A Quadrotor UAV Trajectory Tracking Control Method Based on Preset Performance Control

Abstract

This invention relates to the field of quadrotor unmanned aerial vehicle (UAV) technology, and more particularly to a trajectory tracking control method for quadrotor UAVs based on preset performance control. By establishing a Lagrange model of the quadrotor UAV attitude system and constructing an error dynamics model, a finite-time performance function and inequality constraints of preset performance boundaries are defined. An error transformation function is used to convert the constrained tracking error into an unconstrained tracking error. Then, by combining an adaptive law to estimate the upper bound of external disturbances, constructing a linear sliding mode surface, and designing a finite-time sliding mode controller, the tracking error converges to the neighborhood of the origin within a finite time under external disturbances, and always satisfies the preset performance boundaries throughout the control process. By designing an adaptive law to estimate the upper bound of external disturbances online, the precise upper bound of disturbance information is not required beforehand, significantly improving the robustness and adaptability of the UAV in complex environments and reducing the controller's dependence on model accuracy.

Description

Technical Field

[0001] This invention relates to the field of quadcopter drone technology, and in particular to a quadcopter drone trajectory tracking control method based on preset performance control. Background Technology

[0002] Quadrotor UAVs are a novel type of rotorcraft capable of autonomous vertical takeoff and landing and stable hovering. However, as a four-input, six-output nonlinear underactuated system, its dynamic characteristics are complex due to semi-coupled relationships between system state variables and non-holonomic constraints in the system model, significantly increasing the difficulty of controller design. In actual flight, the inability to accurately model external disturbances such as wind, blade rotation, and geomagnetic influences, which significantly impact the UAV itself, further complicates control. Therefore, ensuring effective control of quadrotor UAVs under external disturbances has become a hot research topic.

[0003] With the continuous development of control theory, various schemes have been applied to the control of quadrotor UAVs. Patent application CN202010801728.X proposes a self-healing quadrotor UAV anti-interference control method and system, designing control schemes based on interference observers for both the position and attitude subsystems to ensure the asymptotic stability of the closed-loop control system. However, according to the definition of asymptotic stability, as time approaches infinity, the system state or state error gradually approaches the origin; such an infinite convergence time is clearly unreasonable. Therefore, finite-time control has received widespread attention in recent years. Furthermore, adaptive control technology can effectively handle external interference caused by wind, geomagnetic influences, etc., achieving better control results. The invention patent application CN201710532250.3 proposes a finite-time adaptive control method for quadrotor UAVs based on non-singular terminal sliding mode. This method aims to ensure the finite-time stability of the quadrotor UAV control system, addressing inertial uncertainties and external disturbances. However, the proposed control algorithm requires an upper bound for the disturbance information, which is often unavailable in practical engineering. Furthermore, the algorithm only considers the steady-state performance of the control system, neglecting transient performance factors such as overshoot and convergence speed. With the rapid development of current technology, controlled objects are becoming increasingly complex, and the requirements for precision and real-time performance of control systems are also increasing. Therefore, existing technologies struggle to quickly achieve control objectives while ensuring the steady-state and transient performance of quadrotor UAV control systems with external disturbances. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a trajectory tracking control method for quadrotor UAVs based on preset performance control, which solves the technical problem that existing technologies struggle to quickly achieve control objectives while ensuring the steady-state and transient performance of quadrotor UAV control systems in the presence of external disturbances.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a trajectory tracking control method for a quadcopter UAV based on preset performance control, applied to the trajectory tracking control of a quadcopter UAV, comprising: S1. Establish a Lagrange model of the attitude system of the quadcopter UAV, and define the tracking error based on the expected trajectory and the actual attitude obtained, so as to construct an error dynamics model; S2. Define a finite-time performance function and construct inequality constraints containing preset performance boundaries to limit the transient and steady-state performance of the tracking error. S3. By using a preset error conversion function, the tracking error constrained by inequality is converted into an unconstrained tracking error. S4. Design an adaptive law for estimating the upper bound of external disturbances in the error dynamics model. Construct a linear sliding surface based on the original tracking error and its first derivative, and design a finite-time sliding controller in conjunction with the unconstrained tracking error. S5. A finite-time sliding mode controller is used to perform trajectory tracking control on the quadcopter UAV, so that the tracking error converges to the neighborhood of the origin within a finite time and always meets the preset performance boundary throughout the entire control process.

[0006] Preferably, when the rate of change of the finite-time performance function is greater than a preset steady-state value, it is proportional to the power of the difference between the function value and the preset steady-state value.

[0007] Preferably, when the initial error is non-negative, the upper bound of the inequality constraint is the finite-time performance function, and the lower bound is the product of the negative finite-time performance function and the preset overshoot parameter. When the initial error is negative, the lower bound of the inequality constraint is the negative finite-time performance function, and the upper bound is the product of the finite-time performance function and the preset overshoot parameter.

[0008] Preferably, the error conversion function is a strictly monotonically increasing function with a range within a preset interval, and the conversion relationship between tracking error and unconstrained tracking error is characterized by the product of the finite-time performance function and the inverse function of the error conversion function.

[0009] Preferably, the control quantities of the finite-time sliding mode controller include at least a feedforward term based on the system dynamics model and reference trajectory, a first linear feedback term proportional to the linear sliding surface, a second nonlinear feedback term proportional to the sign function of the linear sliding surface, a disturbance upper bound compensation term based on adaptive law estimation, and a performance adjustment term related to the unconstrained error variable.

[0010] Preferably, the update rate of the adaptive law is related to the sign function value of the linear sliding surface and an adaptive gain parameter, and includes a correction term to prevent parameter drift, which is proportional to the estimate of the upper bound of the current external disturbance.

[0011] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the described quadcopter unmanned aerial vehicle trajectory tracking control method.

[0012] By employing the above technical solution, the present invention provides a trajectory tracking control method for a quadcopter UAV based on preset performance control, which has at least the following beneficial effects: 1. This invention establishes a Lagrange model of the attitude system of a quadcopter UAV and constructs an error dynamics model. It defines a finite-time performance function and inequality constraints of a preset performance boundary. The constrained tracking error is converted into an unconstrained tracking error using an error transformation function. Then, by combining an adaptive law to estimate the upper bound of external disturbances, constructing a linear sliding surface, and designing a finite-time sliding mode controller, the tracking error is made to converge to the neighborhood of the origin within a finite time under external disturbances. Furthermore, the preset performance boundary is always satisfied throughout the entire control process, taking into account both the transient and steady-state performance of the system.

[0013] 2. This invention estimates the upper bound of external disturbances online by designing an adaptive law, without the need to obtain the precise upper bound of the disturbance information in advance. This overcomes the limitations of traditional control methods that require known upper bounds of disturbances or require disturbances to meet specific statistical characteristics. It significantly improves the robustness and adaptability of UAVs in complex environments and reduces the controller's dependence on model accuracy.

[0014] 3. The finite-time sliding mode controller proposed in this invention has a complete structure, including feedforward terms, linear feedback terms, nonlinear feedback terms, and performance adjustment terms. The control torque is reasonable and easy to implement in engineering. Moreover, this method is not only applicable to attitude tracking control of quadcopter UAVs, but can also be extended to the field of finite-time control of other second-order nonlinear systems, and has good versatility and scalability. Attached Figure Description

[0015] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application 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 of the trajectory tracking and control method for a quadcopter unmanned aerial vehicle (UAV) according to the present invention; Figure 2 This refers to the tracking error of the quadcopter UAV's attitude in the second and third channels of this invention; Figure 3 This refers to the tracking error of the attitude of the quadcopter UAV in the first channel of this invention. Figure 4 This is a diagram showing the change in attitude angle during the tracking process of the quadcopter UAV of this invention; Figure 5 This is a diagram showing the change in control torque during the tracking process of the quadcopter UAV of the present invention. Detailed Implementation

[0016] 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.

[0017] To address the technical challenge of rapidly achieving control objectives while ensuring the steady-state and transient performance of quadrotor UAV control systems under external disturbances, this embodiment provides a quadrotor UAV trajectory tracking control method based on preset performance control. Applied to the trajectory tracking control of quadrotor UAVs, this method introduces a preset performance function to constrain the transient and steady-state performance of the tracking error, and combines it with adaptive sliding mode control technology to achieve high-precision finite-time trajectory tracking under external disturbances. The method includes: S1. Establish the attitude system model and error dynamics model of the quadcopter UAV.

[0018] First, this embodiment uses attitude sensors such as gyroscopes carried by the quadrotor UAV to measure its three-degree-of-freedom attitude data, including pitch, roll, and yaw angles, and establishes a typical Lagrange model for the quadrotor UAV attitude system. The expression of this model is as follows: in, This represents the attitude vector of a quadcopter drone, including the roll angle. Pitch angle and yaw angle , and These are the attitude vectors of the quadcopter UAV. The first and second derivatives, It is the control torque acting on the roll, pitch, and yaw paths, which is the resultant of the lift provided by the rotor rotation driven by the four motors of the UAV. If the rotational speeds of the four motors are known, then the corresponding control force and control torque can be respectively derived from the formulas. and Calculated, where, and Let these represent the control force and control torque on the channel corresponding to the i-th motor, respectively. and This is a coefficient that is related to air density, propeller radius, number of blades, blade geometry, lift, and drag coefficients. Let represent the rotational speed of the i-th motor. The control torque on each attitude channel can then be calculated using the following formula: This represents the bounded external disturbances, such as wind, experienced by the drone during flight, with each term acting on one of the three channels of the attitude system. Inertia matrix. It is a symmetric matrix, defined as: in, , , , , ,in, and Defined separately and , Represents the moment of inertia. Matrix Defined as: in: in, express The first derivative, express The first derivative, express The first derivative.

[0019] Further, define If the desired tracking signal, or the desired trajectory, is given, then the tracking error can be defined as: Let the auxiliary variable be... , Then, both sides of the equation representing the Lagrange model of the quadcopter UAV's attitude system are multiplied by the inertia matrix. inverse matrix Therefore, the attitude system of the quadcopter UAV is converted into the following error dynamics model: in, Representing the inertia matrix The inverse matrix, This represents the normalized external disturbance term. express The first derivative.

[0020] S2. Define the finite-time performance function and construct inequality constraints.

[0021] To ensure the transient and steady-state performance of the quadcopter UAV attitude control system, this embodiment constructs inequality constraints. In this embodiment, when the initial error is non-negative, the upper bound of the inequality constraints is the finite-time performance function, and the lower bound is the product of a negative finite-time performance function and a preset overshoot parameter. When the initial error is negative, the lower bound of the inequality constraints is the negative finite-time performance function, and the upper bound is the product of the finite-time performance function and the preset overshoot parameter. These upper and lower bounds are the preset performance boundaries. Therefore, the inequality constraints in this embodiment can be as follows: in, , representing attitude channels, respectively representing roll, pitch, and yaw. In this embodiment, 0.25 can be used. and They represent the first The tracking error of each attitude channel at time t and the initial time... The value, The finite-time performance function to be defined is, in this embodiment, a finite-time performance function whose rate of change is proportional to the power of the difference between the function value and the preset steady-state value when its function value is greater than the preset steady-state value. Its expression can be as follows: in, It is a positive constant, and in this embodiment it is taken as 0.1. It is a positive constant, and in this embodiment it is taken as 0.6. This is a preset performance threshold, also known as a preset steady-state value, which is set to 0.005 in this embodiment. Based on the performance function defined above, a positive definite candidate Lyapunov function is designed as follows: Differentiating it, we get: According to the finite-time control lemma, we know It will converge to the origin within the preset time.

[0022] S3. Convert the tracking error constrained by inequalities into an unconstrained tracking error.

[0023] Since controller design cannot be directly based on inequality constraints, this embodiment uses time-varying boundary conditions to constrain error evolution in order to transform requirements such as convergence speed, overshoot range, and steady-state accuracy into designable mathematical constraints. Then, through error transformation, the constrained control problem is transformed into a stabilization problem, thereby achieving pre-setting and strict assurance of the system's performance throughout the entire process. In this implementation, a preset error transformation function is used to convert the inequality-constrained tracking error into an unconstrained tracking error. First, the conversion relationship between the tracking error and the unconstrained tracking error is characterized by the product of the finite-time performance function and the inverse function of this error transformation function: in, It is the attitude tracking error vector at time t. This is the transformed, unconstrained tracking error; this function is the error transformation function, and the two form an unconstrained equation relationship. The normalized error vector is defined as follows: This is used to transform boundary-constrained error variables into proportional forms, thereby mapping them to unconstrained variables through an error transformation function. The error transformation function is a strictly monotonically increasing function with a range within a preset interval, and its expression can be represented as: By differentiating the error transformation function and combining it with the finite-time performance function, we obtain the intermediate variables related to the unconstrained tracking error. : Step S3 can be used to determine the constrained tracking error at any time t. Mapped to unconstrained tracking error .

[0024] S4. Design a finite-time sliding mode controller.

[0025] First, based on the original tracking error and its first derivative Constructing a linear sliding surface Its expression is as follows: in, This is represented as the sliding surface combination coefficient, which is set to 2 in this embodiment.

[0026] To address external disturbances in the attitude system of a quadcopter UAV, an adaptive law is designed to estimate the upper bound of external disturbances in the error dynamics model. In this embodiment, the update rate of the adaptive law is related to the sign function value of the linear sliding surface and an adaptive gain parameter, and includes a correction term to prevent parameter drift. This correction term is proportional to the estimated value of the current upper bound of the external disturbance, and its expression is as follows: in, The output of the adaptive law, i.e., the estimated upper bound of the external disturbance, is used for the disturbance compensation term in the controller. The constant gain in the adaptive law is the fixed gain constant. This refers to the time-varying gain term in the adaptive law. In the adaptive law, the error variable measures the current estimated value. The degree of deviation from the upper limit of the interference, Design parameters influence the calculation scale of error variables. As an auxiliary variable, it is used to smooth the update process of the adaptive law and prevent abrupt changes in the estimated value; that is, it is a correction term used to prevent parameter drift. for The first derivative, This is a design constant used to adjust error variables. The threshold, The time constant is used to control auxiliary variables. update rate It is a small constant used for designing time-varying gains. The trigger threshold, For use as auxiliary variables The gain term in the equation is the adaptive gain parameter. The threshold constant is This refers to the term related to the sign function value of the linear sliding surface. In this embodiment, , , , , , , .

[0027] Finally, combining the linear sliding surface and the unconstrained tracking error, a finite-time sliding mode controller is designed. In this embodiment, the control quantity of the finite-time sliding mode controller includes at least a feedforward term based on the system dynamics model and the reference trajectory, a first linear feedback term proportional to the linear sliding surface, a second nonlinear feedback term proportional to the sign function of the linear sliding surface, a disturbance upper bound compensation term based on adaptive law estimation, and a performance adjustment term related to the unconstrained error variable, the expression of which is as follows; in, This represents the control torque vector, which is the actual control quantity applied to the roll, pitch, and yaw channels of a quadcopter UAV. For linear feedback gain coefficient, These are constant parameters in the controller. Let be a diagonal matrix, defined as , The unconstrained tracking error vector is defined as follows: , That is, based on the system dynamics model and the reference trajectory, the feedforward term is used to counteract the coupling effects of the system itself and track the desired trajectory. That is, the first linear feedback term, which is proportional to the linear sliding surface, is used to drive the system state to converge toward the sliding surface. That is, the second nonlinear feedback term, which is proportional to the sign function of the sliding surface, is coupled with the upper bound compensation term for the disturbance in the adaptive law estimation. This refers to the performance adjustment term related to the unconstrained error variable, used to ensure that the tracking error always meets the preset performance boundaries. In this embodiment, , , , .

[0028] S5. A finite-time sliding mode controller is used to perform trajectory tracking control on the quadcopter UAV, so that the tracking error converges to the neighborhood of the origin within a finite time and always meets the preset performance boundary throughout the entire control process.

[0029] S6. Stability analysis and simulation verification.

[0030] Design a positive definite Lyapunov function: Differentiating it, we get: in, according to The properties, further simplified, yield the following: in, The convergence rate coefficient is greater than 0. Therefore, according to the properties of the preset performance function, the system state error will satisfy the inequality constraints mentioned above.

[0031] Finally, digital simulation was performed on this embodiment. As shown in Figures (2) and (3), the attitude tracking error of the quadcopter UAV converges to the origin within 5 seconds under the presence of external disturbances, and both transient and steady-state performance remain within the preset performance boundary PB. As shown in Figure (4), the UAV attitude tracks the desired trajectory within a finite time. As shown in Figure (5), the torque diagram shows that the control torque generated by the controller designed in this embodiment is suitable for application to quadcopter UAVs. Therefore, it can be found that the quadcopter UAV trajectory tracking control law based on preset performance control and adaptive control proposed in this invention can complete the trajectory tracking task within a finite time under the presence of external disturbances.

[0032] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a quadcopter unmanned aerial vehicle trajectory tracking control method.

[0033] 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.

[0034] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0035] 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 trajectory tracking control method for a quadrotor unmanned aerial vehicle (UAV) based on preset performance control, applied to the trajectory tracking control of a quadrotor UAV, characterized in that, include: S1. Establish a Lagrange model of the attitude system of the quadcopter UAV, and define the tracking error based on the expected trajectory and the actual attitude obtained, so as to construct an error dynamics model; S2. Define a finite-time performance function and construct inequality constraints containing preset performance boundaries to limit the transient and steady-state performance of the tracking error. S3. By using a preset error conversion function, the tracking error constrained by inequality is converted into an unconstrained tracking error. S4. Design an adaptive law for estimating the upper bound of external disturbances in the error dynamics model. Construct a linear sliding surface based on the original tracking error and its first derivative, and design a finite-time sliding controller in conjunction with the unconstrained tracking error. S5. A finite-time sliding mode controller is used to perform trajectory tracking control on the quadcopter UAV, so that the tracking error converges to the neighborhood of the origin within a finite time and always meets the preset performance boundary throughout the entire control process.

2. The quadcopter UAV trajectory tracking and control method according to claim 1, characterized in that, The rate of change of the finite-time performance function is proportional to the power of the difference between the function value and the preset steady-state value when the function value is greater than the preset steady-state value.

3. The quadcopter UAV trajectory tracking and control method according to claim 1, characterized in that: When the initial error is non-negative, the inequality constraint has an upper bound of a finite-time performance function and a lower bound of the product of a negative finite-time performance function and a preset overshoot parameter. When the initial error is negative, the lower bound of the inequality constraint is the negative finite-time performance function, and the upper bound is the product of the finite-time performance function and the preset overshoot parameter.

4. The trajectory tracking and control method for a quadcopter UAV according to claim 1, characterized in that: The error conversion function is a strictly monotonically increasing function with a range within a preset interval, and the conversion relationship between tracking error and unconstrained tracking error is characterized by the product of the finite-time performance function and the inverse function of the error conversion function.

5. The trajectory tracking and control method for a quadcopter UAV according to claim 1, characterized in that, The control quantities of the finite-time sliding mode controller include at least a feedforward term based on the system dynamics model and reference trajectory, a first linear feedback term proportional to the linear sliding surface, a second nonlinear feedback term proportional to the sign function of the linear sliding surface, a disturbance upper bound compensation term based on adaptive law estimation, and a performance adjustment term related to the unconstrained error variable.

6. The trajectory tracking and control method for a quadcopter UAV according to claim 1, characterized in that, The update rate of the adaptive law is related to the sign function value of the linear sliding surface and an adaptive gain parameter, and includes a correction term to prevent parameter drift, which is proportional to the estimate of the upper bound of the current external disturbance.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the quadcopter unmanned aerial vehicle trajectory tracking control method as described in any one of claims 1 to 6.

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