A tracking control method for flexible robotic arms

Abstract

The present invention discloses a tracking control method for a flexible robotic arm, comprising the following steps: S1. constructing a model of the flexible robotic arm system; S2. constructing tracking errors of various orders; S3. describing the control objective and designing a feedback controller; S4. constructing a neural network model; S5. designing a virtual controller; and S6. combining Lyapunov's second method to ensure that the Lyapunov function is positive semidefinite and that its time derivative is negative semidefinite. Because the controller design is based on a cost function containing inputs, energy consumption is fully considered, thereby minimizing controller energy consumption, significantly reducing design complexity, and enabling the tracking error to converge to the optimal solution more quickly.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arms, and in particular to a tracking control method applied to a flexible robotic arm. Background Art

[0002] With the continuous development of industrial automation, robots are increasingly used in fields such as medicine, industrial manufacturing, and the military. Flexible robotic arms, with their high flexibility, light weight, and strong load capacity, have shown great potential in unstructured and dynamic environments, and have therefore received widespread attention. However, the elasticity of the flexible robotic arm's joints makes it very easy to deform and vibrate when subjected to driving forces, gravity, and other forces, which greatly increases the difficulty of controlling the robotic arm. At the same time, since the mathematical models of most flexible robotic arms belong to high-order systems, the repeated differentiation of virtual signals may cause a "complexity explosion" problem when designing the controller, and the energy consumption required for control will be relatively large. To overcome these problems, this patent proposes a tracking control method based on optimized backstepping for the tracking control of flexible robotic arms, which enables the angular position of the connecting rod of the flexible robotic arm to track the desired trajectory during movement. Summary of the Invention

[0003] In response to the problems existing in the prior art, the purpose of the present invention is to provide a tracking control method for a flexible manipulator. Based on the analysis of a single-link flexible manipulator model and the measured angular position and angular velocity of the connecting rod and motor shaft as feedback information, a tracking control system based on optimization backstepping is designed, which enables the angular position of the connecting rod of the flexible manipulator to track the desired trajectory during movement. 1) Since the design of the controller is based on a cost function containing an input signal, energy consumption is fully considered, thereby minimizing the energy consumption of the controller; 2) Since a new type of optimization backstepping tracking control scheme is adopted, the unknown terms in the controller design are directly approximated by a neural network to design virtual controllers of various orders and input controllers, greatly reducing the design complexity; 3) The present invention uses an actor-critic architecture to conduct interactive learning between the critic and executor networks, so that the tracking error converges to the optimal solution more quickly.

[0004] In order to solve the above problems, the present invention adopts the following technical solutions

[0005] A tracking control method for a flexible robotic arm, comprising the following steps:

[0006] S1. Build a model of the flexible robotic arm system;

[0007] S2. Construct each order tracking error;

[0008] S3. Describe the control objective and design a feedback controller;

[0009] S4. Build a neural network model;

[0010] S5. Design a virtual controller;

[0011] S6. Combined with Lyapunov's second method, it is ensured that the Lyapunov function is positive semidefinite and the time derivative of the function is negative semidefinite.

[0012] Construct each order tracking error, each order tracking error e i (t), i=1,2,...,n is as follows:

[0013] e1(t)=y(t)-y m (t)

[0014] e i (t) = x i (t)-α i-1 (t),i=2,...,n

[0015] Among them, y(t) is the actual output, y m (t) is the given expected output, α i (t), i=1,...,n is the virtual controller, take n=4, then e1(t) is the difference between the actual output y(t) and the given expected output y m (t), e2(t) is the error value between the state variable x2(t) and the virtual controller α1(t), e3(t) is the error value between the state variable x3(t) and the virtual controller α2(t), and e4(t) is the error value between the state variable x4(t) and the virtual controller α3(t).

[0016] Describe the control objective. Design a feedback controller so that the error of the connecting rod angular position satisfies That is, when time tends to infinity, the actual output y(t) of the link of the flexible manipulator is different from the given expected output y m The error between (t) tends to zero, and the tracking errors of other orders e are achieved at the same time. i (t),i=2,...,n is minimized.

[0017] Constructing a neural network model: Using the following neural network model:

[0018]

[0019] Where χ∈R n is the input vector of the neural network, W T ∈R p×m is the weight matrix, p is the number of neurons,

[0020] S(χ)=ps1(χ),...,s p(χ)] T is a known basis function vector, s i It is generally a Gaussian function, that is:

[0021]

[0022] where μ i =[μ i1 ,...,μ in ] T , μ ij is the center position of the Gaussian function in χ, η i is the width of the Gaussian function.

[0023] In order to make the actual output angular position of the link of the flexible manipulator track the planned output angular position and minimize the overall error of the system, a virtual controller α is designed based on the cost function containing the input. i (t), i=1,2,...,n-1 and the input signal u(t) are as follows:

[0024]

[0025]

[0026] Among them, σ i ,i=1,2...,n are designable parameters; and δ i ,i=1,2,...,n are the known dynamic and control gains in the flexible manipulator system respectively; and are the unknown ideal weights W for critic and actor respectively * Estimates, The update rates are as follows:

[0027]

[0028]

[0029] The update rates are as follows:

[0030]

[0031] in:

[0032]

[0033]

[0034] Among them, λ ci ,i=1,2,...,n and λ ai,i=1,2,...,n are the critic learning rate and actor learning rate respectively, both of which are designable parameters.

[0035] Combined with Lyapunov's second method, as long as the Lyapunov function is positive semidefinite and the time derivative of the function is negative semidefinite, each designable parameter needs to satisfy the following inequality:

[0036]

[0037] Beneficial effects of the present invention

[0038] Compared with the prior art, the advantages of the present invention are:

[0039] Since the controller design is based on a cost function containing inputs, the energy consumption issue is fully considered, thereby minimizing the energy consumption of the controller;

[0040] Because it adopts a new optimized backstepping tracking control scheme, it directly uses neural networks to approximate the unknown terms in the controller design to design virtual controllers of various orders and input controllers, which greatly reduces the design complexity;

[0041] By utilizing the actor-critic architecture to interactively learn the critic and actor networks, the tracking error converges to the optimal solution more quickly. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a model diagram of the single-link flexible robotic arm of the present invention. DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0044] Describe the model and symbols of the flexible manipulator system. Figure 1 The single-link flexible manipulator model shown in the figure is taken as an example, where q1 and q2 are the angular positions of the connecting rod and the motor shaft, respectively, which can be obtained through sensors; u is the input signal, that is, the torque generated by the drive motor; I and J are the inertias of the connecting rod and the rotor, respectively; M is the mass of the connecting rod; l is the position of the center of gravity of the connecting rod; k is the stiffness coefficient. These parameters can be obtained through the identification system and are therefore considered as known quantities in this patent; g is the acceleration of gravity. In order to simplify the design of the controller for the optimized backstepping tracking control scheme, the state variable is selected.

[0045] A tracking control method for a flexible robotic arm comprises the following steps:

[0046] S1. Build a model of the flexible robotic arm system;

[0047] S2. Construct each order tracking error;

[0048] S3. Describe the control objective and design a feedback controller;

[0049] S4. Build a neural network model;

[0050] S5. Design a virtual controller;

[0051] S6. Combined with Lyapunov's second method, it is ensured that the Lyapunov function is positive semidefinite and the time derivative of the function is negative semidefinite.

[0052] Construct each order tracking error, each order tracking error e i (t), i=1,2,...,n is as follows:

[0053] e1(t)=y(t)-y m (t)

[0054] e i (t) = x i (t)-α i-1 (t),i=2,...,n

[0055] Among them, y(t) is the actual output, y m (t) is the given expected output, α i (t), i=1,...,n is the virtual controller, take n=4, then e1(t) is the difference between the actual output y(t) and the given expected output y m (t), e2(t) is the error value between the state variable x2(t) and the virtual controller α1(t), e3(t) is the error value between the state variable x3(t) and the virtual controller α2(t), and e4(t) is the error value between the state variable x4(t) and the virtual controller α3(t).

[0056] Describe the control objective. Design a feedback controller so that the error of the connecting rod angular position satisfies That is, when time tends to infinity, the actual output y(t) of the link of the flexible manipulator is different from the given expected output y m The error between (t) tends to zero, and the tracking errors of other orders e are achieved at the same time. i (t),i=2,...,n is minimized.

[0057] Constructing a neural network model: Using the following neural network model:

[0058]

[0059] Where χ∈R n is the input vector of the neural network, W T ∈R p×m is the weight matrix, p is the number of neurons,

[0060] S(χ)=[s1(χ),...,s p (χ)] T is a known basis function vector, s i It is generally a Gaussian function, that is:

[0061]

[0062] where μ i =[μ i1 ,...,μ in ] T , μ ij is the center position of the Gaussian function in χ, η i is the width of the Gaussian function.

[0063] In order to make the actual output angular position of the link of the flexible manipulator track the planned output angular position and minimize the overall error of the system, a virtual controller α is designed based on the cost function containing the input. i (t), i=1,2,...,n-1 and the input signal u(t) are as follows:

[0064]

[0065]

[0066] Among them, σ i ,i=1,2...,n are designable parameters; and δ i ,i=1,2,...,n are the known dynamic and control gains in the flexible manipulator system respectively; and are the unknown ideal weights W for critic and actor respectively * Estimates, The update rates are as follows:

[0067]

[0068]

[0069] The update rates are as follows:

[0070]

[0071] in:

[0072]

[0073]

[0074] Among them, λ ci ,i=1,2,...,n and λ ai ,i=1,2,...,n are the critic learning rate and actor learning rate respectively, both of which are designable parameters.

[0075] Combined with Lyapunov's second method, as long as the Lyapunov function is positive semidefinite and the time derivative of the function is negative semidefinite, each designable parameter needs to satisfy the following inequality:

[0076]

[0077] The above description is merely a preferred embodiment of the present invention; however, the scope of protection of the present invention is not limited thereto. Any person skilled in the art who, within the technical scope disclosed by the present invention, makes equivalent substitutions or modifications based on the technical solutions and improved concepts of the present invention shall be covered by the scope of protection of the present invention.

Claims

1. A tracking control method for a flexible robotic arm, characterized in that: The following steps are involved: S1. Build a model of the flexible robotic arm system; S2. Construct each order tracking error; S3. Describe the control objective and design a feedback controller; S4. Build a neural network model; S5. Design a virtual controller; S6. Combined with Lyapunov's second method, ensure that the Lyapunov function is positive semidefinite and that its time derivative is negative semidefinite. Construct each order tracking error, each order tracking error e i (t), i=1,2,...,n is as follows: e1(t)=y(t)-y m (t) e i (t)=x i (t)-α i-1 (t),i=2,...,n Among them, y(t) is the actual output, y m (t) is the given expected output, α i (t), i=1,...,n is the virtual controller, take n=4, then e1(t) is the difference between the actual output y(t) and the given expected output y m (t), e2(t) is the error value between the state variable x2(t) and the virtual controller α1(t), e3(t) is the error value between the state variable x3(t) and the virtual controller α2(t), and e4(t) is the error value between the state variable x4(t) and the virtual controller α3(t); Constructing a neural network model: Using the following neural network model: Where χ∈R n is the input vector of the neural network, W T ∈R p×m is the weight matrix, p is the number of neurons, S(χ)=[s1(χ),...,s p (χ)] T is a known basis function vector, s i is a Gaussian function, that is: where μ i =[μ i1 ,...,μ in ] T , μ ij is the center position of the Gaussian function in χ, η i is the width of the Gaussian function; In order to make the actual output angular position of the link of the flexible manipulator track the planned output angular position and minimize the overall error of the system, a virtual controller α is designed based on the cost function containing the input. i (t), i=1,2,...,n-1 and the input signal u(t) are as follows: Among them, σ i ,i=1,2...,n are designable parameters; and δ i ,i=1,2,...,n are the known dynamic and control gains in the flexible manipulator system respectively; and are the unknown ideal weights W for critic and actor respectively * Estimates, The update rates are as follows: The update rates are as follows: in: Among them, λ ci ,i=1,2,...,n and λ ai ,i=1,2,...,n are the critic learning rate and actor learning rate respectively, both of which are designable parameters.

2. The tracking control method for a flexible robotic arm according to claim 1, characterized in that: Describe the control objective and design a feedback controller so that the error of the connecting rod angular position satisfies That is, when time tends to infinity, the actual output y(t) of the link of the flexible manipulator is different from the given expected output y m The error between (t) tends to zero, and the tracking errors of other orders e are achieved at the same time. i (t),i=2,...,n is minimized.

3. The tracking control method for a flexible robotic arm according to claim 1, wherein: Combined with Lyapunov's second method, as long as the Lyapunov function is positive semidefinite and the time derivative of the function is negative semidefinite, each designable parameter needs to satisfy the following inequality:

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