Error tracking control method for hexacopter based on optimal specified performance

Abstract

The application discloses a kind of error tracking control methods of six-rotor unmanned aerial vehicle based on optimal specified performance, it is related to unmanned aerial vehicle control technical field, including the following steps: the physical characteristics of follower unmanned aerial vehicle are modeled, the position dynamics model of unmanned aerial vehicle follower is constructed, and it is converted into state model;Based on the state model, introduce specified performance control, to ensure that the formation tracking error of each follower is strictly constrained within the preset performance boundary, and make actual tracking error can track a pre-set, expected error trajectory;Design fusion fuzzy adaptive and command filter optimization backstepping controller, control follower unmanned aerial vehicle in six-rotor unmanned aerial vehicle system, so that follower can accurately track the trajectory of leader unmanned aerial vehicle, and ensure that its tracking error dynamic and steady-state process strictly satisfy preset performance constraints.The application realizes the convergence of error and the decoupling of expected trajectory, can significantly improve the transient performance and time controllability of formation system.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and more specifically, to an error tracking control method for a six-rotor UAV based on optimal performance specifications. Background Technology

[0002] As a vertical takeoff and landing aircraft with excellent hovering ability and flexible maneuverability, the hexacopter drone has been widely used in fields such as aerial photography and mapping, agricultural plant protection, power line inspection, emergency rescue and even military reconnaissance. With the advancement of flight control algorithms, sensors and energy technologies, it has continued to develop and has now become an indispensable and important platform in the industrial drone market.

[0003] Robust and high-precision position tracking control is the cornerstone for UAVs to achieve autonomous operation in complex tasks. To achieve this goal, backstepping control, as a systematic design method based on Lyapunov stability theory, has been widely used in the field of UAV control because it can effectively handle system nonlinearity and ensure global stability. However, standard backstepping control faces several inherent challenges when applied to hexarotor UAVs: First, UAV systems have significant model uncertainties, and standard backstepping control has limited robustness to such uncertainties; second, although traditional backstepping control can guarantee eventual convergence of the error, it is difficult to pre-constrain and quantitatively guarantee the transient performance (such as overshoot and convergence speed) and steady-state accuracy of the tracking error, which are crucial in many high-standard practical applications.

[0004] To address the aforementioned challenges, existing research has primarily made the following improvements: First, it introduces fuzzy adaptive or neural networks to approximate and compensate for system uncertainties online, thereby enhancing robustness. Second, it combines performance control with a performance function to strictly constrain the dynamic process of tracking error, ensuring it meets preset transient and steady-state indices. However, its convergence time passively depends on the design parameters of the performance function and the initial state of the system, failing to guarantee reaching the steady-state boundary within a finite time, thus making it difficult to meet tasks with strict execution time requirements. Therefore, it is necessary to design a UAV position control method that can strictly guarantee the quality of the dynamic process of tracking error (i.e., transient and steady-state performance) while also ensuring accurate convergence within a preset time, thus unifying process constraints and time constraints. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide an error tracking control method for a hexacopter unmanned aerial vehicle (UAV) based on optimal performance specifications, thereby resolving the issue that it is impossible to simultaneously consider both precise constraints on the dynamic process and precise preset convergence time in the position control of a hexacopter UAV.

[0006] To achieve the above technical objectives, this application provides an error tracking control method for a six-rotor unmanned aerial vehicle based on optimal specified performance, comprising the following steps: The physical characteristics of the follower drone are modeled, a position dynamics model of the drone follower is constructed, and it is converted into a state model; Based on the state model, a specified performance control is introduced to ensure that the formation tracking error of each follower is strictly constrained within a preset performance boundary, and that the actual tracking error can track a pre-set, desired error trajectory. An optimized backstepping controller integrating fuzzy adaptive and command filtering is designed to control the follower drone in a hexacopter UAV system, enabling the follower to accurately track the trajectory of the leader drone and ensuring that the dynamic and steady-state processes of its tracking error strictly meet preset performance constraints.

[0007] Preferably, when obtaining the position dynamics model, the physical characteristics of the follower drone are modeled, and the position dynamics model of the drone follower is as follows: in, Represents a position vector. This represents the linear velocity in the x, y, and z directions. Indicates the quality of the drone. This represents the total thrust generated by the motor. Let represent the rotation matrix, where and Represent and attitude angle , These represent the roll angle, pitch angle, and yaw angle, respectively. , Represents gravitational acceleration. It is an unknown diagonal aerodynamic matrix, in which This represents the air drag coefficient.

[0008] Preferably, when acquiring the position dynamics model, a directed graph is used to describe the directed communication topology between multiple UAVs under control, specifically including: Introducing directed graphs ,in, Represents a set of nodes. Represent edge set; This is the relevant adjacency weight matrix, with weights... Indicates the first The drone can receive signals from the first The communication information of the drone, weight Then it means the first The drone could not receive signals from the first Communication information of the drone; the Laplace matrix is ​​defined as... ,in It is a diagonal matrix. And assume that the directed graph J is a spanning tree with the leader as the root node.

[0009] Preferably, when acquiring the state model, the first The positional relationship equation of the follower hexacopter UAV: in, , , , , , ; They represent the first The drone's position on the x, y, and z axes, They represent the first The speed of the drone in the x, y, and z axes; , They represent the first The components of the total thrust that the drone needs to generate in the x, y, and z axes; This represents the neglected and unmodeled parts of the location system. . They represent the first The drone's position is output along the x, y, and z axes; The design includes an error transformation function: in, It is a synchronization error. Indicates the first drone follower and the first The weight among drone followers Indicates the first The weight between drone followers and leaders, For the first The output of the drone follower system For the first The output of the drone follower system The expected trajectory for leaders.

[0010] Preferably, when the performance is within a preset performance boundary, the preset performance boundary is represented as follows: This performance boundary is determined by an exponential decay function. Define, where is a positive design constant, and represents the initial allowable boundary, steady-state allowable boundary, and convergence rate of the error, respectively.

[0011] Preferably, when constructing the error trajectory, the tracking error between the UAV's position and velocity and the desired position and velocity is defined: the desired error trajectory is constructed by defining an error variable to represent the deviation between the actual error and the desired error trajectory.

[0012] Preferably, when obtaining the optimized backstepping controller, the optimal performance function and the optimal performance index function are established to obtain the adaptive update rate of the fuzzy logic system, and then the optimized backstepping controller is designed.

[0013] Preferably, before controlling the follower drone in the hexacopter drone system, the stability and performance of the designed optimized backstepping controller are verified using Lyapunov candidate functions.

[0014] The present invention discloses the following technical effects: 1. The technical solution of this invention applies time-varying constraints based on performance functions to the original tracking error by specifying performance control, transforming it into an unconstrained error variable. This predefines the behavior specifications of the entire system response process, ensuring that transient performance indicators, including overshoot, convergence rate, and steady-state accuracy, meet preset requirements.

[0015] 2. The technical solution of the present invention tracks the error and designs a desired error trajectory that decays to zero precisely at a user-specified time for the above-mentioned unconstrained error variable. The actual error is then tracked by a controller. This sets strict timed convergence instructions for the system and achieves complete decoupling of convergence time from initial conditions and system parameters.

[0016] 3. The technical solution of this invention utilizes the autonomous learning capability of reinforcement learning algorithms to optimize the parameters of a fuzzy logic system online. Specifically, reinforcement learning, through its autonomous learning ability, continuously learns and approximates the optimal performance function through interaction with the environment, optimizing the parameters of the fuzzy control system in real time online. This enables the UAV to fly smoothly during flight and minimizes energy consumption. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1This is a communication topology diagram based on a hexacopter UAV control system. Figure 2 This is a schematic diagram of the control flow based on a hexacopter UAV control system; Figure 3 This is a trajectory tracking diagram based on a hexacopter UAV control system. Figure 4 This is a two-dimensional trajectory tracking diagram based on a hexacopter UAV control system; Figure 5 This is a convergence plot of the tracking error under the specified performance control of a six-rotor UAV control system; Figure 6 This is a diagram showing the tracking effect of the error trajectory of a six-rotor UAV control system on the desired error trajectory. Figure 7 The tracking error diagram is shown for different desired trajectories based on the control system of a six-rotor UAV. Figure 8 The diagram shows the convergence process of the fuzzy logic system parameters based on the control system of a six-rotor UAV. Figure 9 This is a diagram showing the control inputs in three directions for a six-rotor UAV control system. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0020] like Figures 1-9 As shown, this invention provides an error tracking control method for a hexacopter UAV based on optimal specified performance. It belongs to a hexacopter UAV position control method that combines specified performance control with preset time error tracking. The communication topology and overall process of the control system are as follows: Figure 1 and Figure 2 As shown, the leader of the six-rotor UAVs is labeled LeaderUAV0, and the followers are labeled UAV1, UAV2, UAV3, and UAV4. The method is described in detail using a six-rotor UAV system as an example, and the detailed implementation process includes: Step 1: Establish the positional dynamics model of the drone follower: (1) in, Represents a position vector. This represents the linear velocity in the x, y, and z directions. Indicates the quality of the drone. This represents the total thrust generated by the motor. Let represent the rotation matrix, where and Represent and attitude angle , These represent the roll angle, pitch angle, and yaw angle, respectively. , Represents gravitational acceleration. It is an unknown diagonal aerodynamic matrix, in which This represents the air drag coefficient.

[0021] Step 2: Transform the system dynamics model into a state model: No. The positional relationship equation of a hexacopter UAV (follower): (2) in, , , , , , ; They represent the first The drone's position on the x, y, and z axes, They represent the first The speed of the drone in the x, y, and z axes; , They represent the first The components of the total thrust that the drone needs to generate in the x, y, and z axes; , , . This represents the neglected and unmodeled parts of the location system. . They represent the first The drone outputs its position in the x, y, and z axes.

[0022] The design includes an error transformation function: (3) in, It is a synchronization error. Indicates the first drone follower and the first The weight among drone followers Indicates the first The weight between drone followers and leaders, For the first The output of the drone follower system For the first The output of the drone follower system The expected trajectory for leaders.

[0023] Step 3: Design the specified performance function and construct the error transformation system: Introduce prescribed performance controls to ensure formation tracking error for each follower. Strictly constrained within preset performance boundaries: (4) This performance boundary is determined by an exponential decay function. Define, where is a positive design constant, and represents the initial allowable boundary, steady-state allowable boundary, and convergence rate of the error, respectively.

[0024] To achieve dynamic control of constrained errors Transform it into an unconstrained system and construct a smooth logarithmic error transformation variable. : (5) right Taking the derivative, we obtain its dynamic equation as follows: (6) in, , Thus, the original error was... The performance constraint control problem has been transformed into the problem of controlling the transformed system error variable. The stabilization problem was solved, laying the foundation for the subsequent design of a controller based on the backstepping method.

[0025] Step 4: Construct a "secondary tracking" mechanism for error based on a preset performance function: To achieve precise planning of the dynamic convergence process of tracking error, the control objective is designed to: minimize the actual tracking error. It can track a pre-defined, desired error trajectory. .

[0026] First, define the tracking error between the UAV's position and velocity and the desired position and velocity: (7) in, They represent the first The actual position and speed of the drone Indicates the first The desired position and desired speed of the drone. Indicates position tracking error. This indicates the speed tracking error.

[0027] Based on this, a new error variable is defined. It represents the deviation between the actual error and the expected error trajectory: (8) in, Represents the expected error trajectory. This represents the position tracking error after the transformation. This indicates that the expected dynamics are included. With filter output Speed ​​tracking error.

[0028] Expected error trajectory The construction is as follows: (9) in, , This is the initial error. The derivative of the initial error. yes A continuous function that is smoothly decreasing on the upper surface. , , This is the preset time.

[0029] For error variables Differentiate: (10) but (11).

[0030] Step 5: Design an optimized backstepping controller that integrates fuzzy adaptive and command filtering: Based on the given dynamic model and system state equations of the hexacopter UAV system, the optimal virtual controller and the optimal actual controller are designed respectively. To solve the problem of computational complexity explosion in the backstepping method, a first-order command filter is introduced, and its dynamic equation is defined as follows: (12) in, For virtual control laws, If the filtered output is used, then the filtering error is... It can be represented as . The time constant of the filter, This ensures that the initial value of the filter output is consistent with the input.

[0031] Step 1: Establish the following optimal performance function: (13) in, It is a compact set that includes the origin. It is a permissive control set. It is a virtual controller. It is the optimal virtual controller. It is the cost function.

[0032] Differentiating both sides of equation (13) yields the Hamilton-Jacobi-Bellman (HJB) equation as follows: (14) By solving The optimal virtual controller is obtained as shown below: (15) Will Decomposed into: (16) in, Approximated by fuzzy logic system Substituting formula (16) into formula (15) yields: (17) By using reinforcement learning algorithms to approximate the optimal virtual controller, we can obtain: (18) (19) in, yes The estimated value, yes The estimated value, It is an ideal estimate of the weights of a fuzzy logic system. The ideal weight estimate for executing a fuzzy logic system. Then it is a fuzzy basis function.

[0033] The approximate HJB function is shown below: (20) The Bellman residual is defined as follows: (twenty one) Step 2: Construct the optimal performance metric function as follows: (twenty two) in, It is the actual controller. It is the optimal practical controller. It is the cost function.

[0034] The corresponding Hamilton-Jacobi-Bellman (HJB) equation is as follows: (twenty three) Similar to the first step, an approximate optimal actual controller is obtained through a fuzzy logic system. (twenty four) Among them, fuzzy logic system Used to approximate functions , These are fuzzy basis functions.

[0035] Design an adaptive update rate for a fuzzy logic system: (25) in, For a suitable design constant, It is a positive definite matrix.

[0036] Step Six: Verification of Closed-Loop System Stability and Performance To analyze the design of the virtual controller, the actual controller, and the adaptive law that enable the hexarotor UAV system to stabilize, the following Lyapunov candidate functions are selected. : (26) in, To estimate the error, , , , These are weight estimates. This is the ideal weight.

[0037] For the selected Lyapunov candidate functions By taking the derivative, we can calculate: (27) in, , This is for The smallest eigenvalue, , yes The largest eigenvalue, yes The smallest eigenvalue, , , , , Therefore, it can be proven that all signals of the hexacopter UAV system are consistent and ultimately bounded, and the final tracking error is ultimately bounded, thus proving the stability of the system.

[0038] Step 7: In a six-rotor drone system, the follower can accurately follow the leader, and the dynamic and steady-state processes of tracking error strictly comply with performance constraints.

[0039] To demonstrate the feasibility, effectiveness, and correctness of this example, the present invention conducts the following simulation experiments: In this simulation experiment, an adaptive optimal controller based on optimal performance and error tracking was designed for a hexacopter UAV system to achieve optimal control of the hexacopter UAV system.

[0040] In the optimal controller design process, the system model parameters are set as follows: For the roll, pitch, and yaw channels, the reference trajectory for the leader of the six-rotor UAVs is as follows: The relevant parameters for the designed hexacopter UAV are: UAV mass initial boundary steady-state boundary Convergence coefficient Filter constant The initial state of the follower system is: , .

[0041] Judge fuzzy logic system and And actuator fuzzy logic system and Each contains 7 membership functions, and the center points of the membership functions are evenly distributed in... Above; the initial weights of the fuzzy logic system are: , , The parameters related to the adaptive law are designed as follows: .

[0042] The effectiveness of this simulation is further illustrated by referring to the accompanying diagram: Simulation results are as follows Figures 3-9 , Figure 3 This displays a trajectory tracking diagram of the unmanned aerial vehicle (UAV) system. This indicates the leader's desired trajectory. The diagram shows the actual movement trajectories of the four drone followers under the control method described above. It can be observed that during flight, each follower is able to quickly and stably track the leader's trajectory. Figure 4 This is a two-dimensional trajectory tracking diagram of the unmanned aerial vehicle (UAV) system. Indicates the first The movement trajectories of the four drone followers in the x, y, and z axes indicate that the four drone followers can accurately track the leader's trajectory in all three directions. Figure 5 The diagram shows the tracking error convergence of a hexacopter UAV control system under specified performance control. The specified performance control reduces the system's tracking error... It can be strictly constrained within a preset performance upper bound and performance lower bound, where, They represent the first A drone in axis, axis, Tracking error in the axial direction. Figure 6 It is the error trajectory For the expected error trajectory Tracking effect diagram, preset time The time is 5 seconds, and it can be observed before the preset time. This will enable the achievement of Stable tracking. Figure 7 These are tracking error graphs for different expected trajectories, where These are the errors under three different expected trajectories. Even though the expected trajectories are different, the tracking errors can converge independently, demonstrating the versatility of error tracking. Figure 8 This reflects the convergence process of the parameters of the fuzzy logic system. It can be seen that all parameters can converge to a small neighborhood near the origin without oscillation or divergence, indicating that the adaptive law is effective. Figure 9 It consists of control inputs from four drone followers in three directions, among which They represent the first The control inputs for the drone in the x, y, and z axes.

[0043] This example focuses on a leader-follower system of a hexacopter UAV, investigating a control method combining defined performance control and preset-time error tracking. Defined performance control establishes clear error boundaries and convergence rates. The key to the error tracking method is designing a desired error trajectory that converges precisely to zero at a preset time, providing a foundation for precise control of the error convergence time and improved transient performance. To handle the system's nonlinear dynamics and parameter uncertainties, a fuzzy logic system is used to approximate the unknown nonlinear functions in the system. Based on this, an adaptive actuator-evaluator framework based on the fuzzy logic system is constructed to optimize controller parameters online and approximate ideal control performance, avoiding the difficulty of directly solving complex HJB equations. By designing a corresponding adaptive update law, consistent bounded convergence of fuzzy weights is ensured, thereby optimizing control performance while maintaining system stability. Theoretical analysis and simulation experiments both demonstrate that the proposed control strategy can ensure that the multi-UAV system achieves inclusive control within a predetermined time, and that all signals in the closed-loop system are consistently and eventually bounded, proving the effectiveness of the proposed optimal control scheme.

[0044] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0045] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0046] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for error tracking control of a six-rotor unmanned aerial vehicle (UAV) based on optimal specified performance, characterized in that, Includes the following steps: The physical characteristics of the follower drone are modeled, a position dynamics model of the drone follower is constructed, and it is converted into a state model; Based on the state model, a specified performance control is introduced to ensure that the formation tracking error of each follower is strictly constrained within a preset performance boundary, and that the actual tracking error can track a pre-set, desired error trajectory. Design an optimized backstepping controller that integrates fuzzy adaptive and command filtering to control the follower drone in a hexacopter UAV system, enabling the follower to accurately track the trajectory of the leader drone and ensuring that the dynamic and steady-state processes of its tracking error strictly meet the preset performance constraints. When obtaining the state model, the first The positional relationship equation of the follower hexacopter UAV: in, , , , , , ; They represent the first The drone's position on the x, y, and z axes, They represent the first The speed of the drone in the x, y, and z axes; , Indicates the quality of the drone. They represent the first The components of the total thrust that the drone needs to generate in the x, y, and z axes; This represents the neglected and unmodeled parts of the location system. , They represent the first The drone's position is output along the x, y, and z axes; The design includes an error transformation function: in, It is a synchronization error. Indicates the first drone follower and the first The weight among drone followers Indicates the first The weight between drone followers and leaders, For the first The output of the drone follower system For the first The output of the drone follower system The expected trajectory of leaders; When the performance is within a preset performance boundary, the preset performance boundary is represented as follows: This performance boundary is determined by an exponential decay function. Define, where , where are positive design constants, and represent the initial allowable boundary, steady-state allowable boundary, and convergence rate of the error, respectively; When constructing the error trajectory, the tracking error between the UAV's position and velocity and the desired position and velocity is defined: the desired error trajectory is constructed by defining an error variable to represent the deviation between the actual error and the desired error trajectory. Expected error trajectory The construction is as follows: in, , This is the initial error. The derivative of the initial error. yes A continuous function that is smoothly decreasing on the upper surface. , , This is the preset time.

2. The error tracking control method for a six-rotor UAV based on optimal specified performance according to claim 1, characterized in that: When obtaining the position dynamics model, the physical characteristics of the follower drone are modeled. The position dynamics model of the drone follower is as follows: in, Represents a position vector. This represents the linear velocity in the x, y, and z directions. Indicates the quality of the drone. This represents the total thrust generated by the motor. Let represent the rotation matrix, where and Represent and attitude angle , These represent the roll angle, pitch angle, and yaw angle, respectively. , Represents gravitational acceleration. It is an unknown diagonal aerodynamic matrix, in which This represents the air drag coefficient.

3. The error tracking control method for a six-rotor UAV based on optimal specified performance according to claim 2, characterized in that: When acquiring the position dynamics model, a directed graph is used to describe the directed communication topology relationships between multiple UAVs under control, specifically including: Introducing directed graphs ,in, Represents a set of nodes. Represent edge set; This is the relevant adjacency weight matrix, with weights... Indicates the first The drone can receive signals from the first The communication information of the drone, weight Then it means the first The drone could not receive signals from the first Communication information of the drone; the Laplace matrix is ​​defined as... ,in It is a diagonal matrix. And assume that the directed graph J is a spanning tree with the leader as the root node.

4. The error tracking control method for a six-rotor UAV based on optimal specified performance according to claim 1, characterized in that: When obtaining the optimized backstepping controller, the optimal performance function and the optimal performance index function are established to obtain the adaptive update rate of the fuzzy logic system, and then the optimized backstepping controller is designed.

5. The error tracking control method for a six-rotor UAV based on optimal specified performance according to claim 4, characterized in that: Before controlling the follower drone in the hexacopter UAV system, the stability and performance of the designed optimized backstepping controller are verified using Lyapunov candidate functions.

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