A robot positioning error prediction method and system based on L-SHADE-MLP

Abstract

This invention belongs to the field of robot localization error related technology, and discloses a robot localization error prediction method and system based on L-SHADE-MLP, including the following steps: (1) training the MLP model using the localization error and its corresponding robot joint angle data; (2) converting the MLP parameter model into a population of individuals using an improved L-SHADE algorithm, and initializing the population; (3) performing mutation and crossover operations on the population individuals to obtain experimental individuals; (4) comparing the fitness of the experimental individuals and the initial individuals to select excellent individuals, while adaptively adjusting the evolutionary parameters; (5) determining whether the stopping iteration condition is met; (6) decoding the optimal MLP individual into an MLP parameter model, and completing the local optimization of the MLP model to obtain the final MLP model, thereby predicting the localization error corresponding to the new robot joint angle. This invention overcomes the disadvantage that the MLP model is prone to getting trapped in local optima.

Description

Technical Field

[0001] This invention belongs to the technical field of robot positioning error, and more specifically, relates to a robot positioning error prediction method and system based on L-SHADE-MLP. Background Technology

[0002] The development of industrial robots is limited by their positioning accuracy. To meet the high-precision machining requirements of robots, it is necessary to further reduce their absolute positioning error. Industrial robot positioning errors are mainly divided into geometric errors and non-geometric errors. Current techniques include extended Kalman filtering combined with artificial neural networks, genetic particle swarm optimization (GPSO), deep belief networks, and graph neural networks to predict positioning errors. All of these techniques compensate for geometric errors by modifying the robot's parameter model, and then combine this with a neural network model to predict non-geometric errors.

[0003] The existing technology has the following problems: (1) The kinematic calibration method treats the robot as an ideal model and cannot compensate for non-geometric errors. Moreover, commercial robots usually do not have the authority to modify the robot's geometric parameters, making the technology difficult to implement; (2) For robot localization tasks, robot localization error is usually a prediction problem of a continuous value, and it is difficult and costly to obtain large-scale labeled data. When the dataset is small, complex neural network models are prone to getting stuck in local optima; (3) When predicting new joint angles, graph neural networks and other models need to rebuild the graph, resulting in slow inference speed and poor real-time performance; (4) If non-geometric error compensation is performed on the basis of geometric error compensation, error overlap occurs during the process. Compared with direct prediction of comprehensive error, the prediction accuracy is lower and the inference speed is also slower.

[0004] In summary, existing technologies either have low positioning accuracy or long inference time and poor real-time performance, failing to meet the high accuracy and real-time requirements of robot positioning error prediction. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a robot positioning error prediction method and system based on L-SHADE-MLP. It combines the global search capability of the improved L-SHADE algorithm with the local search capability of the MLP model to directly and efficiently predict the positioning error corresponding to the robot joint angle. This overcomes the disadvantage of the MLP model being prone to getting trapped in local optima and improves the accuracy of robot positioning error prediction.

[0006] To achieve the above objectives, according to one aspect of the present invention, a robot localization error prediction method based on L-SHADE-MLP is provided, the method comprising the following steps:

[0007] (1) Construct a multilayer perceptron model and train the multilayer perceptron model using the positioning error and its corresponding robot joint angle data;

[0008] (2) The MLP parameter model is converted into population individuals of the improved L-SHADE algorithm by real number encoding, and the population is initialized based on Latin hypercube sampling;

[0009] (3) Perform mutation and crossover operations on individuals in the population based on the optimal individual mutation strategy to obtain experimental individuals;

[0010] (4) Compare the fitness of experimental individuals and initial individuals to select superior individuals, and adaptively adjust the evolutionary parameters according to the selected individuals;

[0011] (5) Determine whether the stopping iteration condition is met. If it is met, the iteration process stops and proceeds to step (6); otherwise, proceed to step (3).

[0012] (6) The optimal MLP individual is decoded into an MLP parameter model according to the inverse process of real number encoding, and the local optimization of the MLP model is completed based on the gradient descent method to obtain the final MLP model. Then, the final MLP model is used to predict the positioning error corresponding to the new robot joint angle.

[0013] Furthermore, if the current fitness converges to the minimum or the number of iterations exceeds the maximum number of iterations, the iteration process stops, completing the search for the optimal MLP individual.

[0014] Furthermore, when constructing an MLP model, the formula used to determine the optimal range of the number of neurons is:

[0015]

[0016] In the formula, n and m represent the number of neurons in the input layer and the output layer, respectively, and the constant α∈{1,2,…,10};

[0017] The hidden layer activation function is set to the ELU function:

[0018]

[0019] In the formula, α is the scaling factor, and α = 1 is taken;

[0020] The output layer activation function is set to a linear function:

[0021] f(x) = x (3).

[0022] Furthermore, the encoding process refers to concatenating the weights and biases of the MLP model into a real vector in a certain order. Each dimension of this vector represents a parameter, and the real vector corresponding to the encoded MLP model is called an MLP individual.

[0023] Furthermore, the step of initializing the population using Latin hypercube sampling includes: first, taking each dimension of the parameter space as the MLP individual, and dividing each dimension into N non-overlapping intervals of the same length; then, for each dimension, randomly selecting a point in each interval; finally, forming a D-dimensional variable by randomly selecting points from the initial sampling in each dimension.

[0024] Furthermore, the formula used to guide population mutation in the L-SHADE algorithm using the optimal individual mutation strategy is as follows:

[0025]

[0026] In the formula, From population P G The individuals with the highest fitness among the p·N individuals are randomly selected, where p∈(0,1); They are from P G P G ∪A represents individuals randomly selected from A; A is an external memory that stores individuals successfully selected during previous iterations.

[0027] Furthermore, when the value of an individual dimension exceeds the limit range (-1, 1), the difference vector is corrected:

[0028]

[0029] In the formula, x min =-1; x max =1; v i,j,G With x i,j,G The subscript indicates that the population of generation G is P. G The j-th dimension of the i-th individual.

[0030] Furthermore, the mutation will produce individual v i,j,G With the initial individual x i,j,G Crossover generates new experimental individuals u i,j,G :

[0031]

[0032] In the formula, CR i Let be the crossover rate of the i-th individual;

[0033] Body fitness is f:

[0034]

[0035] In the formula, MSE i The mean square error of the i-th component among the three components of the positioning error; n is the total number of samples; y ij and These are the actual value and the predicted value of the j-th component, respectively.

[0036] Furthermore, the adaptive update strategy for the evolutionary parameters crossover rate CR and scaling factor F is as follows:

[0037]

[0038]

[0039] In the formula, M CR and M F These are the crossover rate CR and scaling factor F set S, stored respectively, for individuals successfully selected during the iterative evolution process. CR Set S F Lehmer mean, M CR M F The update method is as follows:

[0040]

[0041]

[0042]

[0043]

[0044] Δf k =|f(u k,G )-f(x k,G (14)

[0045] In the formula, k in the subscript represents the index of the history memory B; ⊥ is a user-defined termination value; S k For S CR and S F The unified representation of mean; WL (S CR ), mean WL (S F ) are sets S CR S F Lehmer mean; Δf k The fitness gap between the selected experimental individuals and the initial individuals.

[0046] The present invention also provides a robot localization error prediction system based on L-SHADE-MLP. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the robot localization error prediction method based on L-SHADE-MLP as described above.

[0047] In summary, compared with the prior art, the robot localization error prediction method and system based on L-SHADE-MLP provided by this invention mainly have the following characteristics:

[0048] 1. This invention combines the local optimization capability of the MLP model with the global optimization capability of the improved L-SHADE algorithm, solving the problem that neural network models are prone to getting trapped in local optima and improving the prediction capability of robot localization error.

[0049] 2. A data-driven approach is used to directly predict the robot's positioning error. The positioning error is predicted by the robot's joint angles without modifying the robot's geometric parameters, making it easy to implement.

[0050] 3. This invention employs a lightweight MLP neural network model, which, compared to graph neural networks, requires the reconstruction of a separate graph structure for each new joint angle of the robot, greatly improving inference speed and making it suitable for tasks that frequently require prediction of a large number of target points.

[0051] 4. This invention directly predicts both geometric and non-geometric positioning errors. Compared with the step-by-step prediction of existing technologies, it eliminates error overlap in the process and significantly improves positioning accuracy. Attached Figure Description

[0052] Figure 1 This is a flowchart of a robot localization error prediction method based on L-SHADE-MLP provided by the present invention;

[0053] Figure 2 This is a schematic diagram of the MLP model structure provided in an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the individual encoding method of the MLP model provided in the embodiments of the present invention;

[0055] Figure 4 This is a schematic diagram of mutation operation based on optimal individual strategy provided in an embodiment of the present invention;

[0056] Figure 5 This is a schematic diagram of cross-operation provided in an embodiment of the present invention;

[0057] Figure 6 This is a line graph of the positioning error prediction experiment provided in this invention example. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0059] This invention provides a robot localization error prediction method and system based on L-SHADE-MLP. The prediction method mainly includes the following steps:

[0060] Step 1: Measure the robot's actual position using external acquisition equipment, collect robot joint data and its corresponding actual position data, and calculate the positioning error data corresponding to the robot's joint angles based on the theoretical position and the actual position.

[0061] Step two involves constructing a multilayer perceptron model and training it using the positioning error and its corresponding robot joint angle data. The input and output of the multilayer perceptron model are the robot joint angle and the positioning error, respectively.

[0062] When constructing an MLP model, the formula used to determine the optimal range of neurons is:

[0063]

[0064] In the formula, n and m represent the number of neurons in the input layer and the output layer, respectively, and the constant α∈{1,2,…,10}.

[0065] The hidden layer activation function is set to the ELU function:

[0066]

[0067] In the formula, α is the scaling factor, and α = 1 is taken.

[0068] The output layer activation function is set to a linear function:

[0069] f(x)=x (3)

[0070] Step 3: Convert the MLP parameter model into population individuals of the L-SHADE algorithm using real number encoding.

[0071] Encoding and decoding of MLP models: The encoding process refers to concatenating the weights, biases, etc. of the MLP model into a real number vector in a certain order. Each dimension of this vector represents a parameter. The real number vector corresponding to the encoded MLP model is called an MLP individual.

[0072] Decoding is the inverse process of encoding. During the algorithm's evolution, it's necessary to decode the real-number vector into parameters for the MLP model. Based on the encoding method, each element in the real-number vector can be mapped back to its corresponding parameter.

[0073] Step 4: Initialize the population based on Latin hypercube sampling.

[0074] The steps for initializing the population using Latin hypercube sampling include:

[0075] First, take each dimension of the parameter space as the MLP individual and divide each dimension into N non-overlapping intervals of equal length. Then, for each dimension, randomly select a point in each interval. Finally, form a D-dimensional variable by randomly selecting points from the initial sampling in each dimension.

[0076] Step 5: Perform mutation and crossover operations on the individuals in the population based on the optimal individual mutation strategy to obtain experimental individuals.

[0077] The formula used to guide population mutation in the L-SHADE algorithm using the optimal individual mutation strategy is:

[0078]

[0079] In the formula, From population P G The individuals with the highest fitness among the p·N individuals are randomly selected, where p∈(0,1); They are from P G P G ∪A represents individuals randomly selected from A; A is an external memory that stores individuals successfully selected during previous iterations.

[0080] When the value of an individual dimension exceeds the limit range (-1, 1), the difference vector is corrected:

[0081]

[0082] In the formula, x min =-1; x max =1; v i,j,G With x i,j,G The subscript indicates that the population of generation G is P. G The j-th dimension of the i-th individual.

[0083] Step six: Compare the fitness of the experimental individuals with that of the initial individuals according to the set fitness function, and select the superior individuals; at the same time, adaptively adjust the evolutionary parameters according to the selected individuals to complete the population evolution.

[0084] Cross operations include:

[0085] The mutation will produce individual v i,j,G With the initial individual x i,j,G Crossover generates new experimental individuals u i,j,G :

[0086]

[0087] In the formula, CR i Let be the crossover rate of the i-th individual.

[0088] Body fitness is f:

[0089]

[0090] In the formula, MSE i This represents the mean square error of the i-th component among the three components (X, Y, and Z) of the positioning error; n is the total sample size; y ij and These are the actual value and the predicted value of the j-th component, respectively.

[0091] The adaptive update strategy for the evolutionary parameters crossover rate CR and scaling factor F is as follows:

[0092]

[0093] In the formula, M CR and M F These are the crossover rate CR and scaling factor F set S, stored respectively, for individuals successfully selected during the iterative evolution process. CR Set S F Lehmer mean, M CR M F The update method is as follows:

[0094]

[0095]

[0096]

[0097]

[0098] Δf k =|f(u k,G )-f(x k,G (14)

[0099] In the formula, k in the subscript represents the index of the history memory B; ⊥ is a user-defined termination value; S k For S CR and S F The unified representation of mean;WL (S CR ), mean WL (S F ) are sets S CR S F Lehmer mean; Δf k The fitness gap between the selected experimental individuals and the initial individuals.

[0100] Step 7: Retain the current best individual and increment the iteration count by 1. If the current fitness converges to the minimum or the number of iterations exceeds the maximum number of iterations, the iteration process stops, the search for the best MLP individual is completed, and Step 8 is executed. Otherwise, the population size is controlled according to the linear population reduction strategy, and the process returns to Step 5 to continue iterative training.

[0101] The linear population size reduction strategy is as follows:

[0102]

[0103] In the formula, N G+1 The population size for the next generation; round(·) is the floor function; N min N represents the minimum population size. init The initial population size is represented by FES, which is the current fitness evaluation count. MAX This represents the maximum number of fitness evaluations.

[0104] Step 8: Decode the optimal MLP individual into an MLP parameter model according to the inverse process of real number encoding.

[0105] Step 9: Perform local optimization of the MLP model based on gradient descent to obtain the final MLP model.

[0106] Step 10: Use the final MLP model to predict the corresponding positioning error for the new robot joint angles.

[0107] The present invention will be further described in detail below with reference to embodiments. Without loss of generality, the following embodiments all take the improvement of the prediction accuracy of the end-effector positioning error of the UNIVERSAL ROBOTS10 robot (hereinafter referred to as "UR10") as an example to further explain the technical solution of the present invention.

[0108] like Figure 1 As shown, this embodiment of the invention provides a positioning error compensation method for a robot based on L-SHADE-MLP, including the following steps:

[0109] Step 1, build the MLP model. This includes an input layer, hidden layers, and an output layer (see...). Figure 2The MLP model is described. The input layer represents the joint parameters of the robot, and the number of network nodes in the input layer is equal to the number of joint parameters. The output layer represents the position error of the robot's end effector, and the number of nodes in the output layer is equal to the number of position error parameters. The number of hidden layers in the MLP is set to 2. The formula used to determine the optimal range of the number of neurons is:

[0110]

[0111] In the formula, n and m represent the number of neurons in the input layer and the output layer, respectively, and the constant α ∈ {1, 2, ..., 10}. We set the number of neurons in the input layer to 6, the number of neurons in the output layer to 3, and the number of neurons in the two hidden layers to 12 and 8, respectively.

[0112] The hidden layer activation function is set to the ELU function:

[0113]

[0114] In the formula, α is the scaling factor, and α = 1 is taken.

[0115] The output layer activation function is set to a linear function:

[0116] f(x) = x (3).

[0117] Step 2: Iteratively train the MLP model established in Step 1. Data is collected using a UR10 robot and a Leica AT901-MR laser tracker. The sampling range for each joint of the robot is defined as shown in Table 1. Within this range, the theoretical position coordinates are sent to the robot via the host computer, and the joint angles are transmitted. When the robot moves to the specified joint angle, the actual position coordinates of the robot's end effector are measured and recorded using the laser tracker. The difference between the theoretical and actual position coordinates is used to obtain the actual positioning error. The six joint angles of the UR10 robot and their corresponding actual positioning errors form a sample point. 480 points are randomly selected from 510 sample points as training samples, and 30 are used as test samples. The training aims to minimize the difference between the position error output by the MLP model and the actual position error, resulting in a trained MLP model.

[0118] Table 1 Joint Space Sampling Range

[0119]

[0120]

[0121] Step 3: Encode the MLP model into individuals of the improved L-SHADE algorithm population. (See also...) Figure 3The MLP model parameters are encoded using real numbers; the biases and weights in the model are combined into a real number vector, i.e., an MLP individual, in a certain order. Each dimension of the vector represents an MLP parameter, and the MLP individual has a dimension of D = 2^15.

[0122] Step 4: Initialize the population based on Latin hypercube sampling. According to the initial parameters of the MLP model, the values ​​of each dimension of the MLP individuals are uniformly distributed random numbers between (-1.0, 1.0).

[0123] First, the parameter space is defined as each dimension of the MLP individuals, and each dimension is divided into N non-overlapping intervals of equal length. Then, within each interval, a sample point is randomly selected as the initial sampling point, ensuring that each sub-region has only one sample point. Finally, duplicates are eliminated by randomly selecting points from the initial sampling in each dimension to form a D-dimensional variable. The initial population size is N. init =5D=1076.

[0124] Step 5, establish set S CR Set S F The crossover rate (CR) and scaling factor (F) of the individuals successfully selected during the iterative evolution process are stored. The set S is calculated separately. CR Set S F Lehmer mean M CR and M F The formula for calculating the Lehmer mean is:

[0125]

[0126] In the formula, mean L (·) represents the Lehmer mean.

[0127] As shown in Table 2, a historical memory B of size H and a storage set S are established. CR Set S F Lehmer mean M CR and M F M CR M F The initial value of each element is 0.5. For each population iteration, the index value is incremented by one, and the corresponding M is updated. CR and M F The value is set to a maximum index H = 6. If the index exceeds H, it will be updated from 1.

[0128] Based on the historical memory B, during the iteration process, each individual x i Using independent control parameter CR i and F i :

[0129]

[0130]

[0131] In the formula, randn i It follows a normal distribution; r i It is a random integer within the interval [1, H]; when Equal to the termination value, set CR i When the value is equal to 0, the individual undergoes the crossover process in only one dimension; randc i It follows the Cauchy distribution.

[0132] Table 2 Historical Storage B

[0133] <![CDATA[M CR ]]> <![CDATA[M CR,1 ]]> <![CDATA[M CR,2 ]]> <![CDATA[M CR,H ]]> <![CDATA[M F ]]> <![CDATA[M F,1 ]]> <![CDATA[M F,2 ]]> <![CDATA[M F,H ]]>

[0134] Step 6: Mutation operation guided by the optimal individual generation strategy.

[0135] Specifically, please refer to Figure 4 For the G generation population P G The i-th initial individual x i,G Perform the mutation operation. First, from population P... G P G Random selection from ∪A Then, generate mutant individuals v according to the following mutant individual generation strategy. i,G :

[0136]

[0137] In the formula, From population P G The individuals with the highest fitness among the p·N individuals are randomly selected, where p∈(0,1); They are from P G P G ∪A represents randomly selected individuals; A is an external memory that stores successfully selected individuals from the first G-1 generations, with an initial size |A| = round(NP). init ×r arc ), NP init The initial number of individuals in the current population is NP. When the population size exceeds NP, the old individuals in A are randomly replaced by newly selected individuals.

[0138] During the mutation operation, when the value of an individual dimension exceeds the limit range (-1, 1), the difference vector is corrected:

[0139]

[0140] In the formula, x min =-1; x max =1; vi,j,G With x i,j,G The subscript indicates that the population of generation G is P. G The j-th dimension of the i-th individual.

[0141] Step 7, Individual cross-evolution.

[0142] Specifically, please refer to Figure 5 The mutation will produce individual v i,j,G With the initial individual x i,j,G Crossover generates new experimental individuals u i,j,G :

[0143]

[0144] In the formula, CR i Let be the crossover rate of individual i, where the crossover rate is unique among individuals and remains constant throughout the generation calculation; j rand Let j be a random integer within the interval [1, D]. rand This ensures that at least one dimension of the initial individuals has undergone a crossover operation.

[0145] Step 8: Calculate individual fitness using the reciprocal of the mean squared error (MSE) between the predicted and actual values.

[0146]

[0147] In the formula, MSE i This represents the mean square error of the i-th component among the three components (X, Y, and Z) of the positioning error; n is the total sample size; y ij and These are the actual value and the predicted value of the i-th component, respectively. The closer the predicted value of the MLP model is to the actual value, the smaller the mean squared error, the higher the fitness, and the better the MLP individual.

[0148] Calculate the initial individual x respectively i,G and test individual u i,G Based on fitness, select and retain individuals with higher fitness:

[0149]

[0150] In the formula, f is the fitness evaluation function. If an experimental individual is selected to replace the initial individual, the initial individual x... i,G Stored in external memory A.

[0151] Step 9: Update the evolutionary parameters F and CR.

[0152] Specifically, based on the parameter adaptive mechanism of the historical memory, F and CR are dynamically adjusted during the iteration process. M in the historical memory B established in step 5... CR MF The update method is as follows:

[0153]

[0154]

[0155]

[0156]

[0157] Δf k =|f(u k,G )-f(x k,G (14)

[0158] In the formula, k in the subscript represents the index of the history memory B; ⊥ is a user-defined termination value; S k For S CR and S F The unified representation of mean; WL (S CR ), mean WL (S F ) are sets S CR S F Lehmer mean; Δf k The fitness gap between the selected experimental individuals and the initial individuals.

[0159] Step 10: Adaptively adjust the population size N using LSPR.

[0160] Specifically, the population size is adjusted according to the following formula:

[0161]

[0162] In the formula, N G+1 The population size for the next generation; round(·) is the floor function; N min The minimum population size; FES is the number of fitness evaluations; FES MAX This represents the maximum number of fitness evaluations.

[0163] Step 11: Retain the current best individual and increment the iteration count by 1; if the population size N G =N min When the condition is met, the iteration terminates, and the individual with the highest fitness in the population at that time is output, completing the search for the optimal MLP individual; otherwise, return to step 6 to continue iterative training. The main parameter settings for the L-SHADE algorithm are shown in Table 3.

[0164] Step 12: Decode the optimal MLP individual obtained through global search.

[0165] Specifically, the weights and bias parameters of the MLP model are obtained through the real number vectors of the MLP individuals.

[0166] Table 3. Main parameter settings for the L-SHADE algorithm

[0167] D MLP Individual Dimension 215 — <![CDATA[N init ]]> Initial population size 1076 <![CDATA[NP init ≈5D]]> <![CDATA[FES MAX ]]> Maximum number of fitness evaluations 43000 <![CDATA[FES MAX =200D]]> <![CDATA[N min ]]> Minimum population size 4 — <![CDATA[r arc ]]> — 2.6 — |A| Initial size of memory A 2798 <![CDATA[|A|=round(r arc ×NP ini )]]> p — 0.11 — H Maximum index H of memory B 6 —

[0168] Step 13: Local optimization of the MLP model is performed using gradient descent.

[0169] Specifically, first, the parameters of the optimal MLP model are initialized; for robot joint angle input samples, the predicted localization error value of the model is calculated and output through forward propagation; then, the mean squared error of the loss function is calculated by using the model output and the true value to measure the difference between the model's predicted value and the true value; next, the gradient of the parameters is calculated using backpropagation for the error between the model output and the true value, and the gradient of each parameter with respect to the loss function is calculated using the chain rule; finally, the Adam parameter optimizer is used to update the model parameters.

[0170] Repeat the above calculations until the set number of iterations is reached to complete the local optimization and obtain the final MLP model.

[0171] Step 14: Input the new joint angle of the robot into the final MLP model to obtain its corresponding positioning error.

[0172] The present invention, along with existing GBDT hierarchical calibration techniques and neural network techniques, were used to conduct localization error prediction experiments on 30 test samples. The experimental results are shown in Table 4, and the localization error prediction curve is shown below. Figure 6 As shown, compared with other technologies, the model provided by this invention has the smallest fluctuation range and the smallest maximum error in the positioning error line graph obtained from 30 prediction samples. The average prediction error in the three directions is the smallest and the closest, and the prediction accuracy is significantly improved.

[0173] Table 4. Experimental Results of Model Performance Comparison

[0174]

[0175]

[0176] The present invention also provides a robot localization error prediction system based on L-SHADE-MLP. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the robot localization error prediction method based on L-SHADE-MLP as described above.

[0177] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robot localization error prediction method based on L-SHADE-MLP, characterized in that, The method includes the following steps: (1) Construct a multilayer perceptron model and train the multilayer perceptron model using the positioning error and its corresponding robot joint angle data; (2) The MLP parameter model is converted into population individuals of the improved L-SHADE algorithm by real number encoding, and the population is initialized based on Latin hypercube sampling; (3) Perform mutation and crossover operations on individuals in the population based on the optimal individual mutation strategy to obtain experimental individuals; (4) Compare the fitness of experimental individuals and initial individuals to select superior individuals, and adaptively adjust the evolutionary parameters according to the selected individuals; (5) Determine whether the stopping iteration condition is met. If it is met, the iteration process stops and proceeds to step (6); otherwise, proceed to step (3). (6) The optimal MLP individual is decoded into an MLP parameter model according to the inverse process of real number encoding, and the local optimization of the MLP model is completed based on the gradient descent method to obtain the final MLP model. Then, the final MLP model is used to predict the positioning error corresponding to the new robot joint angle.

2. The robot localization error prediction method based on L-SHADE-MLP as described in claim 1, characterized in that: If the current fitness converges to the minimum or the number of iterations exceeds the maximum number of iterations, the iteration process stops, completing the search for the optimal MLP individual.

3. The robot localization error prediction method based on L-SHADE-MLP as described in claim 1, characterized in that: When constructing an MLP model, the formula used to determine the optimal range of neurons is: In the formula, n, m Represents the number of neurons in the input and output layers, a constant. ; The hidden layer activation function is set to function: In the formula, As the scaling factor, take ; The output layer activation function is set to a linear function:

4. The robot localization error prediction method based on L-SHADE-MLP as described in claim 1, characterized in that: The encoding process refers to concatenating the weights and biases of the MLP model into a real vector in a certain order. Each dimension of this vector represents a parameter. The real vector corresponding to the encoded MLP model is called an MLP individual.

5. The robot localization error prediction method based on L-SHADE-MLP as described in claim 1, characterized in that: The steps for initializing the population based on Latin hypercube sampling include: First, taking each dimension of the parameter space as the MLP individual, and dividing each dimension into non-overlapping parts. N First, divide the space into intervals of equal length; then, for each dimension, randomly select a point in each interval; finally, construct the space by randomly selecting points from the initial sample in each dimension. D Dimensional variables.

6. The robot localization error prediction method based on L-SHADE-MLP as described in any one of claims 1-5, characterized in that: The formula used to guide population mutation in the L-SHADE algorithm using the optimal individual mutation strategy is: In the formula, From population The most adaptive The individuals randomly selected from among them ; , They are from Individuals randomly selected from among them; This is an external memory used to store individuals that were successfully selected during previous iterations.

7. The robot localization error prediction method based on L-SHADE-MLP as described in claim 6, characterized in that: When the value of an individual dimension exceeds the limit range (-1, 1), the difference vector is corrected: In the formula, ; ; and The subscript indicates the first Generation population The The first individual dimension; To generate individuals through mutation; This refers to the initial individual.

8. The robot localization error prediction method based on L-SHADE-MLP as described in claim 6, characterized in that: Individuals produced by mutation With the initial individual Crossover, generating new experimental individuals : In the formula, For the first Crossover rate of individual number; Body fitness is : In the formula, This represents the third component of the positioning error. The mean square error of each component; Total sample size; and The first The first component One actual value and one predicted value.

9. The robot localization error prediction method based on L-SHADE-MLP as described in claim 8, characterized in that: Evolutionary parameter crossover rate and scaling factor The adaptive update strategy is as follows: In the formula, and These are the crossover rates of individuals successfully selected during the iterative evolution process. and scaling factor gather ,gather Lehmer mean, , The update method is as follows: In the formula, the subscripts are... Represents historical memory Index; A custom termination value; for and A unified representation; , Sets , Lehmer mean; The fitness gap between the selected experimental individuals and the initial individuals.

10. A robot localization error prediction system based on L-SHADE-MLP, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the robot localization error prediction method based on L-SHADE-MLP as described in any one of claims 1-9.

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