Kinematics Modeling Method of a Large-Deformation Flexible Rod Robot Based on Neural Network

Abstract

This paper proposes a neural network-based kinematic modeling method for a large-deformation flexible rod robot. First, a sensitivity analysis of the system's parameters is performed based on the robot's motion characteristics to identify key parameters with significant impact. Based on the conclusions of the sensitivity analysis, the forward and inverse kinematics of the large-deformation flexible rod robot are established using a neural network algorithm. This involves initially training the network with a simulation dataset to accurately predict the robot's kinematics. Given the differences between simulation models and actual applications, transfer learning techniques are used to optimize network parameters. Actual robot end-point pose data is collected using a multi-camera system, and this data is used to fine-tune the network parameters to improve model accuracy. Finally, combined with visual servo control technology, the target operating point is precisely determined, guiding the robot to accurately reach the predetermined position to perform its task. This method is not only accurate and efficient, significantly improving analysis efficiency, but also exhibits significant model generalization capabilities.

Description

Technical Field

[0001] The present invention belongs to the field of developing more accurate and efficient kinematic modeling methods for large-deformation flexible rod robots, and specifically relates to a kinematic modeling method for large-deformation flexible rod robots based on a neural network. Background Art

[0002] With the continuous development of industrial automation and intelligent manufacturing, the demand for the application of robotics in complex environments is increasing. While traditional rigid robots offer high rigidity and precision, they have strict requirements for their working environment, limiting their scalability and flexibility for diverse tasks. In contrast, flexible robots offer greater adaptability and flexibility, enabling complex operations while maintaining high stability. Flexible robots do not rely on rigid kinematic pairs, thus avoiding friction and wear. They are also compact, lightweight, and offer high precision, making them particularly well-suited for maneuvers in confined spaces. These characteristics give them broad potential for application in aerospace, micromanipulation, medical surgery, and other fields.

[0003] However, the kinematic characteristics of flexible robots are extremely complex. This is mainly due to the significant nonlinear characteristics introduced by the flexible deformation of the rods, which greatly increases the difficulty of kinematic modeling. Currently, the modeling methods for large-deformation flexible rod robots mainly include the finite element method, pseudo-rigid body model method, chain algorithm, beam constraint model method, and elliptic integral method. Although these methods have solved the problem of large-deformation modeling to a certain extent, they still have their own limitations. The finite element method has complex equations, excessive computational effort, and low efficiency; the pseudo-rigid body model method suffers from loss of precision, resulting in large errors; the chain algorithm often fails to converge to the correct solution when solving large-deflection beams with large rotation angles and multiple inflection points on the beam; the beam constraint model method is only applicable to small deformations; and the elliptic integral method has high requirements for initial values.

[0004] Therefore, developing more accurate and efficient kinematic modeling methods for flexible rod robots with large deformations and resolving the complex nonlinear problems encountered by flexible robots under large deformations is crucial for improving their performance and application potential. This not only provides theoretical support for the application of flexible robots in complex environments but also lays the foundation for the development of related fields. Summary of the Invention

[0005] This patent proposes a neural network-based kinematic modeling method for a large-deformation flexible rod robot. First, a sensitivity analysis of the system's parameters is performed to identify key parameters with significant influence on the robot's kinematic characteristics. Based on the sensitivity analysis, the forward and inverse kinematics of the large-deformation flexible rod robot are established using a neural network algorithm. This involves preliminarily training the network using a simulation dataset to accurately predict the robot's kinematics. Given the discrepancies between simulation models and actual applications, this method further optimizes the network parameters using transfer learning techniques. Specifically, a multi-camera system is used to collect data on the actual robot's end-user pose, and this data is used to fine-tune the network parameters to improve the model's accuracy. Finally, combined with visual servo control technology, this method accurately determines the target operating point in space and guides the flexible robot to the desired location to perform its task. In summary, this neural network-based kinematic modeling method for a large-deformation flexible rod robot is not only accurate and efficient, but also eliminates the need for complex derivations and calculations, significantly improving analysis efficiency. In addition, the model has significant generalization capabilities and is more comprehensive than the limitations of traditional kinematic modeling methods in the research process.

[0006] The specific steps include the following five steps, as shown in Figure 1:

[0007] Step 1: Sensitivity analysis of large deformation flexible rod robot; Step 2: Forward kinematics modeling of large deformation flexible rod robot based on neural network; Step 3: Inverse kinematics modeling of large deformation flexible rod robot based on neural network; Step 4: Kinematic model optimization of large deformation flexible rod robot based on transfer learning; Step 5: Accurate target positioning of large deformation flexible rod robot based on visual servoing

[0008] The various steps of the kinematic modeling method for a large-deformation flexible rod robot based on a neural network are described as follows:

[0009] Step 1: Sensitivity analysis of large deformation flexible rod robot

[0010] Before modeling the kinematics of a large-deformation flexible rod robot, a sensitivity analysis of the system parameters is required. This step aims to evaluate whether each system parameter has a significant impact on the robot's kinematic characteristics, thereby determining the input nodes required when constructing the neural network. First, the kinematic characteristics of a large-deformation flexible rod robot are significantly affected by the length of the flexible beam. L 1 and L 2 changes, therefore, these two system parameters can be directly incorporated into the input node without additional analysis. In addition, during the simulation experiment of the large deformation flexible rod robot, it is necessary to set the Young's modulus of the flexible rod.E , Poisson's ratio μ , and the height of the flexible beam cross section a He Kuan b， refer to Figure 2 As shown, it is necessary to pair the parameters { E , μ , a , b The specific process is: take any set of parameters as the benchmark group, that is, E = E 1, μ=μ 1, a=a 1, b= b 1. By driving the large deformation flexible rod L 1 and L 2. Obtain the spatial position of the moving platform, that is X , Y and θ The parameters were then changed by controlling the variables, and the large-deformation flexible rods were driven to obtain the spatial position of the dynamic platform and compare it with the position of the reference group. The difference was used as an evaluation indicator to quantify the influence of each parameter on the system's motion characteristics, and the most sensitive parameters were incorporated into the input nodes of the neural network model.

[0011] Step 2: Forward kinematics modeling of a large-deformation flexible rod robot based on neural network

[0012] According to the sensitivity analysis in step 1, the system parameters that have a significant impact on the kinematics of the large deformation flexible rod robot can be determined. When constructing the forward kinematics model of the large deformation flexible rod robot, it is usually known that the large deformation flexible rod L 1 and L 2, solve the posture of the robot's end moving platform, that is:

[0013] (1)

[0014] in f is the forward kinematics model of a large-deformation flexible rod robot; ( X , Y ) is the position of the end of the moving platform; θ is the posture of the end of the moving platform. According to formula (1), the end posture of the moving platform is also affected by the structure and material of the flexible rod. Based on the analysis of step 1, the number of input neurons can be determined. At the same time, the number of output neurons can be determined according to formula (1). In the process of network construction, the number of hidden layers and the number of neurons in the corresponding layers need to be designed to realize the establishment of the positive kinematic neural network for the large deformation flexible rod robot. Figure 3 In order to optimize the network, the elastic modulus of the flexible beam is first set in the simulation software. E , Poisson's ratio μ and the height of the flexible beam cross section a He Kuan b By driving the large deformation flexible rod L 1 and L 2. Obtain the spatial pose data of the end of the moving platform, that is X , Y and θ In order to eliminate the weight imbalance and numerical calculation problems caused by the large range of eigenvalues and improve the training stability and convergence speed of the model, the parameters of the input neurons are normalized:

[0015] (2)

[0016] in is the original data, is the normalized value; is the minimum value in the data set; is the maximum value in the data set. In order to eliminate the regular interference that may be caused by data sorting, the data order is further randomized to ensure that the model has strong generalization ability. At the same time, to enhance the nonlinear mapping ability of the model, an activation function is introduced between the hidden layers to improve the nonlinear ability of the network regression. After completing the construction of the model, the corresponding loss function needs to be designed, namely:

[0017] (3)

[0018] in is the error between the predicted value and the actual value, 、 and are the error coefficients, X , Y and θ is the actual value, , and For the output neuron of the network, denormalization is used to obtain its predicted value:

[0019] (4)

[0020] in is the denormalized predicted value, is the output value of the network, is the minimum value in the data set, is the maximum value in the data set. The data is input into the network, and after multiple trainings, the network parameters can be optimized.

[0021] Step 3: Inverse kinematics modeling of large deformation flexible rod robot based on neural network

[0022] The inverse kinematics of a large deformation flexible rod robot is to solve the problem of the driving rod when the position of the robot end moving platform is known. L 1 and L The length of 2, that is:

[0023] (5)

[0024] in is the inverse kinematics model of the large deformation flexible rod robot. Similarly, the significance parameter can be determined according to step 1, that is, the number of input neurons can be determined, and the number of output neurons can be determined according to formula (5). In the process of network construction, it is necessary to design the number of hidden layers and the number of neurons in the corresponding layers to realize the establishment of the inverse kinematics neural network for the large deformation flexible rod robot. Figure 4 As shown. In order to optimize the network, the network parameters are optimized using the data obtained from the simulation. Similarly, in order to eliminate the weight imbalance and numerical calculation problems caused by the large range of eigenvalues and improve the training stability and convergence speed of the model, the parameters of the input neurons are normalized with reference to formula (2). In order to eliminate the regular interference that may be caused by data sorting, the data order is further randomized to ensure that the model has a strong generalization ability. At the same time, in order to enhance the nonlinear mapping ability of the model, an activation function is introduced between the hidden layers to improve the nonlinear ability of the network regression. After completing the construction of the model, the corresponding loss function needs to be designed, that is:

[0025] (6)

[0026] in is the error between the predicted value and the actual value, 、 are the error coefficients, L 1 and L 2 is the actual value, and is the predicted value. For the output neurons of the network, refer to formula (4) and use inverse normalization to obtain their predicted values. The data is input into the network, and after multiple trainings, the network parameters can be optimized.

[0027] Step 4: Kinematic model optimization of large deformation flexible rod robot based on transfer learning

[0028] Through steps 2 and 3, the parameters of the forward kinematics and inverse kinematics network models can be preliminarily optimized. Due to the differences between the actual robot platform and the simulation platform, a transfer learning method is proposed to further optimize the network parameters. First, the visual system is used to collect data on the end position of the actual robot. That is, the position and posture of the dynamic platform can be obtained by visually measuring the marker attached to the end of the robot. Figure 5The specific method is to detect the key points of the marker through the visual system, and then obtain the coordinate system based on the marker { M The location information under} is P i ， in i Representative i Key points. According to the coordinate transformation relationship, the pixel coordinates of the key points on the image can be obtained as follows: I i ， The specific expression is:

[0029] (7)

[0030] in is the projection matrix of the visual system, is the marker coordinate system { M}Relative to the camera coordinate system{ C}, the unknown parameters in formula (7) can be solved by optimization algorithm. According to the above method, the pose matrix of the large deformation flexible rod robot in the initial state can be obtained And the pose matrix after movement , and then the position of the moving platform relative to the initial state can be calculated as:

[0031] (8)

[0032] Data collection is achieved by driving the length of the flexible rod to control the movement of the end platform. During the network training process, strict quality control and standardized processes are established to ensure the accuracy and consistency of the training data. In terms of model fine-tuning and hyperparameter optimization, a progressive fine-tuning strategy is adopted to maintain the stability of the core layer structure and adjust the model layer by layer for specific parameters to improve performance and avoid overfitting. At the same time, regularization constraints and early stopping mechanisms are combined to enhance the robustness of the model. During the hyperparameter optimization process, the optimal parameter combination is found through learning rate adjustment, batch size selection and optimizer configuration, using methods such as grid search and Bayesian optimization, thereby improving the convergence speed and prediction accuracy of the model.

[0033] Step 5: Precise target positioning of large deformation flexible rod robot based on visual servoing

[0034] In order to ensure that the large deformation flexible rod robot successfully completes the task, it is also necessary to make the end effector reach the specified position accurately. Therefore, it is proposed to combine the visual servo system to assist the robot in accurately positioning the task target. Through the visual servo system, the robot obtains the target position information in real time, determines its spatial coordinates, and feeds it back to the control system. The control system dynamically adjusts the motion trajectory and posture based on the feedback to ensure that the end effector reaches the target point accurately. Figure 6 shown.

[0035] The beneficial effects of the present invention are:

[0036] 1. The present invention focuses on large-deformation flexible rod robots and proposes a kinematic modeling method based on neural networks. This method is based on sensitivity analysis and uses neural network algorithms and simulation data samples to establish the forward kinematics and inverse kinematics of the robot, thereby enabling accurate prediction of the robot's kinematics. At the same time, the kinematic model is transferred and learned through the motion data of the physical model robot, ensuring the effectiveness and reliability of the model in migrating from the simulation environment to actual applications. Furthermore, the present invention combines the visual servo system to achieve precise positioning of the task target, significantly improving the success rate of task execution and operational accuracy. This design concept utilizes the powerful nonlinear mapping capability of neural networks, which not only avoids the tedious calculations in traditional methods, greatly reduces the computational complexity, but also significantly improves modeling efficiency and generalization capabilities. The precise and efficient kinematic model combined with the visual servo system provides stability and reliability guarantees for the robot to perform tasks in diverse and complex environments, enabling it to accurately locate the task target, thereby improving its adaptability and operational accuracy in actual application scenarios; BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flowchart of the kinematic modeling method for a large-deformation flexible rod robot based on deep learning;

[0038] Figure 2 This is a planar diagram of the flexible beam of a large-deformation flexible rod robot;

[0039] Figure 3 This is a schematic diagram of the forward kinematics neural network structure of a large-deformation flexible rod robot without input variable definition;

[0040] Figure 4 This is a schematic diagram of the inverse kinematics neural network structure of a large-deformation flexible rod robot without input variable definition;

[0041] Figure 5 This is a schematic diagram of the end-user pose measurement system for a large-deformation flexible rod robot based on vision;

[0042] Figure 6This is a block diagram of the target positioning and control system of a large-deformation flexible rod robot based on visual servoing;

[0043] Figure 7 This is a schematic diagram of the sensitivity analysis and comparison results of the large deformation flexible rod robot;

[0044] Figure 8 This is a schematic diagram of the forward kinematic neural network structure of a large-deformation flexible rod robot;

[0045] Figure 9 This is a schematic diagram of the error change curve of the training, verification and testing of the forward kinematics model of the large deformation flexible rod robot;

[0046] Figure 10 This is a schematic diagram of the absolute error distribution between the predicted and actual values of the forward kinematics model of a large-deformation flexible rod robot;

[0047] Figure 11 This is a schematic diagram of the inverse kinematics neural network structure of a large-deformation flexible rod robot;

[0048] Figure 12 This is a schematic diagram of the error change curve of the inverse kinematics model training, verification and testing of a large-deformation flexible rod robot;

[0049] Figure 13 This is a schematic diagram of the absolute error distribution between the predicted and actual values of the inverse kinematics model of a large-deformation flexible rod robot; DETAILED DESCRIPTION

[0050] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention and to make the advantages of the embodiments of the present invention more obvious and easy to understand, the technical solutions in the embodiments of the present invention are further described in detail below with reference to the accompanying drawings:

[0051] The present invention proposes a kinematic modeling method for a large-deformation flexible rod robot based on a neural network, comprising the following steps:

[0052] Step 1: Sensitivity analysis of large deformation flexible rod robot

[0053] First, it is clear that the length of the flexible beam and The change of will inevitably affect the simulation results, and there is no need to further analyze these two system parameters. In addition, the simulation results of the robot also involve Young's modulus , Poisson's ratio and the height of the flexible beam cross section He Kuan b ,Their influence on the simulation results cannot be identified intuitively on the surface, and requires further ,exploration;

[0054] To study Young's modulus , Poisson's ratio , the height of the flexible beam cross section He Kuan b To determine the impact of the flexible beam on the simulation results, it is necessary to study each system parameter independently, that is, when studying one parameter, keep the other three parameters unchanged. 、 The basic length is set to 250mm. When collecting data, the flexible beam length is and Based on the cyclic change of , each system parameter is changed 5 times to obtain the simulation results under different settings, as shown in Table 1. Analyze whether there are differences in the results between different data groups under the same parameter adjustment. However, since the differences between the data groups are subtle and difficult to identify intuitively, the difference between the results of the data groups needs to be used as the comparison benchmark. For specific comparison results, refer to Figure 7 Finally, we can get the Poisson's ratio and the width of the flexible beam cross section The adjustment of has a significant impact on the simulation results and shows a high sensitivity; Young's modulus and the height of the flexible beam cross section The change of has little effect on the simulation results, and the difference in results between data groups is almost 0, showing a weak sensitivity;

[0055] Table 1. Material parameters of flexible rods

[0056]

[0057] Step 2: Forward kinematics modeling of a large-deformation flexible rod robot based on neural network

[0058] When the linear motor in a large-deformation flexible rod robot pushes and pulls the slider along the guide rail, the length of the flexible beam changes, and the moving platform also moves away from its initial position. By determining the position of the end effector at the midpoint of the moving platform, the robot can be used to perform certain tasks. The specific modeling steps are as follows:

[0059] First, define the length of the flexible beam in the finite element analysis software Abaqus and , elastic modulus of the material , Poisson's ratio , cross-sectional side length of flexible beam and , to realize the kinematic simulation of the large deformation flexible rod robot and obtain the coordinates of the end effector at the midpoint of the dynamic platform 、 Y and rotation angle Each set of data has a flexible length and Based on the cyclic change, the side length of the flexible beam cross section and the elastic modulus of the material are changed. , Poisson's ratio Get different data sets. Then import the data into matlab for data preprocessing. Use the randperm function to generate a random index vector. The data is randomly divided into training set and test set in the proportion of . The input data of the training set and test set are normalized and scaled to [-1,1];

[0060] During the model building phase, based on the conclusions of the sensitivity analysis, the length of the flexible beam was 、 , Poisson's ratio and the side length of the flexible beam cross section b The four parameters are set as the input layer nodes, the coordinates of the end effector at the center of the moving platform 、 and rotation angle Set as the output layer node, and set the number of hidden layers and their nodes, refer to Figure 8 As shown. Then configure the neural network training parameters, setting the maximum number of iterations to 1000, the learning rate to 0.01, and the training target minimum error to 0.000001. Use the newwff function to create a feedforward neural network. Starting from the input layer, set the activation function between each two layers to logarithmic sigmoid, tangent sigmoid, and pure linear function. Also specify the training function to be used when training the network as 'trainlm'. Then, use the training set data to train the neural network.

[0061] In the model testing phase, the test set data is imported into the trained model to obtain the prediction results output by the neural network model. The predicted values output by the model are denormalized and compared with the actual values of the test set results. The absolute error diagram of the predicted value and the actual value is shown in the figure. Figure 9 Finally, the correlation coefficient, mean square error, root mean square error, and mean absolute percentage error between the predicted value and the actual value are calculated. Referring to Table 2, it can be seen that the correlation coefficients between them are all greater than 0.999, indicating that the model prediction is accurate and the implementation effect is ideal;

[0062] Table 2. Comparison of Forward Kinematics Model Prediction Performance Evaluation Indexes

[0063]

[0064] Step 3: Inverse kinematics modeling of large deformation flexible rod robot based on neural network

[0065] In practical applications, it is sometimes necessary to obtain the pose of the target point, that is, to use the coordinates of the end effector at the midpoint of the moving platform 、 To solve the length of the two flexible beams and , the specific modeling steps are as follows:

[0066] First, define the length of the flexible beam in the finite element analysis software Abaqus and , elastic modulus of the material , Poisson's ratio , cross-sectional side length of flexible beam a and b , to realize the kinematic simulation of the large deformation flexible rod robot and obtain the coordinates of the end effector at the midpoint of the dynamic platform 、 and rotation angle Each set of data has a flexible length and Based on the cyclic change, the side length of the flexible beam cross section and the elastic modulus of the material are changed. , Poisson's ratio Get different data sets. Then import the data into matlab for data preprocessing. Use the randperm function to generate a random index vector. The data is randomly divided into training set and test set in the proportion of . The input data of the training set and test set are normalized and scaled to [-1,1];

[0067] During the model building phase, based on the conclusions of the sensitivity analysis, the midpoint of the moving platform Coordinates 、 , Poisson's ratio and the side length of the flexible beam cross section b The four parameters are set as the input layer nodes, the length of the flexible beam 、 The two features are set as output layer nodes, and the number of hidden layers and their nodes are set, refer to Figure 11 As shown. Then configure the neural network training parameters, setting the maximum number of iterations to 1000, the learning rate to 0.01, and the training target minimum error to 0.000001. Use the newwff function to create a feedforward neural network. Starting from the input layer, set the activation function between each two layers to logarithmic sigmoid, tangent sigmoid, and pure linear function. Also specify the training function to be used when training the network as 'trainlm'. Then, use the training set data to train the neural network.

[0068] In the model testing phase, the test set data is imported into the trained model to obtain the prediction results output by the neural network model. The predicted values output by the model are denormalized and compared with the actual values of the test set results. The comparison diagram between the actual values and the predicted values is shown in the figure. Figure 12 Finally, the correlation coefficient, mean square error, root mean square error, and mean absolute percentage error between the predicted value and the actual value are calculated. Referring to Table 3, it can be seen that the correlation coefficients between them are all greater than 0.99, indicating that the model prediction is accurate and the implementation effect is ideal;

[0069] Table 3. Comparison of inverse kinematics model prediction performance evaluation indicators

[0070]

[0071] Step 4: Kinematic model optimization of large deformation flexible rod robot based on transfer learning

[0072] Based on steps 2 and 3, a kinematic model optimization experiment for a large-deformation flexible rod robot was carried out. In the experiment, the actual robot end position data was collected through a multi-eye vision system, and the key point position information of the marker was obtained using visual measurement technology. With the transformation matrix Calculate the pixel coordinates of the marker in the image coordinate system I i . Combined with optimization algorithm, solve unknown parameters , further determine the posture matrix of the robot in the initial state and motion state and ;

[0073] Subsequently, the position of the end platform is adjusted by driving the flexible rods, and multiple sets of training data are collected. At the same time, strict data quality control and standardization processes are established to ensure data consistency and accuracy. During the model training process, a progressive fine-tuning strategy is adopted to optimize the model layer by layer for specific parameters, and regularization constraints and early stopping mechanisms are combined to improve model robustness. In hyperparameter optimization, the optimal parameter combination is obtained by adjusting the learning rate, batch size, and optimizer configuration, combining grid search and Bayesian optimization methods;

[0074] Experimental results show that the adaptability of the optimized kinematic model in simulation and actual environments is significantly improved, the pose prediction error is reduced by 90% compared with that before optimization, and the convergence speed and prediction accuracy of the model meet expectations, verifying the effectiveness and practicality of the proposed method in complex environments.

[0075] Step 5: Precise target positioning of large deformation flexible rod robot based on visual servoing

[0076] A visual servo system provides real-time positioning and feedback of the robot's target position, dynamically adjusting its trajectory to ensure the end effector reaches its target point. In a specific experiment, multiple target points were set at different locations, and the deviation between the end effector's actual arrival position and the target position was recorded. The experimental results show that the visual servo positioning method significantly improves the accuracy of end-effector positioning, enabling the robot to reach its target position more stably and accurately, meeting the operational requirements of complex tasks.

Claims

1. The kinematic modeling method of a large-deformation flexible rod robot based on a neural network includes the following five main steps: Step 1: Sensitivity analysis of large deformation flexible rod robot; Before kinematic modeling of the large deformation flexible rod robot, a sensitivity analysis of the system parameters is required as follows: This step aims to evaluate whether the system parameters have a significant impact on the robot's kinematic characteristics, so as to determine the input nodes required when constructing the neural network; First, the kinematic characteristics of the large deformation flexible rod robot are significantly affected by the changes in the flexible beam lengths L1 and L2. Therefore, these two system parameters can be directly included in the input nodes without additional analysis; In addition, during the simulation experiment of the large deformation flexible rod robot, it is necessary to set the Young's modulus E, Poisson's ratio μ, and flexibility of the flexible rod. The height a and width b of the cross section of the flexible beam are determined, so it is necessary to explore the parameters {E, μ, a, b} one by one. The specific process is as follows: take any set of parameters as the benchmark group, that is, E = E1, μ = μ1, a = a1, b = b1, and drive the large-deformation flexible rods L1 and L2 to obtain the spatial position of the moving platform, that is, X, Y and θ; then change the parameter values by controlling the variables, and drive the large-deformation flexible rods to obtain the spatial position of the moving platform and compare it with the benchmark group position; use the difference as an evaluation index to quantify the influence of each parameter on the system's motion characteristics, and incorporate the highly sensitive parameters into the input nodes of the neural network model; Step 2: Forward kinematics modeling of large deformation flexible rod robot based on neural network; After performing sensitivity analysis, the system parameters that have a significant impact on the kinematics of the large-deformation flexible rod robot can be determined. Then, a forward kinematics model of the large-deformation flexible rod robot based on a neural network is constructed: When constructing the forward kinematics model of a large-deformation flexible rod robot, the lengths of the large-deformation flexible rods L1 and L2 are usually known, and the position of the robot's end moving platform is solved, that is: [X,Y,θ] T =f(L1,L2,E,μ,a,b) (1) Where f is the forward kinematics model of the large deformation flexible rod robot; (X, Y) is the position of the end of the moving platform; θ is the posture of the end of the moving platform; According to formula (1), the terminal posture of the moving platform is also affected by the structure and material of the flexible rod. According to formula (1), the number of output neurons can be determined; During network construction, the number of hidden layers and the number of neurons in the corresponding layers need to be designed to establish the forward kinematic neural network for the large-deformation flexible rod robot. To optimize the network, the elastic modulus E, Poisson's ratio μ, and the height a and width b of the flexible beam's cross section are first set in the simulation software. By driving the large-deformation flexible rods L1 and L2, the spatial pose data of the end of the moving platform, namely X, Y, and θ, are obtained. To eliminate weight imbalance and numerical calculation problems caused by an excessively large eigenvalue range and improve the training stability and convergence speed of the model, the parameters of the input neurons are normalized: Where x is the original data, is the normalized value; x min is the minimum value in the data set; x max is the maximum value in the data set; in order to eliminate the regular interference that may be caused by data sorting, the data order is further randomized to ensure that the model has strong generalization ability; at the same time, in order to enhance the nonlinear mapping ability of the model, an activation function is introduced between the hidden layers to improve the nonlinear ability of the network regression; after completing the construction of the model, the corresponding loss function needs to be designed, that is: Loss1=α1(XX′) 2 +α2(YY′) 2 +α3(θ-θ′) 2 (3) Where Loss1 is the error between the predicted value and the actual value, α1, α2 and α3 are error coefficients, X, Y and θ are actual values, and X′, Y′ and θ′ are predicted values. For the output neurons of the network, denormalization is used to obtain their predicted values: y′=y′(y max -and min )+y min (4) Where y′ is the denormalized predicted value, y′ is the output value of the network, and y min is the minimum value in the data set, y max is the maximum value in the data set; input the data into the network, and after multiple trainings, the network parameters can be optimized; Step 3: Inverse kinematics modeling of large deformation flexible rod robot based on neural network; After constructing the forward kinematics model of the large deformation flexible rod robot based on neural network, the inverse kinematics model of the large deformation flexible rod robot based on neural network is constructed: The inverse kinematics of a large deformation flexible rod robot is to solve the lengths of the driving rods L1 and L2 given the position of the robot's end moving platform, that is: [L1, L2] T =f -1 (X,Y,E,μ,a,b) (5) where f -1 is the inverse kinematics model of a large-deformation flexible rod robot; by determining the significance parameter, the number of input neurons can be determined, and the number of output neurons can be determined according to formula (5); During the network construction process, the number of hidden layers and the number of neurons in the corresponding layers need to be designed to realize the establishment of the inverse kinematics neural network for the large deformation flexible rod robot; in order to optimize the network, the network parameters are optimized using the data obtained from the simulation; in order to eliminate the weight imbalance and numerical calculation problems caused by the large range of eigenvalues and improve the training stability and convergence speed of the model, the parameters of the input neurons are normalized with reference to formula (2); in order to eliminate the regular interference that may be caused by data sorting, the data order is further randomized to ensure that the model has a strong generalization ability; at the same time, in order to enhance the nonlinear mapping ability of the model, an activation function is introduced between the hidden layers to improve the nonlinear ability of the network regression; after completing the construction of the model, the corresponding loss function needs to be designed, that is: Loss2=β1(L1-L′1) 2 +β2(L2-L′2) 2 (6) Where Loss2 is the error between the predicted value and the actual value, β1 and β2 are error coefficients, L1 and L2 are actual values, and L′1 and L′2 are predicted values. For the output neurons of the network, refer to formula (4) and use inverse normalization to obtain their predicted values. Input data into the network, and after multiple trainings, the network parameters can be optimized. Step 4: Optimize the kinematic model of the large-deformation flexible rod robot based on transfer learning; Step 5: Accurate target positioning of large-deformation flexible rod robot based on visual servoing.

2. The kinematic modeling method of a large-deformation flexible rod robot based on a neural network according to claim 1, comprising: The parameters of the forward kinematics and inverse kinematics network models can be preliminarily optimized. Due to the differences between the actual robot platform and the simulation platform, a transfer learning method is proposed to further optimize the network parameters: First, the visual system is used to collect data on the actual end position of the robot. That is, the position and posture of the moving platform can be obtained by visually measuring the marker attached to the end of the robot. The specific method is to detect the key points of the marker through the visual system, and the position information based on the marker coordinate system {M} can be obtained as P i , where i represents the i-th key point; according to the coordinate transformation relationship, the pixel coordinates of the key point on the image can be obtained as I i , the specific expression is: Where K is the projection matrix of the visual system, is the homogeneous transformation matrix of the marker coordinate system {M} relative to the camera coordinate system {C}. The unknown parameters in formula (7) can be solved by the optimization algorithm. According to the above method, the pose matrix of the large deformation flexible rod robot in the initial state can be obtained And the pose matrix after movement Then the position of the moving platform relative to the initial state can be calculated as: Data collection is achieved by driving the length of the flexible rod to control the movement of the end dynamic platform; during the network training process, strict quality control and standardized processes are established to ensure the accuracy and consistency of the training data; in terms of model fine-tuning and hyperparameter optimization, a progressive fine-tuning strategy is adopted to maintain the stability of the core layer structure and adjust the model layer by layer for specific parameters to improve performance and avoid overfitting; at the same time, regularization constraints and early stopping mechanisms are combined to enhance the robustness of the model; in the hyperparameter optimization process, through learning rate adjustment, batch size selection and optimizer configuration, grid search and Bayesian optimization methods are used to find the optimal parameter combination, thereby improving the model's convergence speed and prediction accuracy.

3. The kinematic modeling method of a large-deformation flexible rod robot based on a neural network according to claim 1, comprising: After optimizing the kinematic model of the large-deformation flexible rod robot based on transfer learning, precise target positioning of the large-deformation flexible rod robot based on visual servoing is performed: In order to ensure that the large-deformation flexible rod robot successfully completes the task, it is also necessary to make the end effector reach the specified position accurately. Therefore, it is proposed to combine the visual servo system to assist the robot in accurately locating the task target. Through the visual servo system, the robot obtains the target position information in real time, determines its spatial coordinates, and feeds back to the control system. The control system dynamically adjusts the motion trajectory and posture according to the feedback to ensure that the end effector reaches the target point accurately.

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