A method of tendon-driven continuum joint shape estimation

Abstract

The application discloses a kind of flexible cable drive continuum joint shape estimation method.The method first utilizes theoretical angle information, and the end three-dimensional space of continuum joint connecting rod in three directions force and moment information, constructs training sample.Then, each training sample is normalized by minimum maximum value preprocessing and shape remodeling.Coupled with training sample label, the optimal neural network model is trained by inputting into multi-channel common attention recurrent neural network model.For test sample expressed using theoretical angle information and three-direction force and moment information, first, the same minimum maximum value normalization preprocessing and shape remodeling as training sample are carried out on test sample, and then the optimal neural network model obtained by training is inputted to predict the coordinate position information of marker point corresponding to the time point of test sample.Experimental results show that, compared with traditional regression method, the method has better prediction performance, and can accurately estimate the shape of continuum joint.

Description

Technical Field

[0001] This invention belongs to the field of robot kinematics, and in particular relates to a method for estimating the joint shape of a cable-driven continuum. Background Technology

[0002] Inspired by biological structures such as elephant trunks and octopus tentacles, various continuum robots have been designed and applied in minimally invasive surgery in recent years. Unlike traditional rigid linkage robots, continuum robots possess superior flexibility and adaptability, capable of adjusting joint shapes to reach surgical targets through narrow and tortuous paths, and providing sufficient force at the distal end for surgical manipulation. Accurate estimation of the shape of the continuum joints is crucial during surgery. However, due to the complex deformation of continuum joints, it is difficult to establish an accurate kinematic model to estimate their shape. Furthermore, collisions between the continuum joints and surrounding human tissues further reduce the accuracy of model estimation.

[0003] Currently, most studies on the shape estimation of continuum joints employ traditional kinematic methods for modeling. However, the modeling process based on kinematic methods is very complex, requiring tedious parameter identification; and due to the complex nonlinear characteristics of cable-driven continuum joint motion, it is difficult to obtain an accurate shape estimation model. In contrast, data-driven methods learn complex mapping relationships from input data, resulting in more accurate models and improved modeling efficiency. Therefore, this invention proposes a data-driven method based on a multi-channel common attention recurrent neural network for estimating the shape of continuum joints. Summary of the Invention

[0004] Due to the complex deformation characteristics of continuum joints and the unpredictable shape changes resulting from inevitable collisions with human tissue during surgery, accurately and stably controlling the end effector of a continuum surgical robot becomes difficult. Therefore, accurate estimation of the shape changes of continuum joints is needed to alleviate this problem. Addressing the issue that most existing studies rely on traditional kinematic methods for estimating the shape of continuum joints, this invention proposes a data-driven method for estimating the shape of continuum joints.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for estimating the shape of a cable-driven continuum joint is proposed. First, a continuum joint motion dataset for a cable-driven surgical robot is established and divided into training, validation, and test sets according to the load weight at the end of the continuum joint. Then, a sample feature sequence is constructed using three force information, three torque information, and one theoretical angle information input from the dSPACE real-time control system in the XYZ directions of the end of the continuum joint link in three-dimensional space. Simultaneously, the coordinate position information of the marker points on the continuum joint is used as the label sequence for the samples. Further, these feature sequences are overlapped and divided according to a time length T = 50 time points (0.5 s) to construct training, validation, and test samples. In addition, the method independently performs two prediction and regression tasks based on the X and Y coordinate positions of the marker points. In the regression task predicting P (X or Y coordinate), the label for each sample is selected as the X (or Y) coordinate position of the marker point corresponding to the last time point out of T time points. The method includes the following steps:

[0007] Step 1: The training set samples can be represented as Where n represents the number of samples in the training set. The corresponding sample labels are represented as follows: Where y1, y2, ..., y n This represents the X or Y coordinate value of the marker point, depending on the prediction target of the regression task. Then, each feature in the sample undergoes a preprocessing step of minimization (max-min) normalization. The processed training set samples are represented as follows:

[0008] Step 2: Reshape the features of the samples processed in Step 1, splitting the features of each sample into three streams of length T. For any sample... The three flows can be viewed as two-dimensional matrices of dimensions T×3, T×3, and T×1, respectively, corresponding to three force information, three torque information, and one theoretical angle information. The s-th flow can be represented as...

[0009] Step 3: Construct a multi-channel common attention recurrent neural network model to estimate the shape of the continuum joint. Then, feed the training sample set after shape reshaping in Step 2 into the constructed deep neural network along three different channels, and train the deep neural network f(·) using the corresponding sample labels Y to obtain the continuum joint shape estimator.

[0010] Step 4: For any sample x in the test set, first, perform the maximum and minimum value normalization process in Step 1 and the shape reshaping process in Step 2 to obtain the three reshaped flows as follows: and The three streams are then fed into the trained continuum joint shape estimator along three different channels. This is used to estimate the P (X or Y coordinate) of the marked point on the continuum joint of the corresponding test sample for each sample.

[0011] Furthermore, the deep neural network model in step three is a multi-channel common attention recurrent neural network, and the network structure is as follows:

[0012] The first to third layers are three input layers, each receiving three streams of sample features after sequence reshaping, with feature dimensions of T×3, T×3, and T×1, respectively. The fourth to sixth layers are three parallel one-dimensional convolutional layers, each with F filters and K kernel size. s The network has a stride of 1, uses same padding, and employs the tanh activation function. The seventh layer is a common attention layer, taking the outputs of the first and second one-dimensional convolutional layers as input, with an adjustable mapping dimension of m. The eighth layer is a connection layer, concatenating the outputs of the common attention layer and the third one-dimensional convolutional layer. The ninth layer is a shape reshaping layer with a reshaping scale of d. The tenth to twelfth layers are recurrent neural network layers with 128, 64, and 32 nodes, respectively. The thirteenth and fourteenth layers are fully connected layers with 8 and 1 nodes, respectively. Furthermore, the network uses an adaptive moment estimation (Adam) optimizer to minimize the mean squared error (MSE) loss.

[0013] Furthermore, in the deep neural network f(·) constructed in step three, the implementation process of the three one-dimensional convolutional layers from the fourth to the sixth layer is as follows:

[0014] For the samples after maximum and minimum value processing The s-th flow Inputting it into the corresponding one-dimensional convolution channel yields the output of the s-th one-dimensional convolutional layer.

[0015]

[0016] Where F represents the number of filters in the convolutional layer. The output of the j-th filter is expressed as...

[0017]

[0018] Here, tanh(·) represents the tanh activation function. This represents the j-th trainable filter, where K s The kernel size, C represents the convolution kernel size. h This represents the number of channels in the filter. Indicates bias.

[0019] Furthermore, in the deep neural network f(·) constructed in step three, the implementation process of the seventh common attention layer is as follows:

[0020] The outputs of the first and second one-dimensional convolutional layers and The input is fed into a joint attention layer using parallel joint attention to learn the interaction between the two input sequences. First, according to and The similarity matrix was calculated as follows

[0021]

[0022] in, This represents the weight matrix. Then, using the similarity matrix C, two attention maps are obtained respectively.

[0023]

[0024] in, This represents the weight matrix. m represents the adjustable mapping dimension. Next, we will examine the attention map. Perform a linear mapping operation to obtain the attention weights as follows:

[0025]

[0026] in, This represents the mapping matrix. Finally, based on a... v and a q The attention matrices obtained are as follows:

[0027]

[0028] in, Represents a matrix of all ones. This represents the element-wise multiplication operator. It's worth noting that the weighted input features are not summed during the calculation, allowing the attention layer's output to retain temporal order.

[0029] Furthermore, in the deep neural network f(·) constructed in step three, the implementation process of the connection layer in the eighth and ninth layers and the shape reshaping layer is as follows:

[0030] First, the output of the common attention layer and With the output of the third one-dimensional convolutional layer To make a connection, it is represented as Then, O c Remodeling Where the integer d≥1 represents the reshaping scale.

[0031] Furthermore, the implementation process of the tenth to twelfth recurrent neural network layers and the thirteenth and fourteenth fully connected layers is as follows:

[0032] set up The t-th time step is Therefore, for time t, the output of the third recurrent neural network layer can be obtained as follows:

[0033]

[0034] in, Let n1, n2, and n3 represent the mapping processes of the first, second, and third recurrent neural network layers, respectively. n1, n2, and n3 represent the output dimensions of the three recurrent neural network layers at time t. Therefore, the overall output of the third recurrent layer can be expressed as...

[0035]

[0036] Then, use the last time step. The first fully connected layer takes the sample x as input, and the second fully connected layer is used for location prediction. Finally, the predicted P (X or Y coordinate) for sample x is obtained.

[0037]

[0038] in, and These represent the weight matrices and biases of the first and second fully connected layers, respectively. This represents the number of nodes in the first fully connected layer.

[0039] Beneficial Effects: As shown in the figure, the cable-driven continuum joint shape estimation method provided by this invention preprocesses training samples represented using continuum joint force variation information (force information and torque information) and theoretical angle information, and then reshapes the features of the processed samples. These reshaped training samples are then input into a specially constructed deep neural network, and combined with the labels corresponding to the training samples, the optimal deep neural network continuum joint shape estimator is obtained. During the testing phase, test samples represented using continuum joint force variation information (force information and torque information) and theoretical angle information are input into the optimal continuum joint shape estimator to estimate the coordinate positions of the marked points on the continuum joint of the corresponding samples.

[0040] Existing research on the shape estimation of chord-driven continuum joints largely focuses on modeling joint shape changes using traditional kinematic methods. However, due to the flexible deformation capabilities of continuum joints, kinematic modeling methods typically require cumbersome parameter identification processes, making it difficult to generate accurate shape estimation models. Furthermore, during actual surgery, collisions between the continuum joint and human tissues result in unknown shape changes, further reducing the accuracy of continuum joint shape estimation and leading to insufficient adaptability to complex surgical environments.

[0041] Therefore, the present invention employs a data-driven method for estimating the shape of a continuous joint, which is driven by a flexible cable. Experimental results show that this method has better estimation performance than traditional regression methods and can accurately estimate the shape of the continuous joint. Attached Figure Description

[0042] Figure 1 This is a flowchart of a cable-driven continuum joint shape estimation method according to the present invention.

[0043] Figure 2 The X-coordinate of marker point 1 in a training set of data under a load of 5g changes over time.

[0044] Figure 3 The Y-coordinate of marker point 1 in a training set of data under a load of 5g changes over time.

[0045] Figure 4 The theoretical angle of the system input changes over time in a training set of data with a load weight of 5g. Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1As shown, this invention first performs min-maximum normalization preprocessing on training samples represented using the change information of joint forces (force and torque information) and theoretical angle information of the continuum joint, and then reshapes the processed sample features. These features are then input into a constructed deep neural network estimator to predict the coordinate positions of marked points on the continuum joint. During the training phase, the training samples represented using the change information of joint forces (force and torque information) and theoretical angle information of the continuum joint are first preprocessed using min-maximum normalization, and the processed sample features are reshaped. Further, combined with the corresponding training sample labels, the optimal continuum joint shape estimator is obtained. During the testing phase, using the obtained optimal continuum joint shape estimator, combined with test samples represented using the change information of joint forces (force and torque information) and theoretical angle information of the continuum joint, the coordinate positions of marked points on the continuum joint corresponding to each test sample are predicted.

[0048] The following experiment compares the method of this invention with traditional regression methods in terms of mean square error (MSE), mean absolute error (MAE), and Pearson correlation coefficient (PCC).

[0049] The effectiveness of the method in this invention instance was verified by using the cable-driven continuum joint motion dataset from Hefei University of Technology.

[0050] To simulate the stress conditions of a continuous joint in a real surgical environment, the data in this dataset were collected under both unloaded and loaded conditions, totaling 12 sets of data. Specifically, 2 sets of data were collected under unloaded conditions; 2 sets of data were collected under a load of 5g; 4 sets of data were collected under a load of 10g; and 4 sets of data were collected under a load of 15g.

[0051] To conduct a specific study on the shape estimation problem of flexible continuum joints, this invention uses a 3-DOF continuum surgical robot constructed by Hefei University of Technology as an experimental prototype. This prototype contains three degrees of freedom: rotation, translation, and bending of the continuum joint. The prototype mainly consists of a cable-driven module, a rotation and translation module, and a single-DOF continuum joint. The cable-driven module is equipped with three linear motors, several pulleys, and Bowden wires. The three motors drive the movement of three cables, with two providing the power required for the bending motion of the continuum joint, and the other providing the power required for the opening and closing motion of the end effector clamp. The pulleys and Bowden wires mainly guide the two cables driving the bending motion of the continuum joint; one end of each cable is fixed to a linear motor, and the other end, after being guided, is fixed to the end of the continuum joint. In addition, multiple sensors are installed on the prototype. The magnetic grating on the magnetic ring and the optical grating on the translation module are used to detect the overall rotation angle and linear movement distance of the prototype, respectively, while a six-dimensional force sensor is used to detect changes in the force at the end of the continuum. The continuous joint is made of Niti alloy, with an elastic modulus of 65 GPa and a Poisson's ratio of 0.3, giving it good compliance. Considering the limitations of surgical space, the joint's outer diameter was set to 10 mm and its length to 80 mm. Furthermore, four marker points were placed on the continuous joint, with the bottommost marker point being a fixed point. The coordinate positions of the first three marker points were collected for subsequent shape estimation studies. The dSPACE system sends control commands to each motor to control the movement of the entire prototype in three directions and collects data detected by sensors in real time, serving as the data basis for experimental research.

[0052] The linear motor is an LCA-32 linear motor manufactured by SMAC Corporation (USA), with an effective stroke of 12mm, a continuous force of 30N, and a resolution of 5μm, and is equipped with an LCC-10 driver. The DC servo motor is a Weichuan ECG1636 servo motor, used to drive the rotational motion of the overall prototype, with a rated torque of 100.2mNm and a rated speed of 684.2rpm, driven by an ACJ-005-09 driver. The linear module has an effective stroke of 200mm and a lead of 4mm, using a Panasonic MHMF AC servo motor to drive the linear motion of the overall prototype, with a rated torque of 640mNm and a rated speed of 3000rpm, driven by a Panasonic A6 driver. The magnetic grating is an IBB MSR500 model. The optical grating is a Renishaw RH100X30D50A model with a resolution of 1μm. The six-dimensional force sensor is a Kunwei KWR36A sensor, with a force measuring range of 30N and a torque measuring range of 1.5Nm, used to detect changes in force at the end of a continuous body. The force sensor used is model MSQ-1, with a range of 50N and a resolution of 0.1N, used to detect the tension of the driving cable. The dSPACE real-time control system communicates with the linear motor, DC servo motor, and AC servo motor via an RS232 communication module, and with the six-dimensional force sensor via RS485.

[0053] Each data set was sampled for 100 seconds at a sampling rate of 50 Hz, totaling 5000 time points. Each data set also included 16 sequence data points: three force (N) and three torque (N·M) detected by a six-dimensional force sensor (6 sequences); X-coordinates (mm) and Y-coordinates (mm) of three marker points (6 sequences); the actual bending angle (deg) of the continuum joint (1 sequence); the tension (N) of the two flexible cables (2 sequences); and the theoretical input angle (deg) (1 sequence). This invention uses three force and three torque information points in the XYZ directions of the end of the continuum joint link in three-dimensional space, along with a theoretical angle input through the dSPACE real-time control system, to construct sample features. The X (or Y) coordinate information of marker point 1 is selected as the label for the corresponding sample. In this process, the theoretical information is first generated by the host computer using MATLAB / Simulink to write the control program, which is then compiled and imported into dSPACE for execution. dSPACE then sends the control commands to each motor driver via the RS232 communication module and converts the control commands into drive input information for the six-dimensional force sensor via the RS485 communication module. The motor driver then further converts the control commands into drive input information for the LCA-32 linear motor, ECG1636 DC servo motor, and MHMF AC servo motor.

[0054] Considering the contact between the continuous joint and human tissue in practical applications, two sets of data under no-load conditions and two sets of data under a 5g load were used as the training set; four sets of data under a 10g load were used as the validation set; and four sets of data under a 15g load were used as the test set. Furthermore, the number of time points for each sample was set to 50, resulting in 50×7 dimensional sample features. For the overlap between samples, the overlap between the training and validation sets was set to 40, while the overlap between the test sets was set to 49, to predict the P (X or Y coordinate) corresponding to each time point in the test set. Therefore, in each regression task, the number of samples in the training, validation, and test sets were 1984, 1984, and 19804, respectively. The change of the X (or Y) coordinate of marker point 1 in the training set under a 5g load condition over time is shown below. Figure 2 , Figure 3 As shown, the system signal changes over time as follows: Figure 4 As shown.

[0055] It should be noted that although the proposed network structure is the same for regression tasks predicting coordinate X and regression tasks predicting coordinate Y, the specific parameter settings are not entirely the same.

[0056] In the regression task predicting coordinate X, the specific parameters of the network structure are set as follows: the number of filters in each 1DCNN layer is set to 64, the kernel size is set to 3, the stride is set to 1, the padding method is same padding, and the activation function is tanh. Furthermore, the mapping dimension of the common attention layer is set to 32. The reshaping scale d is set to 5, resulting in a reshaping sample feature dimension of 10×960, which is then fed into the recurrent neural network layer for processing. In the three stacked recurrent neural network layers, the number of nodes in the first to third layers are set to 128, 64, and 32, respectively. Finally, the number of nodes in the two stacked fully connected layers is set to 8 and 1, respectively.

[0057] In the regression task predicting coordinate Y, the specific parameters of the network structure are set as follows: the number of filters in each 1DCNN layer is set to 128, the kernel size is set to 3, the stride is set to 1, the padding method is set to same padding, and the activation function is set to tanh. Furthermore, the mapping dimension of the common attention layer is set to 64, and the reshaping scale d is set to 5. Then, for the three stacked recurrent neural network layers, the number of nodes is set to 128, 64, and 32, respectively. Finally, for the two stacked fully connected layers, the number of nodes is set to 8 and 1, respectively.

[0058] However, both tasks employed the same hyperparameter tuning and optimal model preservation strategies. Specifically, the maximum number of training iterations was set to 50, the batch size range was {8, 16, 32, 64, 128}, and the initial learning rate range was set to {0.1, 0.05, 0.01, 0.005, 0.001, 0.0005, 0.0001} to record the best results. Furthermore, the Adaptive Moment Estimation (Adam) optimizer and Mean Squared Error (MSE) were chosen as the network's optimizer and loss function, respectively. For the optimal model preservation strategy, within the hyperparameter range and 50 iteration cycles, the MSE metric of the network model after each iteration was calculated using the validation set, and the optimal model corresponding to the best MSE result was saved. The optimal model was then applied to the test set to evaluate the model's predictive performance.

[0059] In the experiment, to demonstrate the effectiveness of the method of the present invention, the proposed method was compared with other methods applicable to regression tasks. The comparison methods include: SVR (Support Vector Regression), DEN (Dense Network), LSTM (Long Short-Term Memory) / GRU (Gated Recurrent Unit) / Bi-LSTM (Bi-directional Long Short-Term Memory) / Bi-GRU (Bi-directional Gated Recurrent Unit), Multi-Channel LSTM (MC LSTM), Multi-Channel GRU (MC GRU), Multi-Channel Bi-LSTM (MC Bi-LSTM), Multi-Channel Bi-GRU (MC Bi-GRU), Multi-Channel Self-Attention LSTM (MC-SA LSTM), Multi-Channel Self-Attention GRU (MC-SA GRU), and Multi-Channel Self-Attention Bi-LSTM (MC-SA LSTM). The proposed method in this invention is a Multi-Channel Co-Attention GRU (MC-CA LSTM), which includes various multi-channel self-attention Bi-GRU (MC-SA Bi-GRU), multi-channel co-attention Bi-GRU (MC-CA Bi-GRU), and multi-channel co-attention Bi-GRU (MC-CA Bi-GRU).

[0060] In the experiments, for LSTM, GRU, Bi-LSTM, and Bi-GRU, the constructed networks all employed three stacked recurrent neural network layers and two stacked fully connected layers, with the number of nodes per layer set to be consistent with the proposed method. For MCLSTM, MC GRU, MCBi-LSTM, and MC Bi-GRU, the constructed networks used the same multi-channel modules as the proposed method. Furthermore, the number of filters and the kernel size in the convolutional layers were set to {32, 64, 128} and {3, 5}, respectively, for parameter tuning. For MC-SA LSTM, MC-SA GRU, MC-SA Bi-LSTM, and MC-SA Bi-GRU, the constructed networks first merged the multi-channel outputs and then fed them into a self-attention layer. Finally, for MC-CALSTM, MC-CABi-LSTM, and MC-CABi-GRU, the constructed networks introduced a common attention layer between the multi-channel modules and the recurrent neural network modules, and adopted the same parameter settings and tuning strategies as the proposed method.

[0061] Table 1

[0062]

[0063]

[0064] Tables 1 and 2 show the comparison of MSE, MAE, and PCC results of the proposed method and the comparative method on the validation and test sets, respectively, in the task of predicting the X and Y coordinates. Table 1 shows that the proposed method exhibits superior performance on both the validation and test sets, indicating that it can effectively predict the X coordinate of marker point 1. Furthermore, Table 1 also shows that for multi-channel network models, in most cases, the network model with a self-attention layer exhibits worse prediction performance compared to the model without a self-attention layer. This suggests that using a self-attention layer in the network model may reduce the accuracy of the model's prediction of the X coordinate. Moreover, Table 2 shows that on the validation set, the MC-SA GRU method achieves worse experimental results than the MC GRU method, which to some extent indicates that adding a self-attention layer to the network does not necessarily improve the accuracy of the model's prediction of the Y coordinate. However, combining the results in Tables 1 and 2, it can be inferred that for network models based on multi-channel structures, the model with a common attention layer has better prediction performance than the model without a common attention layer. This indicates that using a common attention layer in a network model can effectively learn the correlation between multiple sequences, thereby improving the accuracy of the model in predicting the X and Y coordinates.

[0065] Table 2

[0066]

[0067]

[0068] Next, to observe in more detail the performance of using common attention layers and self-attention layers in the model for the location prediction task, Tables 3 and 4 present a comparison of the experimental results of the MC-SA GRU and MC-CA GRU methods when using different mapping dimensions (m∈{32,64,128}) in the attention layer for the tasks of predicting X-coordinates and Y-coordinates, respectively. It should be noted that for each mapping dimension, the data shown in the tables represent the best results obtained across all hyperparameters in the convolutional layer.

[0069] As shown in Tables 3 and 4, under the same mapping dimension, the MC-CA GRU method outperforms the MC-SA GRU method in all three metrics on both the validation and test sets. This demonstrates that applying a common attention layer to the network model can more effectively improve its performance on the task of predicting coordinate positions. Furthermore, the advantage of the common attention layer is even more pronounced in the task of predicting the X-coordinate position.

[0070] Table 3

[0071]

[0072] Table 4

[0073]

[0074]

[0075] Finally, to comprehensively observe the performance of the network model in the coordinate position prediction task, based on the experimental results in Tables 1 and 2, a network model containing self-attention layers and co-attention layers was selected. Simultaneously, based on the proposed multi-channel module and combined with the Transformer encoder, a multi-channel Transformer (MC Transformer) model was constructed. Then, based on the X and Y coordinate positions predicted by these models, the average Euclidean distance (AED) and average Manhattan distance (AMD) between the true and predicted coordinate positions in the validation and test sets were calculated according to the following formulas.

[0076]

[0077] Among them, (xi ,y i )and represents the actual coordinate position and predicted coordinate position of the marker point corresponding to the i-th sample, respectively, and n represents the number of samples.

[0078] Table 5

[0079]

[0080] Table 5 presents the experimental results of the network model containing self-attention layers and co-attention layers, and the MC Transformer model, on the validation and test sets. The results show that, compared to other methods, the method containing co-attention layers performs better on both the validation and test sets, further demonstrating that the use of co-attention layers can effectively improve the model's performance in the task of predicting coordinate locations.

Claims

1. A tendon-driven continuum joint shape estimation method, characterized by, The method comprises: firstly establishing a tendon-driven surgical robot continuum joint motion data set, and dividing it into a training set, a validation set and a test set according to the load weight of the continuum joint end; then, using three force information, three moment information and one theoretical angle information input through the dSPACE real-time control system in the X, Y and Z directions of the three-dimensional space at the end of the continuum joint link to construct a sample feature sequence; At the same time, the coordinate position information of the marker point on the continuum joint is used as the label sequence of the sample; further, the feature sequences are divided by overlapping according to the time length T = 50 0.5s time points to construct training samples, validation samples and test samples; in addition, the method independently performs two prediction regression tasks according to the X coordinate position and the Y coordinate position of the marker point; in the regression task of predicting the X or Y coordinate of the marker point, the label of each sample is selected as the X or Y coordinate position of the marker point corresponding to the last time point in T time points, and the specific steps of the method comprise: Step one, the training set sample is expressed as Wherein, n represents the sample number of the training set; the corresponding sample label is expressed as Wherein, y1,y2,…,y n The X coordinate value or Y coordinate value of the corresponding mark point, depending on the prediction object of the current regression task; then, the maximum and minimum value normalization preprocessing is performed on each feature in the sample, and the processed training set sample is expressed as Step two, shape remodeling is performed on the features of the sample after processing in step one, and the features of each sample are split into three streams with length T; for any sample The three streams are regarded as two-dimensional matrices with dimensions T x 3, T x 3, and T x 1, respectively, corresponding to three force information, three moment information, and one theoretical angle information, and the s-th stream is expressed as Step three, construct a multi-channel common attention recurrent neural network model for estimating the shape of the continuum joint; then, the training sample set after shape remodeling in step two is sent into the constructed neural network along three different channels, and the corresponding sample label γ is used to train the deep neural network f(·) to obtain the continuum joint shape estimator Step four, for any sample x in the test set, first go through the max-min normalization in step one and the shape reshaping in step two, get the reshaped three flows respectively as and Then input the three flows along three different channels into the trained continuum joint shape estimator In this way, estimate each sample in the test set to get the X or Y coordinates of the labeled points on the continuum joints of the corresponding test sample.

2. The cable-driven continuum kinematics estimation method of claim 1, wherein, The neural network model in step three is a multi-channel common attention recurrent neural network, and the network structure is: The first to third layers are three parallel input layers, receiving three streams of sample features after sequence reshaping: force information, torque information, and theoretical angle information, with feature dimensions of T×3, T×3, and T×1, respectively. The fourth to sixth layers are three parallel one-dimensional convolutional layers, corresponding to the above three streams in turn. The number of filters in each one-dimensional convolutional layer is set to F, and the kernel size is set to K. s The stride is 1, the padding method is same padding, and the activation function is tanh. The seventh layer is a common attention layer, the input of which is the output of the first and second one-dimensional convolutional layers, and the adjustable mapping dimension is set to m. The eighth layer is a connection layer, which connects the outputs of the common attention layer and the third one-dimensional convolution layer; the ninth layer is a shape reshaping layer, and the reshaping scale is set to d; the tenth to twelfth layers are recurrent neural network layers, and the node numbers are 128, 64 and 32 respectively; the thirteenth and fourteenth layers are fully connected layers, and the node numbers are 8 and 1 respectively; in addition, the network uses an adaptive moment estimation optimizer to minimize the mean square error loss.

3. The cable-driven continuum shape estimation method of claim 1, wherein, In the deep neural network f(·) constructed in step three, the implementation process of the three one-dimensional convolution layers in the fourth to sixth layers is as follows: For the sample after max-min processing The s-th stream Input it into the corresponding one-dimensional convolution channel, and the output of the s-th one-dimensional convolution layer is Wherein, F represents the number of filters in the convolution layer; the output of the jth filter is represented as wherein tanh(·) represents a tanh activation function; represents the jth trainable filter, wherein K s represents a kernel size, C h represents a number of channels of the filter; represents a bias.

4. The cable-driven continuum shape estimation method of claim 1, wherein, In the deep neural network f(·) constructed in step three, the implementation process of the seventh layer common attention layer is as follows: The outputs of the first and second one-dimensional convolutional layers are input to a co-attention layer using parallel co-attention to learn the interaction between the two input sequences; first, a similarity matrix is computed as and where and ​ where, represent the weight matrix; then, using the similarity matrix C, two attention maps are obtained respectively as wherein, represents a weight matrix; m represents the adjustable mapping dimension; then, the attention map linear mapping operation is performed to obtain attention weights wherein, represents a mapping matrix; finally, according to a v and a q , the attention matrix is obtained respectively wherein, represents an all-ones matrix, denotes an element-wise multiplication operator; the weighted input features are not summed during the computation, so that the output of the attention layer still has a temporal nature.

5. The cable-driven continuum shape estimation method of claim 1, wherein, In the deep neural network f(·) constructed in step three, the implementation process of the connection layer and the shape reshaping layer of the eighth and ninth layers is as follows: First, the output of the common attention layer is reshaped as and concatenated with the output of the third one-dimensional convolutional layer denoted as Then, O c is reshaped as where the integer d ≥ 1 represents the reshaping scale.

6. The cable-driven continuum shape estimation method of claim 1, wherein, In the deep neural network f(·) constructed in step three, the implementation process of the recurrent neural network layer of the tenth to twelfth layers and the fully connected layer of the thirteenth and fourteenth layers is as follows: Let the t-th time step of Thus, for time t the output of the third recurrent neural network layer is wherein, respectively denote the mapping processes of the first, second, and third recurrent neural network layers; n1, n2, n3 respectively denote the output dimensions of the three recurrent neural network layers at time t; thus, the overall output of the third recurrent layer is denoted as Then, the last time step as input to a first fully connected layer and a second fully connected layer for position prediction; finally, the predicted X or Y coordinate for the sample x is obtained as wherein, and W1and b1represent the weight matrix and bias of the first fully connected layer, respectively, N1is the number of nodes of the first fully connected layer.

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