A pre-set time adaptive neural network collaborative control method for a robotic arm

Abstract

This invention relates to the fields of industry and disciplinary research technology, and discloses a method for pre-time adaptive neural network collaborative control of robotic arms. First, a multi-robotic arm system model with unknown nonlinearities is established. Then, based on backstepping technology, event-triggered mechanisms, neural network adaptive control technology, and pre-time stable control theory, an event-triggered adaptive neural network pre-time stable collaborative controller is designed. Simulation results show that all signals in the multi-robotic arm system are semi-globally stable and bounded, errors can converge to a smaller set within a preset time, and the system does not exhibit the Zeno phenomenon.

Description

Technical Field

[0001] The present invention relates to the field of industry and subject research technology, and in particular to a preset time adaptive neural network collaborative control method for a robotic arm. Background Art

[0002] In recent years, the intelligent manufacturing industry has developed rapidly, and the working mode of robotic arms has also shifted from individual operation to collaborative operation of multiple robotic arms. It is widely used in various industrial fields, subject research, etc.

[0003] For the collaborative operation of multiple robotic arms, it has excellent control performance, including flexible operation, strong robustness and excellent coordination in complex tasks. As the application of collaborative operation of multiple robotic arms becomes more and more extensive, the industry has higher requirements for the control accuracy, stable speed and stability of the collaborative control of multiple robotic arms.

[0004] In past research, scholars have proposed several excellent control methods. However, these traditional control methods can only ensure that the system stabilizes within an indeterminate timeframe. The system's convergence time is uncertain, and the convergence speed does not meet practical requirements. Other scholars have proposed finite-time control methods, which offer significant convergence and robustness advantages. However, the convergence time depends on the initial system state and initial parameter settings, requiring extensive and tedious calculations and making them difficult to control and adjust. Therefore, we propose a pre-timed adaptive neural network collaborative control method for the robotic arm. Summary of the Invention

[0005] (1) Technical problems solved

[0006] In response to the shortcomings of the existing technology, the present invention provides a preset time adaptive neural network collaborative control method for a robotic arm, introduces an event trigger mechanism, and the input gain of the model is a variable gain, which can not only realize the advance setting of the system convergence time, but also compensate the system with the variable gain, solve the impact of the input dead zone on the system, and reduce communication pressure.

[0007] (2) Technical solution

[0008] To achieve the above-mentioned purpose, the present invention provides the following technical solution: a method for collaborative control of a robotic arm with a preset time adaptive neural network, comprising the following steps:

[0009] Step 1: Model the multi-manipulator system with unknown nonlinearities and obtain the state equation of the i-th manipulator;

[0010] Step 2: Define the error variable of the i-th multi-manipulator and design the first virtual control law α i,1 and adaptive law

[0011] Step 3: Define the event trigger mechanism;

[0012] Step 4: Define the second virtual control law α i,2 and adaptive law and

[0013] Step 5: Based on the Matlab experimental platform, conduct simulation experiments and analyze the stability of the system.

[0014] Preferably, the first step specifically includes the following:

[0015] S1: The i-th (i=1,2…,N) robotic arm can be described as:

[0016]

[0017] x i,1 Represents the angular velocity of the i-th robotic arm link, y i and Represent the output signal and input signal of the i-th robot arm respectively, Represents the nonlinear dead zone input, the gain function A i =1.5+0.1sin(x i,1 x i,2 ), B i Represents the viscous friction coefficient, G i Represents the mass of the connecting rod, l i Represents the connecting rod length, J i represents the moment of inertia;

[0018] S2: The input dead zone model is expressed as:

[0019]

[0020] and are the right slope and left slope of the dead zone, respectively, and r ir (t) and r il (t) represent the right and left breakpoints of the dead zone, respectively, satisfying r ir (t)≥0,r il (t)≥0;

[0021] S3: Rewrite the above dead zone model as follows:

[0022] in;

[0023]

[0024]

[0025] S4: The synchronization error of the i-th robot arm can be defined as:

[0026]

[0027] y0 represents the reference output of the virtual leader, B=diag[b1,b2,…,b N ]∈R N×N Represents the adjacency matrix between the leader and the robot. If the robot i can obtain information from the leader, then b i >0, if not then b i =0.

[0028] Preferably, the error variable of the i-th robot arm in the second step is:

[0029]

[0030] where z i,2 is the error variable of the i-th robotic arm, α i,1 is the virtual control law of the i-th multi-manipulator.

[0031] Preferably, the first virtual control law α in the second step i,1 and adaptive law as follows:

[0032] S1: Use radial basis function neural network to analyze the unknown combination part Approximation is performed, which is expressed as:

[0033]

[0034] X i,1 =[x i,1 ,x j,1 ,x j,2 ] T ,σ i,1 (X i,1 )Satisfaction relationship and

[0035] S2: First virtual control law α i,1 and adaptive law The design is as follows:

[0036]

[0037]

[0038] g i,1 g i,1 Input the lower bound of the gain function, and the parameters satisfy ρi,1 >0,l i,1 >0.

[0039] Preferably, the specific content of the third step is:

[0040] S1: Define the event triggering mechanism as follows:

[0041]

[0042] Among them, the design parameters meet

[0043] S2: Define the control signal as:

[0044]

[0045] in

[0046] S3: Pass Yes i Make an estimate, and the estimation error is expressed as:

[0047] In summary, the control signal can be rewritten as:

[0048]

[0049] S4: Construct relative threshold:

[0050]

[0051] When t κ+1 Time, relative error satisfy The output signal Will be updated to event trigger signal

[0052] Preferably, the fourth step includes the following:

[0053] S1: Use radial basis function neural network to analyze the unknown combination part Approximation is performed, which is expressed as:

[0054]

[0055] in and

[0056] S2: According to the second error variable z i,2 The above process uses radial basis function neural network to solve the unknown uncertain part, and uses backstepping design method and Lyapunov function to design the second virtual control law α i,2 , while generating the adaptive law and

[0057]

[0058]

[0059]

[0060] in Design parameter ρ i,2 >0,l i,2 >0, g i,2 g i,2 Lower bound, satisfied g i,2 ≤g i,2 .

[0061] (3) Beneficial effects

[0062] Compared with the prior art, the present invention provides a method for collaborative control of a robotic arm using a preset time adaptive neural network, which has the following beneficial effects:

[0063] This pre-timed adaptive neural network collaborative control method for a robotic arm considers a second-order nonlinear robotic arm model with input deadband and time-varying gain. By estimating the variable input gain bounds, introducing compensation into the control ratio, and designing an adaptive law, it addresses the issues of system instability caused by deadband and external disturbances.

[0064] 2. The preset time adaptive neural network collaborative control method of the robotic arm is proposed in the controller to enable the system stabilization time to be set in advance without being affected by the system state or requiring a large amount of tedious calculations. This method can meet the preset requirements for convergence time.

[0065] 3. This robotic arm's preset time adaptive neural network collaborative control method establishes an event trigger mechanism within the robotic arm system to conserve valuable communication resources. By setting appropriate trigger thresholds, unnecessary communication is reduced while ensuring tracking control. This significantly reduces communication pressure and eliminates Zeno behavior. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a schematic diagram of the nonlinear input dead zone;

[0067] Figure 2 Schematic diagram of communication topology;

[0068] Figure 3 Schematic diagram of the reference signal and the output of each follower;

[0069] Figure 4 It is a schematic diagram of synchronization error;

[0070] Figure 5 Schematic diagram of the control signal of follower 1;

[0071] Figure 6 Schematic diagram of the control signal of follower 2;

[0072] Figure 7 Schematic diagram of the control signal of follower 3;

[0073] Figure 8 Schematic diagram of control signals for follower 4;

[0074] Figure 9 Schematic diagram of the time intervals of trigger events for Follower 1, Follower 2, Follower 3, and Follower 4. DETAILED DESCRIPTION

[0075] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0076] See also Figure 1-9 , a method for collaborative control of a robotic arm with a preset time adaptive neural network, comprising the following steps:

[0077] S01. Model the multi-manipulator system with unknown nonlinearity and obtain the state equation of the i-th manipulator;

[0078] There is an unknown nonlinear multi-manipulator system consisting of a leader and N (N>2) followers, where the i-th (i=1,2…,N) manipulator can be described as

[0079]

[0080] Among them, x i,1 Represents the angular velocity of the i-th robotic arm link, y i and Represent the output signal and input signal of the i-th robot arm respectively, Represents the nonlinear dead zone input, the gain function A i =1.5+0.1sin(x i,1 x i,2 ), B i Represents the viscous friction coefficient, G i Represents the mass of the connecting rod, l iRepresents the connecting rod length, J i Represents the moment of inertia.

[0081] The input dead zone model is expressed as

[0082]

[0083] in, and are the right slope and left slope of the dead zone, respectively, and r ir (t) and r il (t) represent the right and left breakpoints of the dead zone, respectively, satisfying r ir (t)≥0,r il (t)≥0.

[0084] The input can be rewritten as

[0085]

[0086] in

[0087]

[0088]

[0089] The research objective of this invention is to design an event-triggered adaptive neural network preset time stable collaborative controller for a nonlinear multi-manipulator system with input dead zone, so that each manipulator can keep up with the leader's signal within the preset time and have a satisfactory tracking effect.

[0090] Without loss of generality, the following assumptions exist:

[0091] Assumption 1. There are two positive constants and g i,k are the upper and lower bounds of the variable input, respectively, satisfying

[0092]

[0093] Assumption 2. The leader's reference signal is a known bounded continuous function with a second-order derivative.

[0094] For ease of description, we need to refer to the relevant knowledge of algebraic graph theory and regard each robot as a node. The information interaction in a unidirectional directed topology consisting of a virtual leader and N (N>2) robots is represented by a directed graph G = (V, E, A), where V = {1, ..., N} represents the multi-robot node (1, ..., N) and V j ×V i∈E represents the edge from robot node j to robot node i. The adjacency matrix between all robot nodes is A=[a ij ] N×N , if robot arm j can obtain information from robot arm i, then a ij >0, if not then a ij = 0. The degree of the i-th robotic arm is Then its diagonal matrix D=diag[d1,d2,…,d N ]∈R N×N , its Laplace matrix is L=DA∈R N×N The extended graph is described as G′=(V′,E′), where V′={0,1,…,N} represents the leader 0 and multiple agents (1,…,N), and V j ′×V i ′∈E′.

[0095] Assumption 3: A directed graph G can generate a directed tree with leader 0 as its root if there exists at least one directed path from the root node to all other nodes.

[0096] Definition 1. The synchronization error of the i-th robot arm can be defined as:

[0097]

[0098] Here, y0 represents the reference output of the virtual leader, B = diag[b1,b2,…,b N ]∈R N×N represents the adjacency matrix between the leader and the robot. If the robot i can obtain information from the leader, then b i >0, if not then b i =0.

[0099] Neural networks have good approximation capabilities. In this paper, radial basis function neural networks are introduced to approximate any continuous unknown function. It can be expressed as where X=[x1,x2,…,x n ] T is the input vector, W∈R m Represents the weight vector matrix, m represents the number of neurons, which can be expressed as

[0100] M(X)=[M1(X),M2(X),…,M m (X)], where

[0101]

[0102] Here i = 1, 2, ..., m, and i is the width of the Gaussian function, is the center of the Gaussian function.

[0103] Lemma 1. Set Ω∈R n Continuous function on The radial basis function neural network can be used to obtain high accuracy Approximation can be expressed as

[0104]

[0105] Where σ(X) represents the approximation error, satisfying Ideal weight W * It can be expressed as

[0106]

[0107] In order to ensure that the system can be stable within the preset time, this paper introduces a type of conversion function:

[0108]

[0109] Among them, T is the preset time, Φ, Ψ and is a design positive parameter and satisfies k i (0)=1.

[0110] Its derivative is

[0111]

[0112] Obviously, k i (t) is a continuously differentiable function in the interval [0,∞), and its derivative And there are boundaries.

[0113] S02. Define the error variable of the i-th multi-manipulator and design the first virtual control law α i,1 and adaptive law

[0114] Define the error variable of the i-th robotic arm based on graph theory knowledge

[0115]

[0116] where z i,2 is the error variable of the i-th robotic arm, α i,1 is the virtual control law of the i-th multi-manipulator.

[0117] S021, using radial basis function neural network to analyze unknown combination parts

[0118] Approximation can be expressed as

[0119]

[0120] Among them, X i,1 =[x i,1 ,x j,1 ,x j,2 ] T ,σ i,1 (X i,1 )Satisfaction relationship and

[0121] S022, first virtual control law α i,1 and adaptive law The design is as follows:

[0122]

[0123]

[0124] in, g i,1 g i,1 Input the lower bound of the gain function and design the parameters to satisfy ρ i,1 >0,l i,1 >0.

[0125] S03. Define event triggering mechanism;

[0126] In order to reduce communication pressure, the event trigger mechanism is defined as follows

[0127]

[0128] Among them, the design parameters meet

[0129] Define the control signal as

[0130]

[0131] in Γ i =[α i,2 ,1] T ,pass Yes i The estimation error can be expressed as Then the control signal can be rewritten as

[0132]

[0133] At the same time, design and construct a suitable relative threshold

[0134]

[0135] When t κ+1 Time, relative error satisfy The output signal Will be updated to event trigger signal

[0136] S04. Define the second virtual control law α i,2 and adaptive law and

[0137] Since the system model has uncertain parts, the uncertain parts of the second-order nonlinear system model are approximated by neural network; according to the virtual control error z i,2 Design virtual control law α i,2 , and determine the adaptive parameters.

[0138] The step S04 specifically includes:

[0139] S041, using radial basis function neural network to analyze unknown combination parts Approximation can be expressed as

[0140]

[0141] in and

[0142] S042, according to the second error variable z i,2 The above process uses radial basis function neural network to solve the unknown uncertain part, and uses backstepping design method and Lyapunov function to design the second virtual control law α i,2 , while generating the adaptive law and

[0143]

[0144]

[0145]

[0146] in Design parameter ρ i,2 >0,l i,2 >0, g i,2 g i,2 Lower bound, satisfied g i,2 ≤g i,2

[0147] S05. Based on the Matlab experimental platform, simulation experiments are carried out to analyze the stability of the system.

[0148] In order to verify the effectiveness of the proposed method, the algorithm was simulated based on the Matlab experimental platform. Figure 2 This diagram depicts a communication topology with a virtual leader and four followers. In this diagram, robots 1-4 and robot 0 represent the four followers and the virtual leader, respectively. Assume that the output signal (reference signal) of the virtual leader is y0 = sin(t) + 0.1t. Based on the basic principles of graph theory, we can obtain the adjacency matrix B and indegree matrix D:

[0149]

[0150] Design the adaptive neural network controller as follows:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156] in,

[0157] The proposed control method is applied to a multi-manipulator system with input dead zone. The initial state of the system is: x1(0) = [0.1, 0] T , x2(0)=[0.2,0] T , x3(0)=[0.3,0] T , x4(0)=[0.4,0] T , the initial input is u i (0)=[0,0,0,0], the initial adaptive law is and The parameters of the preset stabilization time function are designed to be ψ=0.5, Φ=0.04, and T=0.3.

[0158] The setting values of relevant parameters are as follows: i =0.3, τ i =0.2, η i =2.5, l1=[40,30,25,20] T , l2=[35,20,30,10] T , ρ i,1 =2,ρ i,2 =2,μ i,1 =0.04, μ i,2 =0.01, ξ i =0.01, P i =[1,0;0,1] T , g i,1 =g i,2 =1.8, where i=1,2,3,4.

[0159] The simulation results are shown in the figure:

[0160] Depend on Figure 3-9 It can be seen that all signals are bounded. Figure 2 The reference signal and the output signal of each follower are shown, and good consistent tracking performance can be seen. The synchronization error curve is as follows Figure 4 As shown in Figure 2, the synchronization error enters the 5% error band after about 0.2s, achieving the goal of system convergence within the preset time of 0.3 seconds. The control input signals of the four followers are as follows: Figure 5-8 As shown in Table 2, the event trigger control input w(t) is continuous and smooth, while the control input u(t) is sawtooth. The event trigger statistics are shown in Table 2. The event trigger time intervals of each follower are Figure 9 As shown in Figure 2, the event triggering mechanism saves more than 60% of communication resources and does not suffer from the Zeon phenomenon.

[0161] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for collaborative control of a robotic arm using a preset time adaptive neural network, characterized in that: The following steps are involved: Step 1: Model the multi-manipulator system with unknown nonlinearity and obtain the The state equation of the manipulator; Step 2: Define error variables of multiple manipulators and design the first virtual control law and adaptive law ; Step 3: Define the event trigger mechanism; Step 4: Define the second virtual control law and adaptive law and ; Step 5: Based on the Matlab experimental platform, conduct simulation experiments and analyze the stability of the system; ; ； , for Enter the lower bound of the gain function, and the parameters satisfy ; ； ； ； in , design parameters , for Lower bound, satisfied .

2. The method for collaborative control of a robotic arm using a preset time adaptive neural network according to claim 1, characterized in that: The first step specifically includes the following: S1: , No. A robotic arm can be described as: ； Representative The angular velocity of the robot arm link, and Representing the The output and input signals of the robot arm, Represents the nonlinear deadband input, the gain function , represents the viscous friction coefficient, represents the mass of the connecting rod, represents the connecting rod length, represents the moment of inertia; S2: Input dead zone model is expressed as: ； and are the right and left slopes of the dead zone, respectively, and and Represent the right breakpoint and left breakpoint of the dead zone respectively, satisfying , , , ; S3: Rewrite the above dead zone model as follows: ; in; ； ； S4: The synchronization error of the robot arm can be defined as: ； represents the reference output of the virtual leader, represents the adjacency matrix between the leader and the robot. If the robot If you can get information from the leader, If not, .

3. The method for collaborative control of a robotic arm using a preset time adaptive neural network according to claim 2, characterized in that: In the second step Error variables of the robot arm: ； in For the The error variables of the robot arm, For the A virtual control law for multiple robotic arms.

4. The method for collaborative control of a robotic arm using a preset time adaptive neural network according to claim 3, characterized in that: The first virtual control law in the second step and adaptive law as follows: S1: Use radial basis function neural network to analyze the unknown combination part Approximation is performed, which is expressed as: ； , Satisfaction relationship ,and ; S2: Design the first virtual control law and adaptive law .

5. The method for collaborative control of a robotic arm using a preset time adaptive neural network according to claim 4, characterized in that: The specific contents of the third step are: S1: Define the event triggering mechanism as follows: ； Among them, the design parameters meet ; S2: Define the control signal as: ； in ; S3: Pass right Make an estimate, and the estimation error is expressed as: ; In summary, the control signal can be rewritten as: ； S4: Construct relative threshold: ； when Time, relative error satisfy , then the output signal Will be updated to event trigger signal .

6. The method for collaborative control of a robotic arm using a preset time adaptive neural network according to claim 5, characterized in that: The fourth step includes the following: S1: Use radial basis function neural network to analyze the unknown combination part Approximation is performed, which is expressed as: ； in , ,and ; S2: According to the second error variable The above process uses radial basis function neural network to solve the unknown uncertain part, and uses backstepping design method and Lyapunov function to design the second virtual control law , while generating the adaptive law and .

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