Quadrotor unmanned aerial vehicle control method integrating terminal-constraint-free model predictive control and sliding mode control

Abstract

The invention relates to a quad-rotor unmanned aerial vehicle control method integrating terminal-constraint-free model predictive control and sliding-mode control, and the method comprises the steps: building a nonlinear dynamic model of a quad-rotor unmanned aerial vehicle, setting a reference trajectory of the quad-rotor unmanned aerial vehicle, building a nominal error model based on the reference trajectory, and carrying out the prediction control of the quad-rotor unmanned aerial vehicle. The method comprises the steps of defining an implicit SMC control law for designing an MPC terminal cost function, defining an explicit SMC control law for controlling a real quadrotor system, initializing parameters of an MPC controller, calculating a terminal penalty matrix based on the implicit SMC control law, obtaining the MPC terminal cost function, and obtaining an optimal state trajectory of a quadrotor unmanned aerial vehicle nominal system. And the reference trajectory is transmitted to the explicit SMC controller so as to realize the tracking of the real four-rotor system on the set reference trajectory. According to the method, the calculation burden of a traditional MPC controller is relieved, and the real-time operation capability of the quad-rotor unmanned aerial vehicle is effectively improved while high control precision is kept.

Description

Technical Field

[0001] This invention relates to the field of quadrotor unmanned aerial vehicle (UAV) flight control application technology, and in particular to a quadrotor UAV control method that integrates terminal constraint-free model predictive control and sliding mode control. Background Technology

[0002] As a typical underactuated, strongly coupled, and unstable nonlinear system, the flight control of quadcopter drones is the core foundation for achieving autonomous flight. With the deepening application of drones in complex scenarios such as industrial inspection, precision agriculture, and emergency rescue, extremely high demands are placed on the accuracy, robustness, and adaptability of their control. Quadrotor control systems typically employ a cascaded control structure, consisting of inner-loop attitude control and outer-loop position control, to cope with their complex dynamic characteristics and changing external environments.

[0003] In the field of UAV control, proportional-integral-derivative (PID) control and its variants have been widely used in early UAVs and commercial systems due to their simple structure and ease of implementation. However, PID control has limitations when facing model uncertainties, external disturbances (such as wind disturbances), and dynamic tasks. Its adjustment capability is limited, and parameter tuning relies on experience, making it difficult to maintain optimal performance across the entire flight envelope. To improve control quality, model-based control methods such as linear quadratic regulators (LQR) and model predictive control (MPC) are increasingly being used. LQR achieves optimal control through state feedback, but relies on an exact linearized model of the system, resulting in poor robustness to nonlinear dynamics and sudden disturbances. MPC, on the other hand, utilizes rolling optimization and feedback correction, enabling explicit handling of state and input constraints, making it more suitable for trajectory tracking and disturbance rejection scenarios. However, it has a high computational burden, posing a challenge to the real-time performance of airborne processors. Addressing model uncertainties and strong nonlinearities, active disturbance rejection control (ADRC) significantly improves the adaptability and robustness of the control system under unknown dynamics and disturbances by estimating and compensating for internal and external disturbances in real time, and has been widely used in high-end UAV systems in recent years. Meanwhile, sliding mode control (SMC) has attracted attention due to its strong robustness under matching uncertainties, but its inherent chattering problem is detrimental to the smooth operation of actuators, requiring the use of filtering techniques or higher-order sliding modes for suppression. Currently, research on UAV control algorithms is further developing towards adaptive control and learning-based control. For example, intelligent adaptive systems combining neural networks, fuzzy logic, and traditional control methods can adjust controller parameters and even the structure online to adapt to unknown environments and dynamic system changes. Furthermore, reinforcement learning methods, through interaction with the environment, autonomously learn control strategies, providing new insights for the stable control of UAVs in completely unknown or highly dynamic environments. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a quadrotor UAV control method that integrates terminal-constrained model predictive control and sliding mode control. This method solves the problem of poor real-time performance caused by the large computational burden of traditional MPC-based UAV control methods, as well as the problem of poor mechanism smoothness adaptability caused by chattering in sliding mode control (SMC) methods used to alleviate model uncertainty, which requires filtering techniques or higher-order sliding modes for suppression.

[0005] To address the aforementioned technical problems, this invention provides the following technical solution: a quadrotor unmanned aerial vehicle (UAV) control method integrating unconstrained model predictive control and sliding mode control, comprising the following steps: S1. Establish a nonlinear dynamic model of the quadcopter UAV and set the system state constraints and control input constraints of the nonlinear dynamic model; S2. Set the reference trajectory of the quadcopter UAV and derive the reference trajectory for yaw angle, surge speed, yaw speed and yaw rate; S3. Define the nominal system of the quadcopter UAV, derive the nominal error model for MPC controller optimization based on the trajectory of yaw angle, surge speed, yaw speed, yaw rate and its corresponding reference trajectory, and obtain the error status; S4. Based on the error state, define the implicit SMC control law for designing the MPC terminal cost function, and define the explicit SMC control law for controlling the real quadcopter system. S5. Initialize the parameters of the MPC controller, including the prediction time domain. Sampling interval State weight matrix Control weight matrix And calculate the terminal penalty matrix based on the implicit SMC control law. Construct the final terminal penalty matrix Obtain the MPC terminal cost function ; S6, for the current sampling time , with its error state As the initial state, the MPC controller is used in the time domain. The internal algorithm solves the MPC optimization problem based on the nominal error model, and calculates the optimal state trajectory and optimal control input of the quadrotor UAV nominal system as the MPC nominal signal. S7. Transmit the calculated MPC nominal signal to the explicit SMC control law of the explicit SMC controller; S8. The explicit SMC controller uses the received MPC nominal signal as a reference target, calculates the robust control input for the real quadcopter system based on the explicit SMC control law, drives the real system state to track the optimal state trajectory generated by the MPC controller, and then tracks the reference trajectory of the set quadcopter UAV. S9. Wait for the next sampling moment, and repeat steps S3-S5 to perform rolling optimization and feedback control.

[0006] Furthermore, in step S1, the specific process includes the following steps: S11. The nonlinear dynamic model of the quadcopter UAV is constructed as follows: ; in For rotation matrix, Indicated by angle Rotate. Yaw angle; The system dynamics matrix; The input gain matrix; , , They represent , , For time The first derivative, The system state vector is represented by the pose vector. and velocity vector Composition; Pose Vector Including lateral position Longitudinal position and yaw angle velocity vector Including surge speed sway speed and yaw rate ; It is the control torque, which serves as the control input vector; For disturbance; S12, Set system state constraints and control input constraints ,in For the system state set, To control the input set.

[0007] Furthermore, in step S2, the specific process includes the following steps: S21. Setting up a quadcopter drone based on time. Reference trajectory : ; in , They represent time-based The lateral position reference trajectory and the longitudinal position reference trajectory; S22, based on Derivation of the yaw angle in the nonlinear dynamic model Surge speed sway speed yaw rate Based on time Reference trajectory , , , : ; ; ; ; in, This represents the arctangent function operation. , They represent , for time The first derivative, , They represent , For time The second derivative.

[0008] Furthermore, the reference trajectory of the quadcopter UAV is designed to satisfy the system state constraints and control input constraints of the nonlinear dynamics model.

[0009] Furthermore, in step S3, the specific process includes the following steps: S31. Define the nominal system for quadcopter unmanned aerial vehicles. , denoted as: ; in The nominal state, i.e., without disturbance. state, For nominal control input, For the system model, that is, the disturbance in the nonlinear dynamic model of the quadcopter UAV in step S11. Ignore the obtained model; S32. Obtain the nominal error model by combining each reference trajectory. , denoted as: ; in Represents the nominal error system model; error state , As a reference state, the nominal error system control input , As reference control input, nominal speed error Three-dimensional velocity vector Due to surge speed sway speed and yaw rate trajectory , , Combining and transposing, a three-dimensional velocity reference vector Due to surge speed sway speed and yaw rate Reference trajectory , , Composed of splicing and transposition, nominal yaw angle error , The trajectory representing the yaw angle. The reference trajectory representing the yaw angle. Indicates the time.

[0010] Furthermore, in step S4, the specific process includes the following steps: S41. Define the implicit SMC control law. for: ; in Represents linear state gain. This is an error state. Indicates the switching function, Here is the sliding coefficient matrix. This represents the structure of the sliding coefficient matrix. The row vector, For the control matrix, Positive switching gain, This represents the operation of finding the inverse matrix; S42. Define the explicit SMC control law. for: ; in As an auxiliary sliding mode variable, it is defined as follows: , For sliding mode variables, Represents sliding mode variable For time The first derivative, Represents the sliding coefficient matrix. express The inverse matrix; and These represent the optimal state trajectory and optimal control input obtained by solving the MPC optimization problem, respectively. It is by The optimal vector composed of the first three dimensions, express For time The first derivative, express For time The first derivative, Represents the trajectory of the pose vector. The maximum value of the disturbance. The trajectory is the yaw angle. To achieve the optimal yaw angle, The system dynamics matrix, For the input gain matrix, For rotation matrix, express transpose, express The first derivative of the parameter within the parentheses, This is the symbol for the 2-norm.

[0011] Furthermore, the calculation of the terminal penalty matrix based on the implicit SMC control law in step S5... Construct the final terminal penalty matrix Obtain the MPC terminal cost function The specific process includes the following steps: S51, Nominal error model The system matrix is ​​obtained by linearization near the equilibrium point. and control matrix ; S52, Linear State Gain Based on Implicit SMC Control Law and system matrix and control matrix Obtain the closed-loop system matrix ,in The poles are set to be less than or equal to 0 to obtain a linear state gain. ; S53. Based on SMC sliding mode control theory, set the conditions Solve the sliding coefficient matrix ; S54. Calculate the parameters of the state constraint model. Model mismatch boundary The model mismatch value , This represents the nominal error system model. Indicates the model mismatch quantization parameters. and These are the error state of the nominal error model and the control input of the nominal error system, respectively. and These represent the set of error state constraints and the set of control input constraints for the nominal error model, respectively. This indicates taking the upper bound. The symbol for the second norm; S55. Construct the Lyapunov equations: ; ; Among them, stability adjustment parameters satisfy , Represents the identity matrix and the state cost weight matrix. The weight matrix after transformation related to the input channel This yields the matrix used to construct the terminal penalty matrix. The unique Hermitian positive definite matrix and the unique symmetric real positive semidefinite matrix Finally, the conditions are met. The unique solution : ; in Positive switching gain; S56, Set the terminal penalty matrix Positive switching gain in Conditions to be met: ; In this condition and These represent the maximum and minimum real parts of the eigenvalues ​​of the matrix within the parentheses, respectively. and These represent the maximum and minimum real parts of the non-zero eigenvalues ​​of the matrix within the parentheses, respectively. Indicates taking The maximum value of each parameter; S57, MPC Terminal Cost Function Represented as: ; Among them, the final terminal penalty matrix To ensure system stability coefficient Greater than or equal to 0, express The transpose of .

[0012] Furthermore, in step S6, the solution to the MPC optimization problem is expressed by the following formula: Indicate the cost function, and These are the error state of the nominal error model and the control input of the nominal error system, respectively. and These represent the current sampling time. The error state and nominal error system control input of the corresponding nominal error model. and These represent the set of error state constraints and the set of control input constraints for the nominal error model, respectively. Based on time The nominal error model, This represents the nominal error system model. Indicates that the calculation makes Minimized , Indicates time Integral This is the final terminal penalty matrix.

[0013] The present invention also provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute any of the quadrotor unmanned aerial vehicle control methods integrating unconstrained model predictive control and sliding mode control as described above.

[0014] The present invention also provides a computer-readable storage medium storing computer instructions, which are used to cause a processor to execute the aforementioned quadrotor unmanned aerial vehicle control method integrating unconstrained model predictive control and sliding mode control.

[0015] By employing the above technical solution, the present invention provides a control method for a quadrotor unmanned aerial vehicle that integrates terminal-constraint-free model predictive control and sliding mode control, which has at least the following beneficial effects: (1) This invention provides a quadrotor UAV control method that integrates terminal-constrained model predictive control and sliding mode control. By embedding the sliding mode control law into the terminal cost of MPC, it achieves the effects of eliminating terminal constraints, shortening the prediction time domain of MPC, and increasing the optimal solution space. Thanks to these effects, it solves the problem of excessive computation time when using traditional UAV control methods with terminal-constrained MPC. (2) This invention integrates an explicit SMC controller for controlling a real system. Unlike traditional SMC tracking problems, the tracking trajectory of the explicit SMC in this invention is generated by the optimal state and control input of the MPC without terminal constraints. This establishes a connection between the explicit SMC controller, MPC optimization, and constraints, solving the problem of poor robustness of quadcopter control systems under disturbances without consuming additional computing resources. At the same time, compared with some auxiliary controllers that require optimization, it achieves the effect of saving computing resources. Thanks to this, it solves the problem of quadcopter UAVs consuming too many computing resources for trajectory tracking tasks under system disturbances. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the control of a quadcopter drone according to the present invention; Figure 2 This invention provides a standard system and a practical system for the x-direction, y-direction, and yaw angle. The tracking trajectory; Figure 3 This refers to the actual tracking error of the quadcopter system in the x-direction in the embodiments of the present invention. Figure 4 This refers to the actual tracking error of the quadcopter system in the y-direction in the embodiments of the present invention. Figure 5 This is a real quadcopter system in the embodiment of the invention at a yaw angle. The tracking error of the actual system; Figure 6 This is a comparison of the control input quantities of the nominal system and the actual system in this embodiment of the invention. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0018] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0019] Please refer to Figures 1-6 This illustration shows a specific implementation of the present embodiment. In this embodiment, a nominal error model is constructed based on a reference trajectory. The implicit SMC control law is integrated into the derivation process of the terminal cost term to construct the MPC terminal cost function of the MPC controller. The optimal state trajectory of the nominal system of the quadcopter UAV is obtained and transmitted to the explicit SMC controller to realize the tracking of the set reference trajectory by the real quadcopter system. This alleviates the computational burden of the traditional MPC controller and effectively improves the real-time operation capability of the quadcopter UAV while maintaining high control accuracy.

[0020] Please refer to Figure 1 This embodiment proposes a control method for a quadrotor unmanned aerial vehicle that integrates unconstrained model predictive control and sliding mode control. The method includes the following steps: S1. Establish a nonlinear dynamic model of the quadcopter UAV and set the system state constraints and control input constraints of the nonlinear dynamic model.

[0021] As a preferred embodiment of step S1, the specific process includes the following steps: S11. The nonlinear dynamic model of the quadcopter UAV is constructed as follows: ; in For rotation matrix, Indicated by angle Rotate. Yaw angle; The system dynamics matrix; Let be the input gain matrix, and and All are diagonal matrices, and their diagonal elements , These correspond to the system parameters and control gains on the a, b, and c axes of the body coordinate system, respectively. , , They represent , , For time The first derivative, The system state vector is represented by the pose vector. and velocity vector Composition; Pose Vector Including lateral position Longitudinal position and yaw angle velocity vector Including surge speed sway speed and yaw rate ; It is the control torque, which serves as the control input vector; For disturbance; S12, Set system state constraints and control input constraints ,in For the system state set, To control the input set.

[0022] S2. Set the reference trajectory of the quadcopter UAV and derive the reference trajectory for yaw angle, surge speed, yaw speed and yaw rate.

[0023] As a preferred embodiment of step S2, the specific process includes the following steps: S21. Setting up a quadcopter drone based on time. Reference trajectory : ; in , They represent time-based The lateral position reference trajectory and the longitudinal position reference trajectory; S22, based on Derivation of the yaw angle in the nonlinear dynamic model Surge speed sway speed yaw rate Based on time Reference trajectory , , , : ; ; ; ; in, This represents the arctangent function operation. , They represent , for time The first derivative, , They represent , For time The second derivative.

[0024] More specifically, the reference trajectory of the quadcopter UAV is set to satisfy the system state constraints and control input constraints of the nonlinear dynamics model.

[0025] S3. Define the nominal system of the quadcopter UAV, derive the nominal error model for MPC controller optimization based on the trajectory of yaw angle, surge speed, yaw speed, yaw rate and its corresponding reference trajectory, and obtain the error status.

[0026] As a preferred embodiment of step S3, the specific process includes the following steps: S31. Define the nominal system for quadcopter unmanned aerial vehicles. , denoted as: ; in The nominal state, i.e., without disturbance. state, For nominal control input, For the system model, that is, the disturbance in the nonlinear dynamic model of the quadcopter UAV in step S11. Ignore the obtained model; S32. Obtain the nominal error model by combining each reference trajectory. , denoted as: ; in Represents the nominal error system model; error state , As a reference state, the nominal error system control input , As reference control input, nominal speed error Three-dimensional velocity vector Due to surge speed sway speed and yaw rate trajectory , , Combining and transposing, a three-dimensional velocity reference vector Due to surge speed sway speed and yaw rate Reference trajectory , , Composed of splicing and transposition, nominal yaw angle error , The trajectory representing the yaw angle. The reference trajectory representing the yaw angle. Indicates time. Reference state. , is a six-dimensional augmented vector composed of a three-dimensional reference pose vector and a three-dimensional reference velocity vector, where the reference pose vector is... , for reference trajectory , and The three-dimensional position reference vector is formed.

[0027] S4. Based on the error state, define the implicit SMC control law for designing the MPC terminal cost function, and define the explicit SMC control law for controlling the real quadcopter system.

[0028] As a preferred embodiment of step S4, the specific process includes the following steps: S41. Define the implicit SMC control law. for: ; in Represents linear state gain. This is an error state. Indicates the switching function, This is the sliding coefficient matrix in the implicit SMC control law. This represents the structure of the sliding coefficient matrix. The row vector, For the control matrix, Positive switching gain, This represents the operation of finding the inverse matrix; S42. Define the explicit SMC control law. for: ; in As an auxiliary sliding mode variable, it is defined as follows: , For sliding mode variables, Represents sliding mode variable For time The first derivative, This is the sliding coefficient matrix in an explicit SMC control law. express The inverse matrix; and These represent the optimal state trajectory and optimal control input obtained by solving the MPC optimization problem, respectively. It is by The optimal vector composed of the first three dimensions, express For time The first derivative, express For time The first derivative, Represents the trajectory of the pose vector. The maximum value of the disturbance. The trajectory is the yaw angle. To achieve the optimal yaw angle, The system dynamics matrix, For the input gain matrix, For rotation matrix, express transpose, express The first derivative of the parameter within the parentheses, This is the symbol for the 2-norm.

[0029] S5. Initialize the parameters of the MPC controller, including the prediction time domain. Sampling interval State weight matrix Control weight matrix And calculate the terminal penalty matrix based on the implicit SMC control law. Construct the final terminal penalty matrix Obtain the MPC terminal cost function In this embodiment, the prediction time domain is set. The sampling interval is 0.3 seconds. It takes 0.1 seconds.

[0030] As a preferred embodiment of step S5, the terminal penalty matrix is ​​calculated based on the implicit SMC control law. Construct the final terminal penalty matrix Obtain the MPC terminal cost function The specific process includes the following steps: S51, Nominal error model The system matrix is ​​obtained by linearization near the equilibrium point. and control matrix ; S52, Linear State Gain Based on Implicit SMC Control Law and system matrix and control matrix Obtain the closed-loop system matrix ,in The poles are set to be less than or equal to 0 to obtain a linear state gain. ; S53. Based on SMC sliding mode control theory, set the conditions Solve the sliding coefficient matrix ; S54. Calculate the parameters of the state constraint model. Model mismatch boundary The model mismatch value , This represents the nominal error system model. Indicates the model mismatch quantization parameters. and These are the error state of the nominal error model and the control input of the nominal error system, respectively. and These represent the set of error state constraints and the set of control input constraints for the nominal error model, respectively. This indicates taking the upper bound. The symbol for the second norm; S55. Construct the Lyapunov equations: ; ; Among them, stability adjustment parameters satisfy , Represents the identity matrix and the state cost weight matrix. The weight matrix after transformation related to the input channel This yields the matrix used to construct the terminal penalty matrix. The unique Hermitian positive definite matrix and the unique symmetric real positive semidefinite matrix Finally, the conditions are met. The unique solution : ; in Positive switching gain; S56, Set the terminal penalty matrix Positive switching gain in Conditions to be met: ; In this condition and These represent the maximum and minimum real parts of the eigenvalues ​​of the matrix within the parentheses, respectively. and These represent the maximum and minimum real parts of the non-zero eigenvalues ​​of the matrix within the parentheses, respectively. Indicates taking The maximum value of each parameter; S57, MPC Terminal Cost Function Represented as: ; Among them, the final terminal penalty matrix To ensure system stability coefficient Greater than or equal to 0, express The transpose of .

[0031] This invention achieves the effects of eliminating terminal constraints, shortening the prediction time domain of MPC, and increasing the optimal solution space by embedding the sliding mode control law into the terminal cost of MPC. Thanks to these effects, the drawback of excessively long computation time of traditional UAV control methods with terminal constraint MPC is solved.

[0032] S6, for the current sampling time , with its error state As the initial state, the MPC controller is used in the time domain. The internal algorithm solves the MPC optimization problem based on the nominal error model, and calculates the optimal state trajectory and optimal control input of the nominal system of the quadcopter UAV, which are used as the MPC nominal signal.

[0033] As a preferred embodiment of step S6, the solution to the MPC optimization problem is expressed by the following formula: ; in, Indicates that it is subject to, Represents the cost function, and These are the error state of the nominal error model and the control input of the nominal error system, respectively. and These represent the current sampling time. The error state and nominal error system control input of the corresponding nominal error model. and These represent the set of error state constraints and the set of control input constraints for the nominal error model, respectively. Based on time The nominal error model, This represents the nominal error system model. Indicates that the calculation makes Minimized , Indicates time Integral This is the final terminal penalty matrix.

[0034] In this embodiment, solving this MPC optimization problem (optimal control problem) causes the state of the nominal error model to eventually converge to the origin. At this point, the nominal system trajectory of the quadcopter UAV tracks the reference trajectory, and the optimal state trajectory and optimal control input of the nominal system of the quadcopter UAV are obtained. and .

[0035] S7. Transmit the calculated MPC nominal signal (optimal control and state) to the explicit SMC control law of the explicit SMC controller.

[0036] By integrating an explicit SMC controller for controlling a real system, unlike traditional SMC tracking problems, the tracking trajectory of the explicit SMC in this invention is generated by the optimal state and control input of MPC without terminal constraints. This establishes a connection between the explicit SMC controller and MPC optimization and constraints, solving the problem of poor robustness of quadcopter control systems under disturbances without consuming additional computational resources. Simultaneously, compared to some auxiliary controllers that require optimization, it achieves the effect of saving computational resources. This solves the problem of quadcopter UAVs consuming excessive computational resources for trajectory tracking tasks under system disturbances.

[0037] S8, the explicit SMC controller uses the received MPC nominal signal as a reference target, calculates the robust control input for the real quadcopter system based on the explicit SMC control law, drives the real system state to track the optimal state trajectory generated by the MPC controller, and then tracks the reference trajectory of the set quadcopter UAV.

[0038] like Figure 1 As shown, the SMC controller calculates the control input and transmits it to the quadcopter drone. The state is then fed back to the SMC controller via the brakes inside the quadcopter drone, the constructed nonlinear dynamic model (i.e., nonlinear system), and sensors.

[0039] S9. Wait for the next sampling moment, and repeat steps S3-S5 to perform rolling optimization and feedback control.

[0040] This application also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute any of the quadrotor unmanned aerial vehicle control methods integrating terminal constraint-free model predictive control and sliding mode control as described in the present application.

[0041] This application also provides a computer-readable storage medium storing computer instructions, which are used to cause a processor to execute the aforementioned quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control.

[0042] The nominal system and the actual system differ in the x-direction, y-direction, and yaw angle. The tracking trajectory can be referenced Figure 2 The reference trajectory in step S2 is... Figure 2 The purple dashed line in the diagram indicates this. Figure 2 The orange solid line represents the tracking trajectory (nominal trajectory) of a given quadrotor UAV nominal system, and the blue solid line represents the tracking trajectory (real trajectory) of a real quadrotor system. Figure 2 It can be seen that after a period of time, the real quadcopter system successfully tracked the tracking trajectory of the given quadcopter UAV nominal system. Figure 3 , 4 5 represents the x-axis, y-axis, and yaw angles of a real quadcopter system, respectively. The tracking error can be observed to eventually converge to around 0. Figure 6 The figure shows the nominal system and the actual system in the x-direction, y-direction, and yaw angle. The control inputs are shown in the diagram, where the orange solid line represents the control input of the nominal quadcopter system and the blue line represents the control input of the actual quadcopter system. It can be seen that with this controller design, the nominal quadcopter system successfully tracked the reference trajectory of the given quadcopter, while the actual quadcopter system tracked the trajectory of the nominal quadcopter system. Thus, the actual quadcopter system completed the tracking of the reference trajectory of the given quadcopter.

[0043] In summary, this invention provides a quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control. This method overcomes the drawback of excessive computation time associated with traditional MPC algorithms. Furthermore, the integrated auxiliary sliding mode controller for controlling the real system significantly improves the robustness of the control system under unknown dynamics and disturbances without consuming additional computational resources. Ultimately, even with system disturbances, the quadrotor UAV successfully tracked a given reference trajectory.

[0044] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0045] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0046] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A control method for a quadrotor unmanned aerial vehicle (UAV) integrating unconstrained model predictive control and sliding mode control, characterized in that, Includes the following steps: S1. Establish a nonlinear dynamic model of the quadcopter UAV and set the system state constraints and control input constraints of the nonlinear dynamic model; S2. Set the reference trajectory of the quadcopter UAV and derive the reference trajectory for yaw angle, surge speed, yaw speed and yaw rate; S3. Define the nominal system of the quadcopter UAV, derive the nominal error model for MPC controller optimization based on the trajectory of yaw angle, surge speed, yaw speed, yaw rate and its corresponding reference trajectory, and obtain the error status; S4. Based on the error state, define the implicit SMC control law for designing the MPC terminal cost function, and define the explicit SMC control law for controlling the real quadcopter system. S5. Initialize the parameters of the MPC controller, including the prediction time domain. Sampling interval State weight matrix Control weight matrix And calculate the terminal penalty matrix based on the implicit SMC control law. Construct the final terminal penalty matrix Obtain the MPC terminal cost function ; S6. For the current sampling time , with its error state As the initial state, the MPC controller is used in the time domain. The internal algorithm solves the MPC optimization problem based on the nominal error model, and calculates the optimal state trajectory and optimal control input of the quadrotor UAV nominal system as the MPC nominal signal. S7. Transmit the calculated MPC nominal signal to the explicit SMC control law of the explicit SMC controller; S8. The explicit SMC controller uses the received MPC nominal signal as a reference target, calculates the robust control input for the real quadcopter system based on the explicit SMC control law, drives the real system state to track the optimal state trajectory generated by the MPC controller, and then tracks the reference trajectory of the set quadcopter UAV. S9. Wait for the next sampling moment, and repeat steps S3-S5 to perform rolling optimization and feedback control.

2. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. The nonlinear dynamic model of the quadcopter UAV is constructed as follows: ； in For rotation matrix, Indicated by angle Rotate. Yaw angle; The system dynamics matrix; The input gain matrix; , , They represent , , For time The first derivative, The system state vector is represented by the pose vector. and velocity vector Composition; Pose Vector Including lateral position Longitudinal position and yaw angle velocity vector Including surge speed sway speed and yaw rate ; It is the control torque, which serves as the control input vector; For disturbance; S12, Set system state constraints and control input constraints ,in For the system state set, To control the input set.

3. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 1, characterized in that: Step S2 specifically includes the following steps: S21. Setting up a quadcopter drone based on time. Reference trajectory : ； in , They represent time-based The lateral position reference trajectory and the longitudinal position reference trajectory; S22, based on Derivation of the yaw angle in the nonlinear dynamic model Surge speed sway speed yaw rate Based on time Reference trajectory , , , : ； ； ； ； in, This represents the arctangent function operation. , They represent , for time The first derivative, , They represent , For time The second derivative.

4. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 3, characterized in that: The reference trajectory of the quadcopter UAV is set to satisfy the system state constraints and control input constraints of the nonlinear dynamics model.

5. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 2, characterized in that: Step S3 specifically includes the following steps: S31. Define the nominal system for quadcopter unmanned aerial vehicles. , denoted as: ； in The nominal state, i.e., without disturbance. state, For nominal control input, For the system model, that is, the disturbance in the nonlinear dynamic model of the quadcopter UAV in step S11. Ignore the obtained model; S32. Obtain the nominal error model by combining each reference trajectory. , denoted as: ； in Represents the nominal error system model; error state , As a reference state, the nominal error system control input , As reference control input, nominal speed error Three-dimensional velocity vector Due to surge speed sway speed and yaw rate trajectory , , Combining and transposing, a three-dimensional velocity reference vector Due to surge speed sway speed and yaw rate Reference trajectory , , Composed of splicing and transposition, nominal yaw angle error , The trajectory representing the yaw angle. The reference trajectory representing the yaw angle. Indicates the time.

6. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 1, characterized in that: Step S4 specifically includes the following steps: S41. Define the implicit SMC control law. for: ； in Represents linear state gain. This is an error state. Indicates the switching function, Here is the sliding coefficient matrix. This represents the structure of the sliding coefficient matrix. The row vector, For the control matrix, Positive switching gain, This represents the operation of finding the inverse matrix; S42. Define the explicit SMC control law. for: ； in As an auxiliary sliding mode variable, it is defined as follows: , For sliding mode variables, Represents sliding mode variable For time The first derivative, Represents the sliding coefficient matrix. express The inverse matrix; and These represent the optimal state trajectory and optimal control input obtained by solving the MPC optimization problem, respectively. It is by The optimal vector composed of the first three dimensions, express For time The first derivative, express For time The first derivative, Represents the trajectory of the pose vector. The maximum value of the disturbance. The trajectory is the yaw angle. To achieve the optimal yaw angle, The system dynamics matrix, For the input gain matrix, For rotation matrix, express transpose, express The first derivative of the parameter within the parentheses, This is the symbol for the 2-norm.

7. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 1, characterized in that: Step S5 involves calculating the terminal penalty matrix based on the implicit SMC control law. Construct the final terminal penalty matrix Obtain the MPC terminal cost function The specific process includes the following steps: S51, Nominal error model The system matrix is ​​obtained by linearization near the equilibrium point. and control matrix ; S52, Linear State Gain Based on Implicit SMC Control Law and system matrix and control matrix Obtain the closed-loop system matrix ,in The poles are set to be less than or equal to 0 to obtain a linear state gain. ; S53. Based on SMC sliding mode control theory, set the conditions Solve the sliding coefficient matrix ; S54. Calculate the parameters of the state constraint model. Model mismatch boundary The model mismatch value , This represents the nominal error system model. Indicates the model mismatch quantization parameters. and These are the error state of the nominal error model and the control input of the nominal error system, respectively. and These represent the set of error state constraints and the set of control input constraints for the nominal error model, respectively. This indicates taking the upper bound. The symbol for the second norm; S55. Construct the Lyapunov equations: ； ； Among them, stability adjustment parameters satisfy , Represents the identity matrix and the state cost weight matrix. The weight matrix after transformation related to the input channel This yields the matrix used to construct the terminal penalty matrix. The unique Hermitian positive definite matrix and the unique symmetric real positive semidefinite matrix Finally, the conditions are met. The unique solution : ； in Positive switching gain; S56, Set the terminal penalty matrix Positive switching gain in Conditions to be met: ； In this condition and These represent the maximum and minimum real parts of the eigenvalues ​​of the matrix within the parentheses, respectively. and These represent the maximum and minimum real parts of the non-zero eigenvalues ​​of the matrix within the parentheses, respectively. Indicates taking The maximum value of each parameter; S57, MPC Terminal Cost Function Represented as: ； Among them, the final terminal penalty matrix To ensure system stability coefficient Greater than or equal to 0, express The transpose of .

8. The quadrotor UAV control method integrating unconstrained model predictive control and sliding mode control according to claim 1, characterized in that: In step S6, the solution to the MPC optimization problem is expressed by the following formula: ； in, Indicates that it is subject to, Represents the cost function, and These are the error state of the nominal error model and the control input of the nominal error system, respectively. and These represent the current sampling time. The error state and nominal error system control input of the corresponding nominal error model. and These represent the set of error state constraints and the set of control input constraints for the nominal error model, respectively. Based on time The nominal error model, This represents the nominal error system model. Indicates that the calculation makes Minimized , Indicates time Integral This is the final terminal penalty matrix.

9. An electronic device, characterized in that, The electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute the quadcopter unmanned aerial vehicle control method integrating terminal-free constraint model predictive control and sliding mode control as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that, when executed by a processor, implement the quadrotor unmanned aerial vehicle control method integrating unconstrained model predictive control and sliding mode control as described in any one of claims 1-8.

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