Large-deformation flexible rod piece robot kinematics modeling method based on neural network

Abstract

The invention provides a large-deformation flexible rod piece robot kinematics modeling method based on a neural network. The method comprises the following steps: firstly, carrying out sensitivity analysis on parameters of a system according to motion characteristics of the robot so as to identify key parameters which have obvious influence; according to a conclusion of sensitivity analysis, establishing forward and inverse kinematics of the large-deformation flexible rod piece robot based on a neural network algorithm, namely, performing preliminary training on a network through a simulation data set to accurately predict the kinematics of the robot; in view of differences between a simulation model and actual application, network parameters are optimized by adopting a transfer learning technology, actual robot tail end pose data are acquired by utilizing a multi-view camera system, and the network parameters are finely adjusted by using the data, so that the accuracy of the model is improved; and finally, a target operation point is accurately determined by combining a visual servo control technology, and the robot is guided to accurately arrive at a preset position to execute a task. The method is accurate and efficient, the analysis efficiency is greatly improved, and the generalization ability of the model is remarkable.

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 neural networks. 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. Although traditional rigid robots have high rigidity and precision, they have strict requirements on the working environment, which limits the scalability and flexibility of robots when facing different tasks. In contrast, flexible robots have better adaptability and flexibility, and can perform complex operations while maintaining high stability. Flexible robots do not rely on rigid kinematic pairs, avoid friction and wear problems, and have compact structures, light weight, and high motion precision, especially suitable for operation tasks in narrow spaces. This feature makes them have broad application potential in aerospace, micro-manipulation, medical surgery and other fields.

[0003] However, the kinematic characteristics of flexible robots are extremely complex, mainly because the flexible deformation of the rod introduces significant nonlinear characteristics, which greatly increases the difficulty of kinematic modeling. At present, the modeling methods for large deformation flexible rod robots mainly include 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, too much calculation and low efficiency; the pseudo-rigid body model method will lose accuracy and cause large errors; the chain algorithm often cannot 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 deformation cases; the elliptic integral method has high requirements for initial values.

[0004] Therefore, developing more accurate and efficient kinematic modeling methods for large deformation flexible rod robots and solving complex nonlinear problems of flexible robots under large deformation are of great significance for improving their performance and application potential. This can not only provide theoretical support for the application of flexible robots in complex environments, but also lay the foundation for the development of related fields. Summary of the invention

[0005] The present invention proposes a kinematic modeling method for a large deformation flexible rod robot based on a neural network. First, a sensitivity analysis is performed on the system parameters for the motion characteristics of the large deformation flexible rod robot to identify the key parameters that have a significant impact on the kinematic characteristics; based on the conclusion of the sensitivity analysis, the forward kinematics and inverse kinematics of the large deformation flexible rod robot based on the neural network algorithm are established, that is, the network is preliminarily trained through a simulation data set to achieve accurate prediction of the robot kinematics; in view of the difference between the simulation model and the actual application, this method further uses transfer learning technology to optimize the network parameters. Specifically, a multi-camera system is used to collect data on the end position of the actual robot, and these actual data are used to fine-tune the network parameters to improve the accuracy of the model; finally, combined with visual servo control technology, this method can accurately determine the target operation point in space and guide the flexible robot to accurately reach the predetermined position to perform tasks. In summary, the kinematic modeling method for a large deformation flexible rod robot based on a neural network is not only accurate and efficient, but also does not require complex derivation and calculation, which will greatly improve the 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] Specifically, it includes the following five main steps, as shown in Figure 1: 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 The various steps of the kinematic modeling method of a large deformation flexible rod robot based on a neural network are described as follows: 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. This step aims to evaluate whether each system parameter has a significant impact on the robot's kinematic characteristics, so as to determine the input nodes required when building the neural network. First, the kinematic characteristics of the 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 Kuanb， refer to Figure 2 As shown, we need 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 Then, the parameter values ​​are changed by controlling the variables, and the large deformation flexible rods are driven to obtain the spatial posture of the dynamic platform and compare it with the posture of the reference group. The difference is used as an evaluation index to quantify the influence of each parameter on the motion characteristics of the system, and the parameters with high sensitivity are included in the input nodes of the neural network model.

[0007] Step 2: Forward kinematics modeling of large deformation flexible rod robot based on neural network 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 terminal moving platform, that is: (1) in f It 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 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, and the number of output neurons can be determined according to formula (1). 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 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 high cross-section of the flexible beam a He Kuan b By driving the large deformation flexible rod L 1 and L2. Obtain the spatial posture 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: (2) 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, 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 network regression. After completing the construction of the model, the corresponding loss function needs to be designed, namely: (3) 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, inverse normalization is used to obtain its predicted value: (4) 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 the network parameters can be optimized after multiple trainings.

[0008] Step 3: Inverse kinematics modeling of large deformation flexible rod robot based on neural network The inverse kinematics of a large deformation flexible rod robot is to solve the problem of the driving rod by knowing the position of the moving platform at the end of the robot. L 1 and L The length of 2, that is: (5) in is the inverse kinematics model of the large deformation flexible rod robot. Similarly, according to step 1, the significance parameter can be determined, 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: (6) 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 neuron of the network, refer to formula (4) and use inverse normalization to obtain its predicted value. The data is input into the network, and the network parameters can be optimized after multiple trainings.

[0009] Step 4: Kinematic model optimization of large deformation flexible rod robot based on transfer learning 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, it is proposed to further optimize the network parameters based on the transfer learning method. First, the visual system is used to collect data on the actual robot's end position and posture, that is, the position and posture of the moving platform can be obtained by visually measuring the markers attached to the end of the robot. Figure 5 The 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 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: (7) 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 and posture of the moving platform relative to the initial state can be calculated as: (8) The data is collected by driving the length of the flexible rod to control the movement of the end moving platform. In the process of training the network, a strict quality control and standardized process is 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 keep the core layer structure stable, and adjust the model layer by layer for specific parameters to improve performance and avoid overfitting. At the same time, the regularization constraint and early stopping mechanism are combined to enhance the robustness of the model. In the process of hyperparameter optimization, the optimal parameter combination is found by adjusting the learning rate, selecting the batch size and configuring the optimizer, using grid search and Bayesian optimization methods, thereby improving the convergence speed and prediction accuracy of the model.

[0010] Step 5: Precise target positioning of large deformation flexible rod robot based on visual servoing In order to ensure that the large deformation flexible rod robot successfully completes the task, it is also necessary to make the end effector accurately reach the specified position. Therefore, it is proposed to combine the visual servo system to assist the robot to accurately locate 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 accurately reaches the target point. Figure 6 shown.

[0011] The beneficial effects of the present invention are: 1. The present invention focuses on a large deformation flexible rod robot and proposes a kinematic modeling method based on a neural network. This method is based on sensitivity analysis and uses a neural network algorithm 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, thereby ensuring the effectiveness and reliability of the model in migrating from the simulation environment to actual applications. Furthermore, the present invention combines a 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 capabilities 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 a diverse and complex environment, enabling it to accurately locate the task target, thereby improving its adaptability and operational accuracy in actual application scenarios; BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 It is a flowchart of the kinematic modeling method of a large-deformation flexible rod robot based on deep learning; Figure 2 It is a plane diagram of the flexible beam of the large deformation flexible rod robot; Figure 3 It is a schematic diagram of the structure of the forward kinematics neural network of a large-deformation flexible rod robot without input variable definition; Figure 4 It is a schematic diagram of the inverse kinematics neural network structure of a large deformation flexible rod robot without input variable definition; Figure 5 This is a schematic diagram of the position and posture measurement system of the end of a large-deformation flexible rod robot based on vision; Figure 6 This is a block diagram of the target positioning and control system of a large-deformation flexible rod robot based on visual servoing; Figure 7 This is a schematic diagram of the sensitivity analysis comparison results of the large deformation flexible rod robot; Figure 8 This is a schematic diagram of the positive kinematics neural network structure of a large-deformation flexible rod robot; Fig. 9 It is a schematic diagram of the error variation curve of the training, verification and test of the forward kinematics model of the large deformation flexible rod robot; Fig.10 This is a schematic diagram of the absolute error distribution between the predicted value and the actual value of the forward kinematics model of the large deformation flexible rod robot; Fig.11 It is a schematic diagram of the inverse kinematics neural network structure of a large deformation flexible rod robot; Fig.12 It is a schematic diagram of the error variation curve of the inverse kinematics model training, verification and testing of a large deformation flexible rod robot; Fig.13 This is a schematic diagram of the absolute error distribution between the predicted value and the actual value of the inverse kinematics model of the large deformation flexible rod robot; DETAILED DESCRIPTION

[0013] 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 in conjunction with the accompanying drawings: The present invention proposes a kinematic modeling method for a large deformation flexible rod robot based on a neural network, comprising the following steps: Step 1: Sensitivity analysis of large deformation flexible rod robot 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 effects on the simulation results cannot be identified intuitively through the surface, and need further ,exploration; Young's modulus , Poisson's ratio , the height of the cross section of the flexible beam 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, the value 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 adjustment of the same parameters. However, given that the differences between the data groups are subtle and difficult to identify intuitively, it is necessary to use the difference between the results of the data groups as the comparison benchmark. For specific comparison results, refer to Figure 7 Finally, the Poisson's ratio can be obtained 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; Table 1. Material parameters of flexible rods

[0014] Step 2: Forward kinematics modeling of large deformation flexible rod robot based on neural network When the linear motor pushes and pulls the slider in the large deformation flexible rod robot and slides along the guide rail, the length of the flexible beam will change, and the moving platform will also move away from the initial position. By obtaining the position of the end effector at the midpoint of the moving platform, the robot can be used to perform some tasks. The specific modeling steps are as follows: First, define the length of the flexible beam in the finite element analysis software abaqus and , elastic modulus of the material , Poisson's ratio , side length of the cross section of the 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 moving platform , Y and rotation angle Each set of data has a flexible length and Based on the cyclic changes of the flexible beam, the side length of the 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 the test set are normalized and scaled to [-1,1]; In the model building stage, based on the conclusion of sensitivity analysis, the length of the flexible beam is , , Poisson's ratio And the side length of the cross section of the flexible beam 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 8As shown. Then configure the neural network training parameters, set the maximum number of iterations to 1000, the learning rate to 0.01, and the minimum error of the training target 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 one by one. And specify the training function used when training the network as 'trainlm'. After that, use the training set data to train the neural network; 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. Fig. 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. As shown in Table 2, the correlation coefficients between them are all greater than 0.999, indicating that the model prediction is accurate and the implementation effect is ideal. Table 2. Comparison of evaluation indicators for prediction performance of the forward kinematics model

[0015] Step 3: Inverse kinematics modeling of large deformation flexible rod robot based on neural network In practical applications, it is sometimes necessary to obtain the position 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: First, define the length of the flexible beam in the finite element analysis software abaqus and , elastic modulus of the material , Poisson's ratio , side length of the cross section of the 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 moving platform , and rotation angle Each set of data has a flexible length and Based on the cyclic changes of the flexible beam, the side length of the 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 the test set are normalized and scaled to [-1,1]; In the model building stage, based on the conclusions of the sensitivity analysis, the midpoint of the moving platform Coordinates , , Poisson's ratio And the side length of the cross section of the flexible beam b Four parameters are set as 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 Fig.11 As shown. Then configure the neural network training parameters, set the maximum number of iterations to 1000, the learning rate to 0.01, and the minimum error of the training target 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 one by one. And specify the training function used when training the network as 'trainlm'. After that, use the training set data to train the neural network; 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 value and the predicted value is shown in the figure. Fig.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. As shown in Table 3, the correlation coefficients between them are all greater than 0.99, indicating that the model prediction is accurate and the implementation effect is ideal. Table 3. Comparison of inverse kinematics model prediction performance evaluation indicators

[0016] Step 4: Kinematic model optimization of large deformation flexible rod robot based on transfer learning 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 pose data of the actual robot end 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 Ii . Combined with optimization algorithm, solve unknown parameters , further determine the robot's posture matrix in the initial state and motion state and ; Subsequently, the posture of the end platform is adjusted by driving the flexible rods, and multiple sets of training data are collected. At the same time, a strict data quality control and standardization process is established to ensure the consistency and accuracy of the data. In 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 the robustness of the model. 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; The 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% from that before optimization, and the convergence speed and prediction accuracy of the model are as expected, verifying the effectiveness and practicability of the proposed method in complex environments.

[0017] Step 5: Precise target positioning of large deformation flexible rod robot based on visual servoing The visual servo system is used to perform real-time positioning and feedback of the robot's target position, dynamically adjust the motion trajectory, and ensure that the end effector reaches the target point accurately. In the specific experiment, multiple target points at different positions are set, and the deviation between the actual arrival position of the end effector and the target position is recorded. The experimental results show that the visual servo positioning method significantly improves the accuracy of end positioning, enabling the robot to reach the 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; 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.

2. According to the kinematic modeling method of a large deformation flexible rod robot based on a neural network according to claim 1, before kinematic modeling of the large deformation flexible rod robot is performed, a sensitivity analysis of the system parameters needs to be performed as follows: This step aims to evaluate whether each system parameter has a significant effect on the robot's kinematic characteristics, so as to determine the input nodes required when building the neural network. First, the kinematic characteristics of the 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 , so you need 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 Then, the parameter values ​​are changed by controlling the variables, and the large deformation flexible rods are driven to obtain the spatial posture of the dynamic platform and compare it with the posture of the reference group. The difference is used as an evaluation index to quantify the influence of each parameter on the motion characteristics of the system, and the parameters with high sensitivity are included in the input nodes of the neural network model.

3. After performing sensitivity analysis according to claim 2, 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, it is usually known that the large-deformation flexible rod L 1 and L 2, solve the posture of the robot's terminal moving platform, that is: (1) in f It 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 end posture of the moving platform is also affected by the structure and material of the flexible rod. The number of input neurons can be determined based on the analysis of claim 2, and the number of output neurons can be determined according to formula (1). 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 positive kinematic neural network of the large deformation flexible rod robot. In order to optimize the network, first set the elastic modulus of the flexible beam in the simulation software. E , Poisson's ratio μ and the high cross-section of the flexible beam a He Kuan b By driving the large deformation flexible rod L 1 and L 2. Obtain the spatial posture 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: (2) 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, 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 network regression. After completing the construction of the model, the corresponding loss function needs to be designed, namely: (3) 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, inverse normalization is used to obtain its predicted value: (4) 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 the network parameters can be optimized after multiple trainings.

4. After constructing the forward kinematics model of the large deformation flexible rod robot based on the neural network according to claim 3, construct the inverse kinematics model of the large deformation flexible rod robot based on the neural network: The inverse kinematics of a large deformation flexible rod robot is to solve the problem of the driving rod by knowing the position of the moving platform at the end of the robot. L 1 and L The length of 2, that is: (5) in It is the inverse kinematics model of the large deformation flexible rod robot. Similarly, according to claim 2, the significance parameter can be determined, 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 layer to realize the establishment of the inverse kinematics neural network of the large deformation flexible rod robot. 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: (6) 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 neuron of the network, refer to formula (4) and use inverse normalization to obtain its predicted value. The data is input into the network, and the network parameters can be optimized after multiple trainings.

5. The parameters of the forward kinematics and inverse kinematics network models can be preliminarily optimized through claims 3 and 4. Due to the differences between the actual robot platform and the simulation platform, it is proposed to further optimize the network parameters based on the transfer learning method: First, the visual system is used to collect data on the actual robot's end position and posture. 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 then obtain the coordinate system based on the marker { M The location information under} is P i ， in i Representative i 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: (7) 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 and posture of the moving platform relative to the initial state can be calculated as: (8) The data is collected by driving the length of the flexible rod to control the movement of the end moving platform. In the process of training the network, a strict quality control and standardized process is 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 keep the core layer structure stable, and adjust the model layer by layer for specific parameters to improve performance and avoid overfitting. At the same time, the regularization constraint and early stopping mechanism are combined to enhance the robustness of the model. In the process of hyperparameter optimization, the optimal parameter combination is found by adjusting the learning rate, selecting the batch size and configuring the optimizer, using grid search and Bayesian optimization methods, thereby improving the convergence speed and prediction accuracy of the model.

6. After optimizing the kinematic model of the large deformation flexible rod robot based on transfer learning according to claim 5, accurate 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 to accurately locate 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 based on the feedback to ensure that the end effector reaches the target point accurately.

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