Mechanical arm control method based on bidirectional multi-source knowledge transfer and multi-task optimization

Abstract

The application provides a mechanical arm control method based on bidirectional multi-source knowledge migration multi-task optimization. The evolutionary multi-task optimization method based on bidirectional multi-source knowledge migration adopts an adaptive bidirectional similarity selection strategy ABSSS and an adaptive multi-source knowledge migration strategy AMKTS, and applies the method to a mechanical arm control problem. In view of the fact that the current mechanical arm control technology still has many problems in optimization accuracy and control efficiency, the application combines machine learning and computational intelligence, measures the similarity between tasks from two aspects of information distribution and distribution distance of a task population, and realizes multi-source knowledge migration between target tasks and auxiliary tasks and cross-task knowledge sharing, so that the optimization accuracy and control efficiency of the evolutionary multi-task technology in the mechanical arm control design engineering problem are further improved.

Description

Technical Field

[0001] The present invention relates to two major fields: machine learning and computational intelligence, and mainly relates to an evolutionary multi-task optimization method based on bidirectional multi-source knowledge migration, and relates to a robotic arm control method based on evolutionary multi-task optimization. Background Art

[0002] In recent years, evolutionary multitask optimization has become a hot research topic among scholars, industrial designers, and practical engineering applications both domestically and internationally. Evolutionary multitask optimization aims to simultaneously optimize two or more tasks through knowledge transfer between them, leveraging similarities between tasks to improve optimization efficiency. Evolutionary multitask optimization has a variety of applications, including robotic arm control, sensor coverage, and vehicle crashworthiness design.

[0003] Because task similarity is crucial for promoting positive knowledge transfer between tasks, measuring similarity between tasks has become a key research topic in evolutionary multitasking. Research on evolutionary multitasking optimization is crucial for practical engineering optimization problems and simulations, as it mimics the human brain's ability to simultaneously process multiple tasks. Furthermore, knowledge from evolutionary multitasking can be reused, drawing on relevant knowledge learned from previous processes to reduce the workload of optimizing the target task, ensuring that each task is optimized as efficiently as possible within a multitasking environment.

[0004] Currently, evolutionary multi-task optimization design techniques can be broadly divided into two categories. The first category is suitable for handling a small number of tasks (generally no more than three). This type of technique generally begins by designing an implicit or explicit knowledge transfer strategy to calculate the similarity between tasks. Basic evolutionary algorithms (such as differential evolution and genetic algorithms) are then applied to optimize the tasks using this knowledge transfer. However, since they can only handle a small number of tasks, these techniques have limited practical application. In contrast, the second category is specifically designed for optimizing a large number of tasks (more than three). This type of technique primarily combines computational intelligence algorithms with knowledge from different disciplines (such as machine learning) to design strategies that can measure the similarity between a large number of tasks, thereby achieving the goal of optimizing a large number of tasks. This type of technique achieves the optimization of a large number of tasks through useful knowledge transfer, which solves real-world multi-task optimization scenarios and therefore has high generalization and universal applicability.

[0005] However, while existing evolutionary multi-task optimization techniques have achieved good results in solving a wide range of task optimization problems, they mostly rely on a single measurement method to calculate inter-task similarity. This results in inaccurate results, as task similarity should be measured from multiple perspectives, not just a single one. Furthermore, existing evolutionary multi-task optimization techniques are limited to a single task, hindering cross-task knowledge sharing and improving knowledge transfer efficiency, resulting in slow convergence of the offspring population.

[0006] In the field of robotic arm control, Liu Peng et al. disclosed in Chinese invention patent CN114218715A a "Method for Designing Robotic Arm Structures Based on a Multi-Task Optimization Algorithm." This approach uses evolutionary multi-task optimization technology to solve robotic arm control. This solution uses clustering methods to calculate the similarity between tasks. It then sets a critical threshold b for the best-performing task in the same group and the task to be optimized, deciding whether to perform knowledge transfer. However, relying solely on setting a critical threshold b to determine whether to perform knowledge transfer is clearly crude and arbitrary, and inevitably results in a large amount of negative knowledge transfer, which significantly reduces the accuracy of the algorithm for optimizing robotic arm control problems. Furthermore, this solution fails to consider efficiency and flexibility when transferring knowledge between tasks. Knowledge transfer is performed only between the best-performing task in the same group and the task to be optimized, which is not conducive to cross-task knowledge sharing, improving knowledge transfer efficiency, and resulting in slow convergence of the offspring population. Summary of the Invention

[0007] In order to solve at least one of the problems existing in the prior art, the present invention provides a multi-task optimization robotic arm control method based on bidirectional multi-source knowledge migration. By applying the evolutionary multi-task optimization method to the robotic arm control engineering problem, the robotic arm control can achieve higher accuracy in design.

[0008] Based on computational intelligence algorithms and machine learning algorithms, this paper proposes a novel evolutionary multi-task optimization technology, namely a multi-task optimization manipulator control method based on bidirectional multi-source knowledge transfer, which includes the following steps:

[0009] (1) Initialize the task population P of size N according to the task space. Each task corresponds to a subpopulation P1, P2, ..., P of the same size. K ;

[0010] (2) KLD divergence and maximum mean difference (MMD) are used to calculate the similarity between tasks from the two aspects of population information distribution and distribution distance, respectively, denoted as sim1 and sim2;

[0011] (3) For the target task T k Each individual x i , judge individual xi Whether it satisfies the knowledge transfer optimization, if individual x i If the knowledge transfer optimization conditions are met, then step (4) and step (5) are executed in sequence, otherwise step (6) is executed;

[0012] (4) executing an adaptive bidirectional similarity selection strategy ABSSS, wherein the adaptive bidirectional similarity selection strategy ABSSS determines all auxiliary tasks corresponding to the target task based on sim1 and sim;

[0013] (5) For individual x i Execute the adaptive multi-source knowledge transfer strategy AMKTS to generate variant individuals v i , the adaptive multi-source knowledge transfer strategy AMKTS selects the most suitable auxiliary task for performing knowledge transfer among all auxiliary tasks corresponding to the target task, and applies the EDA method to realize knowledge transfer;

[0014] (6) Use the differential evolution algorithm DE to perform mutation operations to generate mutant individuals v i ;

[0015] (7) Using differential evolution algorithm DE to mutate individual v i Perform crossover to generate trial u i ;

[0016] (8) Using differential evolution algorithm DE to analyze individual x i and u i Perform selection operation to produce offspring individual p i ;

[0017] (9) Using the offspring individual p i Update target task T k The corresponding population P k , update the best solution of all tasks;

[0018] (10) If the stopping condition is met, the iteration ends, otherwise return to step (2).

[0019] The present invention proposes a multi-task optimization method for robotic arm control based on bidirectional multi-source knowledge transfer. This method applies the evolutionary multi-task optimization method of an adaptive bidirectional multi-source knowledge transfer strategy to engineering problems such as robotic arm control design. The present invention consists of two parts: an adaptive bidirectional similarity selection strategy and an adaptive multi-source knowledge transfer strategy. The adaptive bidirectional similarity selection strategy is responsible for calculating the similarity between tasks from two perspectives, while the adaptive multi-source knowledge transfer strategy is used to implement multi-source knowledge transfer. The main innovations of the present invention are as follows:

[0020] (1) In view of the problem that the existing multi-task optimization technology only measures the similarity between tasks from a unilateral perspective, the present invention calculates the similarity from two aspects: the information distribution and the distribution distance of the task population to improve the accuracy of the similarity between tasks, and designs an adaptive bidirectional similarity selection strategy based on the similarities of these two aspects, so that the target task can adaptively perform different aspects of knowledge transfer according to the similarity during the optimization process.

[0021] (2) In view of the low efficiency of existing multi-task optimization technologies in transferring knowledge between target tasks and auxiliary tasks, the present invention designs an adaptive multi-source knowledge transfer strategy, which enables the target task to automatically select different auxiliary tasks for optimization during the optimization process, realizes multi-source knowledge transfer and performs cross-task knowledge sharing, improves the efficiency of knowledge transfer, and promotes the convergence of the offspring population.

[0022] (3) The method of the present invention is applied to robotic arm control engineering problems to improve the accuracy of robotic arm control design, thereby further improving the optimization efficiency of evolutionary multi-tasking technology in processing engineering problems. It can also be applied to engineering problems such as sensor coverage and vehicle crashworthiness design. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of the overall framework of the method provided by the embodiment of the present invention.

[0024] Figure 2 Schematic diagram of the similarity between KLD calculation tasks in an embodiment of the present invention.

[0025] Figure 3 Schematic diagram of the similarity between MMD calculation tasks in an embodiment of the present invention.

[0026] Figure 4 Schematic diagram of the adaptive multi-source knowledge migration strategy in an embodiment of the present invention.

[0027] Figure 5 Schematic diagram of planar robotic arm control in an embodiment of the present invention.

[0028] Figure 6 1 is a convergence curve diagram of the four methods in the embodiments of the present invention at different KACs. DETAILED DESCRIPTION

[0029] The following describes the technology of the present invention in detail in combination with the relevant drawings, first in general and then in detail, and finally uses the method of the present invention to optimize the control of the robotic arm.

[0030] 1. Overall Framework of the Invention

[0031] Attachment Figure 1The overall framework of the application is shown in the schematic diagram. The ABMKT-MTO steps in the application are explained in detail below in combination with the schematic diagram.

[0032] The main components of the overall framework include task space, task similarity calculation, adaptive bidirectional similarity selection strategy ABSSS and adaptive multi-source knowledge transfer strategy AMKTS.

[0033] First, initialize the task population P of size N according to the task space, and each task corresponds to a sub-population P1, P2, …, P K , and evaluate the population individuals based on the objective function Fk, which corresponds to step (1) of the application. Then, task similarity calculation is performed, and the similarities sim1 and sim2 between tasks are calculated from the population information distribution and distribution distance, which corresponds to step (2) of the application. Then, enter the iteration loop, and optimize the target task T k . For each individual x i of the target task T k , if the knowledge transfer probability rmp of the target task T k in the gth generation meets rand < rmp, (rand is a random number between 0 and 1) which corresponds to step (3) of the application, then the adaptive bidirectional similarity selection strategy ABSSS is executed, which corresponds to step (4) of the application, M auxiliary tasks of the target task T i are found, and then the adaptive multi-source knowledge transfer strategy AMKTS is executed, which corresponds to step (5) of the application, and the Estimation of Distribution Algorithm (EDA) is applied to realize knowledge transfer between tasks to generate a mutant individual v k . Otherwise, the target task T i is self-optimized to generate v i , which corresponds to step (6) of the application. Then, the Differential Evolution (DE) is used to perform crossover operation on the mutant individual u i to generate a trial individual u i , which corresponds to step (7) of the application, and the selection operation is performed on the individual x i and the individual p i to produce an offspring individual p i , which corresponds to step (8) of the application. Finally, the offspring individual p k is used to update the population P k of the target task T k , and the optimal solution of all tasks is updated, which corresponds to step (9) of the application. If the algorithm meets the stopping condition G >= Gmax at this time, Gmax is the maximum number of iterations, the iteration stops, otherwise return to step (2), which corresponds to step (10).

[0034] The calculation of the task similarity in step (2) includes:

[0035] In order to more accurately calculate the similarity between tasks, thereby increasing positive knowledge transfer and inhibiting negative knowledge transfer, the present application measures the similarity between tasks according to the information distribution of the task population and the distribution distance, which are respectively denoted as sim1 and sim2.

[0036] First, for the information distribution of the two task populations, KLD divergence (Kullback-Leibler Divergence, KLD) is used to measure. KLD divergence can be understood as how much information is lost when the probability distribution of the target task population is replaced by the probability distribution of the auxiliary task population, thereby obtaining the similarity sim1 between tasks. As shown in the accompanying drawings Figure 2 , suppose the target task T contains 5 units of information (circle), and now replace T with auxiliary tasks A1 (triangle) and A2 (square) respectively. Since the distribution of auxiliary task A1 is closer to the target task T, the auxiliary task T1 obtained by replacing the target task T with auxiliary task A1 is smaller in information loss than the auxiliary task T2 obtained by replacing the target task T with A2, that is, the auxiliary task A1 is more similar to the target task T. Note that a small KLD value indicates that the tasks are more similar. In the present application, a multivariate normal distribution is used to describe the distribution of the kth target task T k :

[0037] T k ~ N(μ k ,∑ k )(1)

[0038] Wherein, μ represents the mean of the distribution of the target task T k ,∑ k is the corresponding covariance matrix, and suppose the target task T k contains m samples, that is, its covariance matrix∑ k is obtained from (2):

[0039]

[0040] Wherein, v i represents the ith individual in the target task T k , and T represents the transpose of the matrix.

[0041] Based on the above information, the KLD of the target task T k and the task A j (k≠j, and k,j=1,2,…,K) is calculated by (3):

[0042] Wherein, represents the inverse matrix of the covariance matrix of task j, tr represents the trace of the matrix, detΣ represents the determinant of the covariance matrix, D represents the dimension of the covariance matrix, μ j and μ k Represent the mean vectors of task j and task k respectively, Σ j ,Σ k denote the covariance matrices of task j and task k respectively.

[0043] Secondly, MMD is used to measure the distribution distance between two task populations. The purpose of MMD is to measure the distance between two distributions in the Reproducing Kernel Hilbert Space (RKHS), that is, to map the task population distribution to a high-dimensional space through RKHS to calculate the difference in the distribution between tasks, thereby obtaining the degree of similarity between tasks. Figure 3 , if the populations of tasks T1, T2, and T3 are shown in two-dimensional coordinates as shown in (a), it is difficult to calculate the distribution distance between them because the distributions between tasks have a lot of overlap. When the populations of tasks are mapped from two-dimensional coordinates to three-dimensional coordinates in (b) using Reproducing Kernel Hilbert Space (RKHS), the distribution distance between them can be more easily calculated. Figure 3 In (b), let task T1 be the target task, and T2 and T3 be auxiliary tasks. Since the distribution distance d1 between T1 and T2 is obviously smaller than the distribution distance d2 between T1 and T3, the target task T1 is more similar to the auxiliary tasks, that is, a small MMD value indicates that the tasks are more similar. Let P1 and P2 be two distributions from the unified population space P, which represent the subpopulation of task T1 and the subpopulation of task T2 respectively. X = (x1, x2, ..., x n ) is the population in P1, x n represents the individuals in P1, and the population in distribution P2 is Y=(y1,y2,…,y m ), y m Denote the individuals in P2, where n and m are the number of individuals in P1 and P2 respectively. Let F represent a type of function that maps the original data space to a high-dimensional space That is, the MMD of distributions P1 and P2 is expressed as:

[0044]

[0045] Among them, E P1 [f(x)], E P2 [f(y)] represents the expectation of f(x) and f(y), f(x) and f(y) represent the functions in P1 and P2, and f(x) represents the relationship between f and the mapping function. Inner product in the reproducing kernel Hilbert space H:

[0046]

[0047] In the present invention, the unit sphere in the reproducing kernel Hilbert space H is selected as F, so we can get:

[0048] ||f|| H ≤1 (6)

[0049] From equations (5) to (6), equation (4) can be further expressed as:

[0050]

[0051] in, Indicates that P1 and P2 are mapped by the function The mathematical expectation after mapping to high-dimensional space, x i 、y i Represent the individuals in P1 and P2 respectively.

[0052] Squaring both sides of formula (7) yields:

[0053]

[0054] Here, x' is a variable from P1 and independent of x, y' is a variable from P2 and independent of y, and k(x,y) is a kernel defined as the inner product of x and y.

[0055] In an embodiment of the present invention, Gaussian is selected to calculate MMD.

[0056] Adaptive bidirectional similarity selection strategy ABSSS steps:

[0057] (1) Input the subpopulations P1, P2, ..., P corresponding to K tasks K , k=1,2,…,K, the number of candidate auxiliary tasks M.

[0058] (2) For any two tasks T i and T j (i≠j), execute the following steps.

[0059] (3) Calculate the task T according to formula (3) i and T j The KLD value kldsim(i,j) is.

[0060] (4) Calculate the task T according to formula (8) i and T j The MMD value mmdsim(i,j) is.

[0061] (5) Complete steps (2) to (4).

[0062] (6) Perform non-dominated sorting NSGAII on kldsim and mmdsim to obtain the rank Rank, and sort kldsim and mmdsim from small to large to obtain the ranks kldR and mmdR respectively.

[0063] (7) For each target task T k , perform the following steps.

[0064] (8) If kldR(Rank(i)) <mmdR(Rank(i)),i=1,2,…,M成立,在kldsim中找到与T k The indexes of M similar tasks are added to the task archive A. k middle.

[0065] (9) If kldR(Rank(i)) <mmdR(Rank(i))不成立,在mmdsim中找到与k对应相似的M个辅助任务的索引,并加入到任务存档A k .

[0066] (10) End steps (7) to (9).

[0067] During task optimization, ABSSS can select appropriate auxiliary tasks to perform different aspects of knowledge transfer based on the non-dominated ranking level of the task's KLD and MMD (a suitable auxiliary task means that its KLD value and MMD value have a good non-dominated level). In the above steps, steps (3) to (4) are to calculate the values ​​of KLD and MMD respectively based on the information distribution and distribution distance of the task population. It should be noted that when i and j are equal, it means that the algorithm is calculating the KLD and MMD of the task itself. In order to distinguish and treat this special case, the present invention sets the KLD value and MMD value at this time to positive infinity, that is, kldsim(i,j)=inf, mmdsim(i,j)=inf, i=j. Steps (8) to (9) select appropriate auxiliary tasks to perform different aspects of knowledge transfer based on the values ​​of KLD and MMD. Since there are two aspects of similarity between tasks, it is not possible to make a decision on the auxiliary tasks based on the similarity of one aspect. The present invention uses the non-dominated sorting method to perform non-dominated sorting on kldsim and mmdsim, and sorts kldsim and mmdsim in ascending order to obtain the corresponding grades kldR and mmdR. Then, suppose that for the kth target task T k Select M similar auxiliary tasks. If the condition of step (8) is met, it means that the task calculated by KLD at this time is the same as the target task T k It is more appropriate to perform knowledge transfer, so the index of the task similar to k in kldsim is added to the task archive A kOtherwise, it is suitable for the target task T k The index of the auxiliary task for performing knowledge transfer is in mmdsim, that is, execute step (9), find the index and add it to A k At this point, all target tasks have archive A k Each has M corresponding auxiliary tasks. Below, the present invention describes in detail how to use these auxiliary tasks and the target task to perform efficient knowledge transfer.

[0068] 2. Adaptive Multi-Source Knowledge Transfer Strategy AMKTS

[0069] For the target task T k Once the appropriate auxiliary task is selected by the adaptive bidirectional similarity selection strategy ABSSS, the next thing to solve is how to make the target task T k Efficiently perform knowledge transfer with M auxiliary tasks, which is the problem that AMKTS needs to solve. k Each individual x in i ,i=1,2,…,n, the adaptive multi-source knowledge transfer strategy AMKTS is based on the Euclidean distance calculation of individual x i The distance between the M auxiliary tasks is then used to implement knowledge transfer. Figure 4 , if the target task T k Individual x in the population i The leftmost black rectangle represents the mean vector and standard deviation vector of the M auxiliary task populations. First, the mean vector Xmean of all auxiliary task populations is obtained by equations (9) to (12). j and standard deviation vector Xstd j , j=1,2,…,M:

[0070]

[0071] Where D represents the dimension of the population, d = 1, 2, ..., D, n represents the size of the task population, Xmean j represents the mean vector of the jth auxiliary task, Xstd j represents the standard deviation vector of the j-th auxiliary task, Xmean j The value of the dth dimension in , Represents Xstd j The value of the dth dimension in x n,d Indicates the value of the dth dimension of the nth individual. In each iteration, the target task T is calculated k Individual x i and the mean vector Xmean of all auxiliary tasks j(j=1,2,…,M) distance. Then find the auxiliary task corresponding to the minimum value of these distances. The auxiliary task at this time is the most suitable one for individual x. i In the present invention, the Empirical Distribution Algorithm (EDA) is used to perform knowledge transfer, as shown in the attached figure. Figure 4 Assume that the mean Xmean2 of the second auxiliary task is the same as the target task individual x i The distance is the shortest, then, according to formula (13), the D-dimensional Cauchy distribution with location parameter Xmean2 and size parameter Xstd2 is used to generate the offspring individual off i Note that only off is drawn in the figure. i The values ​​of the first 3 components.

[0072] off i =Cauchy(Xmean2,Xstd2) (13) Xmean2 and Xstd2 represent the mean vector and standard deviation vector of the second auxiliary task among the M auxiliary tasks, respectively.

[0073] Adaptive multi-source knowledge transfer strategy AMKTS steps:

[0074] (1) Input target task T k The population P k , target task T k Corresponding auxiliary task archive A k .

[0075] (2) For P k Each individual x in i , perform the following steps.

[0076] (3) Calculate archive A according to formulas (9) to (12) k The mean vector Xmean of the M auxiliary tasks j , standard deviation vector Xstd j , j=1,2,…,M.

[0077] (4) Calculate individual x i and mean Xmean j The Euclidean distance dis(i,j) of

[0078] (5) Find the auxiliary task AT corresponding to the minimum value in the Euclidean distance dis, and find the Xmean and Xstd corresponding to the auxiliary task AT.

[0079] (6) Produce offspring individuals according to formula (13) i .

[0080] (7) Complete steps (3) to (6).

[0081] In the above steps, step (3) is to calculate the mean vector and standard deviation vector of the M auxiliary tasks corresponding to the target task. Then, based on these M mean vectors Xmean j , step (4) is to calculate the individual x i The distance dis from the M mean vectors. Then, step (5) is performed in the auxiliary task archive A k Find the individual x i The auxiliary task AT with the smallest distance is obtained, and the mean vector and standard deviation vector of the auxiliary task AT are obtained. Finally, based on the mean vector and standard deviation vector of the auxiliary task AT, step (6) applies the Cauchy distribution to produce the offspring individual off i This knowledge transfer strategy not only allows individuals in the target task to interact with different auxiliary tasks, but also facilitates population convergence through the EDA mechanism for generating offspring individuals. Therefore, AMKTS is able to perform cross-task optimization and implement multi-source knowledge transfer, increasing positive knowledge transfer between tasks and accelerating population convergence.

[0082] In the "ABMKT-MTO" step, the differential evolution algorithm DE is applied to perform step (6) for mutation operation:

[0083] v i =x i +F·(x best -x i )+F·(x r1 -x r2 ) (14)

[0084] Apply the differential evolution algorithm DE to perform step (7) for crossover operation:

[0085]

[0086] Apply the differential evolution algorithm DE to perform step (8) for selection:

[0087]

[0088] Among them, x i represents the current individual, v i is x i The corresponding variant individual, u i is the experimental individual, p i is the offspring individual, x r1 with x r2represents an individual randomly selected from the task population, r1≠r2∈[1,n], j represents the j-th dimension of the individual, j=1,2,…,D, l represents a positive integer randomly selected from [1,D], and rand(0,1) belongs to a random real number in (0,1).

[0089] In some embodiments of the present invention, the aforementioned method of the present invention is applied to mechanical control problems. This embodiment applies the aforementioned method to solve a practical engineering problem of kinematic arm control (KAC).

[0090] like Figure 5 As shown in the figure, the goal of the KAC problem is to find the optimal angle {α1,α2,…,α D}, α D represents the rotation angle of the joint so that the end of the robot arm (end effector) is as close as possible to the target Target in the plane. In other words, the KAC problem aims to find the optimal angle of each joint in the robot arm to minimize the end position P D and the distance between the target position Target. Where D represents the dimension of the KAC problem, which is equal to the total number of links in the robot arm. At the same time, the length between two connected links in KAC is equal, that is, both are L. In mathematical expression, the KAC problem can be solved by minimizing the objective function of formula (17):

[0091] f(α1,α2,…,α D ,[L max ,α max ])=||P D -Target|| (17)

[0092] Among them, {α1,α2,…,α D} represents the independent variable, L max represents the sum of the lengths of all robotic arms, α max Represents the sum of all rotation angles, and the maximum angle of each connection is α max / D, the maximum length of each robot arm is L max / D, ||·|| represents the Euclidean distance.

[0093] The present invention uses ABMKT-MTO to solve the KAC problem. In the experiment, by taking α max With L max Different values ​​of α1,α2,…,α can obtain KAC problems with different numbers of tasks. D The angle range is [0,1], α max With L maxThe value of is generated by CVT (Centroidal Voronoi Tessellation) to obtain KAC for different number of tasks. The end position P of the robot arm D The coordinates of are obtained by iterating equations (18) to (21):

[0094] P i+1 =C i+1 (0,0,0,1) T (18)

[0095]

[0096] L t =L / D (21)

[0097] Where C is a 4×4 matrix, and the initial value C0=I is the unit matrix, α i is the angle of the i-th connection node, L t Indicates the length of each connecting rod, C i Indicates the matrix of the algorithm when it iterates to the i-th generation, P i+1 Represents the position of the end of the i+1th connection section of the robot arm, that is, the coordinate value, i=1,2,…,D.

[0098] The steps for optimizing the planar manipulator control are generally the same as the “ABMKT-MTO steps”. It is only necessary to set some parameters for ABMKT-MTO and change the objective function of the task to Equation (17).

[0099] ABMKT-MTO steps to optimize robot arm control:

[0100] (1) Input the total number of tasks K of the robot arm control to be optimized and set the parameters according to the ABMKT-MTO method.

[0101] (2) Initialize the population in the range [0,1], that is, {α1,α2,…,α D}∈[0,1]. And according to the objective function of the robot arm control task, that is, formula (17), the population individuals are evaluated, and the optimal solution is the rotation angle of the connecting rod {α1,α2,…,α D}, so that the end position of the robot arm P D Get as close to the target as possible.

[0102] (3) Execute the contents of steps (2) to (10) in the “ABMKT-MTO steps of the invented algorithm”.

[0103] Specifically, in order to verify the effectiveness of ABMKT-MTO, experiments were designed to test KAC problems with different numbers of tasks. According to different KAC problems, the number of tasks K was set to 20, 50, and 100, the dimension of the KAC problem D = 20, and the coordinates of the target position Target were [0.5, 0.5]. The parameters of ABMKT-MTO were set according to its steps as follows: the population size Pk of each task n = 100, the knowledge transfer probability parameter rmp = 0.2, the auxiliary task M = 6, the scaling factor F of DE = 0.5, the cross factor CR = 0.9, MaTDE [1] 、EMaTO-MKT [2] and MFEA-DGD [3] The parameter settings are consistent with those in the original paper. The maximum number of iterations Gmax = 1000. All algorithms are run independently 25 times. The average fitness of the tasks is used to evaluate the performance of the method of the present invention. The symbols "+", "-", and "≈" indicate that the compared method is "better", "worse", or "approximately equal" to the ABMKT-MTO method in terms of results.

[0104] The numerical experimental results are shown in Table 1, and the convergence curve of the algorithm is shown in Figure 6 (a) to 6 (c). As can be seen from Table 1, the average fitness of ABMKT-MTO in the KAC problems with 20, 50, and 100 tasks is 0.3044, 0.3113, and 0.3335, respectively. Therefore, although the optimization accuracy of all algorithms decreases with the increase in the number of tasks, ABMKT-MTO is more accurate than MaTDE, EMaTO-MKT, and MFEA-DGD in optimizing KAC problems, and it wins in all three different KAC problems. In addition, Figure 6 Figures (a), (b), and (c) correspond to the convergence curves for 20, 50, and 100 tasks, respectively. These figures also show that ABMKT-MTO achieves the best convergence performance. Clearly, ABMKT-MTO outperforms the other three methods because it combines both the ABSSS and AMKTS strategies. Therefore, considering the practical application scenarios of KAC, ABMKT-MTO can effectively solve various KAC problems.

[0105] Table 1 Experimental results of four algorithms on KAC problems with different task numbers

[0106]

[0107] The robotic arm control method provided in this embodiment combines machine learning and evolutionary multi-task optimization technology, and uses KLD and MMD to calculate the similarity between tasks from two aspects: the information distribution of the task population and the distribution distance of the task population, namely, the adaptive two-way similarity selection strategy ABSSS, which can improve the accuracy of the similarity between tasks and promote the positive knowledge transfer between tasks; then, on the basis of ABSSS, an adaptive multi-source knowledge transfer strategy AMKTS is proposed to perform knowledge transfer between tasks. AMKTS performs knowledge transfer on the basis of ABSSS, which can enable the target task to automatically select different auxiliary tasks for optimization during the optimization process, which is conducive to the execution of multi-source knowledge sharing and the improvement of knowledge transfer efficiency, and accelerates the convergence of the offspring population.

[0108] [1]Chen YL, Zhong JH, Feng L, Zhang J. An adaptive archive-basedevolutionary framework for many-task optimization. IEEE Transactions onEmerging Topics in Computational Intelligence, 2020, 4(3): 369-384.

[0109] [2]Liang ZP, Xu XJ, Liu L, Tu YF, Zhu ZX. Evolutionary many-taskoptimization based on multisource knowledge transfer. IEEE Transactions on Evolutionary Computation, 2022, 26(2): 319-333.

[0110] [3]Liu ZB, Li G, Zhang HL, Liang ZP, Zhu ZX. Multifactorial evolutionary algorithm based on diffusion gradient descent. IEEE Transactions onCybernetics, to be published (online). [doi:10.1109 / TCYB.2023.3270904].

[0111] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-task optimization robotic arm control method based on bidirectional multi-source knowledge transfer, characterized in that: The task of manipulator control is to find the optimal angle of each joint in the manipulator through evolutionary multi-task optimization. , Indicates the rotation angle of the joint to make the end of the robot arm as close as possible to the target position in the plane , the objective function used in optimization To evaluate individuals in a population, represents the sum of the lengths of all robotic arms, represents the sum of the angles of the rotating joints, Indicates the end position of the robotic arm, represents the Euclidean distance, Represents the dimension, which is equal to the total number of links in the robot arm; The steps of evolutionary multi-task optimization include: (1) Input the total number of tasks K to be optimized for the robot control, initialize the task population P of size N according to the task space, and each task corresponds to a subpopulation of the same size , and the range of initialization of each subpopulation is [0,1], that is, ; (2) KLD divergence and maximum mean difference (MMD) are used to calculate the similarity between tasks from the two aspects of population information distribution and distribution distance, respectively, denoted as sim1 and sim2; (3) For target tasks T k , Each individual , judge the individual Whether the knowledge transfer optimization is satisfied, if the individual If the knowledge transfer optimization conditions are met, then execute steps (4) and (5) in sequence, otherwise execute step (6); (4) executing an adaptive bidirectional similarity selection strategy ABSSS, wherein the adaptive bidirectional similarity selection strategy ABSSS determines all auxiliary tasks corresponding to the target task based on sim1 and sim; (5) For individuals Execute the adaptive multi-source knowledge transfer strategy AMKTS to generate variant individuals , the adaptive multi-source knowledge transfer strategy AMKTS selects the most suitable auxiliary task for performing knowledge transfer among all auxiliary tasks corresponding to the target task, and applies the EDA method to realize knowledge transfer; (6) Use the differential evolution algorithm DE to perform mutation operations to generate mutant individuals ; (7) Using differential evolution algorithm DE to mutate individuals Perform crossover operation to generate experimental individuals ; (8) Using differential evolution algorithm DE to and Perform the selection operation to produce the corresponding offspring individual p i ; (9) Use the offspring individual p i Update target tasks T k The corresponding subpopulation P k , update the optimal solution of all tasks; (10) If the stopping condition is met, the iteration ends; otherwise, return to step (2).

2. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to claim 1 is characterized in that: In step (2), the similarity sim1 is: Where, For target tasks T k With Task A j ( and ) of KLD, T represents the transpose of the matrix, represents the inverse matrix of the covariance matrix of task j, It means finding the trace of the matrix, Indicates the determinant of the covariance matrix, D indicates the dimension of the covariance matrix, and Represent the mean vectors of task j and task k respectively, 、 denote the covariance matrices of task j and task k respectively.

3. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to claim 1 is characterized in that: In step (2), let P1 and P2 be two distributions from the task population P, representing the subpopulation of task T1 and the subpopulation of task T2, respectively. is the population in P1, represents the individuals in P1, and the population in P2 is , represents an individual in P2, where n、m are the number of individuals of P1 and P2 respectively, let Represents a type of function that maps the original data space to a high-dimensional space ; Similarity sim2 is: Where, , Indicates that P1 and P2 are mapped by the function 、 The mathematical expectation after mapping to high-dimensional space, 、 represent the individuals in P1 and P2 respectively, is the reproducing kernel Hilbert space, is source P1 and is independent of variables, is source P2 and is independent of variables, For a kernel.

4. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to claim 1 is characterized in that: The steps of the adaptive bidirectional similarity selection strategy ABSSS in step (4) include: Input the subpopulation corresponding to K tasks , the number of candidate auxiliary tasks M ; For any two tasks T i and T j ( ), respectively calculate the task T i and T j KLD value and tasks T i and T j MMD value , denoted as sim1 and sim2; right and Perform non-dominated sorting to obtain the rank , and respectively and Sort from small to large to get the level 、 ; For each target task T k ,if If established, then Find the target task T k Corresponding similar M The index of the task is added to the task archive A k In; if If not established, then Found in k Corresponding similar M The index of the auxiliary task is added to the task archive A k , get all target tasks T k Relative auxiliary tasks.

5. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to any one of claims 1 to 4, characterized in that: In step (5), the steps of the adaptive multi-source knowledge transfer strategy AMKTS include: Enter target task T k subpopulation P k , objectives and tasks T k Corresponding auxiliary task archive A k ; For subpopulations P k Each individual in , computing assistance task archive A k The mean vector of the M auxiliary tasks in and the standard deviation vector , , and then calculate the individual and mean Euclidean distance ; Find the auxiliary task corresponding to the minimum value in the Euclidean distance AT , and find auxiliary tasks AT The corresponding mean vector and standard deviation vector; Based on the mean vector and standard deviation vector as parameters, the Cauchy distribution is used to produce offspring individuals. .

6. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to claim 5 is characterized in that: The mean vector for Where, Indicates the j The mean vector of auxiliary tasks, represents the mean vector Middle d The value of the dimension, Indicates the n Individual d The value of the dimension.

7. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to claim 5 is characterized in that: The standard deviation vector for Where, Indicates the j The standard deviation vector of auxiliary tasks, express Middle d The value of the dimension, express Middle d The value of the dimension, Represents the number of samples, that is, the number of individuals in the population.

8. The multi-task optimization robot arm control method based on bidirectional multi-source knowledge transfer according to claim 5 is characterized in that: Assume that the mean of the second auxiliary task is Target task individuals The distance is the shortest, then the offspring individual The way to generate is Where, Respectively M The mean vector and standard deviation vector of the second auxiliary task in the auxiliary tasks.

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