Robot end load dynamic identification method under safe excitation trajectory

Abstract

The invention relates to the technical field of robot control, solves the technical problem that in the prior art, load parameter identification cannot be carried out on a large component in an existing industrial environment, and particularly relates to a robot tail end load dynamic identification method under a safe excitation track. Comprising the following steps: establishing a comprehensive expression between a load parameter vector and a non-contact force; establishing a dynamic excitation track of each joint of the robot in the feasible working space; and each joint of the robot transforms the posture of the end effector according to the dynamic excitation trajectory, and various parameters of the end load parameter vector of the robot are obtained through a total least square method based on the comprehensive expression. According to the method, the inertia tensor is considered in detail, so that the identification result error of the large-scale component is reduced, the error after external force compensation is further reduced, the external contact force is sensed more accurately, and the application possibility of the large-scale component in a contact type scene taking man-machine cooperation as an example is increased.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a method for dynamically identifying a robot end load under a safe excitation trajectory. Background Art

[0002] Contact force-based methods can improve the efficiency of industrial robots assembling large components in industrial manufacturing. By installing a six-dimensional force sensor at the end of the robot, the gravitational force of the load under the sensor and the actual contact force with the outside world can be effectively sensed. However, the large size and weight of large components make it challenging to accurately estimate the contact force between the load and the operator when handling these large components. Compared to small components, as the weight and size of the workpiece increase, on the one hand, sensor noise and errors will be amplified, and load-related parameters must be fully considered to reduce errors. On the other hand, the identification trajectory of large components during the recognition process must meet safety requirements.

[0003] For example, the Chinese invention patent with the prior art publication number CN114872046A discloses a method for rapid identification of the robot end load based on an excitation trajectory. A six-dimensional force sensor is installed at the end of the robot and a comprehensive expression of gravity and inertial force is designed. By designing the excitation trajectory of the robot end, the posture of the robot end is changed to collect data under different postures of the robot, and the various parameters of the robot end load are obtained by combining the least squares method. However, the above method does not consider the influence of the inertia tensor when establishing the end load, and the consideration of the load parameters is not comprehensive enough. At the same time, the excitation trajectory designed does not take into account the safety issues that may exist for large workpieces during parameter identification. Moreover, the least squares method assumes that there is no error in one direction when performing parameter identification, and only considers the parameter regression in one direction, which makes it have a large error when performing load parameter identification.

[0004] To address these issues, numerous literature has proposed gravity identification algorithms, but their application is still limited to small components. Most methods fail to fully consider the load parameters of large components and pay little attention to safety during the identification process. Consequently, they are unable to meet the requirements for load parameter identification of large components in current industrial environments. Safely identifying the parameters of end-loads remains a crucial research issue. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a method for dynamic identification of robot end load under a safe excitation trajectory, which solves the technical problem that the existing technology cannot meet the requirements of load parameter identification for large components in existing industrial environments.

[0006] To solve the above technical problems, the present invention provides the following technical solution: a method for dynamic identification of robot end load under a safe excitation trajectory, the method comprising the following steps:

[0007] S1. Establish a comprehensive expression between the load parameter vector including the mass, center of mass position and inertia tensor of the load and the non-contact force based on the spatial coordinate system including the robot, sensor and end load;

[0008] S2. Based on the optimization objective function, the start and end constraints, and the safe and feasible space constraints, establish the dynamic excitation trajectory of each joint of the robot in the feasible workspace;

[0009] S3. Each joint of the robot changes the posture of the end effector according to the dynamic excitation trajectory, collects multiple sets of real-time data from sensors in different postures of the robot in real time, and obtains the various parameters of the robot end load parameter vector through the total least squares method based on the comprehensive expression.

[0010] Furthermore, the sensor includes a six-dimensional force sensor and an acceleration sensor installed on the end effector of the robot.

[0011] Furthermore, in step S1, the specific process includes the following steps:

[0012] S11. Establish a spatial coordinate system with the robot base coordinate system as B, the sensor coordinate system as S, and the end load coordinate system as C. The direction of the spatial coordinate system is consistent with the direction of the six-dimensional force sensor coordinate system;

[0013] S12. Assume that the original measurement value of the six-dimensional force sensor is F raw , the non-contact force is F nc =[f nc ,τ nc ] T , the zero point offset value is F0, then the expression of non-contact force is:

[0014] F nc =F raw -F0

[0015] S13. Use the Newton-Euler method to establish the relationship equation between non-contact force, velocity and acceleration, namely:

[0016]

[0017] in,

[0018]

[0019] Where, S Indicates the sensor coordinate system S; m represents the load mass; Sa and S α represents linear acceleration and angular acceleration respectively; S ω represents angular velocity; S g=[ S g x , S g y , S g z ] represents the gravity vector; S c=[ S c x , S c y , S c z ] represents the center of mass position; S I represents the inertia tensor matrix; I xx , I xy , I xz , I yx , I yy , I yz , I zx , I zy , I zz is the inertia tensor on the three linear coordinate axes of the sensor in the inertia tensor matrix; S g x , S g y , S g z Represent the components of the gravity vector on the three linear coordinate axes of the sensor; S c x , S c y , S c z Respectively represent the position of the center of mass on the three linear coordinate axes of the sensor;

[0020] S14. Rewrite the above relationship equation and set the load parameter vector to S Φ=[m,m S c x ,m S c y ,m S c z , S I xx , S I xy , S I xz , S I yy , S I yz , S I zz ] T, thus establishing a comprehensive expression of non-contact force and load weight, center of mass position and inertia tensor:

[0021] S F nc = S A( S a, S α, S ω, S g) S Φ

[0022] Where, S A is the measurement data matrix.

[0023] Furthermore, in step S2, the specific process includes the following steps:

[0024] S21. Setting a feasible workspace for the robot in the actual workspace based on the feasibility and safety of the robot end in the actual space;

[0025] S22. Establish a set of equations related to the robot joint parameters and use them as the excitation equations, that is, consider the non-contact inertial force f without the influence of gravity. iner and moment of inertia τ iner The system of equations is:

[0026]

[0027] The above formula can be reconstructed as:

[0028] S F iner = S C( S a, S α, S ω) S Ω

[0029] in, S C( S a, S α, S ω) is a function of the robot's 4-6 joints (q4, q5, q6); S F iner 、 S Ω is the intermediate variable after reconstruction of the above equations;

[0030] S23, to minimize the robot 4-6 joint minf (q4, q5, q6) contains M S The correlation matrix Υ of C is used as the optimal objective function, that is:

[0031]

[0032] Where,S C Ξ Represents M S The set of C, subscript · Ξ represents a set of 1, 2, ..., M matrices, represents its transpose;

[0033] S24. Based on the optimal objective function, the condition number is introduced as the optimization objective function of the dynamic excitation trajectory, that is:

[0034] minf( S C)=Cond(Y)

[0035] Where Cond(·) represents the optimization objective function;

[0036] S25. Express the excitation trajectory of each joint of the robot with a finite Fourier series, then the angle q of the robot's i-th joint is i (t), angular velocity angular acceleration Respectively expressed as:

[0037]

[0038] Among them, a i,l and b i,l Represent the weights of the sine and cosine functions respectively; ω f =2πf f represents the fundamental angular frequency, f f is the fundamental frequency selected for the Fourier series; N is the number of sine and cosine terms in the Fourier series; l represents the weight; t represents time; q i,0 Indicates the initial position of each joint angle of the robot;

[0039] S26, based on the angle q of the robot's i-th joint i (t), angular velocity angular acceleration Establish start and end condition constraints;

[0040] S27. Establish safe and feasible space constraints for each joint at the beginning and end.

[0041] Furthermore, in step S26, the expressions of the start and end condition constraints are:

[0042]

[0043] Among them, pose represents the end posture of the robot; f k (q1,q2,q3,q4,q5,q6) represents the transformation matrix obtained by forward kinematics; feasible workspace represents the feasible workspace; q i,max 、 Represent the position, velocity, and acceleration of each joint angle respectively.

[0044] Furthermore, in step S27, the expression of the safety feasible space restriction constraint is:

[0045]

[0046] Among them, t0 is the end time; q i (t0), Represent the joint angle position, velocity, and acceleration at the end time respectively.

[0047] Furthermore, in step S3, the specific process includes the following steps:

[0048] Through the collected k items of real-time data, the comprehensive expression based on the non-contact force and load parameter vector is:

[0049] S F nc,Ξ = S A Ξ S Φ

[0050] S F nc,Ξ = S F nc,1 , S F nc,2 ,…, S F nc,k

[0051] S A Ξ = S A1, S A2,…, S A k

[0052] in, S F nc,Ξ 、 S A Ξ Represents a collection of multiple non-contact force and load parameter vectors respectively;

[0053] Load parameter vector S The total least squares solution of Φ is obtained by the following formula:

[0054]

[0055] Among them, ||.|| F represents the Frobenius norm;

[0056] The load parameter vector is obtained by the following formula:

[0057]

[0058] Among them, v 1:n represents the smallest right singular vector; v q Represents the last column of the eigenvector matrix V;

[0059] The load mass, center of mass position and inertia tensor are obtained by solving the load parameter vector.

[0060] By means of the above technical solution, the present invention provides a method for dynamic identification of robot end load under a safe excitation trajectory, which has at least the following beneficial effects:

[0061] 1. This invention establishes a comprehensive expression for identifying robot end-loads, taking into account the relationship between load parameter vectors (including mass, center of mass position, and inertia tensor) and non-contact forces. This detailed consideration of the inertia tensor helps reduce errors in identification results for large components, further minimizing errors after external force compensation and enabling more accurate perception of external contact forces. This increases the potential for large components to be used in contact-based scenarios, such as human-robot collaboration.

[0062] 2. This invention addresses the possibility of varying load sizes at the robot's end-user end, designing a safe feasible space as a constraint to ensure the safety of the identification process. By establishing an optimization objective function, start and end condition constraints, and the safe feasible space constraint, a safe excitation trajectory for load identification is designed, ensuring the speed, effectiveness, and safety of the entire identification process.

[0063] 3. To address the shortcomings of the least squares method in parameter identification, this paper proposes the use of the total least squares method for parameter identification. By using orthogonal regression, the total least squares method simultaneously accounts for noise errors in both the measurement data matrix and the measurement output matrix, thereby achieving more accurate parameter identification results. With smaller parameter identification result errors, external force compensation and perception can be performed more accurately, thus meeting the requirements of contact tasks for various sizes and weights. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0065] Figure 1 Schematic diagram of the sensor coordinate system and the load center of mass position in an embodiment of the present invention;

[0066] Figure 2 A schematic diagram of a safe and feasible space in a terminal posture coordinate system according to an embodiment of the present invention;

[0067] Figure 3 The figure shows the change of the joint angles of the six axes of the robot over time in the embodiment of the present invention. DETAILED DESCRIPTION

[0068] To make the above-mentioned objectives, features, and advantages of the present invention more clearly understood, the present invention is further described below in detail with reference to the accompanying drawings and specific embodiments. This will enable a full understanding of how this application uses technical means to solve technical problems and achieve technical effects, and to implement the invention accordingly.

[0069] When faced with the problem of how to safely identify the parameters of the end load, this embodiment considers the load parameters of large components and the safety of the identification process to meet the requirements of the existing industrial environment for the identification of load parameters of large components. A dynamic identification method for the end load of a robot under a safe excitation trajectory is proposed. By carefully considering the inertia tensor, it helps to reduce the error in the identification results of large components, further reducing the error after external force compensation to more accurately perceive the external contact force, thereby increasing the application possibility of large components in contact scenarios such as human-machine collaboration. The method includes the following steps:

[0070] S1. Based on the spatial coordinate system including the robot, sensor and end load, establish a comprehensive expression between the load parameter vector including the mass, center of mass position and inertia tensor of the load and the non-contact force. The sensor includes a six-dimensional force sensor and an acceleration sensor installed on the end effector of the robot. In this embodiment, a spatial coordinate system including the robot, the six-dimensional force sensor, the acceleration sensor and the end load is established by installing a six-dimensional force sensor and an acceleration sensor on the end effector of the robot. Based on the established coordinate system relationship, the influence formula of the six-dimensional force sensor measurement force and load-related parameters is derived, thereby obtaining a comprehensive expression of the load mass, center of mass position and inertia tensor for the end load identification of the robot. The specific process includes the following steps:

[0071] S11. Establish a spatial coordinate system with the robot base coordinate system as B, the sensor coordinate system as S, and the end load coordinate system as C. The direction of the spatial coordinate system is consistent with the direction of the six-dimensional force sensor coordinate system, such as Figure 1 shown.

[0072] S12. Assume that the original measurement value of the six-dimensional force sensor is F raw , the non-contact force is F nc =[f nc ,τ nc ] T , the zero point offset value is F0, then the relationship between the three is expressed as:

[0073] F raw =Fnc +F0

[0074] Where T represents transpose; f nc , τ nc Represent the non-contact forces on the three linear degrees of freedom and the three rotational degrees of freedom, respectively.

[0075] The zero point offset value can be obtained by reading the initial data of the six-axis force sensor. The expression of the non-contact force is:

[0076] F nc =F raw -F0

[0077] S13. Use the Newton-Euler method to establish the relationship equation between non-contact force, velocity and acceleration, namely:

[0078]

[0079] in,

[0080]

[0081] Where, S Indicates the sensor coordinate system S; m represents the load mass; S a and S α represents linear acceleration and angular acceleration respectively; S ω represents angular velocity; S g=[ S g x , S g y , S g z ] represents the gravity vector; S c=[ S c x , S c y , S c z ] represents the center of mass position; S I represents the inertia tensor matrix; I xx , I xy , I xz , I yx , I yy , I yz , I zx , I zy , I zz is the inertia tensor on the three linear coordinate axes of the sensor in the inertia tensor matrix; S g x , S g y , S gz Represent the components of the gravity vector on the three linear coordinate axes of the sensor; S c x , S c y , S c z Respectively represent the position of the center of mass on the three linear coordinate axes of the sensor; all variables are expressed in the sensor coordinate system after coordinate system conversion.

[0082] S14. Rewrite the above relationship equation and set the load parameter vector to S Φ=[m,m S c x ,m S c y ,m S c z , S I xx , S I xy , S I xz , S I yy , S I yz , S I zz ] T , thus establishing a comprehensive expression of non-contact force and load weight, center of mass position and inertia tensor:

[0083] S F nc = S A( S a, S α, S ω, S g) S Φ

[0084] The superscript S When omitted, the measurement data matrix S A is:

[0085]

[0086] In the formula, the left side S A represents the measurement data matrix, and the right side is the vector to be identified.

[0087] This example establishes a comprehensive expression for identifying the robot's end-load, taking into account the load parameter vector (including mass, center of mass position, and inertia tensor) and non-contact forces. This detailed consideration of the inertia tensor helps reduce errors in the identification results of large components, further minimizing errors after external force compensation and enabling more accurate perception of external contact forces. This increases the potential for large components to be used in contact-based scenarios, such as human-robot collaboration.

[0088] S2. Based on the optimization objective function, the start and end constraints and the safe feasible space constraints, the dynamic excitation trajectory of each joint of the robot in the feasible workspace is established. Furthermore, this embodiment can identify the load-related parameters by changing the posture of the robot end effector. In order to make the selected excitation trajectory represent the identification space and meet the safety requirements in the actual scene, it is necessary to design a joint trajectory in the feasible workspace. The six joints of the robot change the robot end posture according to the set joint trajectory to obtain the load parameter vector. The number of sine and cosine terms in the Fourier series is taken as N=5, and the fundamental frequency f f The selected sampling frequency is 0.1Hz, 250Hz, and a total of 2500 samples are used to calculate the load parameter vector. The specific process includes the following steps:

[0089] S21. According to the feasibility and safety of the robot end in the actual space, set the feasible working space of the robot in the actual working space, such as Figure 2 shown.

[0090] S22. Establish a set of equations related to the robot joint parameters and use them as the excitation equations, that is, consider the non-contact inertial force f without the influence of gravity. iner and moment of inertia τ iner The system of equations is:

[0091]

[0092] The above formula can be reconstructed as:

[0093] S F iner = S C( S a, S α, S ω) S Ω

[0094] in, S C( S a, S α, S ω) is a function of the robot's 4-6 joints (q4, q5, q6); S F iner 、S Ω is the intermediate variable after the reconstruction of the above equations.

[0095] S23, to minimize the robot 4-6 joint minf (q4, q5, q6) contains M S The correlation matrix Υ of C is used as the optimal objective function, that is:

[0096]

[0097] Where, S C Ξ Represents M S The set of C, subscript · Ξ represents a set of 1, 2, ..., M matrices, represents its transpose;

[0098] S24. Based on the optimal objective function, the condition number is introduced as the optimization objective function of the dynamic excitation trajectory, that is:

[0099] minf( S C)=Cond(Y)

[0100] Where Cond(·) represents the optimization objective function;

[0101] S25. Express the excitation trajectory of each joint of the robot with a finite Fourier series, then the angle q of the robot's i-th joint is i (t), angular velocity angular acceleration Respectively expressed as:

[0102]

[0103] Among them, a i,l and b i,l Represent the weights of the sine and cosine functions respectively; ω f =2πf f represents the fundamental angular frequency, f f is the fundamental frequency selected for the Fourier series; N is the number of sine and cosine terms in the Fourier series; l represents the weight; t represents time; q i,0 Indicates the initial position of each joint angle of the robot;

[0104] S26, in order to meet the angle limit of the robot joint, this embodiment is based on the angle q of the robot's i-th joint i (t), angular velocity angular acceleration Establish the start and end condition constraints, the expression is:

[0105]

[0106] Among them, pose represents the end posture of the robot; f k (q1,q2,q3,q4,q5,q6) represents the transformation matrix obtained by forward kinematics; feasible workspace represents the feasible workspace; q i,max 、 Represent the position, velocity, and acceleration of each joint angle respectively;

[0107] S27. Establish the safe and feasible space constraints for each joint at the beginning and end, namely:

[0108]

[0109] Among them, t0 is the end time; q i (t0), Represent the joint angle position, velocity, and acceleration at the end time respectively.

[0110] This embodiment minimizes the optimization objective function minf( S Under the above constraints, the dynamic excitation trajectory can make the robot's posture as diverse as possible to fill the entire recognition space, such as Figure 3 shown.

[0111] Therefore, to address the varying sizes of payloads at the robot's end, a safe feasible space was designed as a constraint to ensure the safety of the identification process. By establishing an optimization objective function, start and end condition constraints, and safe feasible space constraints, a safe excitation trajectory for payload identification was designed, ensuring the speed, effectiveness, and safety of the entire identification process.

[0112] S3. Each joint of the robot changes the posture of the end effector according to the dynamic excitation trajectory, collects multiple sets of real-time data from sensors in different robot postures in real time, and obtains the various parameters of the robot end load parameter vector through the total least squares method based on the comprehensive expression. Specifically, when each joint of the robot changes according to the obtained dynamic excitation trajectory, 2500 sets of real-time data from six-dimensional force sensors and acceleration sensors in different robot postures are collected in real time, and the various parameters of the robot end load parameter vector are obtained through the total least squares method based on the comprehensive expression of non-contact force and load parameter vector. The specific process includes the following steps:

[0113] Through the collected k items of real-time data, the comprehensive expression based on the non-contact force and load parameter vector is:

[0114] S F nc,Ξ = S A ΞS Φ

[0115] S F nc,Ξ = S F nc,1 , S F nc,2 ,…, S F nc,k

[0116] S A Ξ = S A1, S A2,…, S A k

[0117] in, S F nc,Ξ 、 S A Ξ Represents a collection of multiple non-contact force and load parameter vectors respectively;

[0118] To simplify the subscript Ξ will be omitted, the load parameter vector S The total least squares solution of Φ can be obtained by the following formula:

[0119]

[0120] Among them, ||.|| F represents the Frobenius norm, considering all measurements The singular value decomposition of the augmented matrix Z is:

[0121] Z=USV T ,V∈R q×q ,S=(S 1,1 ,…,S q,q )

[0122] Where V represents the eigenvector matrix;

[0123] The load parameter vector is obtained by the following formula:

[0124]

[0125] Among them, v 1:n represents the smallest right singular vector; v q Represents the last column of the eigenvector matrix V.

[0126] The load mass, center of mass position and inertia tensor can be obtained by solving the load parameter vector.

[0127] This embodiment addresses the shortcomings of the least squares method in parameter identification and proposes the use of the total least squares method for parameter identification. By using orthogonal regression, the total least squares method simultaneously accounts for noise errors in both the measurement data matrix and the measurement output matrix, resulting in more accurate parameter identification results. With smaller parameter identification result errors, external force compensation and perception can be performed more accurately, meeting the requirements of contact tasks for various sizes and weights.

[0128] Those skilled in the art will appreciate that all or part of the steps in the above-mentioned embodiment methods can be accomplished by instructing the relevant hardware through a program. Therefore, the present application may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0129] The above embodiments provide a detailed introduction to the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core ideas. At the same time, for those skilled in the art, according to the ideas of the present invention, there may be changes in the specific implementation methods and application scopes. In summary, the contents of this specification should not be understood as limiting the present invention.

Claims

1. A method for dynamic identification of robot end load under safe excitation trajectory, characterized by: The method comprises the following steps: S1. Establish a comprehensive expression between the load parameter vector including the mass, center of mass position and inertia tensor of the load and the non-contact force based on the spatial coordinate system including the robot, sensor and end load; S2. Based on the optimization objective function, the start and end constraints, and the safe and feasible space constraints, establish the dynamic excitation trajectory of each joint of the robot in the feasible workspace; S3. Each joint of the robot changes the posture of the end effector according to the dynamic excitation trajectory, collects multiple sets of real-time data from sensors in different postures of the robot in real time, and obtains the various parameters of the robot end load parameter vector through the total least squares method based on the comprehensive expression.

2. The method for dynamic identification of robot end load according to claim 1, characterized in that: The sensors include a six-dimensional force sensor and an acceleration sensor installed on the end effector of the robot.

3. The method for dynamic identification of robot end load according to claim 2, characterized in that: In step S1, the specific process includes the following steps: S11. Establish a spatial coordinate system with the robot base coordinate system as B, the sensor coordinate system as S, and the end load coordinate system as C. The direction of the spatial coordinate system is consistent with the direction of the six-dimensional force sensor coordinate system; S12. Assume that the original measurement value of the six-dimensional force sensor is F raw , the non-contact force is F nc =[f nc ,τ nc ] T , the zero point offset value is F0, then the expression of non-contact force is: F nc =F raw -F0 S13. Use the Newton-Euler method to establish the relationship equation between non-contact force, velocity and acceleration, namely: in, Where, S Indicates the sensor coordinate system S; m represents the load mass; S a and S α represents linear acceleration and angular acceleration respectively; S ω represents angular velocity; S g=[ S g x , S g y , S g z ] represents the gravity vector; S c=[ S c x , S c y , S c z ] represents the center of mass position; S I represents the inertia tensor matrix; I xx , I xy , I xz , I yx , I yy , I yz , I zx , I zy , I zz is the inertia tensor on the three linear coordinate axes of the sensor in the inertia tensor matrix; S g x , S g y , S g z Represent the components of the gravity vector on the three linear coordinate axes of the sensor; S c x , S c y , S c z Respectively represent the position of the center of mass on the three linear coordinate axes of the sensor; S14. Rewrite the above relationship equation and set the load parameter vector to S Φ=[m,m S c x ,m S c y ,m S c z , S I xx , S I xy , S I xz , S I yy , S I yz , S I zz ] T , thus establishing a comprehensive expression of non-contact force and load weight, center of mass position and inertia tensor: S F nc = S A( S a, S a, S oh, S g) S F Where, S A is the measurement data matrix.

4. The method for dynamic identification of robot end load according to claim 3, characterized in that: In step S2, the specific process includes the following steps: S21. Setting a feasible workspace for the robot in the actual workspace based on the feasibility and safety of the robot end in the actual space; S22. Establish a set of equations related to the robot joint parameters and use them as the excitation equations, that is, consider the non-contact inertial force f without the influence of gravity. iner and moment of inertia τ iner The system of equations is: The above formula can be reconstructed as: S F iner = S C( S a, S a, S oh) S Oh in, S C( S a, S α, S ω) is a function of the robot's 4-6 joints (q4, q5, q6); S F iner 、 S Ω is the intermediate variable after reconstruction of the above equations; S23, to minimize the robot 4-6 joint minf (q4, q5, q6) contains M S The correlation matrix Υ of C is used as the optimal objective function, that is: Where, S C Ξ Represents M S The set of C, subscript · Ξ represents a set of 1, 2, ..., M matrices, represents its transpose; S24. Based on the optimal objective function, the condition number is introduced as the optimization objective function of the dynamic excitation trajectory, that is: minf( S C)=Cond(Υ) Where Cond(·) represents the optimization objective function; S25. Express the excitation trajectory of each joint of the robot with a finite Fourier series, then the angle q of the robot's i-th joint is i (t), angular velocity angular acceleration Respectively expressed as: Among them, a i,l and b i,l Represent the weights of the sine and cosine functions respectively; ω f =2πf f represents the fundamental angular frequency, f f is the fundamental frequency selected for the Fourier series; N is the number of sine and cosine terms in the Fourier series; l represents the weight; t represents time; q i,0 Indicates the initial position of each joint angle of the robot; S26, based on the angle q of the robot's i-th joint i (t), angular velocity angular acceleration Establish start and end condition constraints; S27. Establish safe and feasible space constraints for each joint at the beginning and end.

5. The method for dynamic identification of robot end load according to claim 4, characterized in that: In step S26, the expressions of the start and end condition constraints are: Among them, pose represents the end posture of the robot; f k (q1,q2,q3,q4,q5,q6) represents the transformation matrix obtained by forward kinematics; feasible workspace represents the feasible workspace; q i,max 、 Represent the position, velocity, and acceleration of each joint angle respectively.

6. The method for dynamic identification of robot end load according to claim 5, characterized in that: In step S27, the expression of the safe feasible space restriction constraint is: Among them, t0 is the end time; q i (t0), Represent the joint angle position, velocity, and acceleration at the end time respectively.

7. The method for dynamic identification of the robot end load according to claim 6, characterized in that: In step S3, the specific process includes the following steps: Through the collected k items of real-time data, the comprehensive expression based on the non-contact force and load parameter vector is: S F nc,Ξ = S A Ξ S F S F nc,Ξ = S F nc,1 , S F nc,2 ,…, S F nc,k <h2 style=";text-align:left;direction:ltr"> S <h2 style=";text-align:left;direction:ltr"> A<h2 style=";text-align:left;direction:ltr"> Ξ <h2 style=";text-align:left;direction:ltr"> =<h2 style=";text-align:left;direction:ltr"> S <h2 style=";text-align:left;direction:ltr"> A1,<h2 style=";text-align:left;direction:ltr"> S <h2 style=";text-align:left;direction:ltr"> A2,…,<h2 style=";text-align:left;direction:ltr"> S <h2 style=";text-align:left;direction:ltr"> A<h2 style=";text-align:left;direction:ltr"> k in, S F nc,Ξ 、 S A Ξ Represents a collection of multiple non-contact force and load parameter vectors respectively; Load parameter vector S The total least squares solution of Φ is obtained by the following formula: Among them, ||.|| F represents the Frobenius norm; The load parameter vector is obtained by the following formula: Among them, v 1:n represents the smallest right singular vector; v q Represents the last column of the eigenvector matrix V; the load mass, center of mass position, and inertia tensor are obtained by solving the load parameter vector.

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