A singular value spectrum risk fusion method and system for detecting kinematic singularity of a robot arm

Abstract

The application discloses a singular value spectrum risk fusion method and system for mechanical arm kinematic singularity detection, relates to the technical field of mechanical hands, and solves the problems of inaccurate and untimely mechanical arm kinematic singularity detection in the prior art, has the beneficial effects of realizing accurate, comprehensive and blind area-free detection of the degree of the current configuration of the mechanical arm approaching the kinematic singularity state, and the scheme is as follows: a singular value spectrum risk fusion method for mechanical arm kinematic singularity detection, comprising the following contents: deriving the expression of the Jacobian matrix of the mechanical arm, and calculating the singular value spectrum of the Jacobian matrix; drawing the end-effector manipulability ellipsoid of the mechanical arm for visualizing the singular value spectrum related information; obtaining a normalized minimum singular value index reflecting the movement ability in the most dangerous direction; obtaining a normalized isotropic index reflecting the shape of the manipulability ellipsoid; obtaining a normalized overall movement ability index reflecting the volume of the manipulability ellipsoid; and constructing a singular value spectrum risk fusion index.

Description

Technical Field

[0001] This invention relates to the field of robotic arm technology, and in particular to a singular value spectrum risk fusion method and system for detecting kinematic singularities of robotic arms. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Kinematic singularities of robotic arms are inherent properties of their differential kinematics. To ensure the accuracy, stability, reliability, and safety of robotic arms in performing tasks, kinematic singularities need to be effectively avoided. To achieve this, it is first necessary to accurately and comprehensively detect the kinematic singularities of the robotic arm.

[0004] Currently, commonly used indicators for detecting kinematic singularities include operability, minimum singular value, condition number, and the reciprocal of the condition number. Among these, operability and the reciprocal of the condition number are the most widely used.

[0005] However, existing maneuverability indices and the reciprocal of the condition number still have certain limitations when used to detect kinematic singularities of robotic arms. For maneuverability indices, without dimensionless and scale normalization, maneuverability itself is affected by unit choice. This can cause the numerical range of the maneuverability index to change simply due to unit variations for the same robotic arm. Furthermore, maneuverability indices only reflect the overall volume of the maneuverable ellipsoid, and therefore may overlook severe degradation in a particular direction. For example, when some singular values ​​of the robotic arm configuration are large, while one singular value is small, the volume of the maneuverability ellipsoid may not immediately become small, but the robotic arm configuration in that direction is already close to singularity. For the reciprocal of the condition number index, it only reflects the ratio of the shortest axis to the longest axis of the maneuverability ellipsoid, i.e., the difference between the minimum and maximum singular values, and therefore may overlook situations where all singular values ​​decrease overall.

[0006] In summary, regarding the detection of kinematic singularities inherent in the differential kinematics of robotic arms, which can seriously affect the accuracy, stability, reliability, and safety of robotic arms when performing tasks, the operability index or the reciprocal of the condition number index widely used in the existing technology are difficult to simultaneously take into account the singularity risks such as the reduction of the overall motion capability and the degradation of directional motion capability of the robotic arm when used alone. This can easily lead to problems such as inaccurate and untimely detection of kinematic singularities and the existence of detection blind spots. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a singular value spectrum risk fusion method for detecting kinematic singularities of robotic arms, thereby improving the accuracy, completeness, and reliability of kinematic singularity detection for robotic arms.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solution: A singular value spectrum risk fusion method for kinematic singularity detection of robotic arms includes the following: Establish a forward kinematics model of the robotic arm and obtain the position-level forward kinematics equations of the robotic arm; Derive the expression for the Jacobian matrix of the robotic arm and calculate the singular value spectrum of the Jacobian matrix; Plot a maneuverability ellipsoid at the end of a robotic arm that visualizes singular value spectrum information; Obtain the normalized minimum singular value index that reflects the ability to move in the most dangerous direction; Obtain a normalized isotropic index that reflects the shape of the operability ellipsoid; Obtain a normalized overall motion capability index that reflects the operability ellipsoid volume; Construct a singularity spectrum risk fusion index for detecting kinematic singularities of robotic arms; Verify the performance of the singular value spectrum risk fusion index in detecting kinematic singularities of a robotic arm.

[0009] The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm, as described above, is used when a base coordinate system is selected. When used as a reference coordinate system, the Jacobian matrix of the robotic arm The expression is derived using the vector product method; Singular value decomposition of the Jacobian matrix of the robotic arm yields the singular value spectrum of the Jacobian matrix: in, Describes a left singular vector matrix. Describes a right singular vector matrix. Represents a singular value matrix. for singular values, for The zero vector of dimension, This is the singular value spectrum of the Jacobian matrix under the current configuration of the robotic arm.

[0010] The singular value spectrum risk fusion method for detecting singularity in the kinematics of a robotic arm, as described above, involves drawing a manipulability ellipsoid of the robotic arm end effector that visualizes singular value spectrum-related information. This includes drawing a positional manipulability ellipsoid and an attitude manipulability ellipsoid of the robotic arm end effector, and includes the following: The obtained Jacobian matrix is ​​decomposed as follows: in, for The matrix consisting of the first three rows represents the position Jacobian matrix; for The matrix consisting of the last three rows represents the attitude Jacobian matrix; Draw the positional operability ellipsoid of the robotic arm's end effector, including the following: First, obtain the position vector of the joint variable corresponding to the current configuration of the robotic arm, and substitute it into the obtained position-level positive kinematics equation to calculate the end pose matrix. The vector composed of the first three rows of the fourth column in this matrix is ​​the position vector of the center of the end position operability ellipsoid. The position vector of the joint variable corresponding to the current configuration of the robotic arm is substituted into the expression of the Jacobian matrix to calculate the Jacobian matrix under the current configuration of the robotic arm. The position Jacobian matrix under the current configuration of the robotic arm is extracted from it and singular value decomposition is performed. The directions of the three principal axes of the ellipsoid are determined according to the left singular vector matrix, and the semi-axis lengths of the three principal axes of the ellipsoid are determined according to the three singular values ​​in the singular value matrix. Finally, sampling points are generated on the unit sphere, and a linear transformation is performed on the sampling points to obtain the ellipsoidal surface point set. Combined with the obtained ellipsoidal center position vector, the position operability ellipsoid of the robotic arm end is drawn.

[0011] The singular value spectrum risk fusion method for kinematic singularity detection of a robotic arm, as described above, includes the following steps in drawing the attitude maneuverability ellipsoid of the robotic arm's end effector: Extract the attitude Jacobian matrix of the robot arm in the current configuration from the Jacobian matrix of the calculated robot arm in the current configuration; Singular value decomposition is performed on the Jacobian matrix of the robot arm's current configuration. The directions of the three principal axes of the ellipsoid are determined based on the left singular vector matrix, and the semi-axis lengths of the three principal axes of the ellipsoid are determined based on the three singular values ​​in the singular value matrix. Finally, sampling points are generated on the unit sphere, and a linear transformation is performed on the sampling points to obtain the ellipsoidal surface point set. Combined with the ellipsoidal center position vector calculated in step 3.2, the attitude operability ellipsoid of the robotic arm end is drawn.

[0012] The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm, as described above, includes the following steps for obtaining a normalized minimum singular value index reflecting the ability to move in the most dangerous direction: The risk threshold of the normalized minimum singularity index value is determined by offline calibration using workspace sampling. Safety threshold for normalized minimum singular value index ; The minimum singular value is normalized dimensionlessly using a threshold normalization method:

[0013] in, The normalized minimum singularity index reflects the ability to move in the most dangerous direction. The closer its value is to 0, the closer the robotic arm is to a singular state. This means truncating the result to the interval. Operators in It is a positive number. This represents the smallest singular value.

[0014] The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm, as described above, includes the following steps for obtaining a normalized isotropic index reflecting the shape of the operability ellipsoid: The danger threshold of the normalized isotropic index value was determined by offline calibration using workspace sampling. Safety threshold for normalized isotropic index values ; The isotropic index is processed using a threshold normalization method as follows: in, This is a normalized isotropic index; The reciprocal index of the condition number in the singular value spectrum , It is a positive number.

[0015] The singularity spectrum risk fusion method for detecting kinematic singularities of a robotic arm, as described above, includes the following steps for obtaining a normalized overall motion capability index reflecting the operability ellipsoid volume: The normalized overall motion capability index was determined using a workspace sampling offline calibration method. Danger threshold With normalized overall athletic performance index safety threshold ; The threshold normalization method was used to perform dimensionless normalization on it: in, To normalize the overall athletic performance index, Indicators representing overall athletic ability. It is a positive number.

[0016] The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm, as described above, includes the following: The construction of the singular value spectrum risk fusion index for detecting kinematic singularities of a robotic arm includes the following: Three singular risks are defined, namely, the risk of regression in the weakest direction of movement. Operability and risk of ellipsoidal shape distortion and the risk of overall decline in athletic ability. A fusion mechanism with weakest link penalty characteristics and risk weight adjustment capability is adopted to construct the singular value spectrum risk fusion index for detecting the kinematic singularity of a robotic arm by fusing the three risks, as shown below: in, This represents the singular value spectrum risk fusion index. , and All located in Within the range.

[0017] The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm, as described above, includes the following aspects in verifying the performance of the singular value spectrum risk fusion index in detecting kinematic singularities of the robotic arm: Large-scale sampling was performed in the workspace of the robotic arm to obtain... Each robotic arm configuration is assigned a real label value, depending on whether it is a near-singular or safe configuration. ; Calculate the reciprocal index value of the condition number for each set of robotic arm configurations. Operability index value And the fusion index value of singular value spectrum risk ,calculate , and ,in, A scalar threshold for determining whether a robotic arm configuration is singular. and These are the thresholds for judging whether the robot arm configuration is singular using the reciprocal of the condition number index and the threshold for judging whether the robot arm configuration is singular using the operability index, respectively. For each group of robotic arm configurations, determine them sequentially. , and If true, it indicates that the robot arm configuration detected by the indicators is a near-singular configuration, and the label value of this configuration is... If it is marked as 1, it indicates that the detected robot arm configuration is a safe configuration, and the label value of this configuration is marked. =0; After statistically analyzing the test results of the three indicators, the accuracy of detecting the singularity of the robotic arm is determined based on the values ​​of the three indicators. Accuracy Recall rate as well as Fraction, The fraction is and The harmonized averages are then compared.

[0018] Secondly, the present invention also provides a singular value spectrum risk fusion system for detecting kinematic singularities of a robotic arm, including a computing device, which performs the following: Establish a forward kinematics model of the robotic arm and obtain the position-level forward kinematics equations of the robotic arm; Derive the expression for the Jacobian matrix of the robotic arm and calculate the singular value spectrum of the Jacobian matrix; Plot a maneuverability ellipsoid at the end of a robotic arm that visualizes singular value spectrum information; Obtain the normalized minimum singular value index that reflects the ability to move in the most dangerous direction; Obtain a normalized isotropic index that reflects the shape of the operability ellipsoid; Obtain a normalized overall motion capability index that reflects the operability ellipsoid volume; Construct a singularity spectrum risk fusion index for detecting kinematic singularities of robotic arms; Verify the performance of the singular value spectrum risk fusion index in detecting kinematic singularities of a robotic arm.

[0019] The beneficial effects of the present invention are as follows: This invention is based on the singular value spectrum of the Jacobian matrix of a robotic arm. It extracts and normalizes spectral features that characterize the risk of degradation of motion capability in the weakest direction, the risk of ellipsoidal distortion of operability, and the risk of overall motion capability decay. Through a fusion mechanism with short-board penalty characteristics and risk weight adjustment capabilities, a dimensionless, normalized singular value spectrum risk fusion index is constructed. This index is a comprehensive detection index for the kinematic singularity of the robotic arm. When used to detect singularity, it is not affected by the size and unit selection of the robotic arm. Unlike traditional detection indices that only focus on specific singularity risks such as operability, the reciprocal of the condition number, or the minimum singular value, it can simultaneously take into account three different types of singularity risks: degradation of motion capability in the weakest direction, ellipsoidal distortion of operability, and overall motion capability decay. This enables accurate, comprehensive, and blind-zone-free detection of the degree to which the current configuration of the robotic arm approaches a kinematic singular state. Compared with existing methods that widely use inverse indices based on operability or condition numbers to detect kinematic singularities of robotic arms, the method provided by this invention not only overcomes the problem of detection blind spots under specific robotic arm configurations when using a single index, but also significantly improves the performance of singularity detection in terms of accuracy, precision, and recall, while reducing false alarm and false negative rates. Therefore, the method provided by this invention can provide more timely and reliable singularity warning information for robotic arm systems, and can also be further used for singularity avoidance trajectory planning and control, which is of vital importance to ensuring that robotic arms perform tasks accurately, stably, reliably, and safely. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0021] Figure 1 A schematic diagram of a seven-degree-of-freedom redundant robotic arm and its forward kinematics model according to one or more embodiments of the present invention; Figure 2 A schematic diagram of a set of singular configurations of a robotic arm and its end-effector maneuverability ellipsoid; Figure 3 for Figure 2 A schematic diagram of the singular configuration of a robotic arm and its end-effector maneuverability ellipsoid; Figure 4 A schematic diagram illustrating the blind zone when using the reciprocal of the condition number to detect kinematic singularities of a robotic arm; Figure 5 A schematic diagram illustrating the blind zone when using the operability index to detect kinematic singularities of a robotic arm; Figure 6 This diagram illustrates the performance comparison results when using three metrics to detect the kinematic singularities of a robotic arm. Detailed Implementation

[0022] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0023] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless otherwise expressly indicated by the invention, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof. As described in the background section, there are problems in the prior art. In order to solve the above-mentioned technical problems, this invention proposes a singular value spectrum risk fusion method for detecting kinematic singularities of robotic arms.

[0024] Example 1 In a typical embodiment of the present invention, reference is made to Figure 1 As shown, a singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm includes the following: Step 1: Establish the forward kinematics model of the robotic arm and obtain its position-level forward kinematics equations. The forward kinematics model of the robotic arm was established using the method described in Professor John J. Craig's textbook "Introduction to Robotics," and a coordinate system was set in the established model. As a base coordinate system, coordinate system As the coordinate system of the end effector, and at the same time, the coordinate system Defined as the first A fixed coordinate system for each joint, wherein This represents the number of joints. Based on the above coordinate system setting, the position-level forward kinematics equations of the robotic arm can be derived as follows: (1) in, The position vector representing the joint variables of the robotic arm. Indicates the first The position variables of each joint, with the superscript indicating vector transpose. Let be the pose matrix representing the end effector coordinate system relative to the base coordinate system. Representing the coordinate system Relative to coordinate system The pose matrix is ​​represented.

[0025] Step 2: Derive the expression for the Jacobian matrix of the robotic arm and calculate the singular value spectrum of the Jacobian matrix. Specifically, Step 21: Jacobian Matrix for the Robotic Arm A linear mapping relationship was established between the joint velocity and the Cartesian velocity of the end effector, which is a A 3D matrix This represents the dimension of the operation space. Each column in Indicates the first The transmission ratio of the movement speed of each joint to the movement speed of the end effector of the robotic arm. When a base coordinate system is selected... When used as a reference coordinate system The expression is derived using the vector product method: (2) (3) in, Representing the coordinate system of The axis represents the unit vector in the reference coordinate system. for The zero vector of dimension, Represents the coordinate system of the end effector The origin relative to the coordinate system The position vector is transformed into its representation in the reference coordinate system.

[0026] Step 22: The singular value spectrum is a Jacobian matrix The distribution of all singular values ​​arranged in order of magnitude reflects complete information about the robotic arm's motion capabilities in each principal motion direction under its current configuration. To calculate the singular value spectrum, [the following is a process / step]... Singular value decomposition yields: (4) (5) in, Describes a left singular vector matrix. Describes a right singular vector matrix. Represents a singular value matrix. for singular values, for The zero vector of dimension, This is the singular value spectrum of the Jacobian matrix under the current configuration of the robotic arm.

[0027] Step 3: Plot the maneuverability ellipsoid of the robotic arm end effector, which is related to the visualization of singular value spectrum information. Specifically, Step 31: The singular value spectrum determines the shape, volume, and principal axis length of the maneuverability ellipsoid at the end of the robotic arm. The singular values ​​in the ellipsoid are equal in length to the semi-axis lengths of the maneuverability ellipsoid at the end of the robotic arm, with the minimum singular value being... Equal to half the length of the shortest axis of the ellipsoid, the maximum singular value It is equal to half the length of the longest axis of the ellipsoid. and The ratio reflects the flatness of the ellipsoid, and the product of all singular values ​​is proportional to the volume of the ellipsoid. Therefore, by drawing the maneuverability ellipsoid of the robotic arm's end effector, relevant information of the singular value spectrum can be visualized. However, since this ellipsoid is a six-dimensional ellipsoid, it cannot be drawn directly. Therefore, in practice, a three-dimensional end-effector position maneuverability ellipsoid and a three-dimensional end-effector attitude maneuverability ellipsoid are commonly drawn. To achieve this, the Jacobian matrix derived in step two needs to be decomposed as follows: (6) in, for The matrix consisting of the first three rows represents the position Jacobian matrix; for The matrix consisting of the last three rows represents the attitude Jacobian matrix; Step 32: When drawing the end-effector maneuverability ellipsoid, first obtain the position vector of the joint variables corresponding to the current configuration of the robotic arm. Substitute this equation into the position-level forward kinematics equations obtained in step one to calculate the end-effector pose matrix. The vector formed by the first three rows of the fourth column in this matrix is ​​the position vector of the center of the ellipsoid of the operability of the end position; then... Substituting the Jacobian matrix expression derived in step two, one can calculate the Jacobian matrix under the current configuration of the robotic arm. And extract the position Jacobian matrix of the robotic arm in its current configuration. Further research Perform singular value decomposition According to the left singular vector matrix Determine the directions of the three principal axes of the ellipsoid, and based on the singular value matrix... Three singular values , , Determine the semi-axis lengths of the three principal axes of the ellipsoid; finally, generate sampling points on the unit sphere and utilize... By performing a linear transformation on the sampling points, a set of points on the ellipsoid surface is obtained. Combined with the obtained ellipsoid center position vector, the position operability ellipsoid of the robotic arm end can be drawn. Step 33: When drawing the maneuverability ellipsoid of the robotic arm's end effector, first start from the calculations in Step 32. Extract the pose Jacobian matrix of the robotic arm in its current configuration. Then to Perform singular value decomposition According to the left singular vector matrix Determine the three principal axes of the ellipsoid and, based on the singular value matrix... Three singular values , , Determine the semi-axis lengths of the three principal axes of the ellipsoid; finally, generate sampling points on the unit sphere and utilize... A linear transformation is performed on the sampling points to obtain the point set on the ellipsoid surface. Combined with the ellipsoid center position vector calculated in step 3.2, the attitude operability ellipsoid of the robotic arm end is drawn.

[0028] Step 4: Derive the normalized minimum singular value index that reflects the ability to move in the most dangerous direction. Specifically, Step 41: Singular Value Spectrum middle The minimum singular value is used to characterize the motion capability in the direction corresponding to the shortest semi-axis of the maneuverability ellipsoid of the robotic arm's end effector. When the value approaches zero, the robotic arm approaches a singular state. The value of is easily affected by the dimensions of the robotic arm structure, the scale of the Jacobian matrix, and the selection of the dimensions of the robotic arm's end effector position and attitude. To address this issue, a threshold normalization method is used to perform dimensionless normalization on the minimum singular value: (7) (8) in, The normalized minimum singularity index reflects the ability to move in the most dangerous direction. The closer its value is to 0, the closer the robotic arm is to a singular state. This indicates that the result will be truncated to an interval. Operators in, when hour, This indicates that the indicator is in a dangerous or near-singular state. hour, This indicates that the indicator is in a safe state; Denotes the minimum singular value in the singular value spectrum. ; and These represent the danger threshold and the safety threshold of the normalized minimum singularity index, respectively. It is a very small positive number, such as 0.00002; Step 42: When calculating the normalized minimum singular value index (MMSI) for any configuration of the robotic arm, the risk threshold of the MMSI needs to be used. Safety threshold for normalized minimum singular value index To reasonably determine the values ​​of these two parameters, an offline calibration method using workspace sampling was adopted. First, random sampling was performed within the joint space of the robotic arm. Position vector of joint variables Each set of position vectors corresponds to a set of robotic arm configurations; then, the Jacobian matrix of each set of robotic arm configurations is calculated using the expression for the Jacobian matrix derived in step 21, and the minimum singular value of each set of configurations is obtained using the singular value decomposition method in step 22. Finally, for indivual The risk threshold for the normalized minimum singularity index was determined using the percentile method in statistics, based on the sample composition. Safety threshold for normalized minimum singular value index Value: (9) (10) in, Indicates the 5th percentile. Indicates the 80th percentile; Step 5: Derive the normalized isotropic index reflecting the shape of the operability ellipsoid Specifically, Step 51: Analyze the singular value spectrum. middle and The ratio, which is the reciprocal of the condition number and also known as the isotropic index, is used to characterize the shape balance of the manipulability ellipsoid at the end of a robotic arm. A smaller ratio indicates a more elongated and flattened manipulability ellipsoid, corresponding to more significant differences in the robotic arm's motion capabilities in different directions. When the ratio equals 0, it indicates that the robotic arm is in a singular state. Although the isotropic index is a normalized and dimensionless ratio, it only reflects the proportional relationship between the maximum and minimum singular values, resulting in a blind spot when used to detect kinematic singularities in robotic arms. To facilitate its integration with different risk indicators determined by the singular value spectrum to improve performance, the isotropic index is processed using a threshold normalization method as follows: (11) in, The normalized isotropic index represents the degree of distortion of the operability ellipsoid shape. The closer its value is to 0, the closer the configuration of the corresponding robotic arm is to a singular state. The reciprocal index of the condition number, also known as the isotropic index, is used in singular value spectra. ; and These are the danger threshold and safety threshold for the normalized isotropic index, respectively. Step 52: When calculating the normalized isotropic index value corresponding to any configuration of the robotic arm, the danger threshold of the normalized isotropic index value needs to be used. Safety threshold for normalized isotropic index values Reasonable values ​​for both can be determined using a workspace sampling offline calibration method. This is calculated in step four, two. After obtaining the Jacobian matrix of the robot arm configurations, the minimum singular value of each configuration is obtained using the singular value decomposition method in step 22. and maximum singular value Then calculate the isotropic index value corresponding to each configuration. Finally, for indivual The risk threshold of the normalized isotropic index was determined using the percentile method in statistics for the sample. Safety threshold for normalized isotropic index Value: (12) (13) Step Six: Derive the normalized overall motion capability index reflecting the operability ellipsoid volume. Specifically, Step Six 1: Singular Value Spectrum The product of all singular values ​​is the operability index. This index, proportional to the volume of the operability ellipsoid, characterizes the overall motion capability of the robotic arm in all directions of the task space. Since directly using the product of singular values ​​can result in values ​​that are too large or too small, the geometric mean of all singular value products is used to characterize the robotic arm's motion capability, and this is defined as the overall motion capability index. The larger the index value, the stronger the overall motion capability of the robotic arm; the closer it is to 0, the closer it is to a singular state. Furthermore, this index is related to all singular values, and its numerical range varies significantly with the number of degrees of freedom of the robotic arm and the scale of the Jacobian matrix. Therefore, a threshold normalization method is used to perform dimensionless normalization on it: (14) in, The value is a normalized overall motion capability index. The lower the value, the weaker the robotic arm's motion capability in all directions of the task space. A value of 0 indicates that the robotic arm is in a singular state. Indicates an overall athletic ability index; and These represent the normalized overall athletic performance index. Danger thresholds and safety thresholds; Step 62: When calculating the normalized overall motion capability index value corresponding to any configuration of the robotic arm, it is necessary to use the values ​​representing the normalized overall motion capability index. Danger threshold With normalized overall athletic performance index safety threshold The appropriate values ​​for both can also be determined using the workspace sampling offline calibration method. This is calculated in step four-two. After obtaining the Jacobian matrix of the robot arm configuration, the singular value spectrum of each configuration is obtained using the singular value decomposition method in step 22. Then, calculate the overall motion capability risk index value corresponding to each configuration. Finally, for indivual The sample was used to determine the normalized overall athletic ability index using the percentile method in statistics. Danger threshold With normalized overall athletic performance index safety threshold Value: (15) (16) Step 7: Construct a singular value spectrum risk fusion index for detecting kinematic singularities of robotic arms Specifically, Step 71: In steps four, five, and six, the three singularity feature indices with different dimensions and numerical ranges in the singular value spectrum are thresholded and normalized to map them all to the same dimensionless interval. Based on this, to avoid the problems of inaccurate, untimely, and blind-zone detection of kinematic singularities that can easily occur when using a single index, three singularity risks are first defined: the risk of degradation of kinematic ability in the weakest direction. Operability and risk of ellipsoidal shape distortion and the risk of overall decline in athletic ability. Next, a fusion mechanism with both bottleneck penalty characteristics (a mechanism in multi-objective optimization such as NSGA-III that actively lowers the non-dominated ranking level of an individual when it performs extremely poorly in some objective dimensions) and risk weight adjustment capabilities is adopted to construct the singular value spectrum risk fusion index for detecting the kinematic singularity of the robotic arm, as shown below, after fusing the three risks: (17) (18) (19) (20) in, This represents the singular value spectrum risk fusion index. The closer its value is to 1, the closer the current configuration of the robotic arm is to a kinematic singular state. The closer its value is to 0, the safer the robotic arm configuration is. , and All located in Within the range, the larger the value, the higher the risk of the corresponding type of kinematic singularity; , and , , , These represent the weighting coefficients of the three types of risks mentioned above, and they are related. ; This indicates the penalty index for shortcomings, which meets the following criteria. ; Step 72: In the singular value spectrum risk fusion index By setting The value of can be adjusted to control the sensitivity of this indicator to local high-risk factors, giving it a weakest link penalty characteristic. That is, if any of the risks of deterioration in the weakest direction of motion capability, distortion of the operability ellipsoid shape, or overall motion capability decay significantly increases, the penalty will be applied. The values ​​can all increase promptly. In practical use of the indicators... When detecting kinematic singularities of a robotic arm, as well as , and The value can be determined through offline calibration and performance optimization, or the default parameter value can be used directly. , , and This default parameter set can ensure sensitivity to the risk of motion degradation in the weakest direction, while also taking into account the risks of ellipsoidal shape distortion in operability and overall motion capability attenuation. The penalty effect of addressing weaknesses improves the ability to respond to local high-risk factors.

[0029] Step 8: Verify the performance of the singular value spectrum risk fusion index in detecting the kinematic singularities of the robotic arm. Specifically, Step 81: In use When detecting the kinematic singularities of a robotic arm, theoretically when When this occurs, it indicates that the robotic arm configuration is in a kinematically singular state. However, in practical applications, for ease of use, a scalar threshold is set to determine whether the robotic arm configuration is singular. When the singular value spectrum risk fusion index value of any configuration of the robotic arm to be detected is greater than the threshold, it indicates that the configuration is a singular configuration of the robotic arm. First, in step four-two, the following is calculated... After obtaining the Jacobian matrix of the robot arm configurations, the singular value spectrum risk fusion index value corresponding to each configuration is calculated by combining steps four, five, six, and seven. Finally, for indivual The sample was composed of [variables], and the percentile method in statistics was used to determine [the percentiles]. Value: (twenty one) in, Indicates the 95th percentile; Step 82: The singular value spectrum risk fusion index can theoretically overcome the detection blind spots of a single index, thereby improving the completeness and accuracy of kinematic singularity risk detection for robotic arms. To practically verify the effectiveness and advancement of the singular value spectrum risk fusion index, a comparative experiment was designed to compare its performance in detecting kinematic singularities of robotic arms with the operability index and the reciprocal of the condition number index. To facilitate the experiment, the robotic arm singularity detection problem was set as a binary classification problem, that is, the label value of near-singular configurations of the robotic arm was defined as 1, and the label value of safe configurations was defined as 0. During the experiment, large-scale sampling was first carried out in the workspace of the robotic arm to obtain... Each robotic arm configuration is assigned a real label value, depending on whether it is a near-singular or safe configuration. Then, combining steps four, five, six, seven, and eight, calculate the reciprocal index value of the condition number for each set of robotic arm configurations. Operability index value And the fusion index value of singular value spectrum risk Next, the scalar threshold is calculated in step 81. , and ,in and These are the thresholds for determining whether a robotic arm configuration is singular, calculated using the reciprocal of the condition number and the operability index, respectively. The methods and steps for obtaining these two thresholds are detailed in section 81. The method is the same, but you need to use the 5th percentile. This will not be elaborated upon here; furthermore, the configuration of each robotic arm is determined sequentially. , and If true, it indicates that the robot arm configuration detected by the indicators is a near-singular configuration, and the label value of this configuration is... If it is marked as 1, it indicates that the detected robot arm configuration is a safe configuration, and the label value of this configuration is marked. The result is 0; finally, after statistically analyzing the results of the three indicators, the accuracy of detecting the singularity of the robotic arm using the following formulas is used respectively. Accuracy Recall rate as well as The scores are then compared. If the comparison results show that the singular value spectrum risk fusion index exhibits higher detection performance in all four aspects mentioned above, then the effectiveness and advancement of the proposed singular value spectrum risk fusion index can be verified.

[0030] (twenty two) (twenty three) (twenty four) (25) Among them, accuracy Indicates in The proportion of robotic arm configurations whose tested parameters are correctly identified as "near-singular" or "safe"; accuracy. Recall rate represents the proportion of samples that were judged as near-singular configurations by the detected metric, but are actually near-singular samples; This represents the proportion of all real near-singular samples that were successfully detected by the target indicator. The fraction is and The harmonic mean is used to comprehensively consider the false alarms and false negatives of the detection indicators; the higher the value of the above four indicators, the better the performance of the singularity detection indicators. Furthermore, in formulas (22) to (25), , , and It is based on statistics The calculation formula and meaning of the result obtained by comparing the actual label value and the detected label value of a robotic arm configuration are as follows: (26) (27) (28) (29) in, express The number of true near-singularities in a robotic arm configuration that are correctly detected as near-singularities by the indicators; The number of samples that represent the true safe configuration but are misclassified as near-singular by the index; This represents the number of samples that are true safe configurations and are correctly detected as safe configurations by the index. This represents the number of samples that are true near-singular configurations but were missed by the index as safe configurations; This indicates an indicator function, which is 1 if the condition is true and 0 otherwise.

[0031] Specifically, with Figure 1 Taking the seven-DOF redundant robotic arm shown as an example, the specific implementation steps are as follows: Step 1: Combining Figure 1 The seven-DOF redundant robotic arm shown is modeled using the John J. Craig method, as follows: Figure 1 As shown, the coordinate system in this model The base coordinate system, coordinate system Let the coordinate system be the coordinate system of the end effector. For the first The fixed coordinate system of each joint is established. Based on the above coordinate system setting, the position-level forward kinematics equations of the robotic arm are derived as follows:

[0032] in, The position vector representing the joint variables of the robotic arm. Indicates the first The position variables of each joint This is the pose matrix representing the end effector coordinate system relative to the base coordinate system; Combination Figure 1 As shown in Table 1, the DH parameters corresponding to the forward kinematics model of the robotic arm are obtained by combining the parameter values ​​in Table 1 with the position vectors of the joint variables corresponding to the current configuration of the robotic arm. Substituting these values ​​into the derived position-level forward kinematics equations, the pose matrix can be calculated. The specific value.

[0033] Table 1. Robotic Arm DH Parameters

[0034] Step Two: Combining Figure 1 The DH parameters in Table 1 can be derived using formulas (2) and (3). Figure 1 The robotic arm relative to the base coordinate system Jacobian matrix The expression represents the position vector of the joint variables corresponding to the current configuration. Substituting into the above expression, the matrix can be calculated. The specific value is then calculated using formula (4) for the matrix. By performing singular value decomposition, the left singular vector matrix can be calculated. Right singular vector matrix and singular value matrix Finally from the matrix Extract all the singular values ​​and arrange them in descending order to form a set of numerical distributions. This is the Jacobian matrix of the robotic arm. The singular value spectrum reflects complete information about the motion capabilities of the robotic arm in each main motion direction under the current configuration.

[0035] Step 3: Combine the end-effector pose matrix calculated in Step 1 and the Jacobian matrix calculated in step two This allows for the separate plotting of the maneuverability ellipsoids for the robotic arm's end-effector position and attitude, providing visualization of singular value spectrum information. Specifically, when plotting the end-effector position maneuverability ellipsoid, the process begins with... Extract the vector composed of the first three rows of the fourth column; this vector represents the position vector of the end position and the center of the attitude maneuverability ellipsoid. Then, from the matrix... Extracting the first three rows yields the position Jacobian matrix. Then use formula (4) to... Perform singular value decomposition Based on the calculated left singular vector matrix Determine the directions of the three principal axes of the ellipsoid, and based on the singular value matrix... Three singular values , , Determine the semi-axis lengths of the three principal axes of the ellipsoid; finally, generate sampling points on the unit sphere and utilize... By performing a linear transformation on the sampling points, a set of points on the ellipsoid surface is obtained. Combined with the obtained ellipsoid center position vector, the position operability ellipsoid of the robotic arm end can be drawn. Furthermore, when plotting the end-point attitude operability ellipsoid, first start from the matrix Extracting the last three rows yields the attitude Jacobian matrix. Then use formula (4) to... Perform singular value decomposition According to the left singular vector matrix Determine the three principal axes of the ellipsoid and, based on the singular value matrix... Three singular values , , Determine the semi-axis lengths of the three principal axes of the ellipsoid; finally, generate sampling points on the unit sphere and utilize... By performing a linear transformation on the sampling points, the point set on the ellipsoid surface is obtained. Combined with the calculated ellipsoid center position vector, the attitude operability ellipsoid of the robotic arm end can be drawn.

[0036] Step 4: Combining Figure 1 The DH parameters in Table 1 can be used to derive the normalized minimum singularity index of the robotic arm. First, random sampling is performed within the joint space of the robotic arm. Position vector of joint variables Each set of position vectors corresponds to a set of robotic arm configurations; then, the Jacobian matrix of each set of robotic arm configurations is calculated using formulas (2) and (3). And use formula (4) to apply it to the matrix Perform singular value decomposition to obtain the minimum singular value for each configuration. Then on indivual The risk threshold of the normalized minimum singularity index was determined using the percentile method shown in formulas (9) and (10) for the sample. Safety threshold for normalized minimum singular value index Finally, substituting the two thresholds into formulas (7) and (8), we can obtain the normalized minimum singular value index of the robotic arm as follows:

[0037] in, The normalized minimum singularity index reflects the ability to move in the most dangerous direction. The closer its value is to 0, the closer the robotic arm is to a singular state. express Figure 1 The minimum singular value of the robotic arm shown is in the singular value spectrum. ; It is a very small positive number, which in this embodiment is 1. .

[0038] Step 5: Combining Figure 1 The DH parameters in Table 1 can be used to derive the normalized isotropic index of the robotic arm. First, the normalized isotropic index is calculated in step four. Jacobian matrix of the robot arm configuration Then, use formula (4) to process the matrix. Perform singular value decomposition to obtain the minimum singular value for each configuration. and maximum singular value Then, calculate the isotropic index value corresponding to each configuration. Next, regarding indivual The risk threshold of the isotropic index value was determined using the percentile method shown in formulas (12) and (13) for the sample. and the safety threshold of isotropic index values Finally, substituting the two thresholds into formula (11), we can obtain the normalized isotropic index of the robotic arm as follows:

[0039] in, The normalized isotropic index reflects the degree of distortion of the operability ellipsoid shape. The closer its value is to 0, the closer the configuration of the corresponding robotic arm is to a singular state. express Figure 1 The reciprocal index of the condition number of the robotic arm shown, also known as the isotropic index, is found in the singular value spectrum. .

[0040] Step Six: Combining Figure 1 The DH parameters in Table 1 can be used to derive the normalized overall motion capability index of the robotic arm. First, the following is calculated in step four: Jacobian matrix of the robot arm configuration Then, use formula (4) to process the matrix. Perform singular value decomposition to obtain the singular value spectrum of each configuration. Then, calculate the overall motion capability risk index value corresponding to each configuration. Next, regarding indivual The risk threshold of the normalized overall athletic ability index was determined using the percentile method shown in formulas (15) and (16) for the sample. Safety threshold for normalized overall athletic performance index Finally, substituting the two thresholds into formula (14) yields the normalized overall motion capability index of the robotic arm:

[0041] in, The value is a normalized overall motion capability index, which is proportional to the volume of the operability ellipsoid. The lower the value, the weaker the robot arm's motion capability in all directions of the task space. A value of 0 indicates that the robot arm is in a singular state. express Figure 1 Overall motion capability indicators of the robotic arm.

[0042] Step Seven: Combining Steps Four, Five, and Six, a singular value spectrum risk fusion index for the robotic arm can be constructed. To avoid the problems of inaccurate kinematic singularity detection and blind spots caused by using a single index, the three indices derived in Steps Four, Five, and Six are fused to construct a singular value spectrum risk fusion index for detecting the kinematic singularities of the robotic arm:

[0043] in, This represents the singular value spectrum risk fusion index. The closer its value is to 1, the closer the current configuration of the robotic arm is to a kinematic singular state. The closer its value is to 0, the safer the robotic arm configuration is. , and These represent the risk of degradation of motion capability in the weakest direction, the risk of distortion of the operability ellipsoid shape, and the risk of overall motion capability decay, respectively. , and These represent the weighting coefficients for the three types of risks mentioned above; This indicates the penalty index for weaknesses.

[0044] Step 8: Combining Figures 1-6 As shown, the singular value spectrum risk fusion index constructed in step seven can be verified. Performance. In use When detecting the kinematic singularities of a robotic arm, a scalar threshold can be set for ease of use. When the singular value spectrum risk fusion index value of any configuration of the robot arm to be detected is greater than the threshold, it indicates that the configuration is a near-singular configuration of the robot arm. The value can be determined using the workspace sampling offline calibration method, first calculated in step four two. The Jacobian matrix of the robot arm configuration is obtained, and then the singular value spectrum risk fusion index value corresponding to each configuration is calculated using formula (20). Finally, for indivual The threshold was determined using the percentile method shown in formula (21) for the sample. ; Combination Figure 2 and Figure 3 As shown, after determining the threshold... After the value is determined, one application of the singular value spectrum risk index is to identify... Figure 1 The near-singular configuration of the robotic arm is used to provide early warning information during task execution, such as... Figure 2 and Figure 3 The image shows the usage. Detected Figure 1 A near-singular configuration of a robotic arm. As described in step three, the maneuverability ellipsoid at the end of the robotic arm can visually reflect relevant information about the singular value spectrum corresponding to the current configuration. Therefore, by observing the position and orientation maneuverability ellipsoids of the robotic arm's end, as long as at least one of them has a singular feature, it can be verified that the current robotic arm configuration is a true near-singular configuration. Figure 3 The following is a description of the use of... The detected near-singular configuration's end-effector maneuverability ellipsoid exhibits a significant difference between its longest and shortest axes, indicating highly uneven motion capabilities in different directions for the robotic arm's end effector. Furthermore, the ellipsoid's small volume suggests weak overall robotic arm motion capabilities. In summary, these two singular characteristics indicate... Figure 3 The median shape is a true near-singular shape, thus proving the effectiveness of the singular spectrum risk fusion index in detecting kinematic singularities; Combination Figures 4-5 As shown, the reciprocal of the condition number and the operability index, which are widely used in the prior art, both have blind spots when detecting kinematic singularities of robotic arms. For example, as Figure 4 The image shows two sets of robotic arm configurations and their corresponding end-effector maneuverability ellipsoids obtained using the reciprocal of the condition number index. Configuration 1 has a condition number reciprocal close to 1, but its maneuverability is minimal. In this case, the reciprocal of the condition number index cannot accurately detect that the robotic arm configuration is approaching a singular state. Figure 5 The figure shows two sets of robotic arm configurations and their corresponding end-position maneuverability ellipsoids obtained using the maneuverability index. Configuration 2 has the highest maneuverability, but the reciprocal of the condition number is close to 0. At this point, the maneuverability index cannot accurately detect that the configuration is close to a singular state. The singular value spectrum risk fusion index can theoretically overcome the detection blind spots that exist when the above two indices are used alone. To practically verify the advancement of the singular value spectrum risk fusion index, an experiment comparing the detection performance of the three indices was designed. In the experiment, firstly, random selection... Each robotic arm configuration is assigned a real label value, depending on whether it is a near-singular or safe configuration. Then, combining steps four through eight, the values ​​of three detection indicators corresponding to each group of robotic arm configurations were calculated, namely... , as well as Next, refer to step 81 to calculate the scalar threshold. The method calculates two thresholds. and Furthermore, the configuration of each robotic arm is determined sequentially. , and If true, it indicates that the robot arm configuration detected by the indicators is a near-singular configuration, and the label value of this configuration is... If it is marked as 1, it indicates that the detected robot arm configuration is a safe configuration, and the label value of this configuration is marked. The result is 0; finally, after statistically analyzing the detection results of the three indicators, the accuracy of detecting the singularity of the robotic arm using formulas (22)-(25) is calculated respectively. Accuracy Recall rate as well as Score the results and compare them. For example... Figure 6 The comparison results show that the singular value spectrum risk fusion index exhibits superior performance in all four performance evaluation aspects, thus fully verifying the effectiveness and advancement of the singular value spectrum risk fusion index proposed in this invention. In summary, the method provided in this embodiment effectively solves the problem of blind spots in existing technologies for detecting kinematic singularities, while significantly improving the accuracy, completeness, and reliability of kinematic singularity detection. This provides key technical support for the precise, stable, reliable, and safe execution of tasks by robotic arms.

[0045] In other words, by comparing the performance of the singular value spectrum risk fusion index with the widely used operability and condition number reciprocal index in detecting kinematic singularities through quantitative analysis, it is demonstrated that the proposed method can solve the detection blind zone problem of existing technologies, thereby improving the accuracy, completeness and reliability of kinematic singularity detection of robotic arms.

[0046] Example 2 A singular value spectrum risk fusion system for kinematic singularity detection of a robotic arm includes a computing device that performs the following: Establish a forward kinematics model of the robotic arm and obtain the position-level forward kinematics equations of the robotic arm; Derive the expression for the Jacobian matrix of the robotic arm and calculate the singular value spectrum of the Jacobian matrix; Plot a maneuverability ellipsoid at the end of a robotic arm that visualizes singular value spectrum information; Obtain the normalized minimum singular value index that reflects the ability to move in the most dangerous direction; Obtain a normalized isotropic index that reflects the shape of the operability ellipsoid; Obtain a normalized overall motion capability index that reflects the operability ellipsoid volume; Construct a singularity spectrum risk fusion index for detecting kinematic singularities of robotic arms; Verify the performance of the singular value spectrum risk fusion index in detecting kinematic singularities of a robotic arm.

[0047] For details, please refer to Example 1.

[0048] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm, characterized in that, Includes the following: Establish a forward kinematics model of the robotic arm and obtain the position-level forward kinematics equations of the robotic arm; Derive the expression for the Jacobian matrix of the robotic arm and calculate the singular value spectrum of the Jacobian matrix; Plot a maneuverability ellipsoid at the end of a robotic arm that visualizes singular value spectrum information; Obtain the normalized minimum singular value index that reflects the ability to move in the most dangerous direction; Obtain a normalized isotropic index that reflects the shape of the operability ellipsoid; Obtain a normalized overall motion capability index that reflects the operability ellipsoid volume; Construct a singularity spectrum risk fusion index for detecting kinematic singularities of robotic arms; Verify the performance of the singular value spectrum risk fusion index in detecting kinematic singularities of a robotic arm; The process of obtaining the normalized minimum singular value index, which reflects the ability to move in the most dangerous direction, includes the following: The risk threshold of the normalized minimum singularity index value is determined by offline calibration using workspace sampling. Safety threshold for normalized minimum singular value index ; The minimum singular value is normalized dimensionlessly using a threshold normalization method: in, The normalized minimum singular value index; This indicates that the result will be truncated to an interval. Operators in It is a positive number. Represents the minimum singular value; The process of obtaining the normalized isotropic index reflecting the shape of the operability ellipsoid includes the following: The danger threshold of the normalized isotropic index value was determined by offline calibration using workspace sampling. Safety threshold for normalized isotropic index values ; The isotropic index is processed using a threshold normalization method as follows: in, This is a normalized isotropic index; The reciprocal index of the condition number in the singular value spectrum , It is a positive number; The process of obtaining the normalized overall motion capability index, which reflects the operability ellipsoid volume, includes the following: The normalized overall motion capability index was determined using a workspace sampling offline calibration method. Danger threshold With normalized overall athletic performance index safety threshold ; The threshold normalization method was used to perform dimensionless normalization on it: in, To normalize the overall athletic performance index, Indicators representing overall athletic ability. It is a positive number; The construction of the singular value spectrum risk fusion index for detecting kinematic singularities of robotic arms includes the following: Three singular risks are defined, namely, the risk of regression in the weakest direction of movement. Operability and risk of ellipsoidal shape distortion and the risk of overall decline in athletic ability. A fusion mechanism with weakest link penalty characteristics and risk weight adjustment capability is adopted to construct the singular value spectrum risk fusion index for detecting the kinematic singularity of a robotic arm by fusing the three risks, as shown below: in, This represents the singular value spectrum risk fusion index. , and All located in Within the range.

2. The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm according to claim 1, characterized in that, When a base coordinate system is selected When used as a reference coordinate system, the Jacobian matrix of the robotic arm The expression is derived using the vector product method; Singular value decomposition of the Jacobian matrix of the robotic arm yields the singular value spectrum of the Jacobian matrix: in, Describes a left singular vector matrix. Describes a right singular vector matrix. Represents a singular value matrix. for singular values, for The zero vector of dimension, This is the singular value spectrum of the Jacobian matrix under the current configuration of the robotic arm.

3. The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm according to claim 1, characterized in that, The process of plotting the maneuverability ellipsoid of the robotic arm end effector, which is related to the visualization of singular value spectrum information, includes plotting the position maneuverability ellipsoid and the attitude maneuverability ellipsoid of the robotic arm end effector, and includes the following: The obtained Jacobian matrix is ​​decomposed as follows: in, for The matrix consisting of the first three rows represents the position Jacobian matrix; for The matrix consisting of the last three rows represents the attitude Jacobian matrix; Draw the positional operability ellipsoid of the robotic arm's end effector, including the following: First, obtain the position vector of the joint variable corresponding to the current configuration of the robotic arm, and substitute it into the obtained position-level positive kinematics equation to calculate the end pose matrix. The vector composed of the first three rows of the fourth column in this matrix is ​​the position vector of the center of the end position operability ellipsoid. The position vector of the joint variable corresponding to the current configuration of the robotic arm is substituted into the expression of the Jacobian matrix to calculate the Jacobian matrix under the current configuration of the robotic arm. The position Jacobian matrix under the current configuration of the robotic arm is extracted from it and singular value decomposition is performed. The directions of the three principal axes of the ellipsoid are determined according to the left singular vector matrix, and the semi-axis lengths of the three principal axes of the ellipsoid are determined according to the three singular values ​​in the singular value matrix. Finally, sampling points are generated on the unit sphere, and a linear transformation is performed on the sampling points to obtain the ellipsoidal surface point set. Combined with the obtained ellipsoidal center position vector, the position operability ellipsoid of the robotic arm end is drawn.

4. The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm according to claim 3, characterized in that, The process of drawing the attitude maneuverability ellipsoid of the robotic arm's end effector includes the following: Extract the attitude Jacobian matrix of the robot arm in the current configuration from the Jacobian matrix of the calculated robot arm in the current configuration; Singular value decomposition is performed on the Jacobian matrix of the robot arm's current configuration. The directions of the three principal axes of the ellipsoid are determined based on the left singular vector matrix, and the semi-axis lengths of the three principal axes of the ellipsoid are determined based on the three singular values ​​in the singular value matrix. Finally, sampling points are generated on the unit sphere, and a linear transformation is performed on the sampling points to obtain the ellipsoidal surface point set. Combined with the ellipsoidal center position vector calculated in step 3.2, the attitude operability ellipsoid of the robotic arm end is drawn.

5. The singular value spectrum risk fusion method for detecting kinematic singularities of a robotic arm according to claim 1, characterized in that, The verification of the singular value spectrum risk fusion index's performance in detecting the kinematic singularities of the robotic arm includes the following: Large-scale sampling was performed in the workspace of the robotic arm to obtain... Each robotic arm configuration is assigned a real label value, depending on whether it is a near-singular or safe configuration. ; Calculate the reciprocal index value of the condition number for each set of robotic arm configurations. Operability index value And the fusion index value of singular value spectrum risk ,calculate , and ,in, A scalar threshold for determining whether a robotic arm configuration is singular. and These are the thresholds for judging whether the robot arm configuration is singular using the reciprocal of the condition number index and the threshold for judging whether the robot arm configuration is singular using the operability index, respectively. For each group of robotic arm configurations, determine them sequentially. , and If true, it indicates that the robot arm configuration detected by the indicators is a near-singular configuration, and the label value of this configuration is... If it is marked as 1, it indicates that the detected robot arm configuration is a safe configuration, and the label value of this configuration is marked. =0; After statistically analyzing the test results of the three indicators, the accuracy of detecting the singularity of the robotic arm is determined based on the values ​​of the three indicators. Accuracy Recall rate as well as Fraction, The fraction is and The harmonized averages are then compared.

6. A singular value spectrum risk fusion system for detecting kinematic singularities of a robotic arm, characterized in that, Includes a computing device that executes the singular value spectrum risk fusion method for kinematic singularity detection of a robotic arm as described in claim 1, comprising the following: Establish a forward kinematics model of the robotic arm and obtain the position-level forward kinematics equations of the robotic arm; Derive the expression for the Jacobian matrix of the robotic arm and calculate the singular value spectrum of the Jacobian matrix; Plot a maneuverability ellipsoid at the end of a robotic arm that visualizes singular value spectrum information; Obtain the normalized minimum singular value index that reflects the ability to move in the most dangerous direction; Obtain a normalized isotropic index that reflects the shape of the operability ellipsoid; Obtain a normalized overall motion capability index that reflects the operability ellipsoid volume; Construct a singularity spectrum risk fusion index for detecting kinematic singularities of robotic arms; Verify the performance of the singular value spectrum risk fusion index in detecting kinematic singularities of a robotic arm.

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