Finite-time adaptive autopilot control method for unmanned systems

Abstract

This paper proposes a novel control method for a finite-time adaptive autopilot for unmanned systems. Addressing the widespread inability of current standard autopilots to handle system uncertainties, the present invention, based on a finite-time sliding mode control algorithm framework, designs a finite-time sliding mode surface that avoids singularity and continuously switches. This method proposes a finite-time adaptive rate to track and compensate for the uncertainties of the unmanned system in real time, thereby designing a finite-time adaptive sliding mode control autopilot solution for unmanned systems. This solution enhances the robustness and adaptability of the system, and features plug-and-play modularity. This autopilot solution is not only applicable to a variety of unmanned systems, but also effectively tracks and compensates for the widespread uncertainty issues in these systems. In the presence of uncertain parameter changes and interference, the proposed finite-time adaptive control method enables the system to achieve finite-time eventually uniformly bounded stability.

Description

Technical Field

[0001] The present invention relates to a finite-time adaptive autopilot control method for an unmanned system, belonging to the technical field of intelligent control. Background Art

[0002] Unmanned systems include drones, vehicles, ships, and underwater vehicles. In recent years, they have been widely used in a variety of fields, such as surveillance, logistics, exploration, mapping, and agriculture. Although different unmanned systems have diverse architectures, applications, and operational domains, they all share a common characteristic: the use of autopilots for navigation, guidance, and control. Most unmanned systems are complex, nonlinear systems with coupled longitudinal and lateral dynamics. Drones and underwater vehicles have six degrees of freedom (3D displacement and 3 attitude angles), and are typically controlled by four inputs (roll, pitch, yaw, and throttle). Drones and ships have three degrees of freedom (2D displacement and 1 heading angle), and are typically controlled by two inputs (rudder and throttle). ArduPilot is an open-source autopilot library that supports a variety of unmanned systems. It is developed and maintained by the world's largest community of scientists and engineers. Given ArduPilot's flexibility and widespread application, the method proposed in this proposal will be redeveloped based on the ArduPilot open-source library to make it compatible with a variety of unmanned systems. Currently, almost all standard open-source autopilots use a PID cascade continuous closed-loop architecture (including outer-loop position control and inner-loop speed control). This is because PID controllers are simple to implement and have low computational complexity. However, this linear controller is insufficient to handle the state-dependent and unstructured uncertainties that are prevalent in unmanned systems, such as climate and environmental disturbances, changes in unmanned system load parameters, and unmodeled dynamic system components. When these uncertainties arise, users often need to readjust the PID controller gains in ArduPilot to prevent the autopilot from experiencing reduced control performance or even instability. Therefore, the ArduPilot open-source library currently lacks an adaptive autopilot that can control multiple types of unmanned systems while being compatible with the current standard PID cascade closed-loop architecture. Summary of the Invention

[0003] The technical problem to be solved by the present invention is that unmanned systems are mostly complex nonlinear systems with coupled under-excited longitudinal and lateral dynamic characteristics. The external environment in which they operate is very complex, containing many dependent states and unstructured uncertainties, such as interference from the climate environment, changes in the load parameters of the unmanned system, unmodeled dynamic system parts, etc., and the current mainstream open autopilot libraries such as ArduPilot or PX4 still use linear cascade closed-loop control, which is not sufficient to handle these uncertainties. Although there are many other methods to deal with the uncertainties of these dependent states, most of these methods are targeted at specific unmanned systems, such as the flight control of drones and the pilot of unmanned ships, and they cannot handle multiple types of unmanned systems from a higher level. At the same time, the existing methods are also not compatible with the PID cascade closed-loop control architecture of ArduPilot or PX4.

[0004] Objectives of the present invention: This invention addresses the internal and external environmental uncertainties faced by unmanned systems during mission execution by proposing a finite-time controller. This controller enables the unmanned system's autopilot to adaptively identify these uncertainties, minimizing system failures and rapidly restoring stability within a finite timeframe. Furthermore, the proposed autopilot is compatible with a wide range of existing PID loop cascade systems, including but not limited to ArduPilot and PX4.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows: a finite-time adaptive autopilot control method for an unmanned system, the method comprising the following steps:

[0006] Step 1: Establish the unmanned system dynamics model;

[0007] Step 2: Design a new finite-time sliding surface based on the tracking error;

[0008] Step 3: Extract the uncertainty structure in the system;

[0009] Step 4: Adaptive controller design. This solution is based on adaptive finite-time sliding mode control and adopts a modular design. It can not only be applied to the autopilots of various unmanned systems, but also enables the system to achieve finite-time eventually consistent boundedness, making the system converge and stabilize faster. The specific technical solution is as follows:

[0010] As an improvement of the present invention, step 1: establishing a dynamic model of the unmanned system is as follows: Since most unmanned systems are mechanical systems, such as drones, unmanned vehicles, unmanned ships, etc., the Euler-Lagrangian system is often used to represent the dynamic model of the mechanical system, and its model equation is:

[0011]

[0012] where q, is the n-dimensional state vector of the system and its derivative; M(q) is the mass / inertia matrix of the system; is the Coriolis centripetal force matrix; g(q) is the vector of gravitational moment; are the damping and friction vectors; d represents the external disturbance vector;

[0013] u is the control input. The Euler-Lagrange system has the following properties:

[0014] 1) The norms of matrices and vectors in the Euler-Lagrange system are bounded, that is, there exist positive real numbers c, g, f, a such that

[0015] It should be noted that in this solution, the sizes of c, g, f, and a do not need to be known in advance.

[0016] 2) The matrix M(q) is symmetric and positive definite, satisfying 0 <m1I n ≤M(q)≤m2I n , where m1, m2 are positive constants, I n is the identity matrix,

[0017] 3) Matrix is an antisymmetric matrix, that is, there exists a non-zero vector X with

[0018] Since the Euler-Lagrange system is used to refer to unmanned systems such as drones, unmanned vehicles, and unmanned ships, these unmanned systems will have different M, C, G, F, and d forms when converted into Euler-Lagrange system equations. Here we treat them all as uncertain contents and deal with them accordingly.

[0019] As an improvement of the present invention, step 2: designing a new finite-time sliding mode surface based on the tracking error, specifically as follows:

[0020] This invention provides a control scheme for a finite-time adaptive autopilot for unmanned systems. This scheme, based on finite-time sliding mode control and employing a modular design, can be applied to autopilots for a variety of unmanned systems. It also enables the system to achieve finite-time eventually uniform boundedness, leading to faster convergence and stability. The specific technical solution is as follows:

[0021] First define the error e(t) = q(t)-q d (t), t is the time variable, q d is the target state vector and its norm satisfies ‖q d ‖≤q m , q m and q mmis a positive constant, the finite-time sliding surface is designed as

[0022]

[0023] Where s is the sliding surface, is the time derivative of e, λ p and λ i Refers to the gains of the proportional controller and the integral controller respectively, λ f is a positive constant, Δ(e) is a function of Δ i (e i ) is a vector of elements, defined as follows:

[0024]

[0025] where 0<γ<1, ε is a small positive constant, sign(·) is the sign function, and

[0026] α1=(2-γ)ε γ-1

[0027]

[0028] Then the time derivative in (2) is

[0029]

[0030] where the vector The elements are

[0031]

[0032] Note that the positive constants α1 and α2 ensure that the sliding surface s and the derivative At point|e i |=ε, in addition, the designed sliding surface s and the derivative The singularity in the entire state space is eliminated, and the designed sliding surface can make the error e and Converges in a finite time. At the same time, Δ(e) in formulas (2) and (5) is The following theorem will be satisfied:

[0033]

[0034] As an improvement of the present invention, step 3: extracting the uncertainty structure in the system is as follows. Based on the finite time sliding surface s in formula (2), the uncertainty structure in the Euler system (1) can be extracted. Multiplying both sides of formula (4) by the inertia matrix M and using formula (1) can obtain

[0035]

[0036] where represents the structural uncertainty in system (1), which is state-dependent, is defined as follows:

[0037]

[0038] Next, the goal is to find a suitable state-dependent upper bound for this uncertainty structure and define

[0039]

[0040] where ξ(t) satisfies the following inequality:

[0041]

[0042] According to Theorem (6) and inequality (9), the state-dependent upper bound of the structural uncertainty can be obtained

[0043]

[0044] where is a positive constant:

[0045]

[0046]

[0047]

[0048] Note that these parameters are all unknown. Therefore, later, how to design the controller and the adaptation rate will be introduced, so that the controller can adaptively track the uncertainty and at the same time make the state tracking error converge within a finite time.

[0049] As an improvement of the present invention, Step 4: Adaptive controller design, is specifically as follows: In order to compensate for the uncertainty in formula (10), the controller input is designed as:

[0050]

[0051] where Γ is a positive definite matrix, μ>0, σ>0, 0<v<1, and

[0052]

[0053] i = 0, 1, 2 can be regarded as the estimated values in formula (10), and its adaptation rate is

[0054]

[0055] Its initial value And β i is a positive constant. According to these conditions, we can get Always holds true. Design a Lyapunov function:

[0056]

[0057] in It can be proved in

[0058] It can be seen that the system will be stable in a finite time, and the tracking error e, and It will converge to the boundary region in a finite time.

[0059] The present invention proposes a finite time adaptive rate (13) so that it converges to the uncertainty of the system within a finite time, and the proposed controller is compatible with the ArduPilot unmanned system autopilot system.

[0060] The controller proposed in the present invention is also compatible with other autopilots based on PID loop control, including but not limited to ArduPilot, PX4, etc.

[0061] Compared to the prior art, the present invention has the following advantages: The present invention designs a finite-time adaptive autopilot system for unmanned systems based on ArduPilot. This system addresses the inability of standard open-source PID cascade closed-loop autopilot systems to address the state-dependent and unstructured uncertainties that arise during the operation of unmanned systems. The autopilot control method proposed in the present invention minimizes losses caused by failures, allowing the unmanned system to quickly recover from uncertain disturbances and achieve greater robustness. The adaptive controller of the present invention can estimate and compensate for uncertainties within and outside the unmanned system in real time, allowing the system to converge rapidly within a finite time. The autopilot proposed in the present invention is also compatible with existing PID cascade flight control systems. Its structure can be easily implemented in currently popular autopilots such as ArduPilot and PX4, while also enhancing their performance. Therefore, the present invention can be directly applied to current standard autopilot systems, is simple and easy to implement, and has high economic and practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 The control algorithm flow chart of the adaptive finite-time autopilot in this proposal is shown;

[0063] Figure 2 This paper introduces how to apply the proposed control algorithm to autopilot;

[0064] Figure 3 The control framework diagram of the ArduPilot quadrotor drone adaptive finite-time autopilot is shown. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and technical advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be fully described below with reference to the accompanying drawings.

[0066] Example 1: See Figure 1-Figure 3 , a finite-time adaptive autopilot control method for an unmanned system, the method comprising the following steps:

[0067] Step 1: Establish the unmanned system dynamics model;

[0068] Step 2: Design a new finite-time sliding surface based on the tracking error;

[0069] Step 3: Extract the uncertainty structure in the system;

[0070] Step 4: Adaptive controller design. This solution is based on adaptive finite-time sliding mode control and adopts a modular design. It can not only be applied to the autopilots of various unmanned systems, but also enables the system to achieve finite-time eventually consistent boundedness, making the system converge and stabilize faster. The specific technical solution is as follows:

[0071] Step 1: Establish the unmanned system dynamics model as follows: Since most unmanned systems are mechanical systems, such as drones, unmanned vehicles, and unmanned ships, the Euler-Lagrange system is often used to represent the dynamics model of mechanical systems. Its model equation is:

[0072]

[0073] where q, is the n-dimensional state vector of the system and its derivative; M(q) is the mass / inertia matrix of the system; is the Coriolis centripetal force matrix; G(q) is the vector of gravitational moment; are the damping and friction vectors; d represents the external disturbance vector;

[0074] u is the control input. The Euler-Lagrange system has the following properties:

[0075] 1) The norms of matrices and vectors in the Euler-Lagrange system are bounded, that is, there exist positive real numbers c, g, f, a such that

[0076] It should be noted that in this solution, the sizes of c, g, f, and a do not need to be known in advance.

[0077] 2) The matrix M(q) is symmetric and positive definite, satisfying 0 <m1I n ≤M(q)≤m2I n , where m1, m2 are positive constants, I n is the identity matrix,

[0078] 3) Matrix is an antisymmetric matrix, that is, there exists a non-zero vector X with

[0079] Since the Euler-Lagrange system is used to refer to unmanned systems such as drones, unmanned vehicles, and unmanned ships, these unmanned systems will have different M, C, G, F, and d forms when converted into Euler-Lagrange system equations. Here we treat them all as uncertain contents and deal with them accordingly.

[0080] Step 2: Based on the tracking error, design a new finite-time sliding surface as follows:

[0081] This invention provides a control scheme for a finite-time adaptive autopilot for unmanned systems. This scheme, based on finite-time sliding mode control and employing a modular design, can be applied to autopilots for a variety of unmanned systems. It also enables the system to achieve finite-time eventually uniform boundedness, leading to faster convergence and stability. The specific technical solution is as follows:

[0082] First define the error e(t) = q(t)-q d (t), t is the time variable, q d is the target state vector and its norm satisfies ‖q d ‖≤q m , q m and q mm is a positive constant, the finite-time sliding surface is designed as

[0083]

[0084] Where s is the sliding surface, is the time derivative of e, λ p and λ i Refers to the gains of the proportional controller and the integral controller respectively, λ f is a positive constant, Δ(e) is a function of Δ i (e i ) is a vector of elements, defined as follows:

[0085]

[0086] where 0<γ<1, ε is a small positive constant, sign(·) is the sign function, and

[0087]

[0088] Then the time derivative in (2) is

[0089]

[0090] where the vector The elements are

[0091]

[0092] Note that the positive constants α1 and α2 ensure that the sliding surface s and the derivative At point|e i |=ε, in addition, the designed sliding surface s and the derivative The singularity in the entire state space is eliminated, and the designed sliding surface can make the error e and Converges in a finite time. At the same time, Δ(e) in formulas (2) and (5) is The following theorem will be satisfied:

[0093]

[0094] Step 3: Extract the uncertainty structure in the system. Specifically, based on the finite-time sliding surface s in formula (2), the uncertainty structure in the Euler system (1) can be extracted. Multiplying both sides of formula (4) by the inertia matrix M and using formula (1) yields

[0095]

[0096] in represents the structural uncertainty in system (1), which is state-dependent. The definition of is as follows:

[0097]

[0098] The next goal is to give this uncertainty structure Find a suitable state-dependent upper bound, define

[0099]

[0100] Among them, ξ(t) satisfies the following inequality:

[0101]

[0102] According to Theorem (6) and inequality (9), the state-dependent upper bound of structural uncertainty can be obtained.

[0103]

[0104] where is a positive constant:

[0105]

[0106]

[0107]

[0108] Note that these parameters are all unknown. Therefore, how to design the controller and adaptive rate will be introduced later, so that the controller can adaptively track the uncertainty, and at the same time make the state tracking error converge within a finite time.

[0109] Step 4: Design of the adaptive controller is as follows: In order to compensate for the uncertainty in formula (10), the controller input is designed as:

[0110]

[0111] where Γ is a positive definite matrix, μ > 0, σ > 0, 0 < v < 1, and

[0112]

[0113] i = 0, 1, 2 can be regarded as the estimated value in formula (10), and its adaptive rate is

[0114]

[0115] whose initial value and β i is a positive constant. According to these conditions, it can be obtained that always holds. Design the Lyapunov function:

[0116]

[0117] where It can be proved that where Thus, it can be seen that the system will be stable within a finite time, and the tracking error e, and will converge to the boundary region within a finite time.

[0118] The present invention proposes a finite time adaptive rate (13) so that it converges to the uncertainty of the system within a finite time, and the proposed controller is compatible with the ArduPilot unmanned system autopilot system.

[0119] The controller proposed in this invention is also compatible with other autopilots based on PID loop control, including but not limited to ArduPilot, PX4, etc.

[0120] Example 2: ArduPilot is a popular open-source autopilot library for unmanned systems. It supports the development of a variety of unmanned systems, including drones, unmanned ships, unmanned submarines, and unmanned vehicles. It is maintained by numerous scientists and engineers. This example will use ArduPilot's quadcopter flight control system to illustrate the implementation of the present invention.

[0121] Figure 1 The control algorithm flow chart for the proposed adaptive finite-time autopilot is shown. First, the unmanned system feeds the controller system state and calculates the tracking error. The sliding surface s and error vector ξ are also calculated. The adaptive rate and sliding mode gain ρ are then calculated. This yields the input enhancement term, which is then added to the original PID input to produce the final control input.

[0122] First, let’s review the controller (11) proposed in this invention, which is equivalent to:

[0123]

[0124] Please refer to the above patent requirements for parameter definitions, where Γs1 is equivalent to the PID controller, and the following It can be integrated into the original PID loop, and the entire control loop can achieve finite time convergence. It can be directly embedded into the original flight control's PID loop as a plug-and-play method. The implementation process in the ArduPilot quadrotor drone is as follows:

[0125] 1. Find the five controllers of the flight control in the quadrotor drone, namely the plane position XY controller, height Z controller, roll angle controller, pitch angle controller, and yaw angle controller.

[0126] 2. Confirm the error e of each controller, Note that these errors are the control components in the original PID controller, and the error λ is calculated based on this f Δ(e).

[0127] 3. Calculate the error vector ξ and the finite-time sliding surface s based on these error quantities.

[0128] 4. Calculate the adaptation rate and gain ρ in formulas (12) and (13).

[0129] 5. Calculation The control input is enhanced and added to the original PID frame input, and the final control output is the adaptive finite time control input.

[0130] Figure 2 The steps for applying the proposed control algorithm to an ArduPilot autopilot are presented. Figure 3 This diagram shows the control framework for the ArduPilot quadrotor drone's adaptive finite-time autopilot. The position controller, altitude controller, and attitude controller receive IMU data from the drone. The position controller and altitude controller receive the desired airspeed and altitude from the upper layer. The position controller outputs the desired roll and pitch angles to the attitude controller, while the altitude controller outputs throttle commands to the drone's motors. Each controller is a combination of a native PID controller and an adaptive finite-time controller. Figure 3 The control framework diagram of the ArduPilot quadrotor drone adaptive finite-time autopilot is shown.

[0131] The control algorithm of this proposal is very easy to integrate into existing open source autopilot libraries such as ArduPilot and PX4, and can be applied to various unmanned systems such as drones, unmanned ships, and unmanned vehicles. At the same time, it can enhance the robustness and adaptability of the original PID architecture and better handle the state-dependent and unstructured uncertainty problems that are widely present in unmanned systems. The proposed finite-time adaptive control method enables the system to achieve finite-time eventually uniformly bounded stability.

[0132] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention, and equivalent changes or substitutions made on the basis of the above technical solutions fall within the scope of protection of the claims of the present invention.

Claims

1. A finite-time adaptive autopilot control method for an unmanned system, characterized in that: The method includes the following steps: Step 1: Establish the dynamic model of the unmanned system; Step 2: Design a new finite-time sliding surface according to the tracking error; Step 3: Extract the uncertainty structure in the system; Step 4: Design the adaptive controller; Among them, Step 2: Design a new finite-time sliding surface according to the trajectory tracking error, specifically as follows: First, define the trajectory tracking error vector e(t) = q(t)-q d (t), t is the time variable, q d is the target state vector and its norm satisfies ||q d ||≤q m , q m and q mm is a positive constant, the finite-time sliding surface is designed as Where s is the sliding surface vector, is the time derivative of e, λ p and λ i Refers to the gains of the proportional controller and the integral controller respectively, λ f is a positive constant, Δ(e) is a function of Δ i (e i ) is a vector of elements, which serves the purpose of finite time convergence of the system and is defined as follows: where 0 < γ < 1, ε is a small positive constant, sign(·) is the sign function, and the definitions of α1 and α2 are respectively α1=(2-γ)ε γ-1 α2=(γ-1)ε γ-2 Then the time derivative in equation (2) is where the vector The elements are The constants α1 and α2 ensure that the sliding surface s and the derivative At the point Continuity at , In addition, the designed sliding surface s and the derivative The singularity in the entire state space is eliminated, and the designed sliding surface can make the error e and Converges in a finite time. At the same time, Δ(e) in formulas (2) and (5) is The following theorem will be satisfied:

2. The unmanned system finite time adaptive autopilot control method according to claim 1, characterized in that: Step 1: Establish the dynamic model of the unmanned system, specifically as follows: The Euler-Lagrange system is used to represent the dynamic model of the mechanical system, and its model equation is: where q, is the n-dimensional state vector of the system and its derivative; M(q) is the mass / inertia matrix of the system; is the Coriolis centripetal force matrix; G(q) is the vector of gravitational moment; are the damping and friction vectors; d represents the external disturbance vector; and u is the control input. The Euler-Lagrangian system has the following properties: 1) The norms of matrices and vectors in the Euler-Lagrange system are bounded, that is, there exist positive real numbers c, g, f, a such that ||G(q)||≤g, ||d||≤a. 2) The matrix M(q) is symmetric and positive definite, satisfying 0 <m1I n ≤M(q)≤m2I n , where m1, m2 are positive constants, I n is the identity matrix, 3) Matrix is an antisymmetric matrix, that is, there exists a non-zero vector X with The Euler-Lagrangian system is used to refer to unmanned aerial vehicles, unmanned vehicles, unmanned ships and unmanned systems.

3. The unmanned system finite time adaptive autopilot control method according to claim 2, characterized in that: Step 3: Extract the uncertainty structure in the system, specifically as follows. Based on the finite-time sliding surface s in formula (2), the uncertainty structure in the Euler system (1) can be extracted. Multiply both sides of formula (4) by the inertia matrix M and use formula (1) to obtain in represents the structural uncertainty in system (1), which is state-dependent. The definition of is as follows: The next goal is to give this uncertainty structure Find a suitable state-dependent upper bound, define where T represents the transpose of a vector or matrix, and the matrix ξ(t) satisfies the following inequality: According to Theorem (6) and inequality (9), the state-dependent upper bound of the structural uncertainty can be obtained in A positive constant is:

4. The unmanned system finite time adaptive autopilot control method according to claim 3, characterized in that: Step 4: Design the adaptive controller, specifically as follows: In order to compensate for the uncertainty in formula (10), the controller input u(t) is designed as: where Γ is a positive definite matrix, sign(·) is the sign function, μ > 0, σ > 0, 0 < v < 1, and It can be regarded as the The estimated value, whose adaptive rate is Its initial value And β i is a positive constant, i=0,1,2, according to these conditions we can get Always holds true, design a Lyapunov function: in prove in It can be seen that the system will be stable in a finite time, and the tracking error e, and It will converge to the boundary region in a finite time.

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