Quadrotor unmanned aerial vehicle nonsingular terminal sliding mode formation control method under limited input

Abstract

The invention discloses a quadrotor unmanned aerial vehicle nonsingular terminal sliding mode formation control method under input limitation, relates to the technical field of unmanned aerial vehicle control, and aims to solve the problems of low trajectory tracking and formation control precision, poor stability, buffeting and the like of a quadrotor unmanned aerial vehicle under the conditions of actuator saturation, parameter uncertainty and external interference. The method comprises the following steps: 1) establishing a four-rotor unmanned aerial vehicle second-order kinetic model under limited input, and considering speed instruction amplitude limit; 2) designing a nonsingular terminal sliding mode function based on an exponential reaching law, and ensuring that the system is converged in finite time and has no singular point; 3) introducing a unit vector control method to suppress sliding mode switching buffeting; 4) adopting an RBF neural network to approach to input saturation error and unknown interference; 5) designing an adaptive law to update control parameters online and compensate time-varying characteristics of the parameters; and 6) based on a navigation-following model, expanding to a self-adaptive global rapid nonsingular terminal sliding mode formation control method.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, specifically to a sliding mode control method for a non-singular terminal of a quadrotor UAV under input constraints. It is applicable to high-precision trajectory tracking of a single UAV and swarm control of multiple UAVs, and is particularly suitable for complex scenarios with actuator saturation, time-varying parameters, and external disturbances. Background Technology

[0002] Quadrotor UAVs, due to their high maneuverability and flexible takeoff and landing, have been widely used in military and civilian fields such as battlefield surveillance, fire rescue, and environmental detection. However, in actual control systems, input limitations caused by actuator saturation (such as motor speed limits and thrust amplitude constraints) can seriously affect control accuracy and system stability. At the same time, traditional sliding mode control has defects such as obvious chattering, slow convergence speed, and singularities in terminal sliding mode. In addition, the uncertainty of UAV dynamic parameters and external disturbances (such as airflow disturbances) further exacerbate the control difficulty.

[0003] Existing technologies include backstepping methods for UAV hovering control under input saturation, but these do not consider the rapid convergence of trajectory tracking. Some methods compensate for parameter uncertainty through adaptive control, but fail to effectively suppress sliding mode chattering. While RBF neural networks possess universal approximation properties, their application in saturation error compensation under input-constrained scenarios still requires optimization. In multi-UAV formation control, it is difficult to simultaneously achieve rapid convergence and global stability in the leader-follower model. Therefore, a quadrotor UAV control method that can simultaneously address input constraints, chattering suppression, rapid convergence, and parameter adaptation is urgently needed.

[0004] The technical problem to be solved by this invention:

[0005] 1. Input limitation caused by actuator saturation in quadcopter drones affects the execution effect of control commands;

[0006] 2. Chattering problem and singularity problem in terminal sliding mode of traditional sliding mode;

[0007] 3. Insufficient robustness due to time-varying system parameters and external disturbances;

[0008] 4. The contradiction between rapid convergence and global stability in multi-UAV formation control.

[0009] A search revealed application publication number CN116088548B, which discloses a method for attitude control of a quadrotor UAV based on fast non-singular terminal sliding mode. The method includes the following steps: constructing a mathematical model of the quadrotor UAV; designing an integral terminal sliding mode function to eliminate steady-state errors and achieve finite-time convergence; designing an online adaptive estimation law to compensate for parameter uncertainties and unknown external disturbances; and designing controller parameters γ. φ1 γθ1 and γ ψ1 The selection criteria are as follows. The attitude control method for quadrotor UAVs provided by this invention employs a fast non-singular terminal sliding function with an integral element, which can effectively improve tracking accuracy while maintaining a fast response speed. This method uses an adaptive estimation law to update the control gain online, which eliminates the requirement for upper bound information on disturbances. This invention achieves dynamic adjustment of the control parameters in the sliding mode function, thus simplifying the parameter tuning process to obtain the desired tracking performance while moderately controlling chattering.

[0010] 1. Compared with patent CN116088548B, which only addresses the attitude control of UAVs and does not involve the problem of input limitation (actuator saturation), this invention specifically addresses the formation control of UAVs as point masses and considers the speed command amplitude limitation and actuator saturation characteristics. It uses RBF neural network to approximate the saturation error and specifically solves the control performance degradation caused by input limitation.

[0011] 2. Compared with the integrated terminal sliding mode function used in patent CN116088548B, although it can eliminate steady-state error, it does not optimize the chattering suppression effect. This invention introduces the unit vector control method to replace the sign function, suppressing the chattering amplitude within an acceptable engineering range.

[0012] 3. Compared with patent CN116088548B, which does not extend to multi-UAV formation control, this invention is based on the leader-follower model and designs a global fast non-singular terminal sliding surface, taking into account both the fast convergence and global stability of the formation system.

[0013] 4. Compared with the adaptive law of patent CN116088548B which only updates the control gain, the adaptive law of this invention updates the weights of the RBF neural network and the upper bound of the approximation error simultaneously, providing more comprehensive compensation for time-varying parameters and unknown disturbances. Summary of the Invention

[0014] This invention aims to solve the problems of the prior art. Through a technical approach of "modeling, sliding mode surface design, chatter suppression, adaptive compensation, and formation control," a sliding mode formation control method for non-singular terminals of quadrotor UAVs under input constraints is proposed. The technical solution of this invention is as follows:

[0015] A method for sliding mode formation control of a quadrotor UAV under input constraints without singular terminal involvement includes the following steps:

[0016] S1: Establish a dynamic model of a quadcopter UAV under input constraints. The model considers the speed command amplitude limitation, and the expression is:

[0017]

[0018]

[0019] in, This is the current location of the drone. At the current speed, To control the gain, Accelerate the drone For the drone's velocity vector, For the acceleration vector of the drone;

[0020] S2: Define position tracking error , Design a non-singular terminal sliding mode function for the desired position:

[0021]

[0022] in, , For sliding mode parameters, For terminal index, ;

[0023] S3: Based on the exponential reaching law, a preliminary sliding mode control law is designed, and a unit vector control method is introduced to suppress system chattering. The reaching law expression is:

[0024]

[0025] in, For the gain of the reaching law, These are the parameters for chatter suppression. For sign functions, through unit vectors Approximate substitution sign function; It is a tiny constant;

[0026] S4: Using an RBF neural network to approximate the input saturation error and unknown interference terms. , Let be a saturation function, and let the neural network output be... , The weight matrix, These are radial basis functions;

[0027] S5: Design an adaptive law for online updating of the weights and control parameters of the RBF neural network. The adaptive law expression is:

[0028]

[0029] in, This is the adaptive gain matrix. The attenuation coefficient;

[0030] S6: Substitute the RBF neural network output and the adaptive law into the sliding mode control law, and derive the final control law through the error dynamics relationship.

[0031] Furthermore, it also includes extended steps for multi-drone swarm control:

[0032] S7: Employs a navigator-follower model, defining aircraft 0 as the navigator, i.e., its trajectory is known: position. ,speed acceleration , No. Position error of the follower Speed ​​error ,in The desired distance between the follower and the navigator. Let be the current position vector of the i-th follower. .

[0033] S8: Design a global fast non-singular terminal sliding surface:

[0034]

[0035] in, To approximate the error compensation coefficient, This is the upper bound estimate of the approximation error of the RBF neural network. Let be the globally fast nonsingular terminal sliding surface of the i-th follower. Let p be the p-th power of the position error of the i-th follower.

[0036] S9: Design of formation adaptive control law based on sliding mode arrival conditions, including RBF weight update law and approximation error upper bound estimation law, where the RBF weight update law refers to the law based on sliding mode variables. and radial base The designed adaptive rule is used to adjust the weight matrix of the i-th follower RBF neural network online. This improves the approximation accuracy of saturation error and unknown disturbances. The upper bound estimation law of approximation error refers to the adaptive rule for online estimation of the upper bound of the approximation error of the i-th follower RBF neural network. This error is compensated for to ensure the stability of the formation system.

[0037] Furthermore, in step S6, the output of the RBF neural network and the adaptive law are substituted into the sliding mode control law, and the final control law is derived through the error dynamics relationship. The specific derivation process is as follows:

[0038] The first step is to define the error. Taking the second derivative with respect to time, we obtain the error dynamics equation: After sorting, we can obtain For the desired position vector, This is the current position vector of the drone. For the desired acceleration vector, , These are the derivatives of the desired velocity and the second derivative of the error, respectively.

[0039] The second step is to transform the dynamic model in step S1. Combining this with the above error dynamics equation, we can eliminate... get: Preliminary sorting of control input The expression is: ;

[0040] The third step is to refine the sliding mode function designed in step S2. Taking the derivative, we get ;

[0041] The fourth step is to apply the reaching law based on the unit vector improvement in step S3. Substituting the values ​​into the equation, we get: Organize and solve Related items: ;

[0042] Fifth step: Introduce the saturation error compensation term from the RBF neural network approximation in step S4. Considering compensation for unknown interference under input constraints, the various relations are substituted into the initially sorted... The expression, ultimately derived, yields:

[0043]

[0044] in, , These are the derivative of the desired velocity and the second derivative of the error, respectively.

[0045] Furthermore, the input restrictions in step S1 include speed command amplitude restrictions. In response to the actuator saturation characteristics, the dynamic model modifies the traditional second-order model to match the actual control scenario;

[0046] In step S3, the unit vector control method is used... Substitution symbol function ,in (0, 0.1], achieving jitter amplitude suppression within Within the range.

[0047] Furthermore, in step S4, the radial basis function of the RBF neural network is a Gaussian function. ,in As cluster center, For the width parameter, the network input .

[0048] Furthermore, in step S9, the formation adaptive control law is implemented using a Lyapunov function. Derivation, Let i be the Lyapunov function of the i-th follower. Let i be the sliding surface variable of the i-th follower. Let be the weight matrix of the RBF neural network for the i-th follower. Let be the adaptive gain matrix of the i-th follower. Let be the upper bound estimate of the approximation error of the RBF neural network for the i-th follower. The specific derivation process is as follows:

[0049] The first step is to clarify the relationship between the derivatives of the formation sliding mode variables and the error: based on the formation sliding mode surface Differentiate, and we get ,in , ;

[0050] The second step is to substitute the follower dynamics model. , To follow the speed of the machine, As the input for the follower's acceleration control, combined with the navigator's trajectory information. Organized ;

[0051] The third step is to design the formation sliding mode convergence law. , For the RBF neural network approximation term of the i-th follower, it is compared with the above... Expressions combined;

[0052] The fourth step is to modify the Lyapunov function. Differentiate: ,in , ;

[0053] Fifth step, to make To ensure asymptotic stability of the system, substitute... , , Design a follower weight update law for the input of a follower neural network. Estimation law of upper bound of approximation error Finally, the adaptive control law for the formation was derived. ;

[0054] Through the above derivation, ensure Negative definite, the system is asymptotically stable.

[0055] Furthermore, an indoor optical positioning system experimental platform was established with a Simulink control module for indoor small UAVs, enabling five-UAV trajectory tracking and formation control. The specific method is as follows:

[0056] First, an optical positioning system is used to perform real-time pose estimation for multiple small UAVs, obtaining their three-dimensional position and velocity information. Second, a trajectory tracking control algorithm is designed and implemented in the Matlab / Simulink environment, taking the real-time pose information as input and outputting the desired velocity control command. Finally, the control command is transmitted to the UAVs via a wireless communication module to complete flight control.

[0057] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements a sliding mode formation control method for a quadcopter unmanned aerial vehicle under input constraints as described in any one of the above.

[0058] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a non-singular terminal sliding mode formation control method for a quadrotor unmanned aerial vehicle under input constraints as described in any one of the claims.

[0059] A computer program product includes a computer program that, when executed by a processor, implements a non-singular terminal sliding mode formation control method for a quadrotor unmanned aerial vehicle under input constraints as described in any one of the claims.

[0060] The advantages and beneficial effects of this invention are as follows:

[0061] 1. Solving the problem of limited input: By approximating the saturation error through an RBF neural network, the control performance degradation caused by actuator saturation is effectively compensated, thereby improving system safety;

[0062] 2. Suppressing chattering and avoiding singularities: The unit vector control method keeps chattering amplitude within an acceptable range, and the non-singular terminal sliding mode function avoids the singularity problem of traditional methods;

[0063] 3. Fast convergence and global stability: The exponential approach law combined with the terminal term achieves finite-time convergence, while the linear term ensures the global stability of the system;

[0064] 4. Strong robustness: The adaptive law updates parameters in real time, and the RBF neural network compensates for unknown disturbances and time-varying parameters, maintaining high-precision control even under airflow disturbances and parameter perturbation scenarios;

[0065] 5. Strong engineering practicality: The model is simplified and reasonable, the control law calculation is small, and it can be directly deployed on mainstream flight controllers such as Pixhawk. It can be experimentally verified by Rflysim simulation and indoor optical positioning or outdoor RTK positioning. The trajectory tracking error is less than 0.1m and the formation holding error is less than 0.2m.

[0066] 1. S3 (Unit Vector Control Method) of claim 1: Conventional chattering suppression uses the boundary layer method, which sacrifices control accuracy. This invention uses unit vector control... The alternative sign function, which suppresses chattering while maintaining the robustness of sliding mode control, requires a balance between chattering amplitude and convergence speed, and cannot be directly replaced by conventional methods.

[0067] 2. S4-S5 (RBF + Adaptive Law) of claim 1: Conventional RBF is only used for disturbance approximation. This invention extends it to input saturation error approximation. The adaptive law updates the weights and control parameters at the same time. It is necessary to combine error dynamics and Lyapunov stability derivation. The design complexity is higher than that of conventional adaptive sliding mode.

[0068] 3. S8 (Global Fast Non-Singular Terminal Sliding Surface) of claim 2: The upper bound estimation term for the unfused approximation error of the conventional formation sliding surface is introduced in this invention. Error compensation is achieved through linear terms. To ensure overall stability, it is necessary to balance formation consistency and finite-time convergence, and the design approach is an unconventional combination.

[0069] 4. Lyapunov function design of claim 6: The conventional Lyapunov function only contains sliding mode variables and weights; this invention adds an upper bound estimation term for the approximation error. The negative definite conditions of the coupling terms need to be derived, and the derivation process is not based on conventional stability analysis. Attached Figure Description

[0070] Figure 1 This is a flowchart of a preferred embodiment of the sliding mode formation control method for a quadrotor UAV under input constraints provided by the present invention.

[0071] Figure 2 It is a drone trajectory tracking and control module built in Matlab / Simulink.

[0072] Figure 3 These are the sliding mode variables of the UAV in three directions.

[0073] Figure 4 It is the error variable of the drone.

[0074] Figure 5 It is a verification of single-unit circular trajectory tracking of unmanned aerial vehicles.

[0075] Figure 6 This is the experimental effect of a figure-eight trajectory simulation using Rflysim3D on a drone;

[0076] Figure 7 This is a diagram showing the actual effect of controlling a five-machine circular formation, as recorded by an optical motion capture system. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0078] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0079] 1. System parameter calibration

[0080] Taking a small to medium-sized quadcopter drone as an example, the parameters are set as follows:

[0081] Dynamic parameters: (Control gain) m / s (speed limit value);

[0082] Sliding mode parameters: , , , , , ;

[0083] RBF neural network parameters: 15 hidden layer nodes, cluster centers Evenly distributed in Width parameter ;

[0084] Adaptive parameters: (Identity matrix) , .

[0085] 2. Control Flow Implementation

[0086] Step 1: Initialize the drone position ,speed Expected trajectory (e.g., figure-eight trajectory, circular trajectory);

[0087] Step 2: Real-time calculation of position error With error derivative ;

[0088] Step 3: Calculate the sliding mode function With the law of convergence ;

[0089] Step 4: Calculate using RBF neural network Update adaptive weights upper bound of error ;

[0090] Step 5: Calculate the acceleration command based on the control law. The output is sent to the actuator (motor);

[0091] Step 6: When in multi-aircraft formation, the follower aircraft receives the position information of the navigator aircraft and calculates the formation error. , Repeat Steps 2-5 to achieve formation control.

[0092] 3. Experimental Verification

[0093] (1) Simulation experiment (based on Rflysim platform)

[0094] Simulation environment: CopterSim dynamic model + Rflysim3D 3D display + QGroundControl ground station;

[0095] Experimental scenarios: single UAV figure-eight trajectory tracking, five UAVs in circular formation;

[0096] Results: Position tracking error of a single UAV m, the chattering amplitude is reduced by 60% compared to traditional sliding mode; five-aircraft formation maintains error m, convergence time less than 2s.

[0097] (2) Practical experiment (based on indoor optical positioning system)

[0098] Experimental platform: Phase One X150 quadcopter UAV, indoor infrared positioning system (positioning accuracy ±0.02m);

[0099] Result: Tracking error of the figure-eight trajectory on actual machine Under limited input conditions, the method exhibited no instability and demonstrated stable formation flight, thus verifying its engineering feasibility.

[0100] 4. Stability Analysis

[0101] Define Lyapunov functions:

[0102]

[0103] in, ( (This is the upper bound of the ideal error). By differentiating and substituting the results into the control law and the adaptive law, we can obtain... ( , (where is a constant), according to Lyapunov stability theory, the system is uniformly eventually bounded, i.e. , , All converge to a bounded region near the origin.

[0104] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0105] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0106] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0107] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for sliding mode formation control of a quadrotor unmanned aerial vehicle (UAV) under input constraints without a singular terminal, characterized in that, Includes the following steps: S1: Establish a dynamic model of a quadcopter UAV under input constraints. The model considers the speed command amplitude limitation, and the expression is: in, This is the current location of the drone. At the current speed, To control the gain, Accelerate the drone For the drone's velocity vector, For the acceleration vector of the drone; S2: Define position tracking error , Design a non-singular terminal sliding mode function for the desired position: in, , For sliding mode parameters, For terminal index, ; S3: Based on the exponential reaching law, a preliminary sliding mode control law is designed, and a unit vector control method is introduced to suppress system chattering. The reaching law expression is: in, For the gain of the reaching law, These are the parameters for chatter suppression. For sign functions, through unit vectors Approximate substitution sign function; It is a tiny constant; S4: Using an RBF neural network to approximate the input saturation error and unknown interference terms. , Let be a saturation function, and let the neural network output be... , The weight matrix, These are radial basis functions; S5: Design an adaptive law for online updating of the weights and control parameters of the RBF neural network. The adaptive law expression is: in, This is the adaptive gain matrix. The attenuation coefficient; S6: Substitute the RBF neural network output and the adaptive law into the sliding mode control law, and derive the final control law through the error dynamics relationship.

2. The input-constrained sliding mode formation control method for quadrotor UAVs under non-singular terminal conditions according to claim 1, characterized in that, It also includes extended steps for multi-drone swarm control: S7: Employs a navigator-follower model, defining aircraft 0 as the navigator, i.e., its trajectory is known: position. ,speed acceleration , No. Position error of the follower Speed ​​error ,in The desired distance between the follower and the navigator. Let be the current position vector of the i-th follower. ; S8: Designing Global Fast Non-Singular Terminal Sliding Surfaces: in, To approximate the error compensation coefficient, This is the upper bound estimate of the approximation error of the RBF neural network. Let be the globally fast nonsingular terminal sliding surface of the i-th follower. Let p be the p-th power of the position error of the i-th follower. S9: Design of formation adaptive control law based on sliding mode arrival conditions, including RBF weight update law and approximation error upper bound estimation law, where the RBF weight update law refers to the law based on sliding mode variables. and radial basis functions The designed adaptive rule is used to adjust the weight matrix of the i-th follower RBF neural network online. This improves the approximation accuracy of saturation error and unknown disturbances. The upper bound estimation law of approximation error refers to the adaptive rule for online estimation of the upper bound of the approximation error of the i-th follower RBF neural network. This error is compensated for to ensure the stability of the formation system.

3. The input-constrained sliding mode formation control method for quadrotor UAVs under non-singular terminal conditions according to claim 1, characterized in that, S6 substitutes the RBF neural network output and the adaptive law into the sliding mode control law, and derives the final control law through the error dynamics relationship. The specific derivation process is as follows: The first step is to define error. Taking the second derivative with respect to time, we obtain the error dynamics equation: After sorting, we can obtain For the desired position vector, This is the current position vector of the drone. For the desired acceleration vector, , These are the derivatives of the desired velocity and the second derivative of the error, respectively. The second step is to transform the dynamic model in step S1. Combining this with the above error dynamics equation, we can eliminate... get: Preliminary sorting of control input The expression is: ; The third step is to refine the sliding mode function designed in step S2. Taking the derivative, we get ; The fourth step is to apply the convergence law based on the unit vector improvement in step S3. Substituting the values ​​into the equation, we get: Organize and solve Related items: ; Fifth step: Introduce the saturation error compensation term from the RBF neural network approximation in step S4. Considering compensation for unknown interference under input constraints, the various relations are substituted into the initially organized... The expression, ultimately derived, yields: in, , These are the derivative of the desired velocity and the second derivative of the error, respectively.

4. The input-constrained sliding mode formation control method for quadrotor UAVs under non-singular terminal conditions according to claim 1, characterized in that, The input restrictions in step S1 include speed command amplitude restrictions. In response to the actuator saturation characteristics, the dynamic model modifies the traditional second-order model to match the actual control scenario; In step S3, the unit vector control method is used... Substitution symbol function ,in (0, 0.1], achieving jitter amplitude suppression within Within the range.

5. The input-constrained sliding mode formation control method for quadrotor UAVs under non-singular terminal conditions according to claim 1, characterized in that, In step S4, the radial basis function of the RBF neural network is a Gaussian function. ,in As cluster center, For the width parameter, the network input .

6. The input-constrained sliding mode formation control method for quadrotor UAVs under non-singular terminal conditions according to claim 2, characterized in that, In step S9, the formation adaptive control law is implemented using the Lyapunov function. Derivation, Let i be the Lyapunov function of the i-th follower. Let i be the sliding surface variable of the i-th follower. Let be the weight matrix of the RBF neural network for the i-th follower. Let be the adaptive gain matrix of the i-th follower. Let be the upper bound estimate of the approximation error of the RBF neural network for the i-th follower. The specific derivation process is as follows: The first step is to clarify the relationship between the derivatives of the formation sliding mode variables and the error: based on the formation sliding mode surface Differentiate, and we get ,in , ; The second step is to substitute the follower dynamics model. , To follow the speed of the machine, As the input for the follower's acceleration control, combined with the navigator's trajectory information. Organized ; The third step is to design the formation sliding mode convergence law. , For the RBF neural network approximation term of the i-th follower, it is compared with the above... Expressions combined; The fourth step is to modify the Lyapunov function. Differentiate: ,in , ; Fifth step, to make To ensure asymptotic stability of the system, substitute... , , Design a follower weight update law for the input of a follower neural network. Estimation law of upper bound of approximation error Finally, the adaptive control law for the formation was derived. ; Through the above derivation, ensure Negative definite, the system is asymptotically stable.

7. The input-constrained sliding mode formation control method for quadrotor UAVs under non-singular terminal conditions according to claim 6, characterized in that, A Simulink control module for indoor small UAVs was established based on an indoor optical positioning system experimental platform to achieve five-UAV trajectory tracking and formation control. The specific method is as follows: First, an optical positioning system is used to perform real-time pose estimation for multiple small UAVs, obtaining their three-dimensional position and velocity information. Second, a trajectory tracking control algorithm is designed and implemented in the Matlab / Simulink environment, taking the real-time pose information as input and outputting the desired velocity control command. Finally, the control command is transmitted to the UAVs via a wireless communication module to complete flight control.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the input-constrained non-singular terminal sliding mode formation control method for quadrotor UAVs as described in any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the input-constrained non-singular terminal sliding mode formation control method for quadrotor UAVs as described in any one of claims 1 to 7.

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