxiliary filtering, the composite all-drive control law acting on the second-order all-drive subsystem is distinguished. Compared with actual level input ,in, Used to specify the total drive error variable The closed-loop dynamics The actual control input acting on the horizontal channel of the quadcopter corresponds to each other through the total drive mapping relationship;

[0036] Before constructing the all-drive error variable, a dynamic auxiliary variable for suppressing X-axis oscillation is introduced. :

[0037] ;

[0038] in, This is an adjustment parameter for the dynamic auxiliary variable used to suppress oscillation; this variable is used to smoothly introduce the oscillation angle coupling. And through the weights in the subsequent error variables Adjust the strength of the interaction between position tracking and double pendulum suppression;

[0039] From the above formula, we get: ;

[0040] Before constructing the all-drive mapping state, a second-order continuous reconstruction of the desired waypoints on the horizontal plane is performed, and a standard cycloidal smoothing function is defined:

[0041] ;

[0042] The function satisfies ;

[0043] For any horizontal channel Let the time of the j-th waypoint switch be . The target waypoint after switching is The reference smoothing time is ,Pick ,make This represents the smoothed reference value of the channel before j waypoint switching. For the initial waypoint, assuming the initial swing angle is zero, we have: ,Pick:

[0044] ;

[0045] when At that time, the smooth reference is defined as:

[0046] ;

[0047] when When entering the waypoint holding phase, refer to the following:

[0048] ;

[0049] Within the transition section, the first and second derivatives of the smoothing reference are as follows:

[0050] ;

[0051] at this time, , , All are continuous and bounded, and satisfy the following conditions during the waypoint holding period: ,therefore, and These represent the smoothed desired positions reconstructed from discrete waypoint commands on the X and Y axes, respectively.

[0052] Based on the above reference reconstruction, the X-axis all-drive mapping state variable is defined as follows:

[0053] ;

[0054] in, , The X-axis swing angle coupling weight adjustment parameter;

[0055] right Taking the second derivative yields ;

[0056] Define the composite all-wheel drive control law for Then the X-axis all-drive subsystem is:

[0057] ;

[0058] The finite-time feedback law and UDE perturbation compensation work together to ,Right now:

[0059] ;

[0060] in, Depend on and The mapping relationship between the two drives, the actual horizontal input is ,Will Substituting into the above formula, we obtain the direct expression for the actual horizontal input:

[0061] .

[0062] In some embodiments, when the Y-axis all-drive space isomorphically unfolded, the Y-axis channel isomorphically unfolded according to the X-axis channel.

[0063] Wherein, the definition is: ;

[0064] in ;

[0065] Y-axis total drive mapping relationship ,get:

[0066] ;

[0067] definition: ,but:

[0068] ;

[0069] If the UDE composite finite-time control law is adopted The actual horizontal input on the Y-axis is:

[0070] .

[0071] In some embodiments, the UDE-based finite-time control law design includes: nominal fast finite-time anti-slip control law design and uncertainty and disturbance estimator (UDE) design;

[0072] When designing the nominal fast finite-time anti-slip control law, a non-smooth function is defined:

[0073] ;

[0074] In the all-drive subsystem, the nominal fast finite-time feedback law for the X-axis is designed as follows:

[0075] ;

[0076] in, , , , Among them, with , The two terms are used to guarantee finite-time convergence within the neighborhood of the origin, with , Two of them are used to enhance the fast convergence capability during the large error stage;

[0077] The nominal fast finite-time feedback law for the Y-axis is:

[0078] ;

[0079] in, ;

[0080] When designing the Uncertainty and Disturbance Estimator (UDE), the equivalent disturbance of the entire drive space estimated by the UDE is introduced. Construct the X-axis composite all-drive control law:

[0081] ;

[0082] Based on X-axis all-drive subsystem The equivalent lumped disturbance of the all-drive space is obtained as:

[0083] ;

[0084] Introducing a strict true low-pass filter The UDE estimate satisfies:

[0085] ;

[0086] Will Substituting and rearranging, we obtain the executable frequency domain expression:

[0087] ;

[0088] Select a first-order low-pass filter: ,but:

[0089] ;

[0090] therefore:

[0091] ;

[0092] If the zero initial condition is satisfied Then the time-domain expression is:

[0093] ;

[0094] like Then it is written as:

[0095] ;

[0096] Similarly, the Y-axis perturbation is estimated as follows:

[0097] ;

[0098] exist Under zero initial conditions, the initial term is omitted. .

[0099] The beneficial effects of this invention are as follows: This invention establishes a hierarchical control architecture of "full-drive mapping reconstruction, waypoint reference smoothing, finite-time waypoint tracking and anti-sway, UDE active disturbance rejection compensation, and low-level attitude and thrust execution," which can improve the waypoint tracking accuracy, sway angle suppression effect, and robust flight capability of a quadcopter dual-swing lifting system under conditions where discrete waypoint switching and external wind disturbances coexist. Compared with the prior art, this invention has the following beneficial effects:

[0100] (1) Unification of waypoint tracking and double pendulum cancellation:

[0101] Existing quadrotor dual-swing control methods often handle fuselage position tracking and hook / load sway suppression separately, making it difficult to simultaneously address discrete waypoint tracking and dual-swing suppression within a single control structure. This invention, based on high-order full-drive system (FAS) theory, introduces full-drive mapping state variables to mathematically map the physically coupled and non-directly actuated quadrotor dual-swing underactuated horizontal channel model into a full-drive space model that facilitates controller design. This allows position error, hook swing angle, and load swing angle to be coordinated and adjusted within a unified full-drive space. Therefore, this invention can suppress dual swing of the hook and load while simultaneously achieving discrete waypoint tracking, realizing unified control of waypoint tracking and dual-swing suppression.

[0102] (2) Waypoint switching shock suppression and rapid convergence:

[0103] Existing methods, when handling discrete waypoint tasks, are prone to abrupt changes in control commands due to step switching of the target position, which excites the hook and load swing angles, leading to residual oscillations near the waypoint. This invention, before constructing the all-drive mapping state, performs a second-order continuous smooth reconstruction of the step reference command generated by waypoint switching, and combines a swing suppression dynamic auxiliary variable with a finite-time control law having non-smooth feedback characteristics, enabling the system to quickly enter the target state neighborhood after a waypoint switch. When the nominal disturbance estimation error approaches zero, the all-drive mapping state can achieve finite-time convergence; even with external wind disturbances and estimation errors, the system state can enter an adjustable small neighborhood within a finite time. This mitigates the mechanical excitation caused by discrete waypoint switching, shortens the position response and swing angle decay process, and improves the transient response performance of the UAV lifting system.

[0104] (3) Enhanced wind resistance and composite robustness:

[0105] Existing quadrotor dual-pendulum control methods often rely on high feedback gain or highly accurate model parameters when facing gusts, aerodynamic drag, load parameter variations, and unmodeled coupling terms, resulting in insufficient engineering adaptability. This invention combines an Uncertainty and Disturbance Estimator (UDE) and utilizes strictly true low-pass filtering characteristics to treat external wind disturbances, unmodeled aerodynamic drag, model parameter perturbations, and dual-pendulum nonlinear coupling terms as equivalent lumped disturbances entering the horizontal all-drive subsystem, performing online estimation and active compensation, thereby reducing the sensitivity of control performance to the accuracy of some model parameters. Figures 5 to 7 The simulation results show that the present invention can maintain waypoint tracking performance and suppress double pendulum oscillation under the simultaneous presence of continuous external wind disturbance and double pendulum coupling, thereby improving the robustness and engineering availability of the quadcopter double pendulum hoisting system. Attached Figure Description

[0106] Figure 1 This is a flowchart of the quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection in Embodiment 1 of the present invention;

[0107] Figure 2 This refers to the quadcopter double pendulum system model described in Embodiment 1 of the present invention;

[0108] Figure 3 This refers to the full-drive mapping and active disturbance rejection control framework proposed in Embodiment 1 of the present invention;

[0109] Figure 4 This is a three-dimensional spatial flight trajectory diagram of the quadcopter double-pendulum system in Embodiment 2 of the present invention;

[0110] Figure 5 This is a diagram of the three-axis position tracking response curve in Embodiment 2 of the present invention;

[0111] Figure 6 This is a graph showing the double pendulum angle response in Embodiment 2 of the present invention;

[0112] Figure 7 This is a graph showing the wind disturbance estimation curves along the X and Y axes in Embodiment 2 of the present invention. Detailed Implementation

[0113] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0114] Example 1

[0115] This embodiment provides a quadrotor dual-pendulum finite-time sway elimination method based on full-drive mapping and active disturbance rejection, applied to a quadrotor UAV dual-pendulum lifting system. The method adopts a hierarchical control structure consisting of an outer-loop position and sway elimination control module and an inner-loop bottom-level flight control module. The outer-loop position and sway elimination control module is used to complete the full-drive equivalent mapping, waypoint reference smooth reconstruction, finite-time waypoint tracking, dual-pendulum sway elimination, and horizontal channel active disturbance rejection compensation of the quadrotor dual-pendulum system. The inner-loop bottom-level flight control module is used to realize the attitude stabilization, angular velocity adjustment, and motor mixed control execution of the quadrotor UAV according to the desired attitude angle and thrust command output by the outer loop.

[0116] The method includes the following steps:

[0117] S1. Establish a block matrix dynamic model of the horizontal plane of a quadrotor double pendulum;

[0118] S2, Controller-oriented full-drive state mapping and dynamic reconfiguration;

[0119] S3 and Y-axis all-drive space isomorphic layout;

[0120] S4. Finite-time control law design based on UDE;

[0121] S5. Stability and finite-time convergence analysis of closed-loop systems based on Lyapunov's theorem.

[0122] This embodiment addresses the underactuated, strongly coupled, and nonlinear characteristics exhibited by the quadrotor UAV dual-pendulum hoisting system under the combined effects of discrete waypoint switching, dual-pendulum coupling, and external disturbances. An outer-loop control architecture is constructed, consisting of a full-drive mapping unit, a finite-time control unit, and an active disturbance rejection unit. Specifically, it includes the following units:

[0123] (1) Full drive mapping unit:

[0124] This unit takes the target discrete waypoints, the actual position and velocity of the quadrotor, the swing angle and angular velocity of the hook and load, the mass parameters of the quadrotor, hook, and load, and the sling length parameters as inputs. It is used to mathematically reconstruct the original underactuated horizontal channel into a virtual fully driven subsystem that facilitates controller design. First, under the condition that the altitude channel is stable and satisfies approximately constant altitude, a block matrix dynamic model of the horizontal channel of the quadrotor dual-swing system is established. Simultaneously, to suppress the instantaneous excitation caused by step switching of discrete waypoints, the waypoint commands are reconstructed using a second-order continuous smoothing method, and a swing suppression dynamic auxiliary variable is introduced. Based on the above preprocessing, a fully driven mapping state variable is constructed that integrates position error, swing angle coupling, and auxiliary variables. This transforms the original underactuated dual-swing horizontal channel into an equivalent second-order virtual fully driven subsystem, providing a unified state basis for subsequent waypoint tracking and dual-swing angle suppression control.

[0125] (2) Finite-time control unit:

[0126] This unit takes the all-drive mapping state variables and their dynamic information as input to generate virtual control quantities that meet the requirements of waypoint tracking and double-pendulum angle suppression. Based on the all-drive subsystem, this unit designs a finite-time control law with non-smooth feedback characteristics. By performing closed-loop adjustment of the all-drive mapping state, it improves the system's position tracking accuracy, double-pendulum angle suppression effect, and transient response speed during discrete waypoint switching phases.

[0127] (3) Active interference suppression unit:

[0128] This unit takes the horizontal channel all-drive mapped state variables, the virtual control quantity output by the finite-time control unit, and the system response information as inputs to perform online estimation and active compensation of the equivalent lumped disturbances entering the all-drive subsystem. The equivalent lumped disturbances include external gusts, unmodeled aerodynamic drag, model parameter perturbations, and disturbances caused by the nonlinear coupling of the dual-pendulum system. Based on a low-pass filter structure, this unit constructs an uncertainty and disturbance estimator (UDE) that treats the aforementioned external disturbances and internal uncertainties as a unified horizontal channel lumped disturbance for compensation. This reduces the sensitivity of control performance to accurate model parameters and enhances the disturbance immunity and robustness of the quadcopter dual-pendulum hoisting system under complex operating conditions.

[0129] In the aforementioned outer-loop control architecture, the virtual control quantity output by the finite-time control unit and the disturbance estimate output by the active disturbance rejection unit are combined and then transformed through the inverse transformation of the all-drive mapping relationship to obtain the actual control input of the quadcopter's horizontal channel. This actual control input is then combined with the independent altitude control law of the altitude channel to generate the desired three-dimensional thrust vector, which is then calculated into the desired roll angle, desired pitch angle, and total thrust command. These commands are sent to the inner-loop bottom-level flight control module, which uses them to complete the attitude stabilization, angular velocity adjustment, and motor hybrid control execution of the quadcopter UAV, enabling the quadcopter UAV to move according to the outer-loop control commands, thereby achieving discrete waypoint tracking, double-swing angle suppression, and disturbance rejection flight tasks.

[0130] like Figure 1 As shown, the method in this embodiment is implemented through the following steps:

[0131] S1. Establish a block matrix dynamic model of the quadrotor dual-pendulum horizontal plane. The actual quadrotor dual-pendulum system moves in three-dimensional space. With the inner ring attitude already closed by the underlying control, the outer ring adopts a simplified 7-DOF model of three-dimensional translation plus two sets of projected pendulum angles. This embodiment focuses on solving the waypoint tracking and pendulum disturbance rejection problems on the horizontal plane. First, orthogonal dimensionality reduction and decoupling are performed on the three-dimensional disturbed model.

[0132] S1.1 Construct a set of dynamic equations for a three-dimensional double pendulum with disturbances;

[0133] The quadcopter double-pendulum system addressed in this embodiment is as follows: Figure 2 As shown, the position vector of the quadcopter UAV in the inertial coordinate system is represented as: In this system, These represent the masses of the quadcopter, the hook, and the load, respectively. It is the length of the cable connecting the quadcopter and the hook. It is the length of the cable connecting the hook and the load. These represent the swing angles of the hook and the load in three-dimensional space, respectively. At this point, the control inputs are defined. , This represents the rotation matrix of the quadrotor UAV from its fixed coordinate system to its inertial coordinate system. For total thrust, It is the unit vector of the z-channel. For simplicity, it is defined as follows: , , , ,in .

[0134] Based on the Lagrange dynamics method, and taking into account both external lumped wind disturbance and unmodeled damping, the simplified 7-DOF nonlinear coupled dynamic equations of the quadrotor double pendulum system in three-dimensional space are described as follows:

[0135] ;

[0136] in, Where g is the total mass of the system, and g is the acceleration due to gravity. This is the three-axis equivalent control input acting on the translational channel of the machine body. This refers to the external physical disturbance force acting on the translational channel of the machine body. Here are the angular damping coefficients of the hook and load in the X and Y axes. This is the vertical nonlinear coupling term caused by the oscillation of the double pendulum.

[0137] S1.2, Robust control design of height channel and X-axis disturbance rejection model design;

[0138] In actual hoisting operations, maintaining a stable flight altitude is the top priority. Although the altitude axis dynamics are affected by the double pendulum motion... The coupling has an impact, but this embodiment adopts a layered decoupling strategy: a finite-time height controller is designed first for the Z-axis, and the double pendulum nonlinear coupling of the height axis is decoupled. With lumped interference Treating the bounded lumped disturbance of the height channel as a standard finite-time control law, the following standard finite-time control law is designed:

[0139] ;

[0140] in, , For the feedback gain of the height channel, the non-smooth function is defined as follows: And the finite-time parameters satisfy .

[0141] Under this closed-loop control, the system enters a constant-altitude level flight or hovering state, and it can be reasonably assumed that the vertical acceleration satisfies... Due to the decoupling characteristics defined by the spatial projection angle, the X-axis dynamics, consisting of the first three equations in the 7-DOF nonlinear coupled dynamic equation set, and the Y-axis dynamics, consisting of the fourth to sixth equations, exhibit orthogonal symmetric isomorphism. Therefore, the core control algorithm (full-drive mapping and disturbance observation) in this embodiment will focus on a single horizontal channel (taking the X-axis as an example) for detailed explanation, and its conclusions can be completely equivalently extended to the Y-axis channel.

[0142] To facilitate the clear mathematical separation of nonlinear coupling terms within the system and to prepare for subsequent dimensionality reduction mapping of higher-order fully driven systems (FAS), this embodiment reconstructs the extracted X-axis dynamic equations into a structure separating "driving" and "under-driving" states. Specifically, the X-axis translational displacement is defined as the driving state variable. Define the double-projection swing angle as an underactuated state variable. Based on the above definition, the dynamics of the quadrotor double pendulum system can be rewritten in a standard compact block matrix form:

[0143] ;

[0144] in , , , , ; , , , ; , .

[0145] S2. Full-drive state mapping and dynamic reconfiguration for controllers.

[0146] S2.1, X-axis disturbed dynamic equations and reconstruction of coupled variables;

[0147] To avoid confusion between physical wind disturbance and all-wheel drive space disturbance, this embodiment stipulates: The external physical wind disturbance force acting on the X-axis translational channel, its unit is N. The equivalent lumped disturbance entering the all-drive subsystem has the same dimensions as... Consistent, both satisfy ,in This represents the equivalent disturbance caused by small-angle approximation, unmodeled aerodynamic drag, parametric perturbations, and residual coupling terms, with dimensions similar to... Consistent.

[0148] Therefore, the equation for the controlled translational degree of freedom along the X-axis can be written as:

[0149] ;

[0150] Constructing X-axis coupling auxiliary variables Under the small-angle control model, there is Therefore, the linear approximation form used in the simulation implementation is: .

[0151] From the above definition, the following all-drive mapping relationship can be obtained:

[0152] .

[0153] S2.2, Introducing dynamic auxiliary filtering for sway-free state reconstruction;

[0154] To avoid confusion between the all-drive space control variable and the actual horizontal input of the quadcopter, this embodiment clearly distinguishes the composite all-drive control law acting on the second-order all-drive subsystem. Compared with actual level input .in, Used to specify the total drive error variable The closed-loop dynamics The actual control input acting on the horizontal channel of the quadcopter corresponds to each other through the total drive mapping relationship.

[0155] Before constructing the all-drive error variable, a dynamic auxiliary variable for suppressing X-axis oscillation is introduced. :

[0156] ;

[0157] in, This is an adjustment parameter for the dynamic auxiliary variable used to suppress oscillation; this variable is used to smoothly introduce the oscillation angle coupling. And through the weights in the subsequent error variables Adjusting the strength of the interaction between position tracking and double pendulum suppression, we can obtain the following from the above equation: .

[0158] To reduce the instantaneous excitation of the quadrotor dual-pendulum system during discrete waypoint step switching, this embodiment performs a second-order continuous reconstruction of the desired waypoints on the horizontal plane before constructing the all-drive mapping state. A standard cycloidal smoothing function is defined as follows:

[0159] ;

[0160] The function satisfies .

[0161] For any horizontal channel Let the time of the j-th waypoint switch be . The target waypoint after switching is The reference smoothing time is To ensure the reference trajectory completes its transition before the next waypoint switch, take... ,make This represents the smoothed reference value of the channel before j waypoint switching. For the initial waypoint, assuming the initial swing angle is zero, we have: , can be:

[0162] ;

[0163] when At that time, the smooth reference is defined as:

[0164] ;

[0165] when When entering the waypoint holding phase, refer to the following:

[0166] ;

[0167] Within the transition section, the first and second derivatives of the smoothing reference are as follows:

[0168] .

[0169] Therefore, , , All are continuous and bounded, and satisfy the following conditions during the waypoint holding period: ,therefore, and These represent the smoothed desired positions reconstructed from discrete waypoint commands on the X and Y axes, respectively.

[0170] Based on the above reference reconstruction, the X-axis all-drive mapping state variable is defined as follows:

[0171] ;

[0172] in , This is the parameter for adjusting the X-axis swing angle coupling weight.

[0173] right Taking the second derivative yields .

[0174] Define the composite all-wheel drive control law for Then the X-axis all-drive subsystem is:

[0175] ;

[0176] The finite-time feedback law and UDE perturbation compensation work together to ,Right now:

[0177] ;

[0178] in, Depend on and The mapping relationship between the two drives, the actual horizontal input is ,Will Substituting into the above formula, we obtain the direct expression for the actual horizontal input:

[0179] .

[0180] S3 and Y-axis all-drive space isomorphic layout.

[0181] Since the quadcopter structure is approximately orthogonally symmetrical in the horizontal plane, the Y-axis channel can be isomorphically unfolded according to the X-axis channel.

[0182] definition:

[0183] ;

[0184] in ;

[0185] Y-axis total drive mapping relationship ,get:

[0186] ;

[0187] definition: ,but:

[0188] .

[0189] If the UDE composite finite-time control law is adopted The actual horizontal input on the Y-axis is:

[0190] .

[0191] S4. Finite-time control law design based on UDE.

[0192] S4.1 Design of nominal fast finite-time anti-slip control law;

[0193] Define a non-smooth function:

[0194] ;

[0195] In the all-drive subsystem, the nominal fast finite-time feedback law for the X-axis is designed as follows:

[0196] ;

[0197] in, , , , Among them, with , The two terms are used to guarantee finite-time convergence within the neighborhood of the origin, with , Two of these are used to enhance the fast convergence capability during the large error phase.

[0198] The nominal fast finite-time feedback law for the Y-axis is:

[0199] ;

[0200] in, .

[0201] S4.2 Uncertainty and Interference Estimator (UDE) Design;

[0202] Introducing UDE-estimated all-drive space equivalent disturbance Construct the X-axis composite all-drive control law:

[0203] ;

[0204] Based on X-axis all-drive subsystem The equivalent lumped disturbance of the all-drive space can be obtained as:

[0205] .

[0206] Introducing a strict true low-pass filter The UDE estimate satisfies:

[0207] ;

[0208] Will Substituting and rearranging, we obtain the executable frequency domain expression:

[0209] ;

[0210] Select a first-order low-pass filter: ,but:

[0211] .

[0212] therefore:

[0213] .

[0214] If the zero initial condition is satisfied Then the time-domain expression is:

[0215] ;

[0216] like Then it is written as:

[0217] .

[0218] Similarly, the Y-axis perturbation is estimated as follows:

[0219] ;

[0220] exist Under zero initial conditions, the initial term can be omitted. .

[0221] S5. Stability and finite-time convergence analysis of closed-loop systems based on Lyapunov's theorem.

[0222] After completing the design of the composite finite-time control law based on UDE, this embodiment proves the convergence characteristics of the closed-loop system according to the stability theory of nonlinear control systems. Since the X-axis and Y-axis are physically isomorphic, the theoretical demonstration below only takes the X-axis all-drive subsystem as an example.

[0223] S5.1, Closed-loop error dynamic equation considering interference estimation error;

[0224] Define the disturbance estimation error of UDE ;

[0225] Substituting the composite all-drive control law into the second-order all-drive subsystem, we can obtain the dynamics of the X-axis closed-loop error:

[0226] ;

[0227] when When, construct the Lyapunov function:

[0228] ;

[0229] use Differentiating along the closed-loop trajectory yields:

[0230] ;

[0231] Depend on , It can be known The system is semi-negative definite. According to Lyapunov's stability theorem and Lassalle's invariance principle, the system's state trajectory eventually converges to the maximally invariant set. Within this set Substituting into the closed-loop dynamics, we can obtain Therefore, the nominal closed-loop system is asymptotically stable globally at the origin.

[0232] Furthermore, once the system enters the neighborhood of the origin, higher-order terms decay faster than fractional-power terms, and the dominant dynamic of the closed loop is... Let the scaling transformation be This verifies that the aforementioned dominant system has negative homogeneity relative to the scaling transformation.

[0233] According to the finite-time stability theorem for homogeneous nonlinear systems, the nominal system converges in finite time within the neighborhood of the origin; combined with global asymptotic stability, the conclusion that the nominal closed-loop system converges in finite time can be obtained.

[0234] when When the constant is not zero but is bounded, we have:

[0235] ;

[0236] Therefore, the closed-loop system no longer strictly guarantees reaching the origin in a precise finite time, but rather guarantees convergence in an actual finite time, that is, the state enters the state within a finite time. The upper bound determines the small neighborhood, and the filter remains within that neighborhood. This is achieved by reducing the UDE filtering time constant. By appropriately increasing the feedback gain, the neighborhood can be narrowed. The same applies to the Y-axis.

[0237] S5.2, Inverse mapping of physical states and anti-suspension characteristics;

[0238] In the inverse physical state mapping analysis, both the hook and the load swing angle operate in the small swing angle region, i.e.

[0239] .

[0240] definition Within this swing angle region, the gravity term of the horizontal channel underactuated subsystem is:

[0241] ;

[0242] because ,and exist The interior is monotonous, hence:

[0243] .

[0244] The following uses the X-axis as an example to illustrate the inverse mapping relationship of physical states; the same applies to the Y-axis.

[0245] When the X-axis all-wheel drive mode enters the hold state within a finite time, and the smooth reference enters the waypoint hold segment, then:

[0246] .

[0247] Combined with dynamic auxiliary system And the positive damping term of the underactuated double pendulum system allows us to construct the underactuated energy function. ,in It is a positive definite matrix. Further, the composite energy function is defined. During the waypoint holding period, by , as well as , We can obtain: ,in .

[0248] By Lassalle's invariance principle, the system trajectory converges to satisfy... The largest invariant set. And because... Only by Decide, roll out .

[0249] Furthermore, in this maximally invariant set:

[0250] ;

[0251] Substituting the above relationship into the X-axis underactuated subsystem, we get:

[0252] ;

[0253] Combined with the small swing angle area There will always be a time for it. ,get:

[0254] ;

[0255] Depend on It can be known .

[0256] Then by dynamic auxiliary system We can obtain:

[0257] .

[0258] According to the definition of all-drive mapping state:

[0259] ;

[0260] Can be rewritten as .because ,therefore During the waypoint holding period Therefore Similarly, for the Y-axis, there is , and by get Within the waypoint holding period Therefore .

[0261] Therefore, when the nominal disturbance estimation error approaches zero, there are [conditions / conditions] during the waypoint holding segment. That is, when the quadcopter converges to the target waypoint in the horizontal position, the double swing angle of the hook and load in the X and Y projection directions simultaneously decreases to zero.

[0262] When bounded perturbation estimation errors exist, as can be seen from the aforementioned dynamic analysis of closed-loop errors, Instead of reaching the origin in a strictly finite time, it enters a small neighborhood determined by the upper bound of the disturbance estimation error within a finite time. Accordingly, the above physical state inverse mapping conclusion is relaxed to: during the waypoint holding segment, when the quadcopter enters the target waypoint neighborhood in a horizontal position, the double swing angles of the hook and load in the X and Y projection directions simultaneously decay to the zero neighborhood.

[0263] Example 2

[0264] To further verify the effectiveness of the proposed quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection, numerical simulation experiments were conducted on the MATLAB / Simulink simulation platform. The simulation used a fixed-step solver ode5 (Dormand-Prince) with a step size of 0.001s and a total simulation duration of 40s. At the initial moment of the simulation, the initial position of the quadrotor UAV was... m, initial swing angle is rad.

[0265] In the simulation, the specific parameters are as follows:

[0266] ;

[0267] .

[0268] Select the following parameters for all-drive mapping and sway suppression:

[0269] .

[0270] The time for selecting waypoint reference smooth reconstruction is:

[0271]

[0272] The horizontal channel finite-time control parameters are selected as follows:

[0273] ;

[0274] ;

[0275] .

[0276] Select the Z-axis height channel control parameters as follows:

[0277] .

[0278] The parameters for the UDE estimator are set as follows:

[0279] .

[0280] This embodiment sets up a quadcopter UAV to perform discrete waypoint tracking tasks. The desired altitude value is maintained at [value missing]. The desired waypoint in the horizontal plane is given by a step transition between the desired positions on the X and Y axes:

[0281] ;

[0282] Therefore, the expected waypoints include, in order: , , , , as well as To simulate external gust interference, in Apply continuous step wind disturbance to the system:

[0283] ;

[0284] The equivalent disturbance corresponding to entering the all-wheel drive space is:

[0285] .

[0286] Figure 7 To facilitate comparison with the actual physical wind disturbance force on the same dimension, the estimated value of the all-drive equivalent disturbance output by UDE is converted into the estimated value of the physical wind disturbance force:

[0287] .

[0288] Figures 4 to 7 All simulation results are based on the above simulation environment parameters, quadcopter double pendulum system parameters, controller parameters, discrete waypoint parameters, and external wind disturbance parameters.

[0289] 1. Figure 4 Analysis of flight trajectory in three-dimensional space.

[0290] Figure 4In the diagram, the dashed line represents the desired trajectory, the solid line represents the actual trajectory of the quadcopter, the dot indicates the starting point, and the square indicates the ending point. Based on the waypoint parameters above, the desired trajectory covers a rectangular waypoint area within the horizontal plane, ranging from -1m to 1m along the X-axis and from -1m to 1m along the Y-axis, with the desired altitude maintained around 2m. The actual trajectory starts from the initial position... After departure, head towards the first target waypoint. Movement; then, following the zigzag path formed by switching the desired waypoints, the lateral and longitudinal movements are completed sequentially, eventually reaching the destination. nearby.

[0291] from Figure 4 The relative positions of the solid and dashed lines indicate that there are 2m amplitude step transitions on both the X and Y axes. Despite being subjected to continuous X-axis wind disturbance of 2N and Y-axis wind disturbance of 1.5N, the actual trajectory smoothly transitioned near the waypoint connection lines and did not deviate outside the waypoint area; combined with Figure 5 The altitude curve shows that the actual altitude remains within a narrow range of approximately 1.9995m to 2.001m. Therefore, under the aforementioned mass, rope length, and wind disturbance parameters, this invention can maintain three-dimensional track tracking capability during discrete waypoint switching, while avoiding significant altitude instability caused by double pendulum loads and gust disturbances.

[0292] 2. Figure 5 Analysis of three-axis position tracking response.

[0293] Figure 5 The positional responses along the X, Y, and Z axes are given from 0 to 40 seconds. The expected value along the X-axis is... Switching from 1m to -1m, in Switching from -1m to 1m, in Switching from 1m to -1m. The actual X-axis position curve smoothly rises from 0m to around 1m in the initial stage; Then it transitions from around 1m to around -1m, and at approximately The result largely coincided with the expected value; It then returned to around 1 meter within approximately 4 seconds; It then reached approximately -1m within about 4 seconds. The above curve trend indicates that, under the combined effects of the 2m step waypoint switch on the X-axis and the continuous 2N wind disturbance, the actual position did not oscillate continuously, but instead rapidly entered the target waypoint neighborhood through the finite-time control law of the all-wheel drive.

[0294] In the Y-axis direction, the expected value is Switching from 1m to -1m, in Switching from -1m to 1m. The actual Y-axis position initially rises from 0m to approximately 1m; in Transitioning backward to -1m, and at approximately Then it entered the vicinity of -1m; Transitioning backwards to 1m, and at approximately The result then largely coincided with the expected value. Because the Y-axis is... Subsequently subjected to a 1.5N wind disturbance, the above response indicates that UDE compensation and all-drive mapping control together suppressed the position deviation caused by the wind disturbance.

[0295] The desired height is 2m along the Z-axis. Figure 5 As shown in the curve below, the actual altitude mainly fluctuates briefly around the time of waypoint switching, with the vertical axis ranging from approximately 1.9995m to 2.001m, meaning the altitude deviation is no more than [a certain magnitude]. This result demonstrates that, despite attitude adjustments caused by horizontal discrete waypoint switching and double-pendulum load coupling, the present invention can still maintain altitude channel stability, thereby reducing the risk of load vertical disturbance and flight altitude deviation during hoisting.

[0296] 3. Figure 6 Analysis of the double pendulum response.

[0297] Figure 6 The hook swing angle is given. Load swing angle and hook swing angle Load swing angle The response. In the X-axis direction, in Around 21s and 35s, the desired X-axis position experiences a 2m amplitude shift, resulting in a brief peak response in the hook and load swing angle. The peak swing angle around 9s is approximately in the range of -0.1 rad to 0.2 rad. The peak swing angle around 24s is approximately in the range of -0.2 rad to 0.1 rad. The peak swing angle around 38s was approximately between -0.1 rad and 0.22 rad. After each peak, the swing angle decayed to near zero within a few seconds, without forming a sustained residual oscillation.

[0298] In the Y-axis direction, and Nearby, a 2m amplitude shift occurs at the desired position on the Y-axis, and a brief peak appears corresponding to the swing angle of the hook and the load. Around 16s, the Y-axis swing angle varied within the range of approximately -0.1rad to 0.2rad, and at approximately... It then decays to near zero; Around 30 seconds, the Y-axis swing angle varied within the range of approximately -0.22 rad to 0.1 rad, and remained relatively constant. It then decays to near zero.

[0299] Combination Figure 5The location response indicates that Figure 6 The peak swing angle mainly occurs during waypoint switching and control acceleration changes, while after reaching each target waypoint, the swing angle of both the hook and the load returns to near zero. This indicates that... , , , Under the parameters of the dual-pendulum system, this invention not only enables the UAV fuselage to reach the target waypoint, but also suppresses the dual swing of the hook and load while the fuselage position converges, thus avoiding the continuous accumulation of dual-pendulum energy after waypoint switching.

[0300] 4. Figure 7 Analysis of the UDE wind disturbance estimation response.

[0301] Figure 7 A comparison between the actual wind disturbance and the UDE estimate is presented. Based on the simulation settings, the actual X-axis wind disturbance is... From order 0 to 2N, the actual Y-axis wind disturbance is It jumps from 0 to 1.5N. Figure 7 In the middle, the UDE estimation curve of the X-axis is in It then rapidly rises to around 2N and remains around 2N for most of the subsequent time; the Y-axis UDE estimation curve is... It then rose rapidly to around 1.5N and remained around 1.5N for most of the subsequent time.

[0302] exist Nearby, the X-axis waypoint switch caused a brief fluctuation in the UDE estimation curve, which then returned to around 2N; and Nearby, the Y-axis waypoint switch caused a brief fluctuation in the UDE estimation curve, which then returned to around 1.5N. This phenomenon indicates that the UDE estimate is not only related to... The applied persistent wind disturbance has tracking capability and can recover to near the true disturbance amplitude after transient coupled disturbances introduced by waypoint switching.

[0303] Further integration Figure 5 and Figure 6 It can be seen that, in Even under persistent wind disturbances of 2N on the X-axis and 1.5N on the Y-axis, the system can still achieve position convergence after each waypoint switch, and the hook and load swing angles decay to near zero after a brief peak. Therefore, the combined technical effect of UDE estimation compensation and all-wheel drive finite-time feedback is to reduce position deviation caused by wind disturbances, suppress the double swing angles triggered by waypoint switches, and improve the robustness of the quadcopter double-swing lifting system when external gusts and double-swing coupling coexist.

[0304] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A finite-time pendulum cancellation method for quadrotor dual-pendulum systems based on full-drive mapping and active disturbance rejection, applied to a quadrotor UAV dual-pendulum hoisting system, characterized in that... The method employs a hierarchical control structure consisting of an outer-loop position and anti-sway control module and an inner-loop bottom-level flight control module. The outer-loop position and anti-sway control module is used to complete the full-drive equivalent mapping, waypoint reference smooth reconstruction, finite-time waypoint tracking, anti-sway of the dual-sway system, and active disturbance rejection compensation in the horizontal channel. The inner-loop bottom-level flight control module is used to realize the attitude stabilization, angular velocity adjustment, and motor hybrid control execution of the quadcopter UAV based on the desired attitude angle and thrust command output by the outer loop. The method includes the following steps: Establish a block matrix dynamic model of a quadrotor double pendulum in the horizontal plane; Full-drive state mapping and dynamic reconfiguration for controllers; Y-axis all-drive spatial isomorphic unfolding; Finite-time control law design based on UDE; Stability and finite-time convergence analysis of closed-loop systems based on Lyapunov's theorem.

2. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 1, characterized in that, The outer ring position and anti-sway control module specifically includes the following units: All-drive mapping unit: This unit takes the target discrete waypoints, the actual position and velocity of the quadrotor, the swing angle and angular velocity of the hook and load, the mass parameters of the quadrotor, hook and load, and the sling length parameters as inputs. It is used to mathematically reconstruct the original underactuated horizontal channel into a virtual all-drive subsystem that is convenient for controller design. First, under the condition that the altitude channel is stable and meets the approximate constant altitude condition, the unit establishes a block matrix dynamic model of the horizontal channel of the quadrotor dual-swing system. At the same time, it performs second-order continuous smooth reconstruction of waypoint commands and introduces swing suppression dynamic auxiliary variables to construct an all-drive mapping state variable that integrates position error, swing angle coupling amount and auxiliary variables, thus transforming the original underactuated dual-swing horizontal channel into a second-order virtual all-drive subsystem. Finite-time control unit: This unit takes the all-drive mapping state variables and their dynamic information as input to generate virtual control quantities that meet the requirements of waypoint tracking and double-swing angle suppression. This unit designs a finite-time control law with non-smooth feedback characteristics on the basis of the all-drive subsystem and performs closed-loop adjustment of the all-drive mapping state. Active Disturbance Rejection Unit: This unit takes the horizontal channel all-drive mapped state variables, the virtual control quantity output by the finite-time control unit, and the system response information as inputs to perform online estimation and active compensation for the equivalent lumped disturbances entering the all-drive subsystem. The equivalent lumped disturbances include external gusts, unmodeled aerodynamic drag, model parameter perturbations, and disturbances caused by the nonlinear coupling of the double pendulum. This unit constructs an uncertainty and disturbance estimator based on a low-pass filter structure, and treats external disturbances and internal uncertainties as lumped disturbances in the horizontal channel for compensation.

3. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 1, characterized in that, The inner-loop bottom-level flight control module is used to achieve attitude stabilization, angular velocity adjustment, and motor hybrid control execution of the quadcopter UAV based on the desired attitude angle and thrust commands output by the outer loop. This refers to: The inner ring bottom flight control module receives the desired roll angle, desired pitch angle and total thrust commands output by the outer ring, and generates actual aerodynamic forces and control torques through attitude control, angular velocity control and motor hybrid control, so that the quadcopter UAV moves according to the outer ring control commands.

4. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 1, characterized in that, The establishment of the horizontal plane block matrix dynamic model of the quadrotor double pendulum includes: constructing a set of dynamic equations for the three-dimensional space double pendulum with disturbances, and designing a robust control design for the height channel and an anti-disturbance model for the X-axis.

5. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 4, characterized in that, The aforementioned construction of the three-dimensional spatial dynamic equations for a double pendulum system with disturbances refers to: based on the Lagrange dynamics method, and comprehensively considering external lumped wind disturbances and unmodeled damping, the simplified 7-DOF nonlinear coupled dynamic equations of the quadrotor double pendulum system in three-dimensional space are expressed as follows: ； in, Let be the position vector of the quadcopter UAV in the inertial coordinate system. In this system, These represent the masses of the quadcopter, the hook, and the load, respectively. It is the length of the cable connecting the quadcopter and the hook. It is the length of the cable connecting the hook and the load. Represent the swing angles of the hook and load in three-dimensional space, respectively, and define the control inputs. , This represents the rotation matrix of the quadrotor UAV from its fixed coordinate system to its inertial coordinate system. For total thrust, It is the unit vector of the z-channel, defined , , , , , Where g is the total mass of the system, and g is the acceleration due to gravity. This is the three-axis equivalent control input acting on the translational channel of the machine body. This refers to the external physical disturbance force acting on the translational channel of the machine body. Here are the angular damping coefficients of the hook and load in the X and Y axes. This is the vertical nonlinear coupling term caused by the oscillation of the double pendulum.

6. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 5, characterized in that, The robust control design for the height channel and the disturbance rejection model design for the X-axis adopt a hierarchical decoupling strategy: a finite-time height controller is designed first for the Z-axis, and the double-pendulum nonlinear coupling of the height axis is removed. With lumped interference Treating the bounded lumped disturbance of the height channel as a standard finite-time control law, the following is designed: ； in, , For the feedback gain of the height channel, the non-smooth function is defined as follows: And the finite-time parameters satisfy ; Under this closed-loop control, the system enters a constant-altitude level flight or hovering state, at which point it is assumed that the vertical acceleration satisfies... Due to the decoupling characteristics defined by the spatial projection angle, the X-axis dynamics, which consist of the first three equations in the 7-DOF nonlinear coupled dynamics equation set, and the Y-axis dynamics, which consist of the fourth to sixth equations, exhibit orthogonal symmetric isomorphism. The extracted X-axis dynamic equations are reconstructed into a structure separating "driven" and "underdriven" states, where the X-axis translational displacement is defined as the driving state variable. Define the double-projection swing angle as an underactuated state variable. Based on the above definition, the dynamics of the quadrotor double pendulum system can be rewritten in a standard compact block matrix form: ； in , , , , ; , , , ; , .

7. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 1, characterized in that, The controller-oriented full-drive state mapping and dynamic reconstruction includes: X-axis disturbed dynamic equation and coupled variable reconstruction and anti-sway state reconstruction by introducing dynamic auxiliary filtering.

8. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 7, characterized in that, When reconstructing the X-axis disturbed dynamic equations and coupled variables, the X-axis controlled translation degree of freedom equations are written as follows: ； Based on the rewritten equations above, the following total drive mapping relationship is obtained: ； During the sway-reconstruction process involving the introduction of dynamic auxiliary filtering, the composite all-drive control law acting on the second-order all-drive subsystem is distinguished. Compared with actual level input ,in, Used to specify the total drive error variable The closed-loop dynamics The actual control input acting on the horizontal channel of the quadcopter corresponds to each other through the total drive mapping relationship; Before constructing the all-drive error variable, a dynamic auxiliary variable for suppressing X-axis oscillation is introduced. : ； in, This is an adjustment parameter for the dynamic auxiliary variable used to suppress oscillation; this variable is used to smoothly introduce the oscillation angle coupling. And through the weights in the subsequent error variables Adjust the strength of the interaction between position tracking and double pendulum suppression; From the above formula, we get: ; Before constructing the all-drive mapping state, a second-order continuous reconstruction of the desired waypoints on the horizontal plane is performed, and a standard cycloidal smoothing function is defined: ； The function satisfies ; For any horizontal channel Let the time of the j-th waypoint switch be . The target waypoint after switching is The reference smoothing time is ,Pick ,make This represents the smoothed reference value of the channel before j waypoint switching. For the initial waypoint, assuming the initial swing angle is zero, we have: ,Pick: ； when At that time, the smooth reference is defined as: ； when When entering the waypoint holding phase, refer to the following: ； Within the transition section, the first and second derivatives of the smoothing reference are as follows: ； at this time, , , All are continuous and bounded, and satisfy the following conditions during the waypoint holding period: ,therefore, and These represent the smoothed desired positions reconstructed from discrete waypoint commands on the X and Y axes, respectively. Based on the above reference reconstruction, the X-axis all-drive mapping state variable is defined as follows: ； in, , The X-axis swing angle coupling weight adjustment parameter; right Taking the second derivative yields ; Define the composite all-wheel drive control law for Then the X-axis all-drive subsystem is: ； Finite-time feedback law and UDE perturbation compensation work together ,Right now: ； in, Depend on and The mapping relationship between the two drives, the actual horizontal input is ,Will Substituting into the above formula, we obtain the direct expression for the actual horizontal input: 。 9. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to claim 1, characterized in that, When the Y-axis all-drive space isomorphically unfolded, the Y-axis channel isomorphically unfolded according to the X-axis channel. Wherein, the definition is: ; in ; Y-axis total drive mapping relationship ,get: ； definition: ,but: ； If the UDE composite finite-time control law is adopted The actual horizontal input on the Y-axis is: 。 10. The quadrotor dual-pendulum finite-time pendulum elimination method based on all-drive mapping and active disturbance rejection according to any one of claims 1-9, characterized in that, The UDE-based finite-time control law design includes: nominal fast finite-time anti-slip control law design and uncertainty and disturbance estimator (UDE) design; When designing the nominal fast finite-time anti-slip control law, a non-smooth function is defined: ； In the all-drive subsystem, the nominal fast finite-time feedback law for the X-axis is designed as follows: ； in, , , , Among them, with , The two terms are used to guarantee finite-time convergence within the neighborhood of the origin, with , Two of them are used to enhance the fast convergence capability during the large error stage; The nominal fast finite-time feedback law for the Y-axis is: ； in, ; When designing the Uncertainty and Disturbance Estimator (UDE), the equivalent disturbance of the entire drive space estimated by the UDE is introduced. Construct the X-axis composite all-drive control law: ； Based on X-axis all-drive subsystem The equivalent lumped disturbance of the all-drive space is obtained as: ； Introducing a strict true low-pass filter The UDE estimate satisfies: ； Will Substituting and rearranging, we obtain the executable frequency domain expression: ； Select a first-order low-pass filter: ,but: ； therefore: ； If the zero initial condition is satisfied Then the time-domain expression is: ； like Then it is written as: ； Similarly, the Y-axis perturbation is estimated as follows: ； exist Under zero initial conditions, the initial term is omitted. .

Images