Trajectory tracking method for quadrotor unmanned aerial vehicle based on fixed-time two-channel compensation

Abstract

The application discloses a kind of four rotor unmanned aerial vehicle trajectory tracking methods based on fixed time double channel compensation, belong to unmanned aerial vehicle control technical field.The method establishes four rotor unmanned aerial vehicle dynamics model, and parameter uncertainty term and external disturbance term are unified to be total matching uncertainty term;Fixed time total matching uncertainty observer is designed, total matching uncertainty estimation value is obtained, fixed time filtering parameter estimator is constructed, parameter uncertainty estimation value is obtained, and external disturbance estimation value is reconstructed by the two;Combined with parameter compensation and disturbance compensation, double channel compensation control law is designed, intermediate control input is obtained and is restored as total thrust and attitude control input, drives four rotor unmanned aerial vehicle to execute desired trajectory tracking flight.The application can improve the trajectory tracking precision and anti-interference ability of four rotor unmanned aerial vehicle under the condition of parameter uncertainty and external disturbance, and can be applied to unmanned aerial vehicle autonomous flight task in complex environment.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to a method for tracking the trajectory of a quadcopter UAV based on fixed-time dual-channel compensation. Background Technology

[0002] Quadrotor drones, characterized by vertical takeoff and landing, hovering, high maneuverability, and compact structure, have been widely used in payload transportation, inspection, collaborative operations, and autonomous flight missions in complex environments. In these applications, trajectory tracking control performance directly affects the flight accuracy, mission reliability, and safety of quadrotor drones.

[0003] Quadrotor UAVs are underactuated, multi-input multi-output, strongly coupled nonlinear systems. Their motion is easily affected by deviations in model parameters such as mass, moment of inertia, damping, and channel gain, as well as external environmental disturbances. Existing trajectory tracking methods typically employ techniques such as sliding mode control, disturbance observers, adaptive parameter estimation, and finite-time or fixed-time control. Among these, sliding mode control improves the system's disturbance rejection capability by constructing control terms robust to matching uncertainties; disturbance observers are used for online estimation of unknown disturbances; adaptive parameter estimation is used to identify parameter uncertainties; and finite-time or fixed-time control is used to improve the convergence performance of tracking errors.

[0004] When parameter uncertainty and external disturbances coexist, existing methods typically combine them into a single unknown term for observation and compensation, or only estimate the external disturbance. Since the sources and variation characteristics of parameter uncertainty and external disturbance differ, the above hybrid processing methods struggle to obtain separate estimation information for both. Furthermore, the single compensation term must simultaneously handle both parameter mismatch and external disturbance suppression, hindering targeted compensation based on different uncertainties.

[0005] Furthermore, some methods are designed separately for attitude or position subsystems, lacking a unified dynamic interface between observation, parameter estimation, and control. The convergence time of some finite-time methods still depends on the initial state. Other methods focus on the design of intermediate control inputs without explicitly defining the conversion relationship between these intermediate inputs and the total thrust and attitude control inputs of the quadcopter UAV, thus hindering the direct application of control results to the actual actuators. Therefore, existing technologies still have shortcomings in the unified handling of attitude and position dynamics, the differentiation and targeted compensation of uncertainties from different sources, the guarantee that the upper bound of the tracking error convergence time is independent of the initial state, and the practical implementation of control inputs. Summary of the Invention

[0006] In view of at least one of the above-mentioned technical problems, the present invention provides a trajectory tracking method for a quadrotor UAV based on fixed-time dual-channel compensation. The method unifies parameter uncertainties and external disturbances into a total matched uncertainty. The estimated value of the total matched uncertainty is obtained through a fixed-time total matched uncertainty observer, and the estimated value of the parameter uncertainties is obtained through a fixed-time filtered parameter estimator. Based on this, the estimated value of the external disturbances is reconstructed. Furthermore, a dual-channel compensation control law is constructed that allows for parallel parameter compensation and disturbance compensation to achieve trajectory tracking control under conditions of parameter uncertainty and external disturbances. This solves the problems in the prior art, such as inconsistent attitude and position dynamics interfaces, difficulty in separately estimating and specifically compensating for mixed parameter uncertainties and external disturbances, heavy burden on single compensation terms, difficulty in ensuring that the upper bound of the tracking error convergence time does not depend on the initial state, and unclear conversion relationship between intermediate control inputs and the actual control inputs of the quadrotor UAV.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A trajectory tracking method for a quadrotor UAV based on fixed-time dual-channel compensation, the method comprising:

[0009] A dynamic model of a quadrotor UAV is established, and the sum of parameter uncertainties and external disturbance terms is expressed as the total matching uncertainty in the quadrotor UAV dynamic model; based on the quadrotor UAV state vector and its first derivative Constructing regression vectors or regression matrices ;

[0010] Definition of the first Observation error of each dynamic component Based on the dynamic model of quadcopter UAV, Construct a fixed-time total matched uncertainty observer to obtain the estimate of the total matched uncertainty. ;

[0011] right and Filtering is performed to obtain further estimates of the unknown equivalent parameter vector. ,based on and Obtain the estimate of the parameter uncertainty term ;

[0012] according to and Reconstruct the external disturbance estimate ;

[0013] according to and Construct a dual-channel compensation control law to obtain the intermediate control input. ;

[0014] Will Restored to the total thrust of a quadcopter drone The attitude control inputs represent the roll, pitch, and yaw directions, respectively. , , and according to and , , Drive the quadcopter drone to perform desired trajectory tracking flight.

[0015] Furthermore, according to the quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation, the establishment of a quadrotor UAV dynamic model, and the representation of the sum of parameter uncertainties and external disturbance terms as the total matching uncertainty in the quadrotor UAV dynamic model, includes:

[0016] Considering parameter uncertainties and external disturbances, the dynamic model of the quadcopter UAV is expressed as follows:

[0017] ;

[0018] in, Indicates the sequence number of the dynamic components, corresponding in order to roll angle, pitch angle, yaw angle, altitude, etc. Direction and position Direction and position; , and They represent the first The state quantities, first-order derivatives, and second-order derivatives of each dynamic component; This represents the coordinate vector of a quadcopter drone. Indicates the first Intermediate control input for each dynamic component; and They represent the first Known nominal state coefficients and known nominal control gains for each dynamic component; Indicates the first Known model terms for each dynamic component; Indicates the first The total matching uncertainty of each dynamic component;

[0019] Total Matching Uncertain Items Construct it according to the following formula:

[0020] ;

[0021] in, Indicates the first Each dynamic component is a regression vector or regression matrix constructed from the state variables of the quadrotor UAV. Indicates the first The unknown equivalent parameter vector of each dynamic component; Indicates the first The parameter uncertainty of each dynamic component; Indicates the first External disturbance terms for each dynamic component; the parameter uncertainty terms and the external disturbance term All are associated with the corresponding intermediate control inputs Matching.

[0022] Furthermore, according to the aforementioned quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation, the quadrotor UAV state vector... and its first derivative Constructing regression vectors or regression matrices ,include:

[0023] and The following two-dimensional equivalent forms are used respectively:

[0024] ;

[0025] in, Indicates the first The velocity-related parameter components of each dynamic component; Indicates the first The bias parameter components of each dynamic component.

[0026] Furthermore, according to the aforementioned quadcopter UAV trajectory tracking method based on fixed-time dual-channel compensation, the definition of the first... Observation error of each dynamic component Based on the dynamic model of quadcopter UAV, Construct a fixed-time total matched uncertainty observer to obtain the estimate of the total matched uncertainty. ,include:

[0027] Definition of the first Observation error of each dynamic component Specifically, it is expressed as follows:

[0028] ;

[0029] in, express Observed values;

[0030] For any scalar and positive numbers Define the sign power function The specific implementation is as follows:

[0031] ;

[0032] in, Represents a symbolic function;

[0033] The fixed-time total matched uncertainty observer is represented as:

[0034] ;

[0035] in, For the first The observation error of each dynamic component; express Observed values; Indicates the first Estimate of the total matching uncertainty of each dynamic component; Indicates the first Known model terms for each dynamic component; , , and All are positive observer gains, where the subscripts are... This indicates the corresponding dynamic component, with subscripts 1 to 4 used to distinguish different error correction terms in the observer; and Let represent the lower-order and higher-order power exponents of the observer, respectively, and satisfy . ; For error powers less than 1, The term represents an error power greater than 1. For error powers less than 1, This is an error term with an error power greater than 1.

[0036] Furthermore, according to the aforementioned quadcopter UAV trajectory tracking method based on fixed-time dual-channel compensation, the... and Filtering is performed to obtain further estimates of the unknown equivalent parameter vector. ,based on and Obtain the estimate of the parameter uncertainty term ,include:

[0037] The regression vector or regression matrix is ​​estimated using a fixed-time filtered parameter estimator. and the estimated value of the total matching uncertainty. Filtering is performed to obtain the filtered regression signals. and filtered output signal And construct the auxiliary filter matrix. and auxiliary filter vector Specifically, it is expressed as follows:

[0038] ;

[0039] in, Indicates the first The filtered regression signal is obtained by filtering the regression vector or regression matrix of each dynamic component; Indicates the first The filtered output signal is obtained by filtering the total matching uncertainty estimate of each dynamic component; Denotes the auxiliary filter matrix, and ; Denotes the auxiliary filter vector, and ; Represents the filter coefficients, and ; Represents an unknown equivalent parameter vector dimensionality;

[0040] according to and Construct parameter estimation error signal Specifically, it is expressed as follows:

[0041] ;

[0042] in, Indicates the first Estimates of the unknown equivalent parameter vector of each dynamic component; Indicates the first The parameter estimation error signal of each dynamic component;

[0043] based on Construct a fixed-time parameter update law The specific implementation is as follows:

[0044] ;

[0045] in, Indicates the first Estimates of the unknown equivalent parameter vector of each dynamic component; Indicates the first Symmetric positive definite adaptive gain matrix of each dynamic component; and They represent the first The low-order parameter estimation gain and high-order parameter estimation gain of each dynamic component, and , subscript Indicates the corresponding dynamic components; and Let represent the lower-order and higher-order power exponents of the parameter update law, respectively, and satisfy . ; for The renewal law, for Earn points And thus obtain the first Estimates of parameter uncertainties for each dynamic component .

[0046] Furthermore, according to the aforementioned quadcopter UAV trajectory tracking method based on fixed-time dual-channel compensation, the step of... and Reconstruct the external disturbance estimate ,include:

[0047] Define external disturbance estimate Specifically, it is expressed as follows:

[0048] ;

[0049] in, Indicates the first External disturbance estimates for each dynamic component; Indicates the first Estimate of the total matching uncertainty of each dynamic component.

[0050] Furthermore, according to the aforementioned quadcopter UAV trajectory tracking method based on fixed-time dual-channel compensation, the step of... and Construct a dual-channel compensation control law to obtain the intermediate control input. ,include:

[0051] The dual-channel compensation control law includes parameter compensation terms. and disturbance compensation items ;

[0052] Definition of the first Trajectory tracking error of each dynamic component and its derivative The specific implementation is as follows:

[0053] ;

[0054] in, Indicates the first Trajectory tracking error of each dynamic component; express The derivative; and They represent the first The actual state of each dynamic component and its first derivative; Indicates the first The expected trajectory signal of each dynamic component. This represents the desired trajectory signal of a quadcopter drone; express The derivative; , and These represent the desired roll angle, desired pitch angle, and desired yaw angle, respectively. , and These represent the desired position in the vertical direction, the desired position in the x-direction, and the desired position in the y-direction, respectively; the subscripts in the symbols This represents the corresponding dynamic component;

[0055] Define fixed-time sliding mode variables Specifically, it is expressed as follows:

[0056] ;

[0057] in, and They represent the first The gain of the lower-order error term and the gain of the higher-order error term of each dynamic component. and ; Indicates the lower-order error power exponent. Denotes the higher-order error power exponent and satisfies ; This is a low-order error term. This is a higher-order error term;

[0058] The disturbance compensation term is constructed based on the estimated external disturbance value, and is specifically expressed as follows:

[0059] ;

[0060] in, Indicates the disturbance compensation term; Indicates the disturbance compensation gain; Indicates the smoothing parameter. , ;

[0061] For the One dynamic component, defining the intermediate control input. Specifically, it is expressed as follows:

[0062] ;

[0063] in, Indicates the first Intermediate control input for each dynamic component; Indicates the first The known nominal control gain of each dynamic component; This represents the nominal control term constructed based on the expected trajectory feedforward term, trajectory tracking error, error derivative, fixed-time sliding mode variable, and fixed-time arrival term; Indicates the first Known model terms for each dynamic component.

[0064] Furthermore, according to the quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation, the nominal control term... Including the The expected trajectory second derivative feedforward term of each dynamic component Compensation terms constructed from trajectory tracking error and its derivative, and fixed-time arrival terms. ;

[0065] The fixed-time arrival item is specifically represented as follows:

[0066] ;

[0067] in, , and They represent the first The first arrival term gain, the second arrival term gain, and the third arrival term gain of each dynamic component; Indicates the exponent of the higher-order arrival term. This represents the power exponent of the lower-order arriving term and satisfies... ; and All are smoothing parameters. and .

[0068] Furthermore, according to the aforementioned quadcopter UAV trajectory tracking method based on fixed-time dual-channel compensation, the step of... Restored to the total thrust of a quadcopter drone The attitude control inputs represent the roll, pitch, and yaw directions, respectively. , , and according to and , , Driving a quadcopter drone to perform desired trajectory tracking flight includes:

[0069] For attitude control input, let:

[0070] ;

[0071] For position control input, define the equivalent thrust amplitude. And cause the total thrust of the quadcopter drone to be input Specifically, it is expressed as follows:

[0072] ;

[0073] ;

[0074] in, , and Representing height, Direction and position Intermediate control input for directional position dynamic components; This represents the equivalent thrust amplitude obtained by synthesizing the intermediate control inputs from three positional directions; This indicates the total thrust input of the quadcopter drone; This represents the given desired yaw angle; and They represent according to , , and The desired roll and pitch angles are recovered; satisfying and .

[0075] The beneficial effects of adopting the above technical solution are as follows:

[0076] (1) Unified attitude and position dynamics modeling and control interface: The attitude dynamics and position dynamics of the quadcopter UAV are uniformly represented as six second-order dynamic components, and the parameter uncertainty and external disturbance terms are jointly constructed into a total matched uncertainty, so that each dynamic component adopts a consistent state, observation, estimation and control interface, reducing the structural differences and interface conversion caused by designing the attitude subsystem and position subsystem separately, and facilitating the coordinated realization of six-degree-of-freedom trajectory tracking control.

[0077] (2) Improve the observation response capability of the total matching uncertainty: Set up low-order error feedback term and high-order error feedback term in the total matching uncertainty observer. The low-order error feedback term is used to improve the estimation convergence process in the small error region, and the high-order error feedback term is used to enhance the error decay capability in the large error region. Under the ideal condition that the change rate of the total matching uncertainty is zero, the observation error can converge to zero in a bounded time independent of the initial state, and enter the bounded neighborhood under the general condition that the change rate of the total matching uncertainty is bounded, thereby improving the response capability to the combined effect of parameter uncertainty and external disturbance.

[0078] (3) Achieve posterior separation of parameter uncertainty and external disturbance: By filtering the total matching uncertainty estimate and the regression signal, the unknown equivalent parameter vector estimate and parameter uncertainty estimate are obtained. Then, the external disturbance estimate is reconstructed using the difference between the total matching uncertainty estimate and the parameter uncertainty estimate, so that the parameter uncertainty factor and the external disturbance factor mixed in the total matching uncertainty can be separated, and corresponding estimation information is provided for the two to form compensation quantities respectively.

[0079] (4) Forming a dual-channel structure in which parameter compensation and disturbance compensation work in parallel: The estimated value of the parameter uncertainty term is used to form the parameter compensation term, and the reconstructed external disturbance estimate is processed continuously and boundedly to form the disturbance compensation term. This allows the two compensation terms to work in parallel on the control law, reducing the burden of a single compensation term handling uncertainties from different sources at the same time, and preventing the external disturbance estimate from directly entering the control input in an unsmoothed form. This reduces the direct impact of the estimation residual on the control input and improves the pertinence of compensation and the robustness of trajectory tracking control.

[0080] (5) Realize the recovery of intermediate control input to actual control input: Through the input recovery relationship, the intermediate control input of the six dynamic components is converted into the total thrust of the quadcopter UAV and the roll, pitch and yaw attitude control input, so that the intermediate control quantity calculated by the controller can match the actual actuator of the quadcopter UAV, solve the problem that the intermediate control input cannot be directly applied to the actual actuator, and improve the feasibility of the trajectory tracking method and the reliability of flight control. Attached Figure Description

[0081] Figure 1 This is a flowchart of a quadcopter UAV trajectory tracking method based on fixed-time dual-channel compensation provided in an embodiment of the present invention;

[0082] Figure 2 This is a schematic diagram of a fixed-time dual-channel compensated trajectory tracking control structure provided in an embodiment of the present invention;

[0083] Figure 3A tracking effect diagram of the expected trajectory and actual trajectory of a quadcopter UAV provided in an embodiment of the present invention;

[0084] Figure 4 The graph shows the variation of tracking error of a quadcopter UAV provided in an embodiment of the present invention. Detailed Implementation

[0085] To describe the present invention in more detail, the technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0086] like Figure 2 As shown, this embodiment obtains the trajectory tracking error based on the desired trajectory signal and actual flight state of the quadcopter UAV; using the flight state variables and intermediate control input of the quadcopter UAV, the estimated value of the total matching uncertainty is obtained through a fixed-time total matching uncertainty observer, and the estimated value of the parameter uncertainty is obtained through a fixed-time filtered parameter estimator; the estimated value of the external disturbance is reconstructed based on the estimated value of the total matching uncertainty and the estimated value of the parameter uncertainty; parameter compensation term and disturbance compensation term are formed based on the estimated value of the parameter uncertainty and the estimated value of the external disturbance, respectively, and the parameter compensation term and disturbance compensation term are input together into a dual-channel compensation control law to obtain the intermediate control input; the obtained intermediate control input is converted into the desired trajectory tracking of the quadcopter UAV by the input recovery module, thereby improving the trajectory tracking accuracy and anti-disturbance capability of the quadcopter UAV.

[0087] The embodiments are only used to illustrate the total thrust and attitude control input of the rotary-wing UAV of the present invention to drive the quadcopter UAV to perform desired trajectory tracking flight.

[0088] The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation, such as Figure 1 As shown, it includes the following steps:

[0089] Step 1: Establish a dynamic model of the quadrotor UAV, and express the sum of parameter uncertainties and external disturbance terms as the total matching uncertainty in the quadrotor UAV dynamic model; based on the quadrotor UAV state vector and its first derivative Constructing regression vectors or regression matrices ;

[0090] Considering parameter uncertainties and external disturbances, the dynamic model of the quadcopter UAV is expressed as follows:

[0091] (1)

[0092] in, Indicates the sequence number of the dynamic components, corresponding in order to roll angle, pitch angle, yaw angle, altitude, etc. Direction and position Direction and position; , and They represent the first The state quantities, first-order derivatives, and second-order derivatives of each dynamic component; Here is the state vector of the quadcopter UAV. This represents the coordinate vector of a quadcopter drone. Indicates the first Intermediate control input for each dynamic component; and They represent the first Known nominal state coefficients and known nominal control gains for each dynamic component; Indicates the first Known model terms for kinetic components, where ,when hour, ; Indicates the first The total matching uncertainty of each dynamic component.

[0093] Total Matching Uncertain Items Construct it in the following form:

[0094] (2)

[0095] in, Indicates the first Each dynamic component is a regression vector or regression matrix constructed from the state variables of the quadrotor UAV; Indicates the first The unknown equivalent parameter vector of each dynamic component; Indicates the first The parameter uncertainty of each dynamic component; Indicates the first External disturbance terms for each dynamic component. The parameter uncertainty term. and the external disturbance term All are associated with the corresponding intermediate control inputs They match and are uniformly constituted as the total matching uncertainty.

[0096] In one implementation, and The following two-dimensional equivalent forms are used respectively:

[0097] (3)

[0098] in, Indicates the first The velocity-related parameter components of each dynamic component; Indicates the first The bias parameter components of each dynamic component. The unknown equivalent parameter vector. It is used to characterize the parameter uncertainty caused by one or more of the following: mass deviation, moment of inertia deviation, damping deviation, or dynamic component control gain deviation.

[0099] Step 2: Define the first Observation error of each dynamic component Based on the dynamic model of quadcopter UAV, Construct a fixed-time total matched uncertainty observer to obtain the estimate of the total matched uncertainty. ;

[0100] Definition of the first Observation error of each dynamic component for:

[0101] (4)

[0102] in, express The observed values.

[0103] To uniformly represent the nonlinear power functions in the subsequent fixed-time total matching uncertainty observer, fixed-time parameter update law, fixed-time sliding mode variable, and fixed-time arrival term, for any scalar and positive numbers Define the symbolic power function as:

[0104] (5)

[0105] in, Represents a symbolic function. When... Acting on vectors At that time, the sign exponentiation operation is performed on each element of the vector, that is, the first element of the resulting vector is the first exponentiation operation. The elements are .

[0106] In one implementation, the fixed-time total matched uncertainty observer is represented as:

[0107] (6)

[0108] in, The first one defined by equation (4) The observation error of each dynamic component, in equations (4) and (6) Representing the same physical quantity; express Observed values; Indicates the first Estimate of the total matching uncertainty of each dynamic component; Indicates the first Known model terms for each dynamic component; , , and All are positive observer gains, where the subscripts are... This indicates the corresponding dynamic component, with subscripts 1 to 4 used to distinguish different error correction terms in the observer; and Let represent the lower-order and higher-order power exponents of the observer, respectively, and satisfy . In the implementation using the fixed-time total matched uncertainty observer shown in equation (6), the above range is the power exponent selection condition for the observer structure. and The specific value can be selected within the range based on the quadcopter UAV model parameters and the desired observation performance. This range is not intended to exclude implementations using other equivalent fixed-time observer structures. Therefore, equation (6) obtains the... Simultaneously, obtain the estimated value of the total matching uncertainty term while observing the velocity state of each dynamic component. The total matching uncertainty estimate is used for subsequent parameter estimation and external disturbance reconstruction.

[0109] Equation (6) in the first observation equation For error powers less than 1, The error term is greater than the power of 1; in the second observation equation For error powers less than 1, This refers to error terms of order greater than 1. Through the combined effect of these error correction terms of different orders, the fixed-time total matched uncertainty observer can ensure that the observation error converges to zero or a bounded neighborhood within a fixed time.

[0110] Step 3: [Regarding...] and the estimated value of the total matching uncertainty. Filtering is performed to obtain further estimates of the unknown equivalent parameter vector. ,based on and Obtain the estimate of the parameter uncertainty term ;

[0111] In one implementation, the regression vector or regression matrix is ​​evaluated using a fixed-time filter parameter estimator. and the estimated value of the total matching uncertainty. Filtering is performed to obtain the filtered regression signals. and filtered output signal And construct the auxiliary filter matrix. and auxiliary filter vector :

[0112] (7)

[0113] in, Indicates the first The filtered regression signal is obtained by filtering the regression vector or regression matrix of each dynamic component; Indicates the first The filtered output signal is obtained by filtering the total matching uncertainty estimate of each dynamic component; Denotes the auxiliary filter matrix, and ; Denotes the auxiliary filter vector, and ; Indicates the filter coefficients; Represents an unknown equivalent parameter vector The dimension of . In the two-dimensional equivalent parametric form shown in equation (3), .

[0114] According to the auxiliary filter matrix Auxiliary filter vector Construct parameter estimation error signal :

[0115] (8)

[0116] in, Indicates the first Estimates of the unknown equivalent parameter vector of each dynamic component; Indicates the first The parameter estimation error signal of each dynamic component.

[0117] Based on the parameter estimation error signal Construct a fixed-time parameter update law:

[0118] (9)

[0119] in, Indicates the first Estimates of the unknown equivalent parameter vector of each dynamic component; Indicates the first Symmetric positive definite adaptive gain matrix of each dynamic component; and They represent the first The low-order parameter estimation gain and high-order parameter estimation gain of each dynamic component; subscript Indicates the corresponding dynamic components; and Let represent the lower-order and higher-order power exponents of the parameter update law, respectively, and satisfy . Equation (9) is the first... Estimated values ​​of the unknown equivalent parameter vector of each dynamic component The update law directly gives the update rate of the parameter estimates. Integrating the update rate yields the result. And then from Get the first Estimates of the parameter uncertainties of each dynamic component.

[0120] From the above Estimated values ​​of unknown equivalent parameter vectors Obtain the estimate of the parameter uncertainty term .

[0121] Step 4: Based on the estimated value of the total matching uncertainty term and the estimated value of the parameter uncertainty term Reconstruct the external disturbance estimate The specific formula is as follows;

[0122] (10)

[0123] in, Indicates the first External disturbance estimates for each dynamic component; Indicates the first The estimated value of the total matching uncertainty of the nth dynamic component. The external disturbance estimate is used to characterize the nth... The external disturbance estimation component is obtained from the total matching uncertainty estimate and the parameter uncertainty estimate in each dynamic component.

[0124] Step 5: Estimate the value based on the uncertainties in the parameters. and the external disturbance estimate Construct a dual-channel compensation control law to obtain the intermediate control input. ;

[0125] The dual-channel compensation control law includes a parameter compensation term and a disturbance compensation term, wherein the parameter compensation term is: The disturbance compensation term is derived from the external disturbance estimate. Constructed .

[0126] Definition of the first Trajectory tracking error of each dynamic component and its derivative for:

[0127] (11)

[0128] in, Indicates the first Trajectory tracking error of each dynamic component; Indicates the first The derivative of the trajectory tracking error of each dynamic component; and They represent the first The actual state of each dynamic component and its first derivative; Indicates the first The expected trajectory signal of each dynamic component. This represents the desired trajectory signal of a quadcopter drone; express The derivative; , and These represent the desired roll angle, desired pitch angle, and desired yaw angle, respectively. , and These represent the desired position in the vertical direction, the desired position in the x-direction, and the desired position in the y-direction, respectively; the subscripts in the symbols This represents the corresponding dynamic component.

[0129] Define fixed-time sliding mode variables for:

[0130] (12)

[0131] in, and They represent the first The gain of the lower-order error term and the gain of the higher-order error term of each dynamic component, subscript This represents the corresponding dynamic component; Indicates the lower-order error power exponent. Denotes the higher-order error power exponent and satisfies ; This is a low-order error term. This is a higher-order error term.

[0132] In one implementation, the disturbance compensation term is constructed based on the external disturbance estimate as follows:

[0133] (13)

[0134] in, Indicates the disturbance compensation term; Indicates the disturbance compensation gain; Indicates the smoothing parameter. , .

[0135] For the The intermediate control input is represented by a dynamic component as follows:

[0136] (14)

[0137] in, Indicates the first Intermediate control input for each dynamic component; Indicates the first The known nominal control gain of each dynamic component; This represents the nominal control term constructed based on the expected trajectory feedforward term, trajectory tracking error, error derivative, fixed-time sliding mode variable, and fixed-time arrival term; Indicates the first Known model terms for each dynamic component; Indicates the parameter compensation term; This indicates the disturbance compensation term.

[0138] In one implementation, the nominal control item Including the The expected trajectory second derivative feedforward term of each dynamic component Compensation terms constructed from trajectory tracking error and its derivative, and fixed-time arrival terms. The fixed-time arrival term can be represented as:

[0139] (15)

[0140] in, , and They represent the first The first arrival term gain, the second arrival term gain, and the third arrival term gain of each dynamic component; Indicates the exponent of the higher-order arrival term. This represents the power exponent of the lower-order arriving term and satisfies... and All are smoothing parameters, among which, Used to ensure low-order arrival items exist There is a definition nearby. Used for consecutive bounded terms Perform smoothing processing.

[0141] Through equation (14), the parameter compensation term and disturbance compensation items They are respectively fed into the control law, forming a dual-channel compensation structure.

[0142] Step 6: Input intermediate control Restored to the total thrust of a quadcopter drone and attitude control input , , And according to the total thrust and attitude control input , , Drive the quadcopter drone to perform desired trajectory tracking flight.

[0143] For attitude control input, let:

[0144] (16)

[0145] in, , and These represent the attitude control inputs in the roll, pitch, and yaw directions, respectively.

[0146] For position control input, define the equivalent thrust amplitude. And cause the total thrust of the quadcopter drone to be input The specific implementation is as follows:

[0147] (17)

[0148] (18)

[0149] in, , and Representing height, Direction and position Intermediate control input for directional position dynamic components; This represents the equivalent thrust amplitude obtained by synthesizing the intermediate control inputs from three positional directions; This indicates the total thrust input of the quadcopter drone; This represents the given desired yaw angle; and They represent according to , , and The desired roll and pitch angles are recovered. To ensure the above input recovery relationship is defined, it should satisfy... and The total thrust and attitude control inputs are applied to the quadcopter drone's actuators, enabling the quadcopter drone to perform flight tracking of the desired trajectory.

[0150] To illustrate the effectiveness of the method of this invention, this embodiment uses numerical simulation to construct a trajectory tracking example for a quadcopter UAV. The simulation time is set to 40 s, and the calculation step size is set to 0.001 s. According to the coordinate vector... The arrangement order is given, and the nominal model parameters are taken as follows: , The unknown equivalent parameter vector is taken as... The desired yaw angle and desired position trajectory are set as follows: , , , Expected roll angle and desired pitch angle The input recovery relationship is obtained online according to equation (18). The initial trajectory tracking error and its derivative are set as follows: , .

[0151] To simulate flight conditions where parameter uncertainties and external disturbances coexist, bounded time-varying external disturbances are applied to the six dynamic components. Definition: ;

[0152] Then according to The arrangement order, with external perturbations set as follows: ;

[0153] Substituting the aforementioned parameters, initial trajectory tracking error and its derivative, and desired trajectory into the dynamic model, total matching uncertainty observer, filter parameter estimator, disturbance reconstruction relation, and dual-channel compensation control law described in this embodiment, numerical solutions are obtained to acquire the actual position trajectory of the quadcopter UAV. The actual position trajectory and desired position trajectory are then plotted in the same three-dimensional coordinate system to obtain... Figure 3 The trajectory tracking effect diagram is shown. Further based on... , , Calculate the trajectory tracking error in three positional directions and display its change process in the first 8 seconds. Figure 4 The tracking error variation graph is shown. Figure 3 and Figure 4 This is used to illustrate the trajectory tracking effect in this embodiment and is not intended to limit the scope of protection of this invention.

[0154] Through the above steps, the present invention can achieve a quadrotor-free technical solution under conditions of parameter uncertainty and external disturbance, rather than limiting it; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the present invention.

Claims

1. A trajectory tracking method for a quadrotor unmanned aerial vehicle based on fixed-time dual-channel compensation, characterized in that, The method includes: A dynamic model of a quadrotor UAV is established, and the sum of parameter uncertainties and external disturbance terms is expressed as the total matching uncertainty in the quadrotor UAV dynamic model; based on the quadrotor UAV state vector and its first derivative Constructing regression vectors or regression matrices ; Definition of the first Observation error of each dynamic component Based on the dynamic model of quadcopter UAV, Construct a fixed-time total matched uncertainty observer to obtain the estimate of the total matched uncertainty. ; right and Filtering is performed to obtain further estimates of the unknown equivalent parameter vector. ,based on and Obtain the estimate of the parameter uncertainty term ; according to and Reconstruct the external disturbance estimate ; according to and Construct a dual-channel compensation control law to obtain the intermediate control input. ; Will Restored to the total thrust of a quadcopter drone The attitude control inputs represent the roll, pitch, and yaw directions, respectively. , , and according to and , , Drive the quadcopter drone to perform desired trajectory tracking flight.

2. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 1, characterized in that, The establishment of a quadcopter UAV dynamic model, and the expression of the sum of parameter uncertainties and external disturbance terms as the total matching uncertainty in the quadcopter UAV dynamic model, includes: Considering parameter uncertainties and external disturbances, the dynamic model of the quadcopter UAV is expressed as follows: ； in, Indicates the sequence number of the dynamic components, corresponding in order to roll angle, pitch angle, yaw angle, altitude, etc. Direction and position Direction and position; , and They represent the first The state quantities, first-order derivatives, and second-order derivatives of each dynamic component; This represents the coordinate vector of a quadcopter drone. Indicates the first Intermediate control input for each dynamic component; and They represent the first Known nominal state coefficients and known nominal control gains for each dynamic component; Indicates the first Known model terms for each dynamic component; Indicates the first The total matching uncertainty of each dynamic component; Total Matching Uncertain Items Construct it according to the following formula: ； in, Indicates the first Each dynamic component is a regression vector or regression matrix constructed from the state variables of the quadrotor UAV. Indicates the first The unknown equivalent parameter vector of each dynamic component; Indicates the first The parameter uncertainty of each dynamic component; Indicates the first External disturbance terms for each dynamic component; the parameter uncertainty terms and the external disturbance term All are associated with the corresponding intermediate control inputs Matching.

3. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 1, characterized in that, The state vector based on quadcopter UAV and its first derivative Constructing regression vectors or regression matrices ,include: and The following two-dimensional equivalent forms are used respectively: ； in, Indicates the first The velocity-related parameter components of each dynamic component; Indicates the first The bias parameter components of each dynamic component.

4. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 2, characterized in that, The definition of the first Observation error of each dynamic component Based on the dynamic model of quadcopter UAV, Construct a fixed-time total matched uncertainty observer to obtain the estimate of the total matched uncertainty. ,include: Definition of the first Observation error of each dynamic component Specifically, it is expressed as follows: ； in, express Observed values; For any scalar and positive numbers Define the sign power function The specific implementation is as follows: ； in, Represents a symbolic function; The fixed-time total matched uncertainty observer is represented as: ； in, For the first The observation error of each dynamic component; express Observed values; Indicates the first Estimate of the total matching uncertainty of each dynamic component; Indicates the first Known model terms for each dynamic component; , , and All are positive observer gains, where the subscripts are... This indicates the corresponding dynamic component, with subscripts 1 to 4 used to distinguish different error correction terms in the observer; and Let represent the lower-order and higher-order power exponents of the observer, respectively, and satisfy . ; For error powers less than 1, The term represents an error power greater than 1. For error powers less than 1, This is an error term with an error power greater than 1.

5. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 3, characterized in that, The pair and Filtering is performed to obtain further estimates of the unknown equivalent parameter vector. ,based on and Obtain the estimate of the parameter uncertainty term ,include: The regression vector or regression matrix is ​​estimated using a fixed-time filtered parameter estimator. and the estimated value of the total matching uncertainty. Filtering is performed to obtain the filtered regression signals. and filtered output signal And construct the auxiliary filter matrix. and auxiliary filter vector Specifically, it is expressed as follows: ； in, Indicates the first The filtered regression signal is obtained by filtering the regression vector or regression matrix of each dynamic component; Indicates the first The filtered output signal is obtained by filtering the total matching uncertainty estimate of each dynamic component; Denotes the auxiliary filtering matrix, and ; Denotes the auxiliary filter vector, and ; Represents the filter coefficients, and ; Represents an unknown equivalent parameter vector dimensionality; according to and Construct parameter estimation error signal Specifically, it is expressed as follows: ； in, Indicates the first Estimates of the unknown equivalent parameter vector of each dynamic component; Indicates the first The parameter estimation error signal of each dynamic component; based on Construct a fixed-time parameter update law The specific implementation is as follows: ； in, Indicates the first Estimates of the unknown equivalent parameter vector of each dynamic component; Indicates the first Symmetric positive definite adaptive gain matrix of each dynamic component; and They represent the first The low-order parameter estimation gain and high-order parameter estimation gain of each dynamic component, and , subscript Indicates the corresponding dynamic components; and Let represent the lower-order and higher-order power exponents of the parameter update law, respectively, and satisfy . ; for The renewal law, for Earn points And thus obtain the first Estimates of parameter uncertainties for each dynamic component .

6. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 4, characterized in that, According to and Reconstruct the external disturbance estimate ,include: Define external disturbance estimate Specifically, it is expressed as follows: ； in, Indicates the first External disturbance estimates for each dynamic component; Indicates the first Estimate of the total matching uncertainty of each dynamic component.

7. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 5, characterized in that, According to and Construct a dual-channel compensation control law to obtain the intermediate control input. ,include: The dual-channel compensation control law includes parameter compensation terms. and disturbance compensation items ; Definition of the first Trajectory tracking error of each dynamic component and its derivative The specific implementation is as follows: ； in, Indicates the first Trajectory tracking error of each dynamic component; express The derivative; and They represent the first The actual state of each dynamic component and its first derivative; Indicates the first The expected trajectory signal of each dynamic component. This represents the desired trajectory signal of a quadcopter drone; express The derivative; , and These represent the desired roll angle, desired pitch angle, and desired yaw angle, respectively. , and These represent the desired position in the vertical direction, the desired position in the x-direction, and the desired position in the y-direction, respectively; the subscripts in the symbols This represents the corresponding dynamic component; Define fixed-time sliding mode variables Specifically, it is expressed as follows: ； in, and They represent the first The gain of the lower-order error term and the gain of the higher-order error term of each dynamic component. and ; Indicates the lower-order error power exponent. Denotes the higher-order error power exponent and satisfies ; This is a low-order error term. This is a higher-order error term; The disturbance compensation term is constructed based on the estimated external disturbance value, and is specifically expressed as follows: ； in, Indicates the disturbance compensation term; Indicates the disturbance compensation gain; Indicates the smoothing parameter. , ; For the One dynamic component, defining the intermediate control input. Specifically, it is expressed as follows: ； in, Indicates the first Intermediate control input for each dynamic component; Indicates the first The known nominal control gain of each dynamic component; This represents the nominal control term constructed based on the expected trajectory feedforward term, trajectory tracking error, error derivative, fixed-time sliding mode variable, and fixed-time arrival term; Indicates the first Known model terms for each dynamic component.

8. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 7, characterized in that, The nominal control item Including the The expected trajectory second derivative feedforward term of each dynamic component Compensation terms constructed from trajectory tracking error and its derivative, and fixed-time arrival terms. ; The fixed-time arrival item is specifically represented as follows: ； in, , and They represent the first The first arrival term gain, the second arrival term gain, and the third arrival term gain of each dynamic component; Indicates the exponent of the higher-order arrival term. This represents the power exponent of the lower-order arriving term and satisfies... ; and All are smoothing parameters. and .

9. The quadrotor UAV trajectory tracking method based on fixed-time dual-channel compensation according to claim 8, characterized in that, The Restored to the total thrust of a quadcopter drone The attitude control inputs represent the roll, pitch, and yaw directions, respectively. , , and according to and , , Driving a quadcopter drone to perform desired trajectory tracking flight includes: For attitude control input, let: ； For position control input, define the equivalent thrust amplitude. And cause the total thrust of the quadcopter drone to be input Specifically, it is expressed as follows: ； ； in, , and Representing height, Direction and position Intermediate control input for directional position dynamic components; This represents the equivalent thrust amplitude obtained by synthesizing the intermediate control inputs from three positional directions; This indicates the total thrust input of the quadcopter drone; This represents the given desired yaw angle; and They represent according to , , and The desired roll and pitch angles are recovered; satisfying and .

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