A finite time tracking control method for a vehicle-mounted single-link robotic arm system

Abstract

The present invention discloses a finite time tracking control method for a vehicle-mounted single-link mechanical arm system, comprising: establishing a mathematical model of a vehicle-mounted single-link mechanical arm system with unmodeled dynamics and unknown control direction; obtaining a tracking error based on the position of the mechanical arm and an expected tracking signal according to the mathematical model of the vehicle-mounted single-link mechanical arm system, and constructing a first-order filter in combination with dynamic surface technology; constructing a virtual controller based on a backstepping method, an adaptive method, and a finite time control algorithm; constructing a controller based on a backstepping method, an adaptive method, and a finite time control algorithm, and in combination with a virtual controller, to control the vehicle-mounted single-link mechanical arm system. The control method of the present invention makes the closed-loop system semi-globally finite time stable, so that the system can track the expected trajectory within a finite time.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle-mounted single-link mechanical arm motion control, and in particular to a finite time tracking control method for a vehicle-mounted single-link mechanical arm system. Background Art

[0002] The vehicle-mounted single-link manipulator system is a manipulator system installed on a vehicle. With its outstanding advantages of simple structure, strong flexibility and high reliability, it can operate stably even in harsh environments, thereby greatly improving production efficiency and product quality. In view of this, it is of great significance to study the control method of the single-link manipulator system. As a typical nonlinear system, the backstepping method has been proven to be effective in the design of its controller. However, when the nonlinear system is not completely known, the backstepping method is no longer applicable. In the prior art, fuzzy logic systems (FLSs) and neural networks (NNs) are widely used in the design of adaptive backstepping controllers because of their excellent nonlinear approximation capabilities. It should be noted that the repeated differentiation of virtual control inputs in traditional backstepping control is prone to "computational expansion". If handled improperly, it will increase the online computing burden and reduce system performance. Dynamic surface control technology can overcome this shortcoming. In recent years, there have been research results on adaptive control of nonlinear uncertain systems based on dynamic surface control technology, but these controllers do not consider the situation of unmodeled dynamics and unknown control direction.

[0003] In actual engineering, there are often uncertain nonlinear dynamics that cannot be modeled, that is, unmodeled dynamics. The so-called unmodeled dynamics refers to the fact that measurement noise, external interference and modeling errors often exist in actual applications. If this problem is not taken seriously, the use of this controller will bring disadvantages to the actual system, and in serious cases, it will cause system instability. In addition, due to the inevitable uncertainty of the robotic arm system, the influence of factors such as inaccurate models or changes in the environment, the effect of the control input on the system may change direction over time or with changes in the system state, resulting in unknown control direction. When the control direction is unknown, it is impossible to determine in advance how the change in the control input will specifically affect the system state. This will undoubtedly bring great challenges to the design and analysis of the control system. When designing controllers for robotic arm systems, existing research rarely considers both unmodeled dynamics and unknown control directions.

[0004] In addition, it is of vital importance to achieve fast tracking control of the vehicle-mounted single-link manipulator. Compared with the asymptotic control method, the desired control performance can only be obtained when the convergence time approaches infinity. Obviously, for the manipulator system, achieving the control target within a finite time is more practical. Therefore, compared with the asymptotic control method, the finite time control method has received widespread attention and has been applied to some manipulator systems due to its better anti-interference ability, higher tracking accuracy and faster convergence speed. However, the current research has not conducted in-depth discussions on the situation of unmodeled dynamics and unknown control direction. Summary of the invention

[0005] Technical purpose: In view of the defects in the prior art, the present invention discloses a finite-time tracking control method for a vehicle-mounted single-link robotic arm system, so that the closed-loop system is semi-globally finite-time stable, and the system can track the desired trajectory within a finite time.

[0006] Technical solution: In order to achieve the above technical objectives, the present invention adopts the following technical solution.

[0007] A finite time tracking control method for a vehicle-mounted single-link mechanical arm system, the method comprising:

[0008] Establish a mathematical model of a vehicle-mounted single-link robotic arm system with unmodeled dynamics and unknown control direction;

[0009] According to the mathematical model of the vehicle-mounted single-link robotic arm system, the tracking error is obtained based on the position of the robotic arm and the expected tracking signal, and a first-order filter is constructed in combination with the dynamic surface technology;

[0010] Constructing virtual controllers based on backstepping, adaptive methods, and finite-time control algorithms;

[0011] Based on the backstepping method, adaptive method and finite time control algorithm, a controller is constructed in combination with a virtual controller to control the vehicle-mounted single-link robotic arm system.

[0012] Beneficial effects: Aiming at the control problem of a vehicle-mounted single-link robotic arm, a new finite-time control method based on backstepping is proposed for a single-link robotic arm system with unmodeled dynamics and unknown control direction. The control method can make the closed-loop system semi-globally finite-time stable, so that the system can track the desired trajectory within a finite time. The present invention simultaneously considers the unmodeled dynamics and unknown control direction and processes them by adopting Nussbaum functions and adaptive methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the method of the present invention;

[0014] Figure 2 The state x in the simulation verification process 1 and d Schematic diagram of the curve;

[0015] Figure 3 The state x in the simulation verification process 2 Schematic diagram of the curve;

[0016] Figure 4 is the tracking error in the simulation verification process |x 1 -y d | Schematic diagram of the curve;

[0017] Figure 5 Schematic diagram of the control force curve during the simulation verification process. DETAILED DESCRIPTION

[0018] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0019] For a vehicle-mounted single-link robotic arm system, a finite-time tracking control method for a vehicle-mounted single-link robotic arm system is designed, considering the situation of unmodeled dynamics and unknown control direction. The control direction in the vehicle-mounted single-link robotic arm system is unknown, and the Nussbaum function method is used to process it; the backstepping method is used to design a finite-time controller, but when using the traditional backstepping control method, since each step requires virtual controller information and its derivative, it will lead to the problem of "computational expansion", so the dynamic surface technology is used to avoid the occurrence of this problem; considering that the asymptotically stable control method converges slowly, the convergence speed of the system is accelerated by semi-global finite-time stable control; the output state of the single-link robotic arm system can converge to the desired state within a finite time under the situation of unmodeled dynamics and unknown control direction, so as to realize fast and high-precision tracking control of uncertain single-link robotic arm systems. The method of this embodiment is further explained below.

[0020] As attached Figure 1 As shown, a finite time tracking control method for a vehicle-mounted single-link mechanical arm system of this embodiment includes the following steps:

[0021] Step 1: Establish a mathematical model of a vehicle-mounted single-link robotic arm system with unmodeled dynamics and unknown control direction; the dynamic model of the vehicle-mounted single-link robotic arm system is as follows:

[0022]

[0023] Where N is the mechanical inertia coefficient, M is the viscous friction coefficient; p is the position of the robot arm, and U is the control input signal. are the first and second derivatives of p respectively, R=mgL, where L is the length of the connecting rod, g is the acceleration of gravity, and m is the load mass.

[0024] Let x 1 =p, And considering the unmodeled dynamics and unknown control direction, the mathematical model of the vehicle-mounted single-link robotic arm system can be obtained as follows:

[0025]

[0026] in, Δ 1 (x, z, t) and Δ 2 (x, z, t) is the dynamic disturbance of the vehicle-mounted single-link robotic arm system, that is, the dynamic disturbance of z and x at time t, z is an unmeasurable state, is the unmodeled dynamics of the vehicle-mounted single-link robotic arm system, and is also the first-order derivative of the unmeasurable state z, y is the output of the vehicle-mounted single-link robotic arm system, and q(z, x) is the unknown nonlinear function for z and x. 1 , x 2 ] is the system state, u is the output signal of the controller, and is also the control input signal of the vehicle-mounted single-link robotic arm system;

[0027] Step 2: According to the mathematical model of the vehicle-mounted single-link robotic arm system, the tracking error is obtained based on the position of the robotic arm and the expected tracking signal, and a first-order filter is constructed in combination with the dynamic surface technology; the dynamic surface technology is used to avoid the calculation expansion in the backstepping method; define the following coordinate transformation:

[0028]

[0029] Among them, e 1 is the tracking error, e 2 For state x 2 and α 2，L The difference, η 2 is α 2，L With virtual controller α 1 The difference, y d In order to track the expected signal, there are 77 2 =α 2，L -α 1 , αα 2，L is the output signal of the first-order filter, and the model of the first-order filter is:

[0030]

[0031] Among them, α 1 For virtual controllers, is a positive number; α 1 (0) is the virtual controller α 1 The initial state, α 2，L (0) is the output signal α of the first-order filter 2，L The initial state of

[0032] Step 3: construct a virtual controller based on backstepping method, adaptive method and finite time control algorithm;

[0033] Virtual Controller α 1 The design process is as follows:

[0034] Design a Lyapunov function of the following form:

[0035]

[0036] Among them, V 1 is the Lyapunov function, λ 1 is a constant, for The estimated value of is θ 1 The upper bound of the two-norm of θ 1 is the weight matrix of the fuzzy logic system. for The fuzzy logic system is a common method in the design of the vehicle-mounted single-link robotic arm system controller, which will not be described in detail here.

[0037] According to the Lyapunov function, the virtual controller is:

[0038]

[0039] Among them, 1 For function The variable, ζ 1 The adaptive change law is where π 1 is a designed function, which is specifically expressed as follows in this embodiment:

[0040]

[0041] is a fuzzy basis function, located in a fuzzy logic system, which is a prior art in this field and will not be described in detail here. for The transposed matrix of is the first-order derivative of the desired tracking signal, γ 1 is a constant, X 1 =[x 1 , e 1 , z], ∈1 is a normal number, ∈ is a normal number; γ 1 >0 is a constant, λ 1 >0 is a constant, N(ζ 1 ) is a Nussbaum function, satisfying:

[0042]

[0043] in, For function , S is an independent variable parameter, sup is the supremum, and inf is the infimum;

[0044] Common Nussbaum functions are Etc., in the present invention, can be selected

[0045] Among them, the adaptive method in the virtual controller is embodied in 1 Adaptive change law design;

[0046] Step 4: Based on the backstepping method, adaptive method and finite time control algorithm, a controller is constructed in combination with a virtual controller to control the vehicle-mounted single-link robotic arm system;

[0047] The controller design process is as follows:

[0048]

[0049] Among them, u is the output signal of the controller, which is used to control the vehicle-mounted single-link robotic arm system, corresponding to the vehicle-mounted single-link

[0050] The control input signal in the rod manipulator system, ζ 2 For function The variable of ζ is adaptively changed as follows: π 2 A function designed for is specifically expressed as:

[0051]

[0052] for The estimated value of is θ 2 The upper bound of the two-norm is θ 2 is the weight matrix of the fuzzy logic system, is the fuzzy basis function, for The transposed matrix of 2 >0 is a constant, λ 2 >0 is a constant, X 2 =[x 1 , x 2 , e 1 , e 2 , z], ∈ 2 is a positive constant; N(ζ 2 ) is a Nussbaum function, satisfying:

[0053]

[0054] in, For function Variables;

[0055] Common Nussbaum functions are Etc., in the present invention, can be selected

[0056] Among them, the adaptive method in the controller is embodied in ζ 2 Adaptive change law design.

[0057] The control method of the present invention has been simulated and verified, and the closed-loop stability of the control method of the present invention is demonstrated below in combination with the verification results.

[0058] For the single-link manipulator system, considering the existence of unmodeled dynamics and unknown control direction, the controller and virtual controller designed according to the control method of the present invention, the closed-loop system is semi-global finite-time stable, and the tracking of the desired state, i.e., the tracking error x, is achieved within a finite time. 1 (r)-y d (t) is bounded in finite time.

[0059] The present invention takes the single-link mechanical arm dynamics system as the research object, and the specific parameters of the controller are designed as λ 1 =0.02,λ 2 =0.002,γ 1 =1.5, γx=1.5, x(0)=[x 1 (0), x 2 (0)|=[-0.8, 0], which is the initial value of the system state, y d =0.2sin(0.05t), The simulation results are Figures 2 to 5As shown, it can be seen that the proposed finite-time tracking control scheme of the present invention can still ensure fast and high-precision tracking control of the desired state within a finite time even when the dynamics are not modeled and the control direction is unknown.

[0060] The "first" and "second" in the names such as "first" and "second" (if any) mentioned in the embodiments of the present application are only used as name identifiers and do not represent the first or second in order.

[0061] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A finite time tracking control method for a vehicle-mounted single-link robotic arm system, characterized in that the method include: Establish a mathematical model of a vehicle-mounted single-link robotic arm system with unmodeled dynamics and unknown control direction; According to the mathematical model of the vehicle-mounted single-link robotic arm system, the tracking error is obtained based on the position of the robotic arm and the expected tracking signal, and a first-order filter is constructed in combination with the dynamic surface technology; Constructing virtual controllers based on backstepping, adaptive methods, and finite-time control algorithms; Based on the backstepping method, adaptive method and finite time control algorithm, a controller is constructed in combination with a virtual controller to control the vehicle-mounted single-link robotic arm system; The mathematical model of the vehicle-mounted single-link robotic arm system includes: Among them, z is an unmeasurable state, is the unmodeled dynamics of the single-link robotic arm system, Δ1(x, z, t) and Δ2(x, z, t) are the dynamic disturbances of the vehicle-mounted single-link robotic arm system, y is the output of the vehicle-mounted single-link robotic arm system, q(z, x) is an unknown nonlinear function, p is the position of the robot arm, is the first-order derivative of p, R = mgL, L is the length of the connecting rod, g is the acceleration of gravity, m is the load mass, N is the mechanical inertia coefficient, and M is the viscous friction coefficient; Step 2 also includes: dynamic surface technology is used to avoid the calculation expansion in the backstepping method; define the following coordinate transformation: Among them, e1 is the tracking error, e2 is the state x2 and α 2，L The difference between 2，L The difference with the virtual controller α1, y d is the expected tracking signal; based on the dynamic surface technology, η2=α 2，L -α1, α 2，L is the output signal of the first-order filter, α1 is the virtual controller; The model of the first-order filter is: in, is a positive number; α1(0) is the initial state of the virtual controller α1, α 2，L (0) is the output signal α of the first-order filter 2，L The initial state of The design process of virtual controller α1 includes: Design Lyapunov function: Among them, V1 is the Lyapunov function, λ1 is a constant, for The estimated value of is the upper bound of the two-norm of θ1, that is, θ1 is the weight matrix of the fuzzy logic system; for The square of; According to the Lyapunov function, the virtual controller is: Among them, ζ1 is the variable of function N(ζ1), and the adaptive change law of ζ1 is Where π1 is a designed function; in, is the fuzzy basis function, for The transposed matrix of is the first-order derivative of the desired tracking signal, γ1 is a constant, X1=[x1,e1,z], ∈1 is a normal number, ∈ is a normal number; γ1>0 is a constant, λ1>0 is a constant, and N(ζ1) is the Nussbaum function.

2. The finite time tracking control method of a vehicle-mounted single-link robotic arm system according to claim 1, characterized in that: The controller design process includes: Where, e2 = x2-α 2，L ;u is the output signal of the controller, ζ2 is the function The variable of ζ2 is adaptively changed as follows: π2 is a designed function specifically expressed as: for The estimated value of is the upper bound of the two-norm of θ2, that is, θ2 is the weight matrix of the fuzzy logic system, is the fuzzy basis function, for The transposed matrix, γ2>0 is a constant, λ2>0 is a constant, X2=[x1,x2,e1,e2,z], ∈2 is a normal number; N(ζ2) is the Nussbaum function.

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