A mechanical arm trajectory tracking control method based on improved african vulture algorithm

Abstract

The application discloses a mechanical arm trajectory tracking control method based on an improved African vulture algorithm, and comprises the following steps: acquiring original mechanical arm data; obtaining a trajectory tracking result of the mechanical arm based on a pre-trained mechanical arm trajectory tracking control model according to the original mechanical arm data; and training the mechanical arm trajectory tracking control model by using the improved African vulture algorithm. The application solves the parameter adjustment problem of the controller in the mechanical arm trajectory tracking control model. The improved African vulture algorithm has the advantages of fast convergence speed, strong global search capability and high solution precision, realizes the balance between the global search capability and the local search capability, has excellent performance for the parameters obtained by optimization, and can effectively reduce the parameter adjustment time and effort of scientific researchers.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a robotic arm trajectory tracking control method based on an improved African vulture algorithm. Background Technology

[0002] With the rapid development of industrial automation and robotics, robotic arms are increasingly widely used in manufacturing, aerospace, medical, and other fields. Trajectory tracking control of robotic arms is a key technology to ensure that they can move accurately along a predetermined trajectory, and its performance directly affects production efficiency, quality, and safety. However, in practical applications, robotic arm systems often encounter factors such as nonlinearity, time-varying characteristics, model uncertainties, and external disturbances, which pose significant challenges to the accuracy and stability of trajectory tracking.

[0003] Traditional robotic arm trajectory tracking control methods, such as PID control and sliding mode control, while achieving trajectory tracking to a certain extent, struggle to achieve precise control when dealing with the complexities described above. Linear Active Disturbance Rejection Control (LADRC), as an advanced control method, effectively improves the system's anti-interference capability and control accuracy by extending the state observer to estimate and compensate for internal dynamics and external disturbances in real time. The performance of the LADRC algorithm largely depends on its parameter tuning; however, LADRC suffers from difficult parameter tuning, and conventional parameter tuning methods often fail to yield parameters that provide satisfactory control performance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a robotic arm trajectory tracking control method based on an improved African vulture algorithm, which can solve the parameter tuning problem of the controller in the robotic arm trajectory tracking control model.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] On the one hand, this invention provides a robotic arm trajectory tracking control method based on an improved African vulture algorithm, comprising:

[0007] Obtain raw robotic arm data;

[0008] Based on the original robotic arm data and a pre-trained robotic arm trajectory tracking control model, the trajectory tracking result of the robotic arm is obtained.

[0009] The robotic arm trajectory tracking control model is trained using an improved African vulture algorithm, including:

[0010] Acquire African vulture populations;

[0011] Update the individual positions of each vulture in the African vulture population, and calculate the fitness value of the vulture using the untrained robotic arm tracking control model;

[0012] The satiety rate calculation method considering linear variables is used to divide the global exploration phase into a local exploration phase;

[0013] The vulture's position is updated during both the global and local exploration phases, and the optimal individual position of the vulture is obtained based on the fitness value; an adaptive coefficient is introduced during the global exploration phase.

[0014] The parameters represented by the individual position of the optimal vulture are used as the parameters of the robotic arm trajectory tracking control model.

[0015] Optionally, before updating the individual positions of each vulture in the African vulture population, the African vulture population is initialized using Kent chaotic mapping to generate the individual positions of each vulture in the African vulture population, as shown in the formula:

[0016] ;

[0017] In the formula, For the first The individual position of the vulture in the next iteration; For the first The individual position of the vulture in the next iteration; These are the adjustment parameters for the Kent chaotic map. ; This represents the current iteration number.

[0018] Optionally, the individual positions of each vulture in the African vulture population are updated using a Cauchy back-learning strategy, with the following formula:

[0019] ;

[0020] In the formula, It is a random function; This represents the upper bound of each individual vulture in the African vulture population on the dim dimension; This represents the lower bound of each individual vulture in the African vulture population on the 1st dimension; This represents the location of each individual vulture in the African vulture population in the 1st dimension.

[0021] Optionally, calculating the fitness value of the vulture includes:

[0022] The untrained robotic arm trajectory tracking control model is invoked, and the fitness value of the vulture is calculated using the ITAE metric as the objective function. The formula is as follows:

[0023] ;

[0024] In the formula, t is time, and e is the input and output error signal of the robotic arm.

[0025] Optionally, the formula for the satiety rate calculation method considering linear variables is:

[0026] ;

[0027] ;

[0028] ;

[0029] In the formula, The satiety rate of vultures; A random number between [-1, 1]; A random number between [-1, 1]; This represents the current iteration number; This represents the maximum number of iterations. This is the satiety coefficient; A random number between [-2, 2]; It is a linear variable.

[0030] Optional, when At this time, the vulture is in the global exploration phase. During the global exploration phase, the vulture's position is updated, as shown in the formula:

[0031] ;

[0032] ;

[0033] ;

[0034] In the formula, This represents the vulture's position vector in the next iteration of the global exploration phase. These are adaptive coefficients; One of the best vultures; As the first variable; For global exploration parameters; A random number between [0, 1]; A random number between [0, 1]; The upper bound for optimization during the global exploration phase; The lower bound for optimization during the global exploration phase; A random number between [0, 1]; A random number between [0, 2]; This is the vulture position vector in the current iteration.

[0035] Optional, when At this time, the vulture is in the first partial exploration phase. During the first partial exploration phase, the vulture's position is updated as follows:

[0036] ;

[0037] ;

[0038] In the formula, This is the vulture's position vector in the next iteration of the first local exploration phase; As the first variable; A random number between [0, 1]; As the second variable; One of the best vultures; This is the vulture position vector in the current iteration; These are the parameters for the first local exploration. A random number between [0, 1]; As the third variable; A random number between [0, 1]; It is the fourth variable.

[0039] Optional, when At this time, the vulture is in the second local exploration phase. During the second local exploration phase, the vulture's position is updated as follows:

[0040] ;

[0041] ;

[0042] In the formula, This is the vulture position vector in the next iteration of the second local exploration phase; As the fifth variable; It is the sixth variable; The best vulture in the first group; This is the vulture position vector in the current iteration; For the second local exploration parameters; A random number between [0, 1]; The best vulture in the second group; One of the best vultures; As the second variable; For levy flight operations.

[0043] In a second aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the robotic arm trajectory tracking control method based on the improved African vulture algorithm described in the first aspect.

[0044] Thirdly, the present invention provides a computer system, comprising:

[0045] Memory, used to store computer instructions;

[0046] A processor for executing the computer instructions to implement the steps of the robotic arm trajectory tracking control method based on the improved African vulture algorithm described in the first aspect.

[0047] Beneficial effects

[0048] Compared with existing technologies, the beneficial effects achieved in this aspect are as follows:

[0049] This invention solves the problem of parameter tuning for the controller in the trajectory tracking control model of a robotic arm. The improved African vulture algorithm has the advantages of fast convergence speed, strong global search capability, and high solution accuracy. It achieves a balance between global search and local search capabilities, and performs well in terms of the optimized parameters. It can effectively reduce the time and effort researchers spend on parameter tuning. Attached Figure Description

[0050] Figure 1 The diagram shown illustrates the working principle of the improved African vulture algorithm of the present invention in one embodiment.

[0051] Figure 2 The diagram shown is a flowchart of one embodiment of the improved African vulture algorithm of the present invention;

[0052] Figure 3 The diagram shown is a structural schematic of the robotic arm trajectory tracking control model of the present invention in one embodiment;

[0053] Figure 4 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of this invention and the existing algorithm for the test function F1 in one embodiment;

[0054] Figure 5 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F2 in one embodiment;

[0055] Figure 6 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F3 in one embodiment;

[0056] Figure 7 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of this invention and the existing algorithm for the test function F4 in one embodiment;

[0057] Figure 8 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F5 in one embodiment;

[0058] Figure 9 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F6 in one embodiment;

[0059] Figure 10 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of this invention and the existing algorithm for the test function F7 in one embodiment;

[0060] Figure 11 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F8 in one embodiment;

[0061] Figure 12 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F9 in one embodiment;

[0062] Figure 13 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F10 in one embodiment;

[0063] Figure 14 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F11 in one embodiment;

[0064] Figure 15 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F12 in one embodiment;

[0065] Figure 16 The figure shown is a comparison of the convergence curves of the improved African vulture algorithm of the present invention and the existing algorithm for the test function F13 in one embodiment;

[0066] Figure 17 The figure shown is a comparison of the control angle error of the robotic arm trajectory tracking in one embodiment of the improved African vulture algorithm of the present invention and the African vulture algorithm. Detailed Implementation

[0067] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0068] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0069] Example 1

[0070] like Figure 1 As shown in the figure, this embodiment introduces a robotic arm trajectory tracking control method based on an improved African vulture algorithm, which specifically includes the following steps:

[0071] Obtain raw robotic arm data.

[0072] Based on the original robotic arm data and a pre-trained robotic arm trajectory tracking control model, the trajectory tracking result of the robotic arm is obtained. The structure of the robotic arm trajectory tracking control model is shown below. Figure 3 As shown.

[0073] like Figure 2 As shown, the robotic arm trajectory tracking control model is trained using an improved African vulture algorithm, including:

[0074] Acquire African vulture populations.

[0075] Set the African vulture population size N and the maximum number of iterations. The Kent chaotic mapping is used to initialize the African vulture population, generating the individual locations of each vulture within the population. Specifically:

[0076] Randomly generate one d-dimensional vulture individuals.

[0077] The generated vulture individuals are iteratively processed to generate chaotic sequences of other individuals, as shown in the formula:

[0078] ;

[0079] In the formula, For the first The individual position of the vulture in the next iteration; For the first The individual position of the vulture in the next iteration; These are the adjustment parameters for the Kent chaotic map. ; This represents the current iteration number.

[0080] After iterating based on the set vulture population size, the results are mapped to the search space according to the formula, as follows:

[0081] ;

[0082] In the formula, and These represent the lower and upper limits of the independent variable's value, respectively. This represents the chaos factor generated by the Kent chaos map.

[0083] The individual positions of each vulture in the African vulture population are updated using a Cauchy back-learning strategy. The fitness value of the vultures is calculated using an untrained robotic arm tracking control model. The structure of the robotic arm trajectory tracking control model is as follows: Figure 3 As shown.

[0084] The optimization model formula for the Cauchy back learning strategy is:

[0085] ;

[0086] In the formula, It is a random function; This represents the upper bound of each individual vulture in the African vulture population on the dim dimension; This represents the lower bound of each individual vulture in the African vulture population on the 1st dimension; This represents the position of each individual African vulture in the dim dimension. The specific optimization steps are as follows:

[0087] Define the Cauchy backward jump probability Jr as 0.95, and rand as... Random numbers between;

[0088] When rand≤Jr, generate the Cauchy reverse population of the current population, merge the current vulture population and the Cauchy reverse vulture population, and calculate the individual fitness values ​​of all vultures.

[0089] The untrained robotic arm trajectory tracking control model built in Simulink is called, and the fitness value y of the vulture is calculated with the ITAE metric as the objective function. The specific calculation formula is as follows:

[0090] ;

[0091] In the formula, t is time, and e is the input and output error signal of the robotic arm.

[0092] The satiety rate calculation method considering linear variables is used to divide the global exploration phase into a local exploration phase.

[0093] Fixed parameters The variable is changed to decrease linearly, and the specific calculation formula is as follows:

[0094] ;

[0095] ;

[0096] ;

[0097] In the formula, The satiety rate of vultures; A random number between [-1, 1]; A random number between [-1, 1]; This represents the current iteration number; This represents the maximum number of iterations. This is the satiety coefficient; A random number between [-2, 2]; It is a linear variable.

[0098] In this embodiment, when |F|≥1, the vulture is in the global exploration phase; when |F|<1, the vulture is in the local exploration phase.

[0099] The vulture's position is updated during both the global and local exploration phases, and the optimal individual position of the vulture is obtained based on the fitness value. An adaptive coefficient is introduced during the global exploration phase. By optimizing the satiety rate calculation method and introducing an adaptive coefficient during the global search phase, the algorithm's global search capability is enhanced, avoiding premature finding of local optima during the global exploration phase and balancing the algorithm's global and local exploration capabilities.

[0100] when At this time, the vulture is in the global exploration phase. During the global exploration phase, the vulture's position is updated, as shown in the formula:

[0101] ;

[0102] ;

[0103] ;

[0104] In the formula, This represents the vulture's position vector in the next iteration of the global exploration phase. These are adaptive coefficients; One of the best vultures; As the first variable; For global exploration parameters; A random number between [0, 1]; A random number between [0, 1]; The upper bound for optimization during the global exploration phase; The lower bound for optimization during the global exploration phase; A random number between [0, 1]; A random number between [0, 2]; This is the vulture position vector in the current iteration.

[0105] when At this time, the vulture is in the first partial exploration phase. During the first partial exploration phase, the vulture's position is updated as follows:

[0106] ;

[0107] ;

[0108] In the formula, This is the vulture's position vector in the next iteration of the first local exploration phase; As the first variable; A random number between [0, 1]; As the second variable; One of the best vultures; This is the vulture position vector in the current iteration; These are the parameters for the first local exploration. A random number between [0, 1]; As the third variable; A random number between [0, 1]; It is the fourth variable.

[0109] when At this time, the vulture is in the second local exploration phase. During the second local exploration phase, the vulture's position is updated as follows:

[0110] ;

[0111] ;

[0112] In the formula, This is the vulture position vector in the next iteration of the second local exploration phase; As the fifth variable; It is the sixth variable; The best vulture in the first group; This is the vulture position vector in the current iteration; For the second local exploration parameters; A random number between [0, 1]; The best vulture in the second group; One of the best vultures; As the second variable; For levy flight operations.

[0113] The parameters w0, wc, and b, representing the individual position of the optimal vulture, are used as the parameters w0, wc, and b of the robotic arm trajectory tracking control model.

[0114] Example 2

[0115] like Figure 4-16 As shown, this embodiment is a performance test simulation of the improved African vulture algorithm of the present invention.

[0116] As shown in Table 1, 13 standard algorithm test functions were selected. The optimization performance of the original African Vulture Algorithm (AVOA) and the improved African Vulture Algorithm (EAVOA) of this invention was tested using MATLAB, and compared with the WOA and PSO algorithms. F1-F7 are unimodal test functions, and F8-F13 are multimodal test functions. Unimodal test functions have only one global optimum and no local optima, and can be used to test the search capability and convergence speed of the optimization algorithm. Multimodal test functions, on the other hand, have local optima that increase exponentially with the dimension, and can be used to test the global search capability of the algorithm.

[0117] Table 1 Test Functions

[0118]

[0119] The parameters of the four optimization algorithms were set to be the same (population size 30, maximum number of iterations 300). Each test function was run independently 30 times using MATLAB, and the results were processed. Table 2 shows the optimal value, average value, and standard deviation of the results obtained by the algorithms for solving the 13 test functions. Figure 4-16 The figures shown are comparisons of the convergence curves of the algorithm for the global optimum of 13 test functions. The comparison verifies that the improved African Vulture algorithm of this invention has stronger global search capabilities, faster convergence speed, and higher accuracy.

[0120] Table 2 Experimental Results Data

[0121]

[0122] Example 3

[0123] This embodiment utilizes the robotic arm trajectory tracking control method based on the improved African vulture algorithm described in Embodiment 1. The parameters w0, wc, and b, representing the optimal individual position of the vulture, are set into the controller of the robotic arm trajectory tracking control model. The structure of the robotic arm trajectory tracking control model is as follows: Figure 3 As shown, the output control angle error result is as follows: Figure 17 As shown, the parameters obtained by using the improved African vulture algorithm of this invention have better trajectory tracking performance, smaller input and output errors of the robotic arm joint angles, and higher control precision.

[0124] Example 4

[0125] This embodiment introduces a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the robotic arm trajectory tracking control method based on the improved African vulture algorithm described in Embodiment 1 or 3.

[0126] Example 5

[0127] This embodiment describes a computer system, including:

[0128] Memory, used to store computer instructions;

[0129] A processor is used to execute the computer instructions to implement the steps of the robotic arm trajectory tracking control method based on the improved African vulture algorithm described in Embodiment 1 or 3.

[0130] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied 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.

[0131] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0132] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0133] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0134] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A robotic arm trajectory tracking control method based on an improved African vulture algorithm, characterized in that, include: Obtain raw robotic arm data; Based on the original robotic arm data and a pre-trained robotic arm trajectory tracking control model, the trajectory tracking result of the robotic arm is obtained. The robotic arm trajectory tracking control model is trained using an improved African vulture algorithm, including: Acquire African vulture populations; Update the individual positions of each vulture in the African vulture population, and calculate the fitness value of the vulture using the untrained robotic arm tracking control model; The satiety rate calculation method considering linear variables is used to divide the global exploration phase into a local exploration phase; The vulture's position is updated during both the global and local exploration phases, and the optimal individual position of the vulture is obtained based on the fitness value; an adaptive coefficient is introduced during the global exploration phase. The parameters represented by the individual position of the optimal vulture are used as the parameters of the robotic arm trajectory tracking control model; Before updating the individual positions of each vulture in the African vulture population, the population is initialized using Kent chaotic mapping to generate the individual positions of each vulture, as shown in the formula: ； In the formula, For the first The individual position of the vulture in the next iteration; For the first The individual position of the vulture in the next iteration; These are the adjustment parameters for the Kent chaotic map. ; This represents the current iteration number; The individual positions of each vulture in the African vulture population are updated using a Cauchy back-learning strategy, with the following formula: ； In the formula, It is a random function; This represents the upper bound of each individual vulture in the African vulture population on the dim dimension; This represents the lower bound of each individual vulture in the African vulture population on the 1st dimension; This represents the location of each individual vulture in the African vulture population in the 1st dimension; The formula for calculating the satiety rate considering linear variables is as follows: ； ； ； In the formula, The satiety rate of vultures; A random number between [-1, 1]; A random number between [-1, 1]; This represents the current iteration number; This represents the maximum number of iterations. This is the satiety coefficient; A random number between [-2, 2]; It is a linear variable.

2. The robotic arm trajectory tracking control method based on the improved African vulture algorithm according to claim 1, characterized in that, when At this time, the vulture is in the global exploration phase. During the global exploration phase, the vulture's position is updated, as shown in the formula: ； ； ； In the formula, This represents the vulture's position vector in the next iteration of the global exploration phase. These are adaptive coefficients; One of the best vultures; As the first variable; For global exploration parameters; A random number between [0, 1]; A random number between [0, 1]; The upper bound for optimization during the global exploration phase; The lower bound for optimization during the global exploration phase; A random number between [0, 1]; A random number between [0, 2]; This is the vulture position vector in the current iteration.

3. The robotic arm trajectory tracking control method based on the improved African vulture algorithm according to claim 1, characterized in that, when At this time, the vulture is in the first partial exploration phase. During the first partial exploration phase, the vulture's position is updated as follows: ； ； In the formula, This is the vulture's position vector in the next iteration of the first local exploration phase; As the first variable; A random number between [0, 1]; As the second variable; One of the best vultures; This is the vulture position vector in the current iteration; These are the parameters for the first local exploration. A random number between [0, 1]; As the third variable; A random number between [0, 1]; It is the fourth variable.

4. The robotic arm trajectory tracking control method based on the improved African vulture algorithm according to claim 1, characterized in that, when At this time, the vulture is in the second local exploration phase. During the second local exploration phase, the vulture's position is updated as follows: ； ； In the formula, This is the vulture position vector in the next iteration of the second local exploration phase; As the fifth variable; It is the sixth variable; The best vulture in the first group; This is the vulture position vector in the current iteration; For the second local exploration parameters; A random number between [0, 1]; The best vulture in the second group; One of the best vultures; As the second variable; For levy flight operations.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the robotic arm trajectory tracking control method based on the improved African vulture algorithm as described in any one of claims 1-4.

6. A computer system, characterized in that, include: Memory, used to store computer instructions; A processor for executing the computer instructions to implement the steps of the robotic arm trajectory tracking control method based on the improved African vulture algorithm as described in any one of claims 1-4.

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