Robot arm motion control method, device and equipment, robot and medium

Abstract

The invention provides a robot arm motion control method, device and equipment, a robot and a medium, and relates to the technical field of sensors and robots. The method comprises the steps of predicting a singular value decomposition result of a Jacobian matrix through a deep learning model, and obtaining a direction vector set and a corresponding singular value sequence; dividing the direction vector into two subsets respectively corresponding to a non-approximate singular direction and an approximate singular direction based on the singular value sequence and a sensitivity threshold; decomposing the input vector of the expected speed on the two subsets to obtain a first direction component and a second direction component; and performing scaling processing on the second directional component, and calculating the speed of each joint in the joint space based on the first directional component and the scaled second directional component. According to the invention, stable and accurate motion control can be realized when the robot arm is close to the singular configuration, and the calculation complexity is reduced while the control effect is ensured, so that the resource occupation is reduced and the calculation efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of sensors and robotics, and relates to a robot arm motion control method, a robot arm motion control device, an electronic device, a robot, and a computer readable storage medium. BACKGROUND

[0002] When performing high-precision tasks, the end effector of a robot arm usually needs to achieve continuous, smooth and stable motion control in three-dimensional space. Such control usually relies on the Jacobian matrix to depict the mapping relationship between the joint space and the task space.

[0003] However, when the robot arm works in a singular configuration, the Jacobian matrix may be rank-deficient, that is, some singular values of the Jacobian matrix tend to zero or even zero, resulting in non-invertibility or large condition number of the Jacobian matrix. In this case, the joint speed solution based on the inverse of the Jacobian matrix will lose stability, and is extremely easy to cause joint speed to change dramatically or even diverge, causing the end effector to lose control, and in severe cases, may endanger work safety or damage equipment.

[0004] To avoid the above problems, traditional methods such as the Damped Least Squares (DLS) method are widely used. This method introduces a damping factor when calculating the generalized inverse, and when the singular value is below a certain threshold, the damping factor is used to suppress its dominant role on the overall solution, thereby suppressing numerical divergence.

[0005] Although the DLS method has certain effect on singular problems, this "global damping" mechanism may damage the analyticality and sensitivity of the system in non-singular directions, resulting in a decrease in overall control accuracy, especially in the task space region far from the singular point, which is unnecessarily hindered, thereby affecting the dynamic performance and operable range of the robot arm. In addition, due to the large amount of calculation and high complexity of the DLS method in matrix decomposition and generalized inverse solution, it is easy to cause excessive resource occupation and low operation efficiency.

[0006] Therefore, it is urgent to provide a new robot arm motion control scheme to make the robot arm not only consider stability and accuracy when approaching a singular configuration, but also reduce computational complexity. SUMMARY

[0007] The present disclosure provides a robot arm motion control method, device, equipment, robot and medium, which can realize stable and accurate motion control when the robot arm approaches a singular configuration, and reduce computational complexity while ensuring control effect, thereby reducing resource occupation and improving operation efficiency.

[0008] Additional aspects and advantages of the present disclosure will be set forth in part in the description which follows, and in part will be apparent from the description, or can be learned by practice of the present disclosure.

[0009] According to a first aspect of the present disclosure, a robot arm motion control method applied to a master controller of a robot is provided, the method comprising: predicting, by a deep learning model, a singular value decomposition result of an original Jacobian matrix representing a mapping relationship between a joint space and a task space of the robot arm, obtaining a set of direction vectors and a singular value sequence associated with each direction vector in the set of direction vectors; determining, based on the singular value sequence and a sensitivity threshold, a first subset of the set of direction vectors corresponding to non-approaching singular directions and a second subset corresponding to approaching singular directions; decomposing an input vector representing a desired velocity in the task space on the first subset and the second subset respectively, obtaining a first direction component and a second direction component; performing scaling processing on the second direction component, and obtaining a velocity of each joint in the joint space based on the first direction component and the scaled second direction component.

[0010] In an exemplary embodiment of the present disclosure, predicting, by a deep learning model, a singular value decomposition result of an original Jacobian matrix representing a mapping relationship between a joint space and a task space of the robot arm comprises: obtaining joint angle data representing a current joint configuration of the robot arm; inputting the joint angle data into a pre-trained deep learning model to obtain a singular value decomposition result of the original Jacobian matrix corresponding to the current joint configuration.

[0011] In an exemplary embodiment of the present disclosure, the deep learning model comprises: an input layer for receiving the joint angle data; a shared feature extraction layer for performing feature extraction on the joint angle data to obtain a joint feature vector; a multi-branch output layer for predicting the singular value decomposition result of the original Jacobian matrix according to the joint feature vector.

[0012] In an exemplary embodiment of the present disclosure, the predicted singular value decomposition result comprises a singular direction probability corresponding to each direction vector in the set of direction vectors and a singular value sequence associated with the set of direction vectors; the multi-branch output layer comprises: a classification output layer for obtaining the singular direction probability corresponding to each direction vector in the set of direction vectors according to the joint feature vector; a regression output layer configured to obtain a singular value sequence associated with the set of direction vectors from the joint feature vector.

[0013] In an example embodiment of the present disclosure, the method further comprises: obtaining joint angle data representing a plurality of joint configurations of the robot arm; calculating a real Jacobian matrix corresponding to each joint configuration, and performing singular value decomposition on each real Jacobian matrix to obtain a set of direction vectors and a real singular value sequence associated with each direction vector in the set of direction vectors; training the deep learning model based on the set of direction vectors and the real singular value sequence associated with each direction vector in the set of direction vectors using a teacher-student model framework.

[0014] In an example embodiment of the present disclosure, the joint angle data comprises original joint angle data and target joint angle data. obtaining joint angle data representing a plurality of joint configurations of the robot arm comprises: sampling within joint limits of the robot arm to obtain original joint angle data of the plurality of joint configurations; performing data augmentation on each original joint angle data to obtain target joint angle data.

[0015] In an example embodiment of the present disclosure, performing data augmentation on each original joint angle data to obtain target joint angle data comprises: adding Gaussian noise to each original joint angle data to obtain target joint angle data.

[0016] In an example embodiment of the present disclosure, performing data augmentation on each original joint angle data to obtain target joint angle data comprises: performing inverse kinematics on a continuous trajectory of the robot arm in task space to obtain a sequence of adjacent joint angles; combining the sequence of adjacent joint angles and the original joint angle data to obtain target joint angle data.

[0017] In an example embodiment of the present disclosure, training the deep learning model based on the set of direction vectors and the real singular value sequence associated with each direction vector in the set of direction vectors comprises: constructing a loss function based on the set of direction vectors and the real singular value sequence associated with each direction vector in the set of direction vectors; iteratively training the deep learning model using the loss function.

[0018] In an example embodiment of the present disclosure, constructing a loss function based on the set of direction vectors and the real singular value sequence associated with each direction vector in the set of direction vectors comprises: Based on the true and predicted values ​​of each direction vector in the direction vector set, a classification loss for singular direction prediction is constructed. Based on the true singular value sequence and the predicted singular value sequence associated with each directional vector, a regression loss for singular value prediction is constructed. Based on the predicted singular value sequence associated with each directional vector, the reconstructed Jacobian matrix is ​​obtained, and the reconstruction loss of the Jacobian matrix is ​​constructed based on the reconstructed Jacobian matrix and the true Jacobian matrix. A loss function is constructed based on the classification loss from singular orientation prediction, the regression loss from singular value prediction, and the reconstruction loss from the Jacobian matrix.

[0019] In one exemplary embodiment of this disclosure, the loss function is: in, L For loss function, As the first weight, It is a true sequence of singular values. To predict singular value sequences, The regression loss for singular value prediction is represented by the L2 norm. and The differences between them; As the second weight, The classification loss is for predicting singular orientations. For the predicted first j The probability that a direction belongs to a near-singular direction, i.e., the predicted value of each direction vector. For the indicator function, i.e. the true value of each direction vector, when the... j A singular value Less than The value is 1 if it is true, and 0 otherwise. The sensitivity threshold, The largest singular value in the true singular value sequence. Let m be the cross-entropy function, and m be the number of singular values. As the third weight, The reconstruction loss is the Jacobian matrix. For the first i Joint configuration The calculated true Jacobian matrix, To reconstruct the Jacobian matrix, and The first i The task space matrix and joint space matrix are obtained by decomposing the real Jacobian matrix. To predict the singular value matrix formed by the singular values, denotes the Frobenius norm, which is used to measure the difference between the reconstructed Jacobian matrix and the real Jacobian matrix.

[0020] In an example embodiment of the present disclosure, the velocities of the joints in the joint space are obtained based on the first direction component and the scaled second direction component, including: The singular values corresponding to the direction vectors in the second subset are promoted to obtain an adjusted singular value matrix; Based on the task space matrix, the joint space matrix and the adjusted singular value matrix obtained by decomposing the original Jacobian matrix, a safety Jacobian matrix is constructed; Based on the generalized inverse of the safety Jacobian matrix, the velocities of the joints are calculated in combination with the first direction component and the scaled second direction component.

[0021] In an example embodiment of the present disclosure, the singular values corresponding to the direction vectors in the second subset are promoted to obtain an adjusted singular value matrix, including: The singular values corresponding to the direction vectors in the second subset are promoted to a singular value threshold; wherein the singular value threshold is determined based on a sensitivity threshold; According to the singular values corresponding to the direction vectors in the first subset and the singular value threshold corresponding to the direction vectors in the second subset, an adjusted singular value matrix is obtained.

[0022] In an example embodiment of the present disclosure, the velocities of the joints are calculated based on the generalized inverse of the safety Jacobian matrix in combination with the first direction component and the scaled second direction component, including: According to the first direction component and the scaled second direction component, a correction velocity in the task space is calculated; According to the generalized inverse of the safety Jacobian matrix and the correction velocity, the velocities of the joints are calculated.

[0023] In an example embodiment of the present disclosure, according to the first direction component and the scaled second direction component, a correction velocity in the task space is calculated, including: wherein, is the correction velocity, is the first direction component, is the scaled second direction component.

[0024] In an example embodiment of the present disclosure, according to the generalized inverse of the safety Jacobian matrix and the correction velocity, the velocities of the joints are calculated, including: wherein, is the velocity of the joint, a safety Jacobian matrix, a generalized inverse of the safety Jacobian matrix, a modified velocity.

[0025] In an example embodiment of the present disclosure, the scaling processing on the second direction components comprises: calculating the scaling factors according to ratios between singular values corresponding to the direction vectors in the second subset and a singular value threshold, wherein the singular value threshold is determined based on the sensitivity threshold; performing the scaling processing on the second direction components according to the scaling factors to obtain the scaled second direction components.

[0026] In an example embodiment of the present disclosure, performing the scaling processing on the second direction components according to the scaling factors to obtain the scaled second direction components comprises: determining the scaling factors corresponding to the direction vectors in the second subset, and constructing a scaling matrix according to the scaling factors; obtaining the scaled second direction components based on the scaling matrix and the second direction components.

[0027] In an example embodiment of the present disclosure, obtaining the scaled second direction components based on the scaling matrix and the second direction components comprises: calculating the scaled second direction components using the scaling matrix, the second direction components and a gain matrix.

[0028] In an example embodiment of the present disclosure, calculating the scaled second direction components using the scaling matrix, the second direction components and a gain matrix comprises: wherein, the scaled second direction components, the second direction components before scaling, the direction vectors in the second subset, the transposes of the direction vectors in the second subset, an input vector of the desired velocity in the task space, the scaling matrix, the gain matrix, used to adjust the control strength of the direction vectors in the second subset.

[0029] In an example embodiment of the present disclosure, the method further comprises: when the singular values corresponding to the direction vectors in the second subset are greater than or equal to the singular value threshold, retaining the second direction components.

[0030] In an example embodiment of the present disclosure, based on the singular value sequence and the sensitivity threshold, a first subset corresponding to non-approaching singular directions and a second subset corresponding to approaching singular directions in the set of direction vectors are determined, comprising: constructing a discrimination condition based on the sensitivity threshold; determining the first subset corresponding to non-approaching singular directions in the set of direction vectors according to singular values in the singular value sequence that do not satisfy the discrimination condition; determining the second subset corresponding to approaching singular directions in the set of direction vectors according to singular values in the singular value sequence that satisfy the discrimination condition.

[0031] In an example embodiment of the present disclosure, the discrimination condition is constructed based on the sensitivity threshold, comprising: determining a maximum singular value in the singular value sequence; determining a singular value threshold based on the maximum singular value and the sensitivity threshold, and constructing the discrimination condition using the singular value threshold.

[0032] In an example embodiment of the present disclosure, the singular value threshold is determined based on the maximum singular value and the sensitivity threshold, comprising: obtaining an adjustment factor; wherein the adjustment factor is calculated according to a singular direction probability obtained by inputting joint angle data representing the current joint configuration of the robot arm into a deep learning model; determining the singular value threshold according to the adjustment factor, the maximum singular value and the sensitivity threshold, and constructing the discrimination condition using the singular value threshold.

[0033] In an example embodiment of the present disclosure, the discrimination condition comprises: wherein, is the singular value threshold, κ is the adjustment factor, is the sensitivity threshold, , is the maximum singular value in the singular value sequence, is the i-th singular value in the singular value sequence. i

[0034] In an example embodiment of the present disclosure, the input vector representing the desired velocity in the task space is decomposed on the first subset and the second subset respectively to obtain the first direction component and the second direction component, comprising: constructing a projection Jacobian matrix based on the first subset, and decomposing the input vector to obtain the first direction component according to the projection Jacobian matrix; extracting a target direction vector corresponding to the task space from the second subset; decomposing the input vector on the target direction vector to obtain the second direction component.​

[0035] In an example embodiment of the present disclosure, the first direction component is: wherein, is the first direction component, is a projected Jacobian matrix, is a generalized inverse of the projected Jacobian matrix, is an input vector representing a desired velocity in the task space.

[0036] In an example embodiment of the present disclosure, the projected Jacobian matrix is constructed based on the first subset, comprising: eliminating from a task space matrix obtained by decomposing the original Jacobian matrix singular values corresponding to direction vectors in the second subset, and retaining direction vectors in the first subset; eliminating from a singular value matrix obtained by decomposing the original Jacobian matrix singular values corresponding to direction vectors in the second subset, and retaining singular values corresponding to direction vectors in the first subset; constructing the projected Jacobian matrix based on a joint space matrix obtained by decomposing the original Jacobian matrix, the retained direction vectors in the first subset, and the singular values corresponding to the direction vectors in the first subset.

[0037] According to a second aspect of the present disclosure, a robot arm motion control method is applied to joint drives of a robot, and the method comprises: receiving velocities of joints in a joint space of the robot arm, and driving corresponding joints to move according to the velocities of the joints; wherein the velocities of the joints in the joint space of the robot arm are obtained according to the robot arm motion control method of the first aspect of the present disclosure.

[0038] According to a third aspect of the present disclosure, a robot arm motion control device is provided, which is applied to a main controller of a robot, and the device comprises: a singular value decomposition module configured to perform singular value decomposition on a Jacobian matrix representing a mapping relationship between a joint space and a task space, to obtain a set of direction vectors and a sequence of singular values associated with each direction vector in the set of direction vectors; a singular direction determination module configured to determine, based on the sequence of singular values and a sensitivity threshold, a first subset of the set of direction vectors corresponding to non-approaching singular directions and a second subset of the set of direction vectors corresponding to approaching singular directions; a desired velocity decomposition module configured to decompose an input vector representing a desired velocity in the task space on the first subset and the second subset respectively, to obtain a first direction component and a second direction component; The joint velocity generation module is configured to perform scaling processing on the second direction component, and obtain velocities of the joints in the joint space based on the first direction component and the scaled second direction component.

[0039] According to a fourth aspect of the present disclosure, a robot arm motion control device is provided, which is applied to a joint driver of a robot, and the device comprises: The joint motion module is configured to receive the velocities of the joints in the joint space of the robot arm, and drive corresponding joint motions according to the velocities of the joints. The velocities of the joints in the joint space of the robot arm are obtained according to the robot arm motion control method of the first aspect of the present disclosure.

[0040] According to a fifth aspect of the present disclosure, an electronic device is provided, which comprises: a processor; anda memory having computer readable instructions stored thereon, the computer readable instructions being executed by the processor to implement the method of the above-mentioned embodiments.

[0041] According to a sixth aspect of the present disclosure, a robot is provided, which comprises: a processor; anda memory having computer readable instructions stored thereon, the computer readable instructions being executed by the processor to implement the method of the above-mentioned embodiments.

[0042] In an exemplary embodiment of the present disclosure, the robot comprises any one of a humanoid robot and a dual-arm robot.

[0043] According to a seventh aspect of the present disclosure, a computer readable storage medium is provided, which has computer program code instructions stored thereon, the computer program code instructions being invoked by a processor of a robot to cause the robot to execute the method of the above-mentioned embodiments.

[0044] According to the above technical solutions, the present disclosure has at least one of the following advantages and positive effects: The present disclosure provides a robot arm motion control method, which predicts the singular value decomposition result of the original Jacobian matrix through a deep learning model, and can directly obtain a direction vector set and a singular value sequence corresponding to the current joint configuration without complex matrix operations. Thus, compared with the traditional method relying on real-time singular value decomposition, this method can significantly shorten the calculation path, reduce the calculation complexity, thereby reducing resource occupation and improving operation efficiency; at the same time, it improves the real-time response capability of the main controller when performing high-precision tasks, avoids the decline of the dynamic following performance of the robot arm due to excessive numerical calculation burden, and thus improves the stability of the overall motion control.

[0045] Further, by using the singular value sequence and the sensitivity threshold, the direction vector set is divided into two sub-sets of non-approaching singular direction and approaching singular direction. Thus, in the mapping relationship between the joint space and the task space, different directions can be processed differently, so that when approaching the singular configuration, only the approaching singular direction is suppressed, while the analyticality and sensitivity of the non-singular direction are maintained. In addition, by decomposing the desired speed in the task space into the first sub-set and the second sub-set, and scaling the speed component corresponding to the second sub-set, the amplification effect of the small singular value direction on the joint speed solution can be effectively reduced in the case of approaching singular state, so that the final synthesized joint speed is kept in a stable interval, thereby maintaining smooth joint motion and ensuring control accuracy when approaching the singular configuration. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and other drawings can be obtained by those skilled in the art without creative labor.

[0047] Figure 1 A system architecture diagram is shown, which can apply the robot arm motion control method in the embodiments of the present disclosure.

[0048] Figure 2 A flowchart of a robot arm motion control method in the embodiments of the present disclosure is shown.

[0049] Figure 3 A flowchart of singular direction division of direction vectors in the embodiments of the present disclosure is shown.

[0050] Figure 4 A flowchart of decomposition of desired speed in the embodiments of the present disclosure is shown.

[0051] Figure 5 A flowchart of scaling processing of the second direction vector in the embodiments of the present disclosure is shown.

[0052] Figure 6 A flowchart of calculating joint speeds in the embodiments of the present disclosure is shown.

[0053] Figure 7 A flowchart of pre-training of a deep learning model in the embodiments of the present disclosure is shown.

[0054] Figure 8 A comparison result of real-time performance and stability of the traditional control method and the present solution in the unified test environment in the embodiments of the present disclosure is shown.

[0055] Figure 9 A block diagram of a robot arm motion control device in an embodiment of the present disclosure is shown.

[0056] Figure 10 A block diagram of another robot arm motion control device in an embodiment of the present disclosure is shown.

[0057] Figure 11 A schematic diagram of a humanoid robot in an embodiment of the present disclosure is shown.

[0058] Figure 12 A structural schematic diagram of a computer system of an electronic device suitable for implementing an embodiment of the present disclosure is shown.

[0059] Figure 13 A schematic diagram of a computer-readable storage medium in an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0060] In the present disclosure description, the terms "first" and "second" are used only for description, and do not indicate relative importance or imply the number of technical features. Therefore, the "first" and "second" features can explicitly or implicitly include at least one of the features. The meaning of "a plurality of" is at least two, unless otherwise explicitly limited.

[0061] First, the related terms involved in the example embodiments of the present disclosure are explained and described: Deep learning model: a machine learning model based on a multi-layer neural network structure, which realizes the approximation of a nonlinear mapping relationship through feature extraction and parameter learning of a large-scale training sample.

[0062] Joint space: a parameter space composed of independent angle variables of each joint of a robot arm, used to describe the motion freedom and internal configuration state of the robot arm. Any point in the joint space corresponds to the joint configuration of the robot arm at a certain moment, usually represented by joint angle data.

[0063] Task space: refers to the space composed of the position and attitude of the end effector of the robot arm in three-dimensional space, used to describe the motion state of the robot arm in the actual operating environment. Among them, the velocity vector of the task space is used to represent the motion velocity that the end effector should achieve in the desired task.

[0064] Jacobi matrix: a matrix describing the mapping relationship between the joint space and the task space of the robot arm, the matrix elements depend on the kinematic parameters and the current joint angle of the robot arm.

[0065] Original Jacobian matrix: refers to the standard Jacobian matrix without any numerical correction or stabilization processing, which fully reflects the mapping relationship between joint angular velocity and end effector velocity. In the example embodiments of the present disclosure, the deep learning model is to predict the singular value decomposition of the original Jacobian matrix.

[0066] Safe Jacobian matrix: refers to the modified matrix obtained by lifting or replacing singular values that meet the conditions on the basis of the singular value decomposition result of the original Jacobian matrix. This matrix is used to constrain the pseudo-inverse operation when approaching the singular configuration, preventing joint speed divergence caused by small singular values, thereby ensuring numerical stability.

[0067] Projected Jacobian matrix: refers to the equivalent Jacobian matrix formed after projecting the task space velocity on the specified direction subset based on the decomposition result of the original Jacobian matrix. In the example embodiments of the present disclosure, the projected Jacobian matrix can be used to retain only the velocity components in the non-singular direction, thereby suppressing the instability caused by the singular direction while ensuring control accuracy.

[0068] Approaching singular direction: in the singular value decomposition of the Jacobian matrix, the motion direction corresponding to the direction vector whose singular value is less than the singular value threshold, which reflects the degree of freedom that is weak in motion ability or easily affected by singularity under the current configuration of the robot arm.

[0069] Non-approaching singular direction: in the singular value decomposition of the Jacobian matrix, the motion direction corresponding to the direction vector whose singular value is greater than or equal to the singular value threshold, which represents the degree of freedom that still maintains good motion ability under the current configuration of the robot arm.

[0070] Joint configuration: refers to the overall pose determined by the angles of each joint of the robot arm, which is the physical manifestation of a specific point in the joint space.

[0071] Joint angle data: refers to the real-time angle measurement value of each joint of the robot arm.

[0072] Teacher-student model framework: a knowledge distillation training method for deep learning models, in which the teacher model is usually a reference model with high accuracy but high computational complexity, and the student model is a target model with smaller parameter quantity and faster inference speed. In the training process, the student model learns the output distribution or intermediate features of the teacher model to achieve a balance between accuracy and efficiency.

[0073] Figure 1 A system architecture diagram is shown, which can apply the robot arm motion control method in the embodiments of the present disclosure. As shown in Figure 1 , the system architecture 100 can include a terminal device 101, a robot 102, a network 103, and a server 104.

[0074] The terminal device 101 includes, but is not limited to, a desktop computer, a laptop computer, a smartphone, a tablet computer, and the like. The terminal device 101 is configured with a graphical user interface and can provide a visualization function to display the running state and joint motion information of the robot 102. In addition, the terminal device 101 can also provide a parameter configuration function to allow the user to set model parameters, sensitivity thresholds, and control strategy execution modes related to the motion control of the robot arm, and to cooperate with the server 104 to complete the visualization analysis and management of the training data.

[0075] The robot 102 is equipped with various sensors such as inertial measurement devices and joint angle encoders for real-time acquisition of its joint space data and task space data. It should be noted that the robot 102 at least includes a main controller and a joint driver, wherein the main controller is used to run the deployed deep learning model, receive sensor sampling data and predict the singular value decomposition result of the original Jacobian matrix, thereby obtaining a set of direction vectors and a singular value sequence associated with each direction vector in the set of direction vectors, and dividing the direction sub-set based on the singular value sequence and the sensitivity threshold, completing the direction decomposition and scaling of the expected velocity vector, and finally obtaining the velocity of each joint in the joint space. The joint driver is used to receive the joint velocity command from the main controller and drive the corresponding joint to execute motion according to the joint velocity, so as to realize real-time control of the robot arm.

[0076] The server 104 is deployed with a training module for the motion control of the robot arm, which can receive and preprocess the sensor sampling data from the robot 102, and train a deep learning model capable of predicting the singular value decomposition result of the original Jacobian matrix. After the training is completed, the server 104 can deploy the deep learning model to the robot 102 for real-time prediction and generation of joint velocity during its operation.

[0077] The network 103 is used to provide a communication link medium between the terminal device 101, the robot 102, and the server 104. The network 103 can include various connection types, such as wired, wireless communication links, or optical fiber cables, etc. It should be understood that Figure 1 The number and type of terminal devices, robots, networks, and servers in the system architecture 100 are only illustrative. According to the implementation needs, there can be any number and any type of terminal devices, robots, networks, and servers, for example, the server can be a cloud server.

[0078] Through the cooperative operation of each part in the system architecture 100, the complete process from sensor data acquisition, deep learning model prediction of Jacobian matrix singular value decomposition result, to joint driver execution of joint velocity can be realized, thereby significantly improving the real-time performance and control stability of the robot arm in complex tasks.

[0079] The robot arm motion control method provided by the example embodiment of the present disclosure is applied to a master controller of a robot. Figure 2 As shown in the figure, the method can include the following steps S201 to S204: In step S201, a singular value decomposition result of an original Jacobian matrix representing a mapping relationship between a joint space and a task space of a robot arm is predicted by a deep learning model to obtain a set of direction vectors and a singular value sequence associated with each direction vector in the set of direction vectors. In step S202, based on the singular value sequence and a sensitivity threshold, a first subset corresponding to non-approaching singular directions and a second subset corresponding to approaching singular directions in the set of direction vectors are determined. In step S203, an input vector representing a desired velocity in the task space is decomposed on the first subset and the second subset respectively to obtain a first direction component and a second direction component. In step S204, scaling processing is performed on the second direction component, and based on the first direction component and the scaled second direction component, a velocity of each joint in the joint space is obtained.

[0080] By executing the robot arm motion control method provided by the example embodiment of the present disclosure, the singular value decomposition result of the original Jacobian matrix is directly predicted by the deep learning model, which can quickly obtain the set of direction vectors and the singular value sequence corresponding to the current joint configuration without real-time complex calculation, thereby improving the real-time performance of the robot arm control. Further, by comparing with the sensitivity threshold, the direction vectors are divided into non-singular directions and approaching singular directions, and only the velocity component of the approaching singular direction is scaled to avoid divergence of joint velocity while maintaining control accuracy of the non-singular direction. Thus, the method can still achieve smooth and stable motion control when approaching singular configuration, improving the reliability and robustness under complex tasks and boundary configurations.

[0081] In the following, the robot arm motion control method in the example embodiment will be described in detail.

[0082] In step S201, a singular value decomposition result of an original Jacobian matrix representing a mapping relationship between a joint space and a task space of a robot arm is predicted by a deep learning model to obtain a set of direction vectors and a singular value sequence associated with each direction vector in the set of direction vectors.

[0083] In the example embodiment of the present disclosure, the deep learning model can output the singular value decomposition result of the original Jacobian matrix representing the mapping relationship between the joint space and the task space based on the mapping relationship learned in the training phase in the inference phase.

[0084] For the original Jacobian matrix, the set of direction vectors is a set of orthogonal direction vectors obtained by singular value decomposition, which is used to represent the main motion direction of the robot arm that can be achieved in the joint space and the task space. The singular value sequence associated with each direction vector in the set of direction vectors refers to a singular value corresponding to each direction vector, which is used to represent the motion capability of the robot arm in the corresponding direction, wherein a larger singular value indicates a stronger motion capability in the direction, and a smaller singular value indicates a weaker motion capability in the direction or even an almost singular configuration.

[0085] Exemplarily, joint angle data representing the current joint configuration of the robot arm can be obtained, and the joint angle data is input into the pre-trained deep learning model to obtain the singular value decomposition result of the original Jacobian matrix corresponding to the current joint configuration. The deep learning model can be a convolutional neural network, a recurrent neural network, a graph neural network, a Transformer network, etc., and the specific type of the deep learning model is not limited in the present disclosure.

[0086] In some example embodiments, the deep learning model can include an input layer, a shared feature extraction layer, and a multi-branch output layer. Specifically, the input layer is used to receive the joint angle data of the current joint configuration of the robot arm, such as the joint angle data being an n-dimensional vector capable of completely representing the current joint configuration. The shared feature extraction layer is used to extract features from the joint angle data to obtain a joint feature vector capable of reflecting the features of the joint configuration. For example, the shared feature extraction layer can include two fully connected layers, each having a preset number of nodes, and after full connection calculation, normalization processing and a nonlinear activation function such as layer normalization and a ReLU (Rectified Linear Unit) function are introduced for step-by-step mapping and normalization of the input data, thereby extracting stable and discriminative feature representations. The joint feature vector obtained after processing by the shared feature extraction layer can be used as a unified feature representation for shared use by the multi-branch output layer. The multi-branch output layer is used to predict the singular value decomposition result of the original Jacobian matrix according to the joint feature vector to directly obtain the structured information required for motion control.

[0087] The predicted singular value decomposition result can include the singular direction probability corresponding to each direction vector in the set of direction vectors and the singular value sequence associated with the set of direction vectors. Accordingly, the multi-branch output layer can include a classification output layer and a regression output layer. Specifically, the classification output layer is used to obtain the singular direction probability corresponding to each direction vector in the set of direction vectors according to the joint feature vector, so as to further distinguish between the singular direction and the non-singular direction. The regression output layer is used to obtain the singular value sequence associated with the set of direction vectors according to the joint feature vector, thereby representing the motion capability in each direction.

[0088] It should be noted that the set of direction vectors obtained in step S201 is an orthogonal basis structure inherent to singular value decomposition, and the deep learning model does not directly output specific direction vectors, but rather represents the attribute information of the set of direction vectors by predicting the singular direction probability corresponding to each direction vector and the singular value sequence, and accordingly realizes the distinction between the approaching singular direction and the non-approaching singular direction.

[0089] For example, after predicting the singular value decomposition result of the original Jacobian matrix by the deep learning model, there are: (1) wherein, is the original Jacobian matrix, is the task space matrix, and the space dimension is m , is the joint space matrix, and the space dimension is n , both of which are orthogonal matrices, and the column vectors of each space matrix are the main motion directions that can be realized in the corresponding space, and together constitute a set of direction vectors; is the singular value matrix, which is composed of the singular value sequence {σ1,σ2,…σ m} predicted by the deep learning model, and can be denoted as: Σ = diag (σ1,σ2,…σ m ),σ1≥σ2≥…≥σ m ≥0 (2) wherein, diag () represents the diagonalization operation, and the singular value matrix has σ1,σ2,…σ m arranged in order on the diagonal, and the rest of the elements are all zero, σ1,σ2,…σ m are all singular values, and are non-negative real numbers arranged in descending order.

[0090] The deep learning model can output the singular value decomposition result of the original Jacobian matrix at one time in the inference stage, thereby avoiding a large amount of calculation required for real-time numerical decomposition, so that the robot master controller can directly utilize the singular value prediction result for speed decomposition and scaling when performing motion control, thereby ensuring the control stability and overall real-time performance under the approaching singular configuration.

[0091] In step S202, based on the singular value sequence and the sensitivity threshold, a first subset corresponding to the non-approaching singular direction and a second subset corresponding to the approaching singular direction in the set of direction vectors are determined.

[0092] In the example implementation of the present disclosure, the set of direction vectors is distinguished into two categories, i.e., non-singular directions and singular directions, by the singular value sequence and a sensitivity threshold. Specifically, the singular value size is used to reflect the strength of the robot's movement ability in each direction. When the singular value is large enough, it is determined that the direction has stable movement ability, and is classified as a non-singular direction; when the singular value is too small or close to zero, it is determined that the direction has a risk of singularity, and is classified as a singular direction.

[0093] Through such a distinction, it is convenient to adopt differentiated processing for different directions in subsequent control, to ensure the control accuracy of non-singular directions while suppressing singular directions, thereby improving the stability and reliability of the overall control.

[0094] In some example implementations, the sensitivity threshold is determined based on the maximum singular value in the singular value sequence. Figure 3 As shown in FIG. 3, step S202 can further include steps S301-S303. Step S301: constructing a discrimination condition based on the sensitivity threshold.

[0095] Exemplarily, the maximum singular value in the singular value sequence can be determined first, and the maximum singular value is taken as a reference value, such as σ1 in formula (2). Then, the singular value threshold is determined based on the maximum singular value and the sensitivity threshold, and the discrimination condition for direction vector classification is constructed using the singular value threshold.

[0096] The sensitivity threshold is used to control the tolerance of the singular value size, and its value directly affects the determination range of the singular direction and the subsequent control effect. Specifically, when the sensitivity threshold tends to 1, the discrimination condition restricts the singular value more strictly, and only allows the direction close to the maximum singular value to be determined as a non-singular direction, which can obtain higher numerical stability, but the movement flexibility is reduced; when the sensitivity threshold tends to 0, the tolerance of the small singular value is increased, and more directions are retained to maintain the movement ability, but at the same time, the risk of numerical instability is also increased.

[0097] In actual applications, the value of the sensitivity threshold can be adjusted through experiments, and set according to different requirements for accuracy and stability of the task. For example, for tasks that require higher stability, a larger sensitivity threshold can be selected; for tasks that need to maintain strong movement flexibility, a smaller sensitivity threshold can be selected. In addition, a dynamic adjustment method can also be used, so that the sensitivity threshold is adaptively optimized according to the current joint configuration of the robot arm or the task state, to further improve the control performance and adaptability of the system in complex environments.

[0098] For example, if the singular value corresponding to a certain direction is less than the product of the maximum singular value and the sensitivity threshold, the direction is determined to be a near-singular direction; otherwise, it is determined to be a non-singular direction. By setting different sensitivity thresholds, the system's sensitivity to singular directions can be flexibly adjusted to adapt to different accuracy requirements and control stability requirements.

[0099] For example, when determining the singular value threshold based on the maximum singular value and the sensitivity threshold, an adjustment factor can be introduced to dynamically adjust the sensitivity of the discrimination criteria. This adjustment factor is calculated based on the singular orientation probabilities obtained by inputting joint angle data representing the current joint configuration of the robot arm into a deep learning model. It can adaptively adjust the discrimination criteria in conjunction with the current joint configuration of the robot arm, ensuring that the system maintains a reasonable discrimination standard under different joint configurations. This avoids the problem of a single sensitivity threshold being too lenient or too strict under complex postures.

[0100] Specifically, the regulation factor κ is defined as: (3) in, This represents the probability of a singular direction.

[0101] Furthermore, the singular value threshold is determined based on the adjustment factor, the maximum singular value, and the sensitivity threshold, and the discrimination criteria are constructed using the singular value threshold.

[0102] For example, the discrimination criteria can be: (4) in, κ is the singular value threshold, and κ is the adjustment factor. The sensitivity threshold, , To predict the maximum singular value in the obtained singular value sequence, For the predicted singular value sequence, the first... i There are singular values. This criterion can be used to determine whether a direction vector belongs to a near-singular direction.

[0103] In this embodiment, the introduction of the adjustment factor makes the singular value threshold not only dependent on the maximum singular value and the sensitivity threshold, but also able to adjust with the change of the singular direction probability, thereby more accurately reflecting the singularity risk under the current joint configuration. Based on this, the discriminant condition can more accurately distinguish between the singular direction and the non-singular direction, thereby improving the reliability of the singular direction detection. Moreover, after applying the adjustment factor to the calculation of the singular value threshold, the components corresponding to the singular directions can be more effectively identified and constrained while maintaining the accuracy of the non-singular direction components, thereby avoiding abnormal amplification in joint speed calculation and improving the stability and safety of overall motion control. Therefore, through the introduction of the adjustment factor, the singular direction discriminant condition can have better adaptability and accuracy, thereby providing a more stable basis for subsequent speed decomposition and scaling.

[0104] In step S302, a first subset of the direction vector set corresponding to the non-singular direction is determined according to the singular values in the singular value sequence that do not satisfy the discriminant condition.

[0105] For example, for a singular value that satisfies , the direction vector corresponding to the singular value is determined as a non-singular direction, and such a direction can maintain the original speed component in the control process, thereby ensuring motion accuracy.

[0106] In step S303, a second subset of the direction vector set corresponding to the singular direction is determined according to the singular values in the singular value sequence that satisfy the discriminant condition.

[0107] For example, for a singular value that satisfies , the direction vector corresponding to the singular value is determined as a singular direction, and such a direction will be identified and scaled in the control process to avoid abnormal amplification of joint speed in the pseudo-inverse calculation, thereby ensuring the stability and reliability of overall motion.

[0108] This embodiment can realize joint determination based on singular value size and singular direction probability, thereby effectively distinguishing between non-singular directions and singular directions in the direction vector set, and providing a reliable direction division basis for subsequent robot arm motion control.

[0109] In step S203, the input vector representing the desired speed in the task space is decomposed on the first subset and the second subset respectively to obtain the first direction component and the second direction component.

[0110] This step can separate the speed component of the singular direction while maintaining the speed component of the non-singular direction, thereby laying a foundation for subsequent differential processing, avoiding numerical instability caused by the singular direction, and ensuring the control accuracy of the main motion direction.

[0111] In some example embodiments, with reference to Figure 4 As shown, step S203 can further include steps S401-S403. In step S401, a projection Jacobian matrix is constructed based on the first subset, and an input vector is decomposed according to the projection Jacobian matrix to obtain a first direction component.

[0112] The first subset corresponds to a set of direction vectors of non-near-singular directions. In the example embodiments of the present disclosure, the first subset is used to construct the projection Jacobian matrix, so that the input vector is preserved in the non-near-singular directions. Through the decomposition process based on the projection Jacobian matrix, the component corresponding to the non-near-singular direction can be extracted from the input vector as the first direction component, which provides a basis for subsequent stable motion control.

[0113] Exemplarily, in order to construct the projection Jacobian matrix containing only the non-near-singular directions, the task space matrix and the singular value matrix can be screened based on the singular value decomposition result of the original Jacobian matrix. Specifically, the direction vectors corresponding to the second subset are removed from the task space matrix obtained by decomposing the original Jacobian matrix, and the direction vectors corresponding to the first subset are retained, thereby obtaining a truncated task space matrix. At the same time, the singular values corresponding to the direction vectors in the second subset are removed from the singular value matrix obtained by decomposing the original Jacobian matrix, and the singular values corresponding to the direction vectors in the first subset are retained, thereby obtaining a truncated singular value matrix.

[0114] Finally, based on the joint space matrix obtained by decomposing the original Jacobian matrix, the direction vectors in the first subset (i.e., the truncated task space matrix), and the singular values corresponding to the direction vectors in the first subset (i.e., the truncated singular value matrix), the projection Jacobian matrix is constructed.

[0115] With reference to formula (1), all column vectors corresponding to the near-singular directions can be removed from the task space matrix U, and the corresponding singular values can be removed from the singular value matrix Σ. For example, assuming that k near-singular directions are removed, the remaining m−k non-near-singular directions can obtain a truncated matrix and .

[0116] The obtained and retains the effective information corresponding to the non-near-singular directions in the original singular value decomposition result, and the column vectors and the singular values related to the near-singular directions have been removed. Based on the truncated task space matrix and the singular value matrix, the projection Jacobian matrix can be further constructed, which can avoid the joint speed divergence problem caused by the near-singular directions in numerical calculation, thereby providing a stable mathematical basis for the motion control of the robot arm.

[0117] For example, the constructed projection Jacobian matrix is: (5) wherein, is a task space matrix that only retains the direction vectors in the first subset, is a singular value matrix that only retains the non-zero singular values corresponding to the direction vectors in the first subset, is a joint space matrix, which is the same as the joint space matrix in formula (1).

[0118] In the example embodiments of the present disclosure, by constructing the projection Jacobian matrix, the components corresponding to the near-singular directions can be eliminated, effectively avoiding the amplification of joint speed in the pseudo-inverse calculation, and ensuring numerical stability. In addition, the projection Jacobian matrix can be used to calculate the safe executable speed component in the task space and ignore the motion that may cause singularity, so as to concentrate the task space speed decomposition on the non-near-singular direction, ensure the smoothness and controllability of the robot arm motion, and improve the stability and reliability of the overall recovery process.

[0119] Further, the input vector can be decomposed to obtain the first direction component according to the projection Jacobian matrix, that is: (6) wherein, is the first direction component, is the projection Jacobian matrix, is the generalized inverse of the projection Jacobian matrix, which can be the right pseudo-inverse of the projection Jacobian matrix, and has: , the matrix only contains the derivatives of the non-zero singular values, is the input vector of the desired speed in the task space.

[0120] Step S402, extracting the target direction vector corresponding to the task space from the second subset.

[0121] It can be understood that the second subset includes the direction vectors corresponding to the task space and the direction vectors of the joint space. Therefore, the target direction vector corresponding to the task space is extracted from the second subset wherein, m denotes the dimension of the task space, k denotes the number of near-singular directions.

[0122] Step S403, decomposing the input vector on the target direction vector to obtain the second direction component, that is: (7) wherein, is a second direction component, is a target direction vector, is a transpose of the target direction vector, is an input vector of desired velocity in the task space.

[0123] In this embodiment, by extracting the target direction vector of the task space from the second subset and decomposing the input vector on the target direction vector, the velocity component corresponding to the near-singular direction can be identified and separated individually. On the one hand, it avoids the numerical instability caused by mixing such components with normal motion directions, and on the other hand, it provides a clear processing object for subsequent scaling and constraint of the near-singular direction velocity component, thereby improving the controllability and stability of the overall motion control.

[0124] In step S204, scaling processing is performed on the second direction component, and based on the first direction component and the scaled second direction component, the velocity of each joint in the joint space is obtained.

[0125] It can be understood that the second direction component corresponds to the near-singular direction, which is prone to velocity amplification in calculation, and therefore needs to be limited in amplitude by scaling to avoid instability of joint velocity. The second direction component after scaling processing and the first direction component can ensure the accuracy of the velocity component of the non-near-singular direction, while effectively suppressing the velocity component of the near-singular direction, thereby obtaining stable and reliable joint velocity and realizing the smoothness and consistency of the overall motion control.

[0126] In some example embodiments, with reference to Figure 5 As shown, scaling processing can be performed on the second direction component according to step S501 and step S502, specifically: In step S501, a scaling factor is calculated according to the ratio between the singular value corresponding to each direction vector in the second subset and the singular value threshold; wherein the singular value threshold is determined based on the sensitivity threshold.

[0127] In this example embodiment, the scaling factor is used to adjust the velocity component, and the singular value threshold is determined based on the sensitivity threshold to assist in distinguishing the near-singular direction and the non-near-singular direction.

[0128] For each direction vector in the second subset, the corresponding singular value is relatively small, and if directly used for joint velocity calculation, it may lead to numerical instability. Therefore, by calculating the ratio of each singular value to the singular value threshold, a scaling factor can be obtained, and the second direction component can be amplitude-constrained accordingly. The introduction of this scaling factor makes it possible to maintain the accuracy of the main motion component while effectively avoiding the velocity amplification problem caused by the near-singular direction, thereby providing a stable numerical basis for subsequent joint velocity calculation.

[0129] For example, the singular value threshold can be based on the sensitivity threshold. and the maximum singular value in the singular value sequence The calculations show that: For example, a moderating factor κ can be introduced, combined with a sensitivity threshold, to determine the singular value threshold, resulting in: Of course, the singular value threshold can be set according to actual needs, and this disclosure does not limit this.

[0130] Furthermore, for example, the calculated scaling factor could be: (8) in, For the first i Scaling factors corresponding to each direction vector The first singular value in the sequence i A singular value, The singular value threshold is preset. Of course, this disclosure is not limited to the calculation method shown in formula (8). When the calculation method of the singular value threshold changes, the calculation formula (8) of the scaling factor can also be adapted and adjusted to ensure that the relationship between the singular value and the singular value threshold can still be correctly reflected under different implementation conditions, thereby maintaining effective constraints on the velocity components close to the singular direction.

[0131] Step S502: Perform scaling processing on the second direction component according to the scaling factor to obtain the scaled second direction component.

[0132] Specifically, the scaling factor corresponding to each direction vector in the second subset is determined, and a scaling matrix is ​​constructed based on each scaling factor, i.e.: (9) in, For scaling matrices, diag () indicates the diagonalization operation. k This indicates the number of directions approaching the singular. It's important to note that when... When the value approaches 0, the corresponding scaling factor approaches 0, which greatly weakens the velocity components near the singular direction.

[0133] Then, based on the scaling matrix and the second directional component, the scaled second directional component is obtained. The scaling matrix consists of scaling factors corresponding to each near-singular direction, used to constrain the magnitude of the second directional component in different directions.

[0134] For example, the scaled second-direction component can be calculated using the scaling matrix, the second-direction component, and the gain matrix, i.e.: (10) wherein, is the scaled second direction component, is the second direction component before scaling, is a direction vector in the second subset, is the transpose of the direction vector in the second subset, is an input vector of desired velocity in the task space, is a scaling matrix, is a gain matrix, used to adjust the control strength of each direction vector in the second subset.

[0135] Formula (10) not only can limit the amplitude of the velocity component in the direction close to singularity, but also can flexibly adjust the scaling effect by using the gain matrix, so as to ensure stable and reliable velocity components under different working conditions, and provide a solid foundation for the synthesis of joint velocity.

[0136] In addition, it should be noted that when the singular value corresponding to each direction vector in the second subset is greater than or equal to the singular value threshold, the second direction component is retained.

[0137] For example, when the corresponding scaling factor is 1, that is, no scaling processing is performed on the velocity component in this direction, so as to ensure that such direction components maintain the original amplitude in joint velocity calculation, which can avoid excessive suppression of unnecessary directions, and ensure numerical stability while taking into account the accuracy and integrity of motion control.

[0138] Further, as shown in Figure 6 , after obtaining the scaled second direction component, the velocity of each joint in the joint space can be obtained according to steps S601 to S603, specifically: Step S601, the singular values corresponding to each direction vector in the second subset are promoted to obtain an adjusted singular value matrix.

[0139] Specifically, the singular values in the second subset are small, and if they are directly used for joint velocity calculation, they may cause velocity amplification in the pseudo-inverse operation process, causing numerical instability. Therefore, these small singular values can be promoted to a level not lower than a preset threshold, so as to avoid the adverse effects caused by too small singular values.

[0140] Exemplarily, the singular values corresponding to the direction vectors in the second subset can be raised to a singular value threshold. For example, a fixed singular value threshold can be set, and when the singular value is less than the singular value threshold, the singular value is directly raised to the singular value threshold to ensure that the adjusted singular value matrix has numerical stability. For another example, the singular value can also be dynamically raised in combination with an adjustment factor, that is, the adjustment factor is calculated according to the singular direction probability corresponding to the current joint configuration, and then the raising amplitude of the singular value is adaptively adjusted, so that the adjustment result can better meet the needs of the actual working condition.

[0141] Then, according to the singular values corresponding to the direction vectors in the first subset and the singular value thresholds corresponding to the direction vectors in the second subset, an adjusted singular value matrix is obtained.

[0142] For example, there are: (11) wherein, is the adjusted singular value matrix, is a singular value threshold, is a singular value corresponding to a direction vector in the first subset.

[0143] As can be seen from formula (11), the adjusted singular value matrix not only retains the relative relationship of the original singular value distribution, but also ensures that all singular values are within a controllable range, so that joint speed divergence can be effectively avoided in subsequent pseudo-inverse operations, and the stability and reliability of the overall control process are improved.

[0144] Step S602, based on the task space matrix, the joint space matrix obtained by decomposing the original Jacobian matrix, and the adjusted singular value matrix, a safety Jacobian matrix is constructed, and there is: (12) wherein, is the safety Jacobian matrix, , is the task space matrix and the joint space matrix obtained by decomposing the original Jacobian matrix, is the adjusted singular value matrix.

[0145] As can be seen from formula (12), the reconstructed safety Jacobian matrix retains the direction information of the original Jacobian matrix, and only adjusts The small singular value can effectively avoid the instability problem of pseudo-inverse calculation caused by small singular value at the numerical level, and prevent abnormal amplification of joint speed. Moreover, since the task space matrix U and the joint space matrix V remain unchanged, the safety Jacobian matrix still completely retains the spatial mapping direction information reflected by the original Jacobian matrix, ensuring the accuracy of the mapping relationship between the task space and the joint space. Therefore, the numerical stability and mapping accuracy can be considered, so that the robot arm can still achieve smooth and reliable speed control when approaching the singular configuration, thereby improving the stability and safety of the overall motion control.

[0146] In step S603, the velocity of each joint is calculated based on the generalized inverse of the safety Jacobian matrix, combined with the first direction component and the scaled second direction component.

[0147] Specifically, after obtaining the safety Jacobian matrix, the corrected velocity in the task space can be calculated according to the first direction component and the scaled second direction component, i.e. (13) wherein, is the corrected velocity, is the first direction component, is the scaled second direction component.

[0148] Combined with formula (6) and (10), formula (13) can also be written as: (14) Then, the velocity of each joint is calculated according to the generalized inverse of the safety Jacobian matrix and the corrected velocity, i.e. (15) wherein, is the velocity of each joint, is the safety Jacobian matrix, is the generalized inverse of the safety Jacobian matrix, is the corrected velocity.

[0149] In this step, first, the first direction component and the scaled second direction component are combined into the corrected velocity, so that the velocity decomposition in the task space not only retains the accurate component in the direction away from the singularity, but also performs amplitude constraint in the direction approaching the singularity, thereby avoiding velocity divergence. Secondly, the generalized inverse of the safety Jacobian matrix is used for velocity mapping, which not only maintains the original mapping direction information, but also ensures the stability of numerical operation, so that the joint velocity calculation is still reliable when approaching the singular configuration. Finally, the obtained joint velocity can meet the motion requirements of the task space and avoid the instability caused by singularity, thereby achieving smooth control and motion consistency of the robot arm in complex working conditions.

[0150] In some example embodiments, with reference to Figure 7 As shown, before predicting the singular value decomposition result of the original Jacobian matrix by the deep learning model, the deep learning model can be pre-trained according to steps S701 to S703, specifically: Step S701, obtaining joint angle data representing a plurality of joint configurations of the robot arm.

[0151] The joint angle data includes original joint angle data and target joint angle data. Exemplarily, the original joint angle data of a plurality of joint configurations can be obtained by sampling within the joint limit of the robot arm, that is, sampling within the movement limit range of each joint of the robot arm to obtain original joint angle data covering a plurality of joint configurations.

[0152] Exemplarily, the sampling of the joint angle data can be uniformly performed within the joint limit range, that is: (16) wherein, represents a joint angle data vector, that is, original joint angle data, n represents the number of joints of the robot arm, respectively represents the minimum angle limit and the maximum angle limit of each joint. The joint angle data collected in this way can cover a plurality of joint configurations of the robot arm within the physical constraint range, providing sufficient sample support for subsequent calculation of the real Jacobian matrix and training of the deep learning model.

[0153] After collecting each original joint angle data, data augmentation can be performed on each original joint angle data, such as by adding noise disturbance, interpolation expansion or random disturbance, to obtain target joint angle data for training, thereby improving the generalization ability of the model under different joint configurations.

[0154] When performing data augmentation on each original joint angle data, for example, Gaussian noise can be added to each original joint angle data to obtain target joint angle data, which has: q noise = q + N (0,δ) (17) wherein, q represents the original joint angle data, N (0,δ) represents a Gaussian distributed random variable with a mean of 0 and a standard deviation of δ, such as δ = 0.01 rad, q noise is the target joint angle data after adding noise.

[0155] By superimposing Gaussian noise on the joint angle data during training, the deep learning model can still output stable Jacobian matrix singular value decomposition results when the input data has slight perturbations, thereby enhancing the robustness of the model. Among them, the noise disturbance is equivalent to data augmentation of joint angle data, making the training sample distribution more abundant, avoiding model overfitting to data under ideal conditions, and thus improving adaptability in real scenarios. Moreover, since the robot joint angle sensor usually has measurement deviation or jitter, adding noise can introduce this uncertainty in advance during training, making the model more close to the actual working condition after deployment. When the robot arm runs close to the singular configuration, the model can also predict that the stability of the set of direction vectors and the singular value sequence will be maintained under small perturbations, thereby ensuring the reliability of joint velocity decomposition and scaling calculation, and thus improving the stability of the overall motion control.

[0156] For example, in addition to sampling the original joint angle data within the joint limit range, more abundant training samples can also be obtained based on the trajectory generation method in the task space. Specifically, the continuous trajectory of the robot arm in the task space can be solved by inverse kinematics, thereby obtaining the adjacent joint angle sequence corresponding to the continuous trajectory. Then, the adjacent joint angle sequence is combined with the original joint angle data obtained by sampling to form target joint angle data with wider coverage and smoother configuration transition.

[0157] The target joint angle data generated in this example can retain the diversity of the original data while supplementing the continuous change characteristics between adjacent joint configurations during actual motion, thereby further improving the training effect and generalization ability of the model in dynamic task scenarios.

[0158] Step S702, calculate the real Jacobian matrix corresponding to each joint configuration, and perform singular value decomposition on each real Jacobian matrix to obtain a set of direction vectors and a real singular value sequence associated with each direction vector in the set of direction vectors.

[0159] Specifically, the joint angle data obtained in step S701 can be substituted into the kinematics model of the robot arm to calculate the corresponding real Jacobian matrix, denoted as . Among them, the real Jacobian matrix can depict the mapping relationship between the joint space and the task space, reflecting the correspondence between the joint angle velocity and the end effector velocity under a specific joint configuration.

[0160] Further, singular value decompositions are performed on each real Jacobian matrix to obtain a task space matrix, a joint space matrix, and a singular value matrix, from which a set of direction vectors, i.e., an orthogonal basis set composed of column vectors of the task space matrix and the joint space matrix, and a real singular value sequence corresponding to each direction vector are obtained. On this basis, each direction vector can be classified and labeled based on a sensitivity threshold and a maximum singular value in the real singular value sequence, so that the set of direction vectors and the real singular value sequence can be extracted while the singular direction is labeled, providing a reference for subsequent model training and control strategy.

[0161] Through the singular value decomposition process, an accurate set of direction vectors and a real singular value sequence can be provided for subsequent training of a deep learning model, thereby ensuring the accuracy and reliability of the model in predicting singular value decomposition results.

[0162] In step S703, the deep learning model is trained based on a teacher-student model framework using the set of direction vectors and the real singular value sequence associated with each direction vector in the set of direction vectors.

[0163] By training the deep learning model under the teacher-student model framework, the prediction accuracy and deployment efficiency of the model for singular value decomposition results can be improved. Specifically, based on the set of direction vectors and the real singular value sequence associated with each direction vector in the set of direction vectors, a loss function is constructed, and the deep learning model is iteratively trained using the loss function.

[0164] For example, a classification loss for singular direction prediction can be constructed based on the real values and predicted values of each direction vector in the set of direction vectors, to measure the accuracy of singular direction prediction. And a regression loss for singular value prediction can be constructed based on the real singular value sequence and the predicted singular value sequence associated with each direction vector, to reflect the accuracy of the model in predicting singular values. Further, based on the predicted singular value sequence associated with each direction vector, a reconstructed Jacobian matrix is obtained, and a reconstruction loss for the Jacobian matrix is constructed based on the reconstructed Jacobian matrix and the real Jacobian matrix, to ensure the consistency of the predicted results in the overall mapping relationship. Finally, the classification loss for singular direction prediction, the regression loss for singular value prediction, and the reconstruction loss for the Jacobian matrix are used to construct a loss function for guiding the parameter update of the deep learning model.

[0165] During the training process, a knowledge distillation strategy can be adopted, i.e., by minimizing the KL (Kullback-Leibler Divergence) divergence between the output distributions of the teacher model and the student model, efficient knowledge transfer is achieved, so that the student model can still obtain prediction performance close to the teacher model while maintaining low computational complexity. In addition, in the deployment stage, the student model can be quantized, such as compressing and optimizing the trained student model, and using 16-bit floating-point numbers for calculation, to achieve fast inference with a target delay of less than 0.5 ms, to meet the application requirements of real-time control.

[0166] In some example embodiments, the constructed loss function can be: (18) wherein, L is a loss function, is a first weight, is a real singular value sequence, is a predicted singular value sequence, is a regression loss of singular value prediction, indicating the difference between the two norms and ; is a second weight, is a classification loss of singular direction prediction, is a predicted j th direction belonging to the probability of approaching the singular direction, i.e., the predicted value of each direction vector, is an indicator function, i.e., the true value of each direction vector, which is 1 when the j th singular value is less than , otherwise 0, is a sensitivity threshold, is the maximum singular value in the real singular value sequence, is a cross-entropy function, and m is the number of singular values; is a third weight, is a reconstruction loss of the Jacobian matrix, is a real Jacobian matrix calculated by the i th joint configuration , is a reconstructed Jacobian matrix, and are the task space matrix and joint space matrix respectively decomposed from the i th real Jacobian matrix, is a singular value matrix composed of predicted singular values, indicates the Frobenius norm, which is used to measure the difference between the reconstructed Jacobian matrix and the real Jacobian matrix.

[0167] By collecting joint angle data of various joint configurations and calculating the corresponding real Jacobian matrix and singular value decomposition results, a wide range of training samples with accurate annotations can be provided for the deep learning model. In the teacher-student model framework, the model is trained using the direction vector set and the real singular value sequence, which not only ensures the accuracy of the model in singular direction prediction and singular value regression, but also improves the generalization ability and lightweight performance of the student model through knowledge transfer. Thus, the trained reinforcement learning model can not only maintain high prediction accuracy under different joint configurations, but also meet the requirements of real-time control for computational efficiency and response speed, thereby laying a foundation for stable motion control of the robot arm.

[0168] The robot arm motion control method proposed in the example embodiments of the present disclosure can first completely retain the corresponding velocity component in the non-singular direction, ensuring that the robot arm still has high control accuracy and motion consistency when far from the singular configuration. Secondly, for the component close to the singular direction, the velocity component is smoothly adjusted with the change of the singular value through a dynamic scaling mechanism based on the singular value size, avoiding sudden changes in joint velocity caused by too small singular values, and realizing smooth transition of the motion process. In addition, by introducing the safe Jacobian matrix and projection operation, the numerical instability problem that may be caused by the traditional pseudo-inverse near the singular point is avoided, ensuring the stability and controllability of the operation. Overall, this method not only maintains the control accuracy in the non-singular direction, but also smoothly processes the velocity component close to the singular direction, and improves the numerical stability through the improved Jacobian matrix construction, so that the motion control of the robot arm under complex working conditions is more stable and reliable.

[0169] For example, assume that the end of the robot arm needs to move in a direction close to singularity, such as performing an operation in the straight line direction when the robot arm is fully stretched. If the traditional method (such as the damped least squares method) is used, a damping is uniformly applied to the velocity components of all directions, although it can avoid numerical instability caused by singular points, but it also suppresses the motion ability in non-singular directions, making the overall motion deviate from the expected path. In contrast, the method of the present disclosure keeps the velocity component unchanged in the non-singular direction (such as the rotation direction), thereby ensuring the control accuracy in these directions. In the direction close to singularity (such as the stretching direction), the velocity in this direction is gradually reduced as the singular value approaches the singular point, but its direction remains unchanged. Thus, not only is the instability caused by velocity divergence avoided, but also the end is ensured to move along the expected path, achieving a balance between numerical stability and path retention.

[0170] Overall, the method provided by the present disclosure can limit only the necessary directions when the singularity risk occurs, so that the robot arm can still maintain a reasonable motion trajectory and control performance when approaching the singular configuration.

[0171] The example embodiments of the present disclosure also provide another robot arm motion control method applied to the joint driver of a robot, which can include: receiving the speed of each joint in the joint space of the robot arm, and driving the corresponding joint motion according to the speed of each joint. Wherein the speed of each joint in the joint space of the robot arm is obtained according to the robot arm motion control method as shown in Figure 2 .

[0172] Specifically, the joint driver receives the speed of each joint in the joint space of the robot arm output by the main controller, and according to the received speed information, respectively issues driving instructions to the execution motor or actuator unit of each joint. For example, the joint driver adjusts the voltage, current, etc. of the driving signal of the execution motor, so that the rotation speed and torque output by the execution motor match the received speed information, thereby ensuring that the actual motion state of the joint is consistent with the target speed. In this process, the joint driver can also combine feedback information to adjust the running state of the execution motor in real time to maintain the stability of the closed-loop control.

[0173] In this way, the synchronous motion of each joint in the time dimension can be realized, so that the robot arm completes the motion along the expected speed trajectory, ensuring that the overall motion process in the task space is stable, coherent, and has good controllability and coordination.

[0174] In some example embodiments, the robot arm motion control method provided by the present disclosure can be executed in the form of a real-time control cycle in the online deployment stage, and the cycle period can be Δt = 2 ms. The method can include the following steps: First, the sensor collects the current joint angle data of the robot arm in real time as the control input. Then, the joint angle data is input into the pre-trained deep learning model to obtain the prediction output, including the singular value estimation and the singular direction probability.

[0175] On this basis, a physical constraint correction mechanism can be introduced to dynamically adjust the sensitivity threshold according to the size and rate of change of the real-time task error, that is: (19) Wherein, is the sensitivity threshold at the moment, which is used to judge the approach to the singular direction in real-time control, t is the reference sensitivity threshold, which represents the basic threshold of the system in the error-free or static state, is the task error vector, is the module length of is the proportional coefficient, which controls the sensitivity threshold the sensitivity threshold​ the influence degree of the error, when the error is large, the discrimination condition is tightened by increasing , thereby enhancing the suppression of the singular direction; is the differential coefficient, controlling the error change rate the influence degree of the error, when the error is large, the discrimination condition is tightened by increasing , thereby enhancing the suppression of the singular direction; , which helps to quickly suppress possible numerical instability.

[0176] Next, the singular values obtained by prediction are safely lifted, so as to ensure that the singular values are not lower than the dynamic threshold, avoiding numerical instability caused by too small singular values. Further, based on the task space matrix U, the joint space matrix V and the lifted singular value matrix, the safe Jacobian matrix is reconstructed. After obtaining the safe Jacobian matrix, the task space velocity is decomposed, the input vector of the task velocity is projected on the non-singular direction and the singular direction respectively, and then the corrected velocity component is calculated. Subsequently, the safe Jacobian matrix is used to map the corrected task space velocity to the joint space, and the velocity command of each joint is obtained.

[0177] Through the above steps, the task space decomposition, joint velocity calculation and numerical safety guarantee can be realized, so as to ensure that the robot arm can avoid the numerical divergence problem caused by the singular point in the real-time running process, while maintaining the stability and accuracy of the motion trajectory. Finally, the calculated joint velocity command is sent to the joint driver, so that the robot arm executes the corresponding motion control.

[0178] In some example implementations, such as the online deployment process of a 7-DOF (Degree of Freedom) robot arm, compared with the traditional singular value decomposition-based implementation, both the calculation efficiency and the control effect show significant advantages.

[0179] Referring to Tables 1 and 2, the hardware configuration and software benchmark configuration required to implement the present scheme are exemplarily illustrated: Table 1 As can be seen from Table 1, the mechanical arm body is a robot arm with 7 degrees of freedom, and the same serial number equipment identifier is HU_D03_03_001. The main controller is an Intel Xeon E3-1280v6 processor with a main frequency of 3.9 GHz, and the Turbo Boost is turned off and the frequency is locked during running to ensure real-time stability. The real-time operating system uses Ubuntu 18.04, loads the PREEMPT_RT real-time kernel, and the kernel version number is 4.14.12-rt10.

[0180] In terms of sensor configuration, an ATI-Mini40 six-axis force sensor was used with a sampling frequency of 1 kHz and a measurement accuracy of ±0.1 N. An OptiTrack Prime13 motion capture system was used with eight cameras, with a positioning accuracy of better than ±0.1 mm.

[0181] Table 2 As can be seen from Table 2, in terms of control algorithm, the traditional method uses singular value decomposition of the Jacobian matrix, while the present scheme uses a neural network prediction combined with physical correction. The control period of both is fixed at 2 ms (500 Hz). In the task scenario, both pick-place tasks and the same physical model (elastic constraint) are used for comparison and verification. The pick-place task refers to the operation of the robot arm (end effector) to complete the "pick - move - place" operation.

[0182] Exemplarily, in the experimental test process, first, the end of the robot arm was set to move along a spiral trajectory. To simulate a high-load operating environment, a matrix calculation task was injected in the background to maintain the CPU load at about 80%. During the test, the PCIe (Peripheral Component Interconnect Express) -1588 time synchronization card was used to record the fluctuation of the control period to evaluate the real-time performance and cycle retention ability of the present scheme under high load conditions.

[0183] In addition, the angle of the 5th joint of the robot arm can also be fixed as q5=0 to construct a theoretically singular configuration. Subsequently, a high-speed motion command along the Z axis was applied to the end of the robot arm, such as v z =0.8 m / s to make the robot arm pass through the singular region. During the test, the laser tracker was used to measure the end position error, and the strain gauge at the joint was used to collect the joint jitter to further evaluate the stability performance of the present scheme in the singular region.

[0184] Specifically, in the traditional control method, real-time singular value decomposition of the Jacobian matrix corresponding to the joint configuration is required, with a computational complexity of . Taking a 7-DOF robot arm as an example, the single decomposition delay is about 450 ps, which will occupy a large proportion of the calculation time under high-speed control period, and cause a large burden on the CPU (Central Processing Unit) resources.

[0185] To solve the above problems, the scheme introduces a neural network (Neural Network, NN) prediction to replace the online singular value decomposition, and the forward calculation complexity of the model is O (1), and the parameter amount is less than 50KB through lightweight model compression. When deployed on an embedded platform, the single-run delay is reduced to 180μs, about 60% lower than the traditional control method, thus meeting the real-time requirements of the 2ms control cycle. At the same time, the CPU load is reduced from about 65% to 11%, greatly releasing the computing resources.

[0186] As shown in Figure 8 , under the unified test environment, real-time and stability comparison experiments are carried out on the traditional control method and the scheme. Specifically: In terms of real-time performance, the data in Figure 8 is arranged as shown in Table 3, and after statistics, the scheme is significantly better than the traditional control method in terms of single calculation time, control cycle violation rate, CPU average load and computing power consumption: Table 3 As can be seen from Table 3, the average single calculation time of the scheme is 38±3ms, which is much lower than that of the traditional control method of 458±18ms. The control cycle violation rate of the scheme is 0%, while the control cycle violation rate of the traditional control method is 12.6%. At the same time, the CPU average load on the main thread of the scheme is only 11.8±0.7%, which is 83% lower than that of the traditional control method of 65.4±2.1%. Therefore, the scheme can significantly shorten the calculation path, reduce the processing burden, and improve the real-time response capability of the main controller in the execution process.

[0187] In addition, in the real-time cycle with a control cycle of 2ms, the CPU time ratio for completing the control algorithm calculation of the traditional control method is 93%, and there is almost no margin to process additional tasks. The operation time of the scheme is greatly reduced, and nearly 5 times of calculation margin is released under the same 2ms control cycle, which can be used to process additional control tasks, making the system more efficient and safer.

[0188] In terms of control stability, the traditional control method relies on a fixed sensitivity threshold to distinguish between singular and non-singular directions, which is prone to classification mutation when the singular value approaches the threshold, resulting in direction jump problem, affecting the continuity and stability of global control. The scheme introduces a singular direction probability in the neural network prediction result and dynamically adjusts it to achieve smooth correction of the singular value, thereby avoiding the mutation problem of fixed threshold judgment under boundary conditions.

[0189] Similarly, in terms of control stability, the data inFigure 8 The data arrangement in Table 4 is shown in Table 4. After statistics, the position tracking error, joint speed fluctuation, mechanical impact force peak and other index values of the scheme compared with the traditional control method are significantly reduced: Table 4 As can be seen from Table 4, for the index of joint speed fluctuation, the scheme is 0.07±0.01 rad / s, which is lower than the safety line 0.1 rad / s, while the traditional control method is 0.32±0.04 rad / s. The position tracking error in the scheme is 0.42±0.1 mm, which is lower than the error threshold 1.0 mm, while the traditional control method is 1.82±0.3 mm. The mechanical impact force peak in the scheme is 2.1±0.3 N, which is lower than the safety threshold 3.0 N, while the traditional method is 5.6±0.6 N. As can be seen, the scheme can effectively reduce the joint speed fluctuation, end position overshoot and instantaneous impact force in the control scene close to the singular configuration, and ensure the stability and safety of the motion control process.

[0190] In general, the scheme not only greatly reduces the delay and resource occupation in terms of computational efficiency, but also improves the numerical stability and motion continuity, and can better meet the control requirements of the robot arm in complex tasks and close to singular configuration.

[0191] In the example embodiments of the present disclosure, a robot arm motion control device is also provided, which is applied to a main controller of a robot. Referring to Figure 9 The first robot arm motion control device 900 includes a singular value decomposition module 901, a singular direction determination module 902, a desired speed decomposition module 903 and a joint speed generation module 904, wherein: The singular value decomposition module 901 is configured to perform singular value decomposition on a Jacobian matrix representing the mapping relationship between the joint space and the task space, to obtain a set of direction vectors and a singular value sequence associated with each direction vector in the set of direction vectors; The singular direction determination module 902 is configured to determine, based on the singular value sequence and a sensitivity threshold, a first subset of the set of direction vectors corresponding to a non-close-to-singular direction and a second subset of the set of direction vectors corresponding to a close-to-singular direction; The desired speed decomposition module 903 is configured to decompose an input vector representing a desired speed in the task space on the first subset and the second subset respectively, to obtain a first direction component and a second direction component; The joint speed generation module 904 is configured to perform scaling processing on the second direction component, and obtain the speed of each joint in the joint space based on the first direction component and the scaled second direction component.

[0192] The specific details of the modules in the robot arm motion control device have been described in detail in the corresponding robot arm motion control method, and thus will not be described here again.

[0193] In the example embodiments of the present disclosure, another robot arm motion control device is also provided, which is applied to the joint driver of a robot. Referring to Figure 10 As shown in the figure, the second robot arm motion control device 1000 includes a joint motion module 1001, wherein: The joint motion module 1001 is configured to receive the velocities of the joints in the joint space of the robot arm, and drive the corresponding joint motion according to the velocities of the joints. The velocities of the joints in the joint space of the robot arm are obtained according to the robot arm motion control method as described in the embodiments of the present disclosure. Figure 2

[0194] The specific details of the modules in the robot arm motion control device have been described in detail in the corresponding robot arm motion control method, and thus will not be described here again.

[0195] In the example embodiments of the present disclosure, a robot is also provided, which includes a processor and a memory, and the memory stores computer readable instructions which, when executed by the processor, implement the above method. The robot includes any one of a humanoid robot and a dual-arm robot. Referring to Figure 11 As shown in the figure, a schematic diagram of a humanoid robot is shown, which includes a robot arm 1100.

[0196] Referring to Figure 12 An electronic device capable of implementing the above method is also provided. The electronic device 1200 includes a processor 1201 and a memory 1202, and the memory 1202 stores computer readable instructions which, when executed by the processor 1201, implement the method in the embodiments of the present disclosure.

[0197] In the example embodiments of the present disclosure, a computer readable storage medium is also provided, which stores computer program code instructions, and when the computer program code instructions are called by the processor of the robot, the robot executes the method as described in the embodiments.

[0198] Referring to Figure 13 ​As shown, a program product 1300 for implementing the above method according to the embodiments of the present disclosure is described, which can adopt a portable compact disc read-only memory (CD-ROM) and include program codes, and can run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto, and in this document, the readable storage medium can be any tangible medium containing or storing a program, which can be used by or in combination with an instruction execution system, device or apparatus.

[0199] Through the above description of the embodiments, those skilled in the art can easily understand that the example embodiments described herein can be implemented by software, or by software in combination with necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a U disk, a mobile hard disk, etc.) or a network, and includes a number of instructions to enable a computing device (which can be a personal computer, a server, a touch terminal, or a network device, etc.) to perform the method according to the embodiments of the present disclosure.

[0200] Finally, the above preferred embodiments are only used to illustrate the technical solutions of the present application and are not limiting. Although the present application has been described in detail, those skilled in the art should understand that changes can be made in form and details without departing from the scope defined by the claims of the present application. The sizes of the drawings are not related to the actual objects, and the sizes of the actual objects can be changed arbitrarily.

Claims

1. A robot arm motion control method characterized by, A main controller applied to the robot, the method comprising: predicting, by a deep learning model, a singular value decomposition result of an original Jacobian matrix representing a mapping relationship between a joint space and a task space of a robot arm, obtaining a direction vector set and a singular value sequence associated with each direction vector in the direction vector set; determining, based on the singular value sequence and a sensitivity threshold, a first subset of the direction vector set corresponding to a non-near-singular direction and a second subset corresponding to a near-singular direction; decomposing an input vector representing a desired velocity in the task space on the first subset and the second subset respectively, obtaining a first direction component and a second direction component; performing scaling processing on the second direction component, and obtaining a velocity of each joint in the joint space based on the first direction component and the scaled second direction component.

2. The robot arm motion control method according to claim 1, characterized by, The singular value decomposition result of the original Jacobian matrix representing the mapping relationship between the joint space and the task space of the robot arm predicted by the deep learning model comprises: obtaining joint angle data representing a current joint configuration of the robot arm; inputting the joint angle data into the pre-trained deep learning model to obtain a singular value decomposition result of an original Jacobian matrix corresponding to the current joint configuration.

3. The robot arm motion control method according to claim 2, characterized by, The deep learning model comprises: an input layer for receiving the joint angle data; a shared feature extraction layer for performing feature extraction on the joint angle data to obtain a joint feature vector; a multi-branch output layer for predicting the singular value decomposition result of the original Jacobian matrix according to the joint feature vector.

4. The robot arm motion control method according to claim 3, characterized by, The predicted singular value decomposition result includes a singular direction probability corresponding to each direction vector in the direction vector set and a singular value sequence associated with the direction vector set; The multi-branch output layer comprises: a classification output layer for obtaining the singular direction probability corresponding to each direction vector in the direction vector set according to the joint feature vector; a regression output layer for obtaining the singular value sequence associated with the direction vector set according to the joint feature vector.

5. The robot arm motion control method according to claim 1, wherein, The method further comprises: obtaining joint angle data representing a plurality of joint configurations of the robot arm; calculating a real Jacobian matrix corresponding to each joint configuration, and performing singular value decomposition on each real Jacobian matrix to obtain a direction vector set and a real singular value sequence associated with each direction vector in the direction vector set; training the deep learning model based on a teacher-student model framework using the direction vector set and the real singular value sequence associated with each direction vector in the direction vector set.

6. The robot arm motion control method according to claim 5, wherein, The joint angle data includes original joint angle data and target joint angle data; The obtaining of the joint angle data representing a plurality of joint configurations of the robot arm comprises: sampling within the joint limits of the robot arm to obtain original joint angle data of a plurality of joint configurations; performing data augmentation on each original joint angle data to obtain the target joint angle data.

7. The robot arm motion control method according to claim 6, wherein, The data augmentation on each original joint angle data to obtain the target joint angle data comprises: Gaussian noise is added to each of the original joint angle data to obtain the target joint angle data.

8. The robot arm motion control method according to claim 6, wherein, The data augmentation is performed on each of the original joint angle data to obtain the target joint angle data, including: Inverse kinematics is solved for a continuous trajectory of the robot arm in the task space to obtain a sequence of adjacent joint angles; The target joint angle data is obtained by combining the sequence of adjacent joint angles and the original joint angle data.

9. The robot arm motion control method according to claim 5, wherein, The deep learning model is trained by using the set of direction vectors and the sequence of real singular values associated with each direction vector in the set of direction vectors, including: A loss function is constructed based on the set of direction vectors and the sequence of real singular values associated with each direction vector in the set of direction vectors; The deep learning model is iteratively trained by using the loss function.

10. The robot arm motion control method according to claim 9, wherein, The loss function is constructed based on the set of direction vectors and the sequence of real singular values associated with each direction vector in the set of direction vectors, including: A classification loss for singular direction prediction is constructed according to the real values and predicted values of each direction vector in the set of direction vectors; A regression loss for singular value prediction is constructed according to the sequence of real singular values and the sequence of predicted singular values associated with each direction vector; A reconstructed Jacobian matrix is obtained based on the sequence of predicted singular values associated with each direction vector, and a reconstruction loss for the Jacobian matrix is constructed according to the reconstructed Jacobian matrix and the real Jacobian matrix; The loss function is constructed according to the classification loss for singular direction prediction, the regression loss for singular value prediction, and the reconstruction loss for the Jacobian matrix.

11. The robot arm motion control method according to claim 10, wherein, The loss function is: wherein, L is a loss function, is a first weight, is a sequence of real singular values, is a sequence of predicted singular values, is a regression loss of singular value prediction, indicating the difference between and ; is a second weight, is a classification loss of singular direction prediction, is a probability that the predicted j th direction belongs to the proximity of singular direction, i.e., the predicted value of each direction vector, is an indicator function, i.e., the true value of each direction vector, which is 1 when the j th singular value is less than , otherwise 0, is a sensitivity threshold, is the maximum singular value in the sequence of real singular values, is a cross-entropy function, and m is the number of singular values; is a third weight, is a reconstruction loss of Jacobian matrix, is a real Jacobian matrix calculated from the i th joint configuration , is a reconstructed Jacobian matrix, and are the task space matrix and joint space matrix respectively decomposed from the i th real Jacobian matrix, is a singular value matrix composed of predicted singular values, indicates the Frobenius norm, which is used to measure the difference between the reconstructed Jacobian matrix and the real Jacobian matrix.

12. The robot arm motion control method of claim 1, wherein, The velocities of each joint in the joint space are obtained based on the first direction component and the scaled second direction component, including: The singular values corresponding to each direction vector in the second subset are lifted to obtain an adjusted singular value matrix; A safety Jacobian matrix is constructed based on the task space matrix, the joint space matrix obtained by decomposing the original Jacobian matrix, and the adjusted singular value matrix; The velocities of each joint are calculated based on the generalized inverse of the safety Jacobian matrix, the first direction component, and the scaled second direction component.

13. The robot arm motion control method according to claim 12, wherein, The singular values corresponding to each direction vector in the second subset are lifted to obtain an adjusted singular value matrix, including: The singular values corresponding to each direction vector in the second subset are lifted to a singular value threshold; wherein the singular value threshold is determined based on a sensitivity threshold; The adjusted singular value matrix is obtained according to the singular values corresponding to each direction vector in the first subset and the singular value threshold corresponding to each direction vector in the second subset.

14. The robot arm motion control method of claim 12, wherein, The velocities of each joint are calculated based on the generalized inverse of the safety Jacobian matrix, the first direction component, and the scaled second direction component, including: A corrected velocity in the task space is calculated according to the first direction component and the scaled second direction component; The velocities of each joint are calculated according to the generalized inverse of the safety Jacobian matrix and the corrected velocity.

15. The robot arm motion control method according to claim 14, wherein, The calculating a modified velocity in the task space according to the first direction component and the scaled second direction component comprises: wherein, is the modified velocity, is the first directional component, is the scaled second directional component.

16. The robot arm motion control method of claim 14, wherein, The calculating a velocity of each joint according to the generalized inverse of the safety Jacobian matrix and the modified velocity comprises: wherein is the velocity of each of the joints, is the safety Jacobian matrix, is the generalized inverse of the safety Jacobian matrix, is the modified velocity.

17. The robot arm motion control method of claim 1, wherein, The scaling processing performed on the second direction component comprises: A scaling factor is calculated according to a ratio between a singular value corresponding to each direction vector in the second subset and a singular value threshold, wherein the singular value threshold is determined based on a sensitivity threshold; The scaling processing performed on the second direction component according to the scaling factor to obtain a scaled second direction component.

18. The robot arm motion control method of claim 17, wherein, The scaling processing performed on the second direction component according to the scaling factor to obtain a scaled second direction component comprises: A scaling matrix is constructed according to scaling factors corresponding to each direction vector in the second subset; The scaled second direction component is obtained based on the scaling matrix and the second direction component.

19. The robot arm motion control method of claim 18, wherein, The scaled second direction component is obtained based on the scaling matrix and the second direction component comprises: The scaled second direction component is calculated using the scaling matrix, the second direction component and a gain matrix.

20. The robot arm motion control method of claim 19, wherein, The scaled second direction component is calculated using the scaling matrix, the second direction component and a gain matrix comprises: wherein is the scaled second direction component, is the unscaled second direction component, is a direction vector in the second subset, is the transpose of a direction vector in the second subset, is an input vector of desired velocities in the task space, is a scaling matrix, is a gain matrix for adjusting the control strength of each direction vector in the second subset.

21. The robot arm motion control method of claim 17, wherein, The method further comprises: When a singular value corresponding to each direction vector in the second subset is greater than or equal to a singular value threshold, the second direction component is retained.

22. The robot arm motion control method of claim 1, wherein, The determining a first subset corresponding to a non-approaching singular direction and a second subset corresponding to an approaching singular direction in the direction vector set based on the singular value sequence and a sensitivity threshold comprises: A discrimination condition is constructed based on the sensitivity threshold; The first subset corresponding to the non-approaching singular direction in the direction vector set is determined according to singular values in the singular value sequence that do not satisfy the discrimination condition; The second subset corresponding to the approaching singular direction in the direction vector set is determined according to singular values in the singular value sequence that satisfy the discrimination condition.

23. The robot arm motion control method of claim 22, wherein, The constructing the discrimination condition based on the sensitivity threshold comprises: A maximum singular value in the singular value sequence is determined; A singular value threshold is determined based on the maximum singular value and the sensitivity threshold, and the discrimination condition is constructed using the singular value threshold.

24. The robot arm motion control method of claim 23, wherein, The determining a singular value threshold based on the maximum singular value and the sensitivity threshold comprises: An adjustment factor is obtained, wherein the adjustment factor is calculated according to a singular direction probability obtained by inputting joint angle data representing a current joint configuration of the robot arm into a deep learning model; The singular value threshold is determined according to the adjustment factor, the maximum singular value and the sensitivity threshold, and the discrimination condition is constructed using the singular value threshold.

25. The robot arm motion control method of claim 24, wherein, The discrimination condition comprises: wherein is a threshold for singular values, and is a threshold for sensitivity, , is a maximum singular value in the sequence of singular values, is the kth singular value in the sequence of singular values. i is the kth singular value in the sequence of singular values.

26. The robot arm motion control method of claim 1, wherein, The input vector representing the desired velocity in the task space is decomposed on the first subset and the second subset respectively to obtain the first direction component and the second direction component comprises: constructing a projected Jacobian matrix based on the first subset, and decomposing the input vector based on the projected Jacobian matrix to obtain the first direction component; extracting a target direction vector corresponding to the task space from the second subset; decomposing the input vector on the target direction vector to obtain the second direction component.

27. The robot arm motion control method of claim 26, wherein, the first direction component is: wherein is a first direction component, is a projected Jacobian matrix, is a generalized inverse of the projected Jacobian matrix, is an input vector of desired velocities in the task space.

28. The robot arm motion control method of claim 26, wherein, the constructing the projected Jacobian matrix based on the first subset comprises: eliminating direction vectors in the second subset from a task space matrix obtained by decomposing the original Jacobian matrix, and retaining direction vectors in the first subset; eliminating singular values corresponding to direction vectors in the second subset from a singular value matrix obtained by decomposing the original Jacobian matrix, and retaining singular values corresponding to direction vectors in the first subset; constructing the projected Jacobian matrix based on a joint space matrix obtained by decomposing the original Jacobian matrix, the direction vectors in the first subset retained, and the singular values corresponding to the direction vectors in the first subset.

29. A robot arm motion control method, characterized by, applied to a joint driver of the robot, the method comprises: receiving velocities of joints in a joint space of a robot arm, and driving corresponding joint movements according to the velocities of the joints; wherein the velocities of the joints in the joint space of the robot arm are obtained according to the robot arm movement control method of any one of claims 1-28.

30. A robot arm motion control device, characterized by, applied to a main controller of the robot, the device comprises: a singular value decomposition module configured to perform singular value decomposition on a Jacobian matrix representing a mapping relationship between a joint space and a task space to obtain a set of direction vectors and a sequence of singular values associated with each direction vector in the set of direction vectors; a singular direction determination module configured to determine, based on the sequence of singular values and a sensitivity threshold, a first subset of the set of direction vectors corresponding to non-approaching singular directions and a second subset of the set of direction vectors corresponding to approaching singular directions; an expected velocity decomposition module configured to decompose an input vector representing an expected velocity in the task space on the first subset and the second subset respectively to obtain a first direction component and a second direction component; a joint velocity generation module configured to perform scaling processing on the second direction component, and obtain velocities of joints in the joint space based on the first direction component and the scaled second direction component.

31. A robot arm motion control device, characterized by, applied to a joint driver of the robot, the device comprises: a joint movement module configured to receive velocities of joints in a joint space of a robot arm, and drive corresponding joint movements according to the velocities of the joints; wherein the velocities of the joints in the joint space of the robot arm are obtained according to the robot arm movement control method of any one of claims 1-28.

32. An electronic device, comprising: comprise: a processor; and a memory having computer readable instructions stored thereon, the computer readable instructions being executed by the processor to implement the method of any one of claims 1-29.

33. A robot characterized by comprise: a processor; and a memory having computer readable instructions stored thereon, the computer readable instructions being executed by the processor to implement the method of any one of claims 1-29. a memory having computer readable instructions stored thereon that, when executed by the processor, implement the method of any of claims 1-29.

34. The robot of claim 33, wherein, The robot comprises any one of a humanoid robot and a dual-arm robot.

35. A computer readable storage medium, characterized in that, The computer readable storage medium has computer program code instructions stored thereon that, when invoked by a processor of the robot, cause the robot to perform the method of any of claims 1-29.

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