Four-rotor unmanned aerial vehicle all-drive specified time control method based on error tracking

Abstract

A four-rotor unmanned aerial vehicle all-drive specified time control method based on error tracking belongs to the technical field of unmanned aerial vehicle flight control, and comprises the following steps: firstly, establishing a rigid body model of a four-rotor unmanned aerial vehicle system, initializing the state and control parameters of the system, and converting the model into an all-drive system to realize decoupling of a control channel; secondly, a monotonic expectation error curve is constructed, an error system model is converted, and a system error convergence track is planned; designing a smooth time-varying gain function of an index-polynomial combination; designing a virtual controller, and constructing a specified time expansion state observer to estimate internal and external total disturbance; and finally, designing a specified time controller based on the expected error curve. According to the invention, it can be ensured that the position and attitude tracking error of the quad-rotor unmanned aerial vehicle converges to a minimum neighborhood near an original point within a predetermined time, and the method has very strong robustness to disturbance; trajectory tracking with high precision, high robustness and excellent transient performance is realized.

Description

Technical Field

[0001] This invention belongs to the field of UAV flight control technology. It proposes a quadrotor UAV full-drive specified time control method based on error tracking, which addresses the underactuated characteristics, external environmental interference, and unmodeled internal dynamics in quadrotor UAV systems, as well as the strict convergence time requirements of the system. Background Technology

[0002] Quadrotor drones, due to their simple structure, strong vertical takeoff and landing capabilities, and high maneuverability, have been widely used in complex tasks such as logistics transportation, disaster relief, agricultural and forestry plant protection, and military reconnaissance. With the increasing complexity of application scenarios, the performance requirements for quadrotor drone control systems are no longer limited to simple hovering or low-speed flight. Instead, more stringent requirements are being placed on the system's rapid trajectory tracking capabilities, strong anti-interference capabilities, and timeliness in completing tasks within a specified timeframe.

[0003] However, a quadcopter UAV is a typical underactuated, strongly coupled, and nonlinear system. On the one hand, it has only four control inputs but needs to control six degrees of freedom, resulting in highly coupled system dynamic equations and posing significant challenges to controller design. On the other hand, during actual flight, the UAV inevitably suffers from external environmental disturbances such as gusts and turbulent airflow, while also experiencing internal unmodeled dynamics such as load variations and inaccurate aerodynamic parameters. These combined internal and external disturbances severely impact flight stability, posing a significant challenge to high-precision tracking control.

[0004] Traditional quadcopter UAV control methods, such as PID control, backstepping, and sliding mode control, are mostly based on asymptotic stability theory. While these methods are widely used in engineering, theoretically, the time required for the system state to converge to the equilibrium point tends to be infinite, making it difficult to meet the time-sensitive requirements of emergency rescue or tactical strike missions. To improve convergence speed, finite-time and fixed-time control theories have been introduced into UAV control. Although fixed-time control can ensure that the convergence time has an upper bound independent of the initial state, this upper bound often depends on a complex combination of controller parameters, making it difficult to directly set the exact convergence time with a simple parameter. This leads to a "trial and error" dilemma for designers during actual debugging.

[0005] The all-drive system approach proposed in recent years has provided a new perspective for solving the control problem of underactuated systems, transforming high-order nonlinear systems into linear systems with all-drive characteristics through model transformation. Meanwhile, specified-time control theory allows users to directly specify the physical time constant. However, existing combined methods still have shortcomings: First, to achieve specified-time convergence, traditional methods often require infinite control gain at the terminal moment, leading to "gain explosion" and easily causing actuator saturation or even damage; second, conventional observers struggle to accurately estimate complex disturbances within a specified time; furthermore, the lack of quantitative planning for transient errors during trajectory tracking may result in excessive overshoot.

[0006] In summary, the current field of UAV control urgently needs a control scheme that can simultaneously meet the following conditions: it can solve the underactuated coupling problem through a full-drive system approach, achieve convergence within a user-defined time, effectively compensate for total disturbances using an observer, and ensure the smoothness and boundedness of control commands. This invention is proposed based on the aforementioned background and technological gaps. Summary of the Invention

[0007] To address the challenges of achieving specified-time convergence, high-precision anti-interference, and smooth control input under underactuated constraints and complex disturbances in existing quadrotor UAVs, this invention proposes a specified-time all-drive control method for quadrotor UAVs based on error tracking. The proposed method first establishes a rigid body model of the quadrotor UAV and transforms it into an all-drive system model, achieving decoupling of the control channels. Second, a monotonic expected error curve is constructed to plan the system convergence trajectory. Next, a smooth time-varying gain function combining exponential and polynomial functions is designed, and a specified-time extended state observer is constructed to estimate the total internal and external disturbances. Finally, a specified-time controller based on the expected error curve is designed by combining a filter compensation function. This design ensures that the position and attitude tracking errors of the quadrotor UAV converge to a minimal neighborhood near the origin within a predetermined time and exhibits strong robustness to disturbances.

[0008] The proposed technical solution to address the above-mentioned technical problems is as follows: A method for all-wheel drive time-specified control of a quadrotor UAV based on error tracking, the method comprising the following steps: Step 1: Establish a rigid body model of the quadcopter UAV system, initialize the system's state and control parameters, and transform the model into a fully driven system to achieve decoupling of the control channel; Step 2: Construct a monotonic expected error curve and transform the error system model to plan the system error convergence trajectory; Step 3: Design a smooth time-varying gain function of exponential-polynomial combination; design a virtual controller and construct a time-extended state observer to estimate the total internal and external disturbances; Step 4: Design a specified time controller based on the desired error curve.

[0009] Furthermore, the process of step 1 is as follows: 1.1 Considering the influence of external disturbances, the rigid body model of the quadcopter UAV is represented as follows: (1); in, This indicates the position of the quadcopter drone relative to the inertial coordinate system; yes The derivative; yes The second derivative; This represents the attitude angle of a quadcopter drone relative to an inertial coordinate system. yes The derivative; yes The second derivative; These represent the mass and gravitational acceleration of the quadcopter drone, respectively. These represent quadcopter drones in Moment of inertia on the shaft; Indicates the aerodynamic coefficient; This indicates uncertain disturbances in the external environment in terms of position and attitude. For control input of quadcopter drones; This indicates the control torque of a quadcopter drone; 1.2 Defining Virtual Control Variables for Quadrotor UAVs : (2); (3); (4); The rigid body model of a quadcopter UAV can be rewritten as an all-drive system model: (5); in, The position and attitude angles of the quadcopter drone; for The derivative; Six control inputs for the quadcopter drone; Unmodeled dynamics inside the quadcopter drone; This represents an uncertain disturbance in a bounded external environment; It is the sum of the internal unmodeled dynamics and the total external disturbance; 1.3 Definition of Tracking Error for Quadrotor UAVs for: (6); in, The desired trajectory for a quadcopter drone.

[0010] Furthermore, the process of step 2 is as follows: 2.1 Constructing a monotonic expected error curve for: (7); in, This indicates the specified convergence time constant; when time... hour, The specific formula is as follows: (8); in ; This represents the initial value for the tracking error of the quadcopter drone; 2.2 Defining the Expected Tracking Error of a Quadrotor UAV for: (9); Differentiating equation (9) and substituting it into equation (5), we get: (10); (11); in, They represent The first and second derivatives; They represent The first and second derivatives.

[0011] Furthermore, the process of step 3 is as follows: 3.1 Construct the following exponential-polynomial time-varying gain function. To ensure convergence and smooth transition at a specified time: (12); in, It is a positive parameter; 3.2 Construct a time-dilated state observer to estimate the internal unmodeled dynamics and the total external disturbance: (13); in, for The estimated value; for The derivative; It is the gain variable of the extended state observer; 3.3 Define the error of the state observer for a specified time extension for: (14); Differentiating equation (14) and substituting it into equations (5) and (13), we get: (15); in, The Herwitz matrix; It is a constant matrix; This represents the actual total disturbance. 3.4 Define virtual error for: (16); in, for The derivative; For virtual control law, the design is as follows: (17); in, For virtual controller gain; 3.5 Taking the derivative with respect to the virtual error, we get: (18).

[0012] The process of step 4 is as follows: Design a time-specific controller based on the desired error curve. for: (19); in, This is the controller gain.

[0013] The method further includes the following steps: Step 5: Prove the stability of the specified time-dilation state observer and controller, as follows: 5.1 Based on the inversion recursion idea, the first step is to design the following Lyapunov function and prove that the observer of the extended state at a specified time is stably convergent: (20); in, It is a positive definite matrix; Differentiating equation (20), we get: (twenty one); in, ; for The maximum value, i.e. ; It is a positive definite matrix; 5.2 Based on the inverse recursive idea, the second step designs the following Lyapunov function, proving that the controller based on the expected error curve converges stably at a specified time: (twenty two); Differentiating equation (22), we get: (twenty three); in, ; This indicates taking the minimum value among the three. for The maximum value, i.e. ; Based on the above analysis, it is shown that the extended state observer and tracking error at a specified time can not only converge quickly within a specified time, but also converge stably to a very small neighborhood.

[0014] This invention presents a time-defined control method for all-wheel drive of a quadrotor UAV based on error tracking. By constructing a monotonic expected error curve, the convergence process of the tracking error is constrained within a preset boundary, and the constrained error system is transformed into an equivalent unconstrained system. A time-varying gain function is designed to achieve a smooth transition of the system state from transient to steady state, avoiding non-smooth behavior caused by control law switching. Based on this, a time-defined extended state observer and a controller based on the expected error curve are constructed, thereby ensuring that the position and attitude tracking errors of the quadrotor UAV converge to the origin neighborhood within the user-specified time and strictly meet the preset transient and steady-state performance requirements, achieving high-precision and robust tracking of the quadrotor UAV under external disturbances and unmodeled dynamics.

[0015] The technical concept of this invention is as follows: Addressing the tracking control problem of a quadrotor UAV with external interference, unmodeled dynamics, and strict time-bound convergence requirements, a rigid body model of the system is first established and transformed into an all-drive system. A class of monotonic expected error curves is constructed, converting user-specified performance indicators such as convergence time and steady-state accuracy into quantitative constraints on the tracking error. Error transformation transforms the originally constrained tracking problem into an unconstrained stabilization problem. Furthermore, a smooth time-varying gain function combining exponential and polynomial functions is designed and embedded into an extended state observer, ensuring continuous and bounded gain before and after a specified time. This achieves fast and smooth estimation of the total system disturbance, overcoming the peak or chattering problems that may occur in traditional observers during transient phases. Finally, combining the estimation information and error feedback, a time-bound controller based on the expected error curve is designed, and a filter compensation mechanism is used to handle computational complexity, ensuring that all signals in the closed-loop system are bounded and that the tracking error converges within a preset specified time.

[0016] The main advantages of this invention are: it enables the tracking error of a quadcopter UAV to converge within a user-preset time, and the convergence time is completely independent of the system's initial state and control parameters; it achieves direct and quantitative constraints on system overshoot, convergence speed, and steady-state accuracy through the expected error curve, simplifying the controller parameter tuning process; the time-varying gain extended state observer used can smoothly and accurately estimate composite disturbances, avoiding abrupt changes in the estimated values; the proposed specified-time controller has a clear structure, combining feedforward compensation and feedback stabilization, effectively suppressing model uncertainty and external interference, and significantly improving the tracking accuracy, anti-interference capability, and engineering applicability of the quadcopter UAV in complex environments. Attached Figure Description

[0017] Figure 1 This is the control flowchart of the present invention; Figure 2 The position tracking error curve under initial condition ①; Figure 3 The attitude tracking error curve under initial condition ①; Figure 4 The position tracking error curve under initial condition ②; Figure 5 The attitude tracking error curve under initial condition ②; Figure 6 The control torque curve under initial condition ①; Figure 7 The control torque curve under initial condition ②; Figure 8 This is a three-dimensional spiral ascent curve under initial condition ①; Figure 9 This is a three-dimensional spiral ascent curve under initial condition ②; Figure 10 The extended state observer tracking curve under initial condition ①; Figure 11 The extended state observer tracking curve under initial condition ②; Detailed Implementation

[0018] The invention will now be further described with reference to the accompanying drawings.

[0019] Reference Figures 1-11 A method for time-specified all-wheel drive control of a quadrotor UAV based on error tracking, comprising the following steps: Step 1: Establish a rigid body model of the quadcopter UAV system, initialize the system's state and control parameters, and transform the model into an all-drive system. The process is as follows: 1.1 Considering the influence of external disturbances, the rigid body model of the quadcopter UAV is represented as follows: (1); in, This indicates the position of the quadcopter drone relative to the inertial coordinate system; yes The derivative; yes The second derivative; This represents the attitude angle of a quadcopter drone relative to an inertial coordinate system. yes The derivative; yes The second derivative; These represent the mass and gravitational acceleration of the quadcopter drone, respectively. These represent quadcopter drones in Moment of inertia on the shaft; Indicates the aerodynamic coefficient; This indicates uncertain disturbances in the external environment in terms of position and attitude. For control input of quadcopter drones; This indicates the control torque of a quadcopter drone; 1.2 Defining Virtual Control Variables for Quadrotor UAVs : (2); (3); (4); The rigid body model of a quadcopter UAV can be rewritten as an all-drive system model: (5); in, The position and attitude angles of the quadcopter drone; for The derivative; Six control inputs for the quadcopter drone; Unmodeled dynamics inside the quadcopter drone; This represents an uncertain disturbance in a bounded external environment; It is the sum of the internal unmodeled dynamics and the total external disturbance; 1.3 Definition of Tracking Error for Quadrotor UAVs for: (6); in, The desired trajectory for a quadcopter drone; Step 2: Construct the monotonic expected error curve and transform the error system model. The process is as follows: 2.1 Constructing a monotonic expected error curve for: (7); in, This indicates the specified convergence time constant; when time... hour, The specific formula is as follows: (8); in ; This represents the initial value for the tracking error of the quadcopter drone; 2.2 Defining the Expected Tracking Error of a Quadrotor UAV for: (9); Differentiating equation (9) and substituting it into equation (5), we get: (10); (11); in, They represent The first and second derivatives; They represent The first and second derivatives; Step 3, design the time-extended state observer and virtual controller, the process is as follows: 3.1 Construct the following exponential-polynomial time-varying gain function. To ensure convergence and smooth transition at a specified time: (12); in, It is a positive parameter; 3.2 Construct a time-dilated state observer to estimate the internal unmodeled dynamics and the total external disturbance: (13); in, for The estimated value; for The derivative; It is the gain variable of the extended state observer; 3.3 Define the error of the state observer for a specified time extension for: (14); Differentiating equation (14) and substituting it into equations (5) and (13), we get: (15); in, The Herwitz matrix; It is a constant matrix; This represents the actual total disturbance. 3.4 Define virtual error for: (16); in, for The derivative; For virtual control law, the design is as follows: (17); in, For virtual controller gain; 3.5 Taking the derivative with respect to the virtual error, we get: (18); Step 4, design a specified time controller based on the desired error curve, the process is as follows: Design a time-specific controller based on the desired error curve. for: (19); in, For controller gain; Step 5: Prove the stability of the specified time-dilation state observer and controller, as follows: 5.1 Based on the inversion recursion idea, the first step is to design the following Lyapunov function and prove that the observer of the extended state at a specified time is stably convergent: (20); in, It is a positive definite matrix; Differentiating equation (20), we get: (twenty one); in, ; for The maximum value, i.e. ; It is a positive definite matrix; 5.2 Based on the inverse recursive idea, the second step designs the following Lyapunov function, proving that the controller based on the expected error curve converges stably at a specified time: (twenty two); Differentiating equation (22), we get: (twenty three); in, ; This indicates taking the minimum value among the three. for The maximum value, i.e. ; Based on the above analysis, it is shown that the extended state observer and tracking error at a specified time can not only converge quickly within a specified time, but also converge stably to a very small neighborhood.

[0020] To verify the effectiveness of the proposed method, a simulation experiment was conducted on the control effect shown in equation (19). The initial conditions and control parameters in the experiment were set as follows: mass of the quadcopter UAV gravitational acceleration The sampling step size is 0.001s. The moment of inertia and aerodynamic coefficient on the shaft are selected as follows: ; and The external interference is selected as follows: ; Selected as The desired trajectory is set as follows: ; Time-varying gain function Virtual controller and controller The parameters in are set to respectively The parameters for the time-spread state observer are selected as follows. To verify that the proposed control strategy is independent of the initial conditions, two different initial attitudes were selected for simulation: ; ; Figures 2 to 11 The diagram shows the principle and simulation results of the proposed time-controlled method for quadrotor UAVs. Figures 2 to 5 The position and attitude tracking error curves under different initial conditions are shown. As can be seen from the figures, the system state errors converge rapidly to near the equilibrium point within a user-preset specified time, exhibiting high steady-state accuracy, demonstrating the superiority of this method in terms of dynamic response and control accuracy. Figures 6 to 7 The corresponding control input torque curve is shown. The control signal is smooth and bounded. After the system stabilizes, it can quickly reach the equilibrium value without violent jitter or strange phenomena. Figures 8 to 9 The actual tracking effect of the three-dimensional spiral upward trajectory is demonstrated. The actual curve matches the expected curve well, which verifies the accuracy of trajectory tracking. Figures 10 to 11The extended state observer's tracking performance for the total system disturbance is demonstrated. The observed values ​​quickly follow the actual disturbance changes, indicating that the observer has good estimation capabilities and robustness. In summary, this specified-time control method can achieve rapid convergence of system errors within a user-defined time, while ensuring smooth control input, accurate trajectory tracking, and strong disturbance rejection capabilities. It is suitable for high-precision, high-dynamic-requirement quadrotor UAV control tasks.

[0021] The above description illustrates the superiority of the designed method as demonstrated by simulation experiments presented in this invention. Clearly, this invention is not limited to the examples described above; various modifications can be made without departing from the fundamental spirit and scope of the invention. The control method designed in this invention exhibits excellent control performance for quadrotor UAV systems with model uncertainties and external disturbances, effectively achieving rapid convergence and high-precision maintenance of UAV position and attitude errors within a user-specified time period. This significantly improves the speed, accuracy, and robustness of the quadrotor UAV flight control system.

[0022] The above describes the good effects shown by one embodiment of the present invention. Obviously, the present invention is not only suitable for the above embodiment, but can also be implemented with various changes without departing from the basic spirit of the present invention and without exceeding the content involved in the substantive content of the present invention.

Claims

1. A method for time-specified all-drive control of a quadrotor unmanned aerial vehicle based on error tracking, characterized in that, The method includes the following steps: Step 1: Establish a rigid body model of the quadcopter UAV system, initialize the system's state and control parameters, and transform the model into a fully driven system to achieve decoupling of the control channel; Step 2: Construct a monotonic expected error curve and transform the error system model to plan the system error convergence trajectory; Step 3: Design a smooth time-varying gain function of exponential-polynomial combination; design a virtual controller and construct a time-extended state observer to estimate the total internal and external disturbances; Step 4: Design a specified time controller based on the desired error curve.

2. The method for all-wheel drive time-specified control of a quadrotor UAV based on error tracking as described in claim 1, characterized in that, The process of step 1 is as follows: 1.1 Considering the influence of external disturbances, the rigid body model of the quadcopter UAV is represented as follows: （1）； in, This indicates the position of the quadcopter drone relative to the inertial coordinate system; yes The derivative; yes The second derivative; This represents the attitude angle of a quadcopter drone relative to an inertial coordinate system. yes The derivative; yes The second derivative; These represent the mass and gravitational acceleration of the quadcopter drone, respectively. These represent quadcopter drones in Moment of inertia on the shaft; Indicates the aerodynamic coefficient; This indicates uncertain disturbances in the external environment in terms of position and attitude. For control input of quadcopter drones; This indicates the control torque of a quadcopter drone; 1.2 Defining Virtual Control Variables for Quadrotor UAVs : （2）； （3）； （4）； The rigid body model of a quadcopter UAV can be rewritten as an all-drive system model: （5）； in, The position and attitude angles of the quadcopter drone; for The derivative; Six control inputs for the quadcopter drone; Unmodeled dynamics inside the quadcopter drone; This represents an uncertain disturbance in a bounded external environment; It is the sum of the internal unmodeled dynamics and the total external disturbance; 1.3 Definition of Tracking Error for Quadrotor UAVs for: （6）； in, The desired trajectory for a quadcopter drone.

3. The method for all-wheel drive time-specified control of a quadrotor UAV based on error tracking as described in claim 1, characterized in that, The process of step 2 is as follows: 2.1 Constructing a monotonic expected error curve for: （7）； in, This indicates the specified convergence time constant; when time... hour, The specific formula is as follows: （8）； in ; This represents the initial value for the tracking error of the quadcopter drone; 2.2 Defining the Expected Tracking Error of a Quadrotor UAV for: （9）； Differentiating equation (9) and substituting it into equation (5), we get: （10）； （11）； in, They represent The first and second derivatives; They represent The first and second derivatives.

4. The method for all-wheel drive time-specified control of a quadrotor UAV based on error tracking as described in claim 1, characterized in that, The process of step 3 is as follows: 3.1 Construct the following exponential-polynomial time-varying gain function. To ensure convergence and smooth transition at a specified time: （12）； in, It is a positive parameter; 3.2 Construct a time-dilated state observer to estimate the internal unmodeled dynamics and the total external disturbance: （13）； in, for The estimated value; for The derivative; It is the gain variable of the extended state observer; 3.3 Define the error of the state observer with specified time extension for: （14）； Differentiating equation (14) and substituting it into equations (5) and (13), we get: （15）； in, The Herwitz matrix; It is a constant matrix; This represents the actual total disturbance. 3.4 Define virtual error for: （16）； in, for The derivative; For virtual control law, the design is as follows: （17）； in, For virtual controller gain; 3.5 Taking the derivative with respect to the virtual error, we get: （18）。 5. The method for all-wheel drive time-specified control of a quadrotor UAV based on error tracking as described in claim 1, characterized in that, The process of step 4 is as follows: Design a time-specific controller based on the desired error curve. for: （19）； in, This is the controller gain.

6. The method for all-wheel drive time-specified control of a quadrotor UAV based on error tracking as described in any one of claims 1 to 5, characterized in that, The method further includes the following steps: Step 5: Prove the stability of the specified time-dilation state observer and controller, as follows: 5.1 Based on the inversion recursion idea, the first step is to design the following Lyapunov function and prove that the observer of the extended state at a specified time is stably convergent: （20）； in, It is a positive definite matrix; Differentiating equation (20), we get: （21）； in, ; for The maximum value, i.e. ; It is a positive definite matrix; 5.2 Based on the inverse recursive idea, the second step designs the following Lyapunov function, proving that the controller based on the expected error curve converges stably at a specified time: （22）； Differentiating equation (22), we get: （23）； in, ; This indicates taking the minimum value among the three. for The maximum value, i.e. ; Based on the above analysis, it is shown that the extended state observer and tracking error at a specified time can not only converge quickly within a specified time, but also converge stably to a very small neighborhood.

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