A modeling and estimation method of robot pneumatic clamping force based on CNN-LSTM

Abstract

The present invention discloses a modeling and estimation method of the pneumatic clamping force of a robot based on CNN-LSTM. Firstly, the input parameters of the clamping force estimation model are reasonably selected by analyzing the pneumatic clamping control system of the industrial robot to reflect the complex hysteresis nonlinear characteristics of the system, and then a CNN feature extraction layer is introduced. The CNN is used to optimize the LSTM network to solve the problem that the traditional LSTM model is difficult to effectively obtain data association features. Compared with the traditional electric claw control, the invention is a sensorless and low-cost effective estimation method for pneumatic clamping force.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial robots, and in particular to a modeling and estimation method of a robot's pneumatic clamping force based on CNN-LSTM. Background Art

[0002] With the continuous development of the Industrial 4.0 era, pneumatic systems are widely used in the end effectors of industrial robots due to their clean, efficient, and cost-effective advantages. Industrial robots with pneumatic end effectors are increasingly widely used in mechanical precision manufacturing, transportation, chemical industry and other fields. However, due to the complex nonlinearity of industrial robots with pneumatic end effectors, the compressibility of the working medium, and the susceptibility to environmental interference, this poses a great challenge to the high-precision clamping force control of the industrial robot end effectors. In addition, the use of clamping force detection is a key factor in improving the performance of the robot system, and traditional clamping force detection methods usually rely on force sensors, which will increase costs and be susceptible to electromagnetic interference.

[0003] In recent years, research has been conducted on the estimation of sensorless gripping force of the robot pneumatic end. For example, based on the pneumatic system and robot dynamics model, and considering the influence of the pneumatic system air path contraction and expansion, a sensorless gripping force estimation method based on the system mechanism model is proposed; for the pneumatic muscle-enabled robot system, a sensorless force estimation scheme based on adaptive gain integral terminal sliding mode control is proposed. In addition, in order to improve the estimation effect of the system under disturbance, another document proposes a time-varying adaptive optimal force estimation scheme, which uses a delay estimation method to approximate the nonlinearity and disturbance in the system to reduce the influence of system friction. However, since the pneumatic system is susceptible to environmental interference and the system model parameters are time-varying, it is difficult for the above method to obtain accurate model parameters and the model calculation is complex.

[0004] In order to overcome this shortcoming, some literatures have proposed a clamping force estimation scheme based on neural network for the problem of pneumatic end force estimation of robots. The neural network is used to establish a relationship model between the clamping force and the input control signal. This method is simpler and more effective, but when the air pressure changes, the estimation accuracy of the model will decrease. Due to the nonlinear characteristics of the pneumatic clamping system, it is difficult to achieve the desired effect using a single neural network force estimation method. In order to improve the accuracy of the clamping force estimation model, some literatures have proposed a neural network clamping force estimation scheme based on genetic algorithm optimization; some literatures have used PSO to optimize the BP neural network and combined with the joint torque disturbance observer to propose a clamping force estimation method. Although this type of method can improve the estimation accuracy compared to a single network, the above methods do not take into account the hysteresis strong nonlinear characteristics unique to the pneumatic system, which limits the further improvement of the clamping force estimation accuracy. Summary of the invention

[0005] The present invention aims to solve the problem that the existing robot pneumatic clamping force modeling estimation accuracy is low, and provides a robot pneumatic clamping force modeling estimation method based on CNN-LSTM.

[0006] To solve the above problems, the present invention is achieved through the following technical solutions:

[0007] A modeling and estimation method of robot pneumatic clamping force based on CNN-LSTM includes the following steps:

[0008] Step 1: Construct a CNN-LSTM combined neural network clamping force estimation model;

[0009] The CNN-LSTM combined neural network clamping force estimation model is mainly composed of an improved CNN neural network and an LSTM neural network; the input of the improved CNN neural network is used as the input of the CNN-LSTM combined neural network clamping force estimation model, the output of the improved CNN neural network is connected to the input of the LSTM neural network, and the output of the LSTM neural network is used as the output of the CNN-LSTM combined neural network clamping force estimation model;

[0010] Step 2: First obtain the output air pressure and estimated clamping force of the industrial robot pneumatic clamping control system, that is, the output air pressure P at time t-1 t-1 , output pressure P at time t t , estimated clamping force h at time t-2 t-2 and the estimated clamping force h at time t-1 t-1 ; Then use the time t-2 to estimate the clamping force h t-2 and the estimated clamping force h at time t-1 t-1 Calculate the estimated clamping force change increment E, where E = h t-1 -h t-2 , the positive and negative E values ​​reflect the positive and reverse characteristics of the hysteresis characteristics; these five features are then normalized and used as the model input vector X at time t t =(P t ,P t-1 ,h t-1 ,h t-2 ,E) T ;

[0011] Step 3: Input the model at time t into vector X tThe data is sent to the CNN-LSTM combined neural network clamping force estimation model; in the CNN-LSTM combined neural network clamping force estimation model, the data features of the model input vector are first extracted through two convolutional layers, and then the extracted data features are flattened using the flattening layer. The flattened data features are then sent to the LSTM neural network for prediction, and the model output vector h at time t is estimated. t That is, estimate the clamping force at time t.

[0012] In the above step 1, the improved CNN neural network includes an input layer, two convolutional layers and a flattening layer. The input of the input layer forms the input of the improved CNN neural network, the output of the output layer of the input layer is connected to the input of the first convolutional layer, the output of the first convolutional layer is connected to the input of the second convolutional layer, the output of the second convolutional layer is connected to the input of the flattening layer, and the output of the flattening layer forms the output of the improved CNN neural network.

[0013] In step 1 above, the mathematical model of the LSTM neural network is as follows:

[0014] f t =σ(W f,h h t-1 +W f,x x t +b f )

[0015] i t =σ(W i,h h t-1 +W i,x x t +b i )

[0016]

[0017] o t =σ(W o,h h t-1 +W o,x x t +b o )

[0018]

[0019] h t =o t ⊙tanh(C t )

[0020] Among them, h t-1 is the output of the LSTM neural network at time t-1, i.e., the estimated clamping force at time t-1, x t is the input of the LSTM neural network at time t, i.e., the flattened data features at time t; f tis the state of the forget gate at time t, W f,h and W f,x They are respectively the forget gate and h t-1 and x t The corresponding weight, b f is the bias of the forget gate; i t is the state of the input gate at time t, W i,h and W i,x are respectively the input gate and h t-1 and x t The corresponding weight, b i is the bias of the input gate; is the intermediate state of the memory unit at time t, W c,h and W c,x are respectively the memory unit and h t-1 and x t The corresponding weight, b c is the bias of the memory unit; o t is the state of the output gate at time t, W o,h and W o,x are the output gate and h t-1 and x t The corresponding weight, b o is the bias of the output gate; C t is the state of the memory unit at time t, C t-1 is the state of the memory unit at time t-1; h t is the output of the LSTM neural network at time t, i.e., the estimated clamping force at time t; ⊙ is the Hadamard product operation; σ(x) is the Sigmoid function, and tanh(x) is the hyperbolic tangent function.

[0021] Compared with the prior art, the present invention proposes a force-free sensor and low-cost clamping force estimation method based on the CNN-LSTM model, aiming at the strong nonlinear hysteresis characteristics exhibited by the pneumatic gripper at the end of the industrial robot. First, the input parameters of the clamping force estimation model are reasonably selected by analyzing the pneumatic gripping control system of the industrial robot to reflect the complex hysteresis nonlinear characteristics of the system, and then the CNN feature extraction layer is introduced, and the LSTM network is optimized by CNN to solve the problem that the traditional LSTM model is difficult to effectively obtain data association features. Compared with the traditional electric gripper control, the invention is a sensorless, low-cost effective pneumatic gripping force estimation method. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is the structural diagram of the pneumatic clamping control system of a traditional industrial robot.

[0023] Figure 2 This is the characteristic curve of the pneumatic clamping control system of the industrial robot.

[0024] Figure 3 This is the structural diagram of the CNN-LSTM combined neural network clamping force estimation model.

[0025] Figure 4 This is the LSTM structure diagram. DETAILED DESCRIPTION

[0026] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific examples.

[0027] Aiming at the complex hysteresis nonlinear characteristics presented by the pneumatic clamping control system of the industrial robot, realizing low-cost air gripper clamping force estimation without force sensor through modeling method is an effective way to reduce system cost and improve the control accuracy of pneumatic end clamping of the industrial robot. From the perspective of the system, the present invention comprehensively considers various interference factors affecting the clamping force, and combines the hysteresis nonlinear characteristics between the pneumatic clamping force of the industrial robot and the air pressure. On the basis of LSTM (Long and Short-Term Memory, long and short-term memory artificial neural network), a CNN (Convolutional Neural Network) feature extraction layer is introduced to construct a CNN-LSTM combined neural network clamping force estimation model, thereby realizing a low-cost model-based pneumatic clamping force estimation method.

[0028] Traditional industrial robot pneumatic gripper control system Figure 1 As shown, the electric proportional valve is used as the air pressure control module. According to existing research results, the compressibility of the gas and the inherent nonlinear friction of the system lead to obvious hysteresis in the system during operation, and the combination of these two factors will make the nonlinear characteristics between the input air pressure and the output clamping force of the system more complex, thus seriously affecting the control accuracy of the air gripper. According to the experimental data of the air gripper clamping system obtained from the experiment, it is found that the input air pressure and the output clamping force show a hysteresis characteristic relationship, as shown in the following figure. Figure 2 As shown in the experimental results, the air pressure-clamping force complex hysteresis phenomenon of the pneumatic clamping system has the following characteristics: 1) There is a multi-value mapping in the reciprocating motion: when the air pressure P a =P b When the corresponding clamping force F a ≠F b , one input corresponds to different outputs, that is, there is uncertainty in the output; 2) The air pressure inside the gas path is not only determined by the current air pressure P at time t t The decision also depends on the historical output pressure (the pressure P at the moment before the current moment, i.e., at moment t-1) t-1 ) and the historical output clamping force (the clamping force F at the moment before the current moment, i.e., at moment t-1) t-1and the clamping force F at the moment before t-1, i.e. at t-2 t-2 ), where ΔF(k-1)=F(k-1)-F(k-2) is the forward and reverse stroke characteristics in reciprocating motion, such as ΔF(k-1)>0 and ΔF(k-1)<0 represent the forward and reverse strokes respectively.

[0029] Based on the above analysis, considering that the past behavior of the air path will also affect the gripping force of the end gripper of the industrial robot, the present invention selects the actual output air pressure P of the air pump at the current time t t , the actual output pressure of the air pump at the moment before the current moment t, that is, at the moment t-1, P t-1 、Estimated clamping force at time t-1 h t-1 , estimated clamping force h at time t-2 t-2 , and the clamping force change increment E (change increment E = h t-1 -h t-2 , which is used to indicate the characteristics of the forward and reverse strokes in the forward and reverse reciprocating motions) These five features are used as the input vector X of the CNN-LSTM combined neural network clamping force estimation model. t =(P t ,P t-1 ,h t-1 ,h t-2 ,E) T By selecting such input feature information, the CNN convolution technology of the CNN-LSTM combined neural network clamping force estimation model can be used to extract the hysteresis multi-value mapping feature law. In addition, the above input vector X t Before entering the CNN-LSTM combined neural network clamping force estimation model, normalization and other preprocessing are required, and then feature extraction is performed.

[0030] Since the pneumatic clamping control system of industrial robots has complex hysteresis nonlinear characteristics and is easily affected by factors such as air pressure leakage and environment, there is a complex coupling relationship between the influencing factors. The traditional single LSTM model is difficult to guarantee the accuracy of the estimation results, while CNN can effectively extract the feature information in the air pressure-clamping force data and reduce the interference of redundant input information on the prediction results. The present invention intends to combine CNN with LSTM and propose a CNN-LSTM combined neural network clamping force estimation model, such as Figure 3 shown.

[0031] Traditional CNN is a feedforward neural network capable of feature extraction, which includes input layer, convolution layer, pooling layer, fully connected layer and output layer. The core components of CNN are convolution layer and pooling layer. First, the correlation features between input information are extracted through the convolution layer, and then the features extracted by the convolution layer are passed to the pooling layer. Pooling is used to reduce the dimension of the data, thereby improving the network training speed and preventing overfitting. In practical applications, the features that can be extracted by only one convolution layer are often limited. In order to obtain more complete data features, multiple convolution layers are usually stacked together to form a multi-layer convolutional network.

[0032] Taking into account the multi-value mapping characteristics of the hysteresis of the pneumatic clamping control system of the industrial robot, in order to reflect the input vector of the multi-value mapping characteristics when modeling the hysteresis characteristics, the present invention improves the structure of the traditional CNN, and the improved CNN is mainly composed of an input layer, two convolutional layers and a flattening layer. The improved CNN abandons the pooling layer of the traditional CNN and only uses two convolutional layers of the traditional CNN as feature extraction layers to complete the feature extraction of feature parameters, where the number of convolutions of the two convolutional layers is 16 and 32 respectively, and the convolution size is 2×1. Each convolutional layer contains a ReLU activation layer, and its expression is:

[0033] C o =f(X T *W c +b c ) (1)

[0034] In the formula, C o is the output of the convolutional layer, X T is the convolutional layer input, W c is the shared weight of the convolutional layer; b c is the convolution layer bias; * represents the convolution operation; f(x) represents the ReLU activation function, f(x) = max{0,x}.

[0035] Since CNN is commonly used for image processing, the output is in matrix form. In order to adapt to the temporal characteristics of air pressure information, the improved CNN first extracts features from the input data through two convolutional layers, and then uses a flattening layer to replace the fully connected layer and output layer of the traditional CNN. In this way, the original output 3x2 matrix can be expanded to a 1x6 matrix, and the extracted features are sent to the LSTM network for prediction.

[0036] The clamping force is not only related to the current air pressure input signal, but also the historical behavior of the pneumatic clamping system (such as historical input, historical output, etc.) will also affect the clamping force. Compared with the traditional RNN, the LSTM network has better memory function and can more effectively obtain the historical correlation features in the air pressure-clamping force data. Therefore, the present invention uses the LSTM network to construct a clamping force estimation model without force sensor. LSTM uses the threshold method to control and update the state of the memory unit, which solves the gradient disappearance and gradient explosion problems in the RNN training process. The LSTM network consists of N LSTM units. The unit output and memory unit state of the i-th unit at time t are respectively and Where j = 1, 2, ..., N, in this embodiment, N = 32. The core of LSTM lies in its three threshold structures and memory units. The specific LSTM structure is as follows Figure 4 As shown in the figure. The LSTM neural network extracts important input information through the input gate, forget gate and output gate, and passes the extracted information to the memory unit. The memory unit is updated by the forget gate and the input gate, and the important information of the historical moment is selectively remembered according to the training, or the redundant information in the memory state at a certain moment is removed, and the memory state of the memory unit is updated, and then the information is output.

[0037] 1) Input of LSTM neural network:

[0038] [h t-1 ,x t ]

[0039] 2) Forget gate of LSTM neural network:

[0040] f t =σ(W f,h h t-1 +W f,x x t +b f ) (2)

[0041] 3) Input gate of LSTM neural network:

[0042] i t =σ(W i,h h t-1 +W i,x x t +b i ) (3)

[0043]

[0044] 4) Output gate of LSTM neural network:

[0045] o t =σ(Wo,h h t-1 +W o,x x t +b o )

[0046] 5) Output of LSTM neural network:

[0047]

[0048] h t =o t ⊙tanh(C t ) (6)

[0049] Among them, h t-1 is the output of the LSTM neural network at time t-1, i.e., the estimated clamping force at time t-1, x t is the input of the LSTM neural network at time t, i.e., the flattened data features at time t; f t is the state of the forget gate at time t, W f,h and W f,x They are respectively the forget gate and h t-1 and x t The corresponding weight, b f is the bias of the forget gate; i t is the state of the input gate at time t, W i,h and W i,x are respectively the input gate and h t-1 and x t The corresponding weight, b i is the bias of the input gate; is the intermediate state of the memory unit at time t, W c,h and W c,x are respectively the memory unit and h t-1 and x t The corresponding weight, b c is the bias of the memory unit; o t is the state of the output gate at time t, W o,h and W o,x are the output gate and h t-1 and x t The corresponding weight, b o is the bias of the output gate; C t is the state of the memory unit at time t, C t-1 is the state of the memory unit at time t-1; h t is the output of the LSTM neural network at time t, i.e., the estimated clamping force at time t; ⊙ is the Hadamard product operation; σ(x) is the Sigmoid function, and tanh(x) is the hyperbolic tangent function.

[0050] Formula (2-6) shows that the output h of the LSTM neural network at the current time t is t Both the input x of the LSTM neural network at the current time t t It is also related to the output h of the LSTM neural network at the historical time t-1 t-1 , and also the memory cell state C of the LSTM neural network at the current time t t related.

[0051] The loss function E of the LSTM neural network t for:

[0052] E t =1 / 2(F t -h t ) 2 (7)

[0053] In the formula, F t is the target clamping force at the current moment t, h t Estimate the clamping force at the current time t.

[0054] Based on the above analysis, the present invention proposes a modeling and estimation method for the pneumatic clamping force of a robot based on CNN-LSTM, which includes the following steps:

[0055] Step 1: Construct a CNN-LSTM combined neural network clamping force estimation model.

[0056] The CNN-LSTM combined neural network clamping force estimation model is mainly composed of an improved CNN neural network and an LSTM neural network; the input of the improved CNN neural network is used as the input of the CNN-LSTM combined neural network clamping force estimation model, the output of the improved CNN neural network is connected to the input of the LSTM neural network, and the output of the LSTM neural network is used as the output of the CNN-LSTM combined neural network clamping force estimation model.

[0057] The improved CNN neural network includes an input layer, two convolutional layers and a flattening layer. The input of the input layer forms the input of the improved CNN neural network, the output of the output layer of the input layer is connected to the input of the first convolutional layer, the output of the first convolutional layer is connected to the input of the second convolutional layer, the output of the second convolutional layer is connected to the input of the flattening layer, and the output of the flattening layer forms the output of the improved CNN neural network.

[0058] The mathematical model of the LSTM neural network is as follows:

[0059] f t =σ(W f,h h t-1 +W f,x x t +bf )

[0060] i t =σ(W i,h h t-1 +W i,x x t +b i )

[0061]

[0062] o t =σ(W o,h h t-1 +W o,x x t +b o )

[0063]

[0064] h t =o t ⊙tanh(C t )

[0065] Among them, h t-1 is the output of the LSTM neural network at time t-1, i.e., the estimated clamping force at time t-1, x t is the input of the LSTM neural network at time t, i.e., the flattened data features at time t; f t is the state of the forget gate at time t, W f,h and W f,x They are respectively the forget gate and h t-1 and x t The corresponding weight, b f is the bias of the forget gate; i t is the state of the input gate at time t, W i,h and W i,x are respectively the input gate and h t-1 and x t The corresponding weight, b i is the bias of the input gate; is the intermediate state of the memory unit at time t, W c,h and W c,x are respectively the memory unit and h t-1 and x t The corresponding weight, b c is the bias of the memory unit; o t is the state of the output gate at time t, W o,h and W o,x are the output gate and h t-1 and x t The corresponding weight, b o is the bias of the output gate; Ct is the state of the memory unit at time t, C t-1 is the state of the memory unit at time t-1; h t is the output of the LSTM neural network at time t, i.e., the estimated clamping force at time t; ⊙ is the Hadamard product operation; σ(x) is the Sigmoid function, and tanh(x) is the hyperbolic tangent function.

[0066] The CNN-LSTM combined network structure adopted by the present invention mainly consists of two parts. The first part is CNN feature extraction. The data passing through the CNN feature extraction layer is transferred to LSTM for clamping force estimation after the dimension is adjusted by the flattening layer. The second part uses the LSTM clamping force estimation model to realize clamping force estimation, thereby obtaining the final output result. Parameter learning in CNN-LSTM modeling is completed using the conventional steepest descent method.

[0067] Step 2: First obtain the output air pressure and estimated clamping force of the industrial robot pneumatic clamping control system, that is, the output air pressure P at time t-1 t-1 , output pressure P at time t t , estimated clamping force h at time t-2 t-2 and the estimated clamping force h at time t-1 t-1 ; Then use the time t-2 to estimate the clamping force h t-2 and the estimated clamping force h at time t-1 t-1 Calculate the estimated clamping force change increment E, where E = h t-1 -h t-2 ; Then, these five features are normalized and used as the model input vector X at time t t =(P t ,P t-1 ,h t-1 ,h t-2 ,E) T .

[0068] Step 3: Input the model at time t into vector X t The data is sent to the CNN-LSTM combined neural network clamping force estimation model; in the CNN-LSTM combined neural network clamping force estimation model, the data features of the model input vector are first extracted through two convolutional layers, and then the extracted data features are flattened using the flattening layer. The flattened data features are then sent to the LSTM neural network for prediction, and the model output vector h at time t is estimated. t That is, estimate the clamping force at time t.

[0069] The estimated value of the clamping force obtained through the modeling method provides basic clamping force feedback information for the closed-loop control of the clamping force of the industrial robot end pneumatic gripper, which can achieve high-precision control of the clamping force and will effectively expand the application range of pneumatic grippers.

[0070] It should be noted that, although the embodiments of the present invention described above are illustrative, they are not intended to limit the present invention, and therefore the present invention is not limited to the above specific embodiments. Without departing from the principles of the present invention, any other embodiments obtained by those skilled in the art under the guidance of the present invention are deemed to be within the protection of the present invention.

Claims

1. A modeling and estimation method for robot pneumatic clamping force based on CNN-LSTM, characterized in that: The steps include: Step 1: Construct a CNN-LSTM combined neural network clamping force estimation model; The CNN-LSTM combined neural network clamping force estimation model is composed of an improved CNN neural network and an LSTM neural network; the input of the improved CNN neural network is used as the input of the CNN-LSTM combined neural network clamping force estimation model, the output of the improved CNN neural network is connected to the input of the LSTM neural network, and the output of the LSTM neural network is used as the output of the CNN-LSTM combined neural network clamping force estimation model; Step 2: First obtain the output air pressure and estimated clamping force of the industrial robot pneumatic clamping control system, that is, the output air pressure P at time t-1 t-1 , output pressure P at time t t 、Estimated clamping force h at time t-2 t-2 and the estimated clamping force h at time t-1 t-1 ; Then use the time t-2 to estimate the clamping force h t-2 and the estimated clamping force h at time t-1 t-1 Calculate the estimated clamping force change increment E, where E = h t-1 -h t-2 , the positive and negative E values ​​reflect the positive and reverse characteristics of the hysteresis characteristics; these five features are then normalized and used as the model input vector X at time t t =(P t ,P t-1 ,h t-1 ,h t-2 ,E) T ; Step 3: Input the model at time t into vector X t The data is sent to the CNN-LSTM combined neural network clamping force estimation model; in the CNN-LSTM combined neural network clamping force estimation model, the data features of the model input vector are first extracted through two convolutional layers, and then the extracted data features are flattened using the flattening layer. The flattened data features are then sent to the LSTM neural network for prediction, and the model output vector h at time t is estimated. t That is, estimate the clamping force at time t.

2. According to a modeling and estimation method of a robot pneumatic clamping force based on CNN-LSTM according to claim 1, in step 1, the improved CNN neural network includes an input layer, two convolutional layers and a flattening layer, the input of the input layer forms the input of the improved CNN neural network, the output of the input layer is connected to the input of the first convolutional layer, the output of the first convolutional layer is connected to the input of the second convolutional layer, the output of the second convolutional layer is connected to the input of the flattening layer, and the output of the flattening layer forms the output of the improved CNN neural network.

3. The modeling and estimation method of the robot pneumatic clamping force based on CNN-LSTM according to claim 1 is characterized in that: In step 1, the mathematical model of the LSTM neural network is as follows: f t =σ(W f,h h t-1 +W f,x x t +b f ) i t =σ(W i,h h t-1 +W i,x x t +b i ) o t =σ(W o,h h t-1 +W o,x x t +b o ) h t =o t ⊙tanh(C t ) Among them, h t-1 is the output of the LSTM neural network at time t-1, i.e., the estimated clamping force at time t-1, x t is the input of the LSTM neural network at time t, i.e., the flattened data features at time t; f t is the state of the forget gate at time t, W f,h and W f,x They are respectively the forget gate and h t-1 and x t The corresponding weight, b f is the bias of the forget gate; i t is the state of the input gate at time t, W i,h and W i,x are respectively the input gate and h t-1 and x t The corresponding weight, b i is the bias of the input gate; is the intermediate state of the memory unit at time t, W c,h and W c,x are respectively the memory unit and h t-1 and x t The corresponding weight, b c is the bias of the memory unit; o t is the state of the output gate at time t, W o,h and W o,x are the output gate and h t-1 and x t The corresponding weight, b o is the bias of the output gate; C t is the state of the memory unit at time t, C t-1 is the state of the memory unit at time t-1; h t is the output of the LSTM neural network at time t, i.e., the estimated clamping force at time t; ⊙ is the Hadamard product operation; σ(x) is the Sigmoid function, and tanh(x) is the hyperbolic tangent function.

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