Mechanical arm kinematics identification method and equipment based on enhanced adaptive parameters
By introducing predefined boundaries of filtering processing and PPF function in robotic arm kinematic identification, the adaptive parameter estimation rate is designed, which solves the problem of insufficient accuracy when handling noise and interferes with data, and achieves more efficient parameter estimation and Kinematic identification effect.
Patent Information
- Application Number
- CN202411212425.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-30
- Publication Date
- 2025-01-03
AI Technical Summary
In a complex and changeable working environment, the six-degree of freedom robotic arm system is affected by factors such as friction, load changes and external interference. Traditional parameter estimation methods such as least squares method are difficult to achieve ideals when processing actual data containing a large amount of noise and interference. The estimation accuracy of the kinematic model has limited the error compensation effect, limiting the improvement of the robotic arm's motion accuracy.
Using the kinematic identification method of robotic arm based on enhanced adaptive parameters, a kinematic model is established through the standard DH parameter method, linearly split into the product formula of constant unknown parameters and regression matrix, filtering processing and auxiliary matrix are introduced to construct intermediate variables, and design The predefined boundary of the PPF function combines intermediate variables and transform errors to design the adaptive parameter estimation rate, and enhance the adaptive parameter estimator to achieve kinematic identification of the robotic arm.
By constructing an auxiliary matrix to obtain error information for parameter estimation, the identification algorithm is simplified, the parameter estimation convergence rate is improved, the system model parameter uncertainty is overcome, and the accuracy and efficiency of robotic arm kinematic identification is significantly improved.
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Figure CN119238492A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of mechanical arm dynamics, and in particular to a mechanical arm kinematics identification method and device based on enhanced adaptive parameters. Background Art
[0002] As an important part of industrial automation and robotics technology, the kinematic accuracy of the six-degree-of-freedom robot directly affects the quality and efficiency of the work task. Kinematic identification, as a key technology to improve the positioning accuracy of the robot, has always received widespread attention. Traditionally, the kinematic modeling of the six-degree-of-freedom robot mainly relies on the Denavit-Hartenberg (DH) method, which establishes the kinematic model of the robot by assigning four independent parameters (link length, torsion angle, link offset, and joint rotation angle) to each link. However, when the adjacent joint axes of the robot are parallel or nearly parallel, the DH method will have the problem of parameter mutation, resulting in singularity in the model, which affects the kinematic accuracy of the robot.
[0003] To solve the above problems, the Modified-Denavit-Hartenberg (MDH) modeling method was proposed. By adding a parameter rotating around the Y axis to improve the DH method, the parameter mutation problem was effectively solved, and the advantages of the DH method, such as simple modeling and wide application range, were inherited. Based on the MDH modeling method and combined with the differential transformation theory, a positioning error identification model for the end of the manipulator can be established. The geometric parameter errors in the model can be solved by optimization algorithms such as the least squares method, and the absolute positioning accuracy of the manipulator can be improved by correcting these parameters.
[0004] However, although the MDH method and the kinematic parameter identification technology based on this method have achieved remarkable results in improving the positioning accuracy of the robot arm, they still face some challenges in practical applications. Especially in complex and changeable working environments, the robot arm system is often affected by various uncertain factors such as friction, load changes, and external interference. In addition, traditional parameter estimation methods such as the least squares method often find it difficult to achieve ideal estimation accuracy when processing actual data containing a lot of noise and interference, resulting in limited error compensation effects of the kinematic model, which in turn limits the further improvement of the robot arm's motion accuracy. Summary of the invention
[0005] The purpose of the present invention is to solve the problem of estimation accuracy of kinematic identification in the prior art when processing actual data containing complex interference. The present invention provides a method and device for kinematic identification of a manipulator based on enhanced adaptive parameters. The method for kinematic identification of a manipulator based on enhanced adaptive parameters mainly includes the following steps: S1. Establish the kinematic model of the robot arm based on the standard DH parameter method; S2, linearize the kinematic model of the robot arm and split it into the product of constant unknown parameters and regression matrix; S3, filter the product formula and introduce an auxiliary matrix to construct an intermediate variable containing the estimation error. S4, converting the estimation error into a transformation error, by introducing an inverse matrix, and designing a predefined boundary based on the PPF function; S5, designing the adaptive parameter estimation rate by combining the intermediate variables with the transformation error and the convergence performance of the estimation error within the predefined bounds; S6. Enhance the adaptive parameter estimator with preset convergence performance to achieve kinematic identification of the robot arm within predefined boundaries.
[0006] Furthermore, the mathematical expression of the kinematic model of the robot arm is as follows:
[0007] in, Indicates the position and posture information of the end of the robot. is the degrees of freedom of the task space; is the positive kinematic function; q represents the joint vector of the robot arm, and N is the degree of freedom in the joint space; The forward kinematics function is obtained by multiplying the transformation matrices of adjacent joints of the robot arm in sequence. The mathematical form of is as follows:
[0008] Where n is the ordinal number of the joint; d is the offset of the connecting rod; is the connecting rod torsion angle; a is the connecting rod length. Multiply the transformation matrix of the coordinate system established by each joint , the total transformation matrix of the manipulator's end coordinate system relative to the base coordinate system is obtained, which is the forward kinematics equation of the manipulator.
[0009] Furthermore, the Jacobian matrix is calculated by the partial differential of the kinematic model of the robot arm, and the calculation formula is:
[0010] in, Indicates the speed of the end effector of the robot arm; is the Jacobian matrix of the robot, is the parameter vector; represents the joint velocity; The end motion of the manipulator actuator is linearly affected by the joint angle. The above equation is linearized to separate the product of the regression matrix and the constant variable. The mathematical expression is as follows:
[0011] in, represents the separated regression matrix; Represents the constant parameter vector in the separated kinematic parameters.
[0012] Furthermore, step S3 is specifically as follows: S31. In order to reduce the impact of noise on the system and improve the accuracy of the estimation process, a low-pass linear filter is used to filter the product of the regression matrix and the constant variable. The mathematical expression is as follows:
[0013] in, and Respectively represent the velocity and regression matrix of the end effector of the robot arm after filtering. The filtered waveform satisfies the following mathematical form:
[0014] Among them, k>0 is the transfer parameter; , They represent the regression matrix and velocity of the end effector of the robot arm respectively; From the mathematical form of the waveform, the relationship between the speed and position of the end effector of the robot arm is as follows:
[0015] S32. An auxiliary matrix is introduced to define an intermediate variable containing error information. The specific mathematical expression of the definition is as follows:
[0016] in, is the auxiliary matrix, is the auxiliary vector, , They are , The derivative of; v represents the forgetting factor of the filter matrix, and satisfies v>0; P is the intermediate variable, is the estimated value of the constant parameter vector; The definition of the auxiliary matrix is differentiated and solved as follows:
[0017] Combined with the definition of the auxiliary matrix, we can get T=D , and then we can conclude that the intermediate variable P contains estimation errors, which can be expressed mathematically as:
[0018] in, Estimation error of the constant parameter vector.
[0019] Furthermore, the error conversion converts the estimation error into a transformation error and a rate of change of the transformation error.
[0020] Among them, the rate of change of the transformation error is expressed as a function, which can be simply expressed as follows:
[0021] in, is the transformation error; is the error transformation function, which is a monotonically increasing bounded function. The inverse function of the error transformation function can be obtained.
[0022] in, is an intermediate variable.
[0023] Furthermore, the transformation error and the rate of change of the transformation error satisfy the following properties:
[0024] in, is a constant greater than 0.
[0025] Furthermore, the mathematical expression of the predefined boundary is as follows:
[0026] in, is a constant greater than 0; ; represents the time-dependent transient estimation error; is the PPF function, which is a designed monotonically decreasing function, in order to ensure the estimation The transient and steady-state convergence performance of the error within predefined boundaries is mathematically expressed as follows:
[0027] in, > >0; l>0 is a priori selected constant.
[0028] The following bounds can be used to predefine the transient estimation error convergence (e.g., overshoot and convergence rate). Note that the PPF function and boundary conditions in this paper are designed for constant parameters. With this bound, the estimation error The transient performance can be adjusted by ,l, and to specify quantitatively and formulate a priori.
[0029] Furthermore, the condition for the convergence of the estimation error within the predefined boundary is that Z and S(Z) are bounded, where S(Z) is a bounded function, and the boundedness of Z is maintained.
[0030] When the estimation error converges, when the regression matrix R satisfies the PE condition, it can be concluded that the matrix D is a positive definite matrix and is reversible.
[0031] However, it is not easy to calculate the inverse matrix online, so we introduce a matrix as follows:
[0032] Solving the above equation for differentials yields
[0033] From the above formula, we can see that under the initial conditions In this case, the matrix Q approaches the inverse of D, and Q is introduced as the inverse matrix of matrix D. At this time, for matrices D and Q, D(t)Q(t)=I−M(t) holds, where I is the identity matrix, is the residual matrix, representing the initial conditions and converges to zero with the exponential t→∞.
[0034] After introducing the transformation error, the constraint equation can be written as
[0035] Since S(Z) is strictly increasing, the inverse function of S(Z) is expressed as:
[0036] Can get , and then get the intermediate vector The expression is:
[0037] Furthermore, considering the constant unknown parameter , whose adaptive update law can be used as a “virtual control input” to converge the transformation error Z.
[0038] In order to keep Z bounded, an adaptive law is given according to the dynamics of Z, and the derivative of Z is:
[0039] in, is a diagonal matrix with For the boundary, and is a non-zero matrix 0.
[0040] Furthermore, the mathematical expression of the designed adaptive estimation rate is:
[0041] in, represents the adaptive estimate of the parameter; is the learning gain matrix.
[0042] Next we use the Lyapunov function to prove its stability. Considering , we have
[0043] The Lyapunov function is defined as , then its time derivative is:
[0044] By choosing the appropriate gain , the above inequality can be simplified to
[0045] in, is a normal number, from which we can conclude that Z is convergent and tends to zero. The proof is complete.
[0046] A computer device includes: a processor and a storage medium; the processor loads and executes instructions and data in the storage medium to implement a mechanical arm kinematics identification method based on enhanced adaptive parameters.
[0047] The beneficial effects of the technical solution provided by the present invention are as follows: the present invention simplifies the identification algorithm and improves the parameter estimation convergence rate by obtaining the error information of parameter estimation by constructing an auxiliary matrix, integrates PPF into the APE framework to design an adaptive parameter estimation rate, effectively overcomes the uncertainty of system model parameters caused by changes in measurement methods and environmental parameters, predetermines the transient estimation error performance of the robot arm parameter estimation, and greatly improves the convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS
[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which: Figure 1 is a flow chart of a method for kinematic identification of a robotic arm based on enhanced adaptive parameters in an embodiment of the present invention; Figure 2 is a schematic diagram of DH parameters of the PUMA560 robot arm in an embodiment of the present invention; Figure 3 is a schematic diagram of the simulation results of the PUMA560 robotic arm in an embodiment of the present invention; Figure 4is a schematic diagram of DH parameters of the MyCobot280 robot arm in an embodiment of the present invention; Figure 5 Schematic diagram of the circular track of the MyCobot280 robot arm joint in an embodiment of the present invention; Figure 6 is a schematic diagram of the simulation results of MyCobot280 in an embodiment of the present invention; Figure 7 It is a schematic diagram of the operation of the hardware device in the embodiment of the present invention. DETAILED DESCRIPTION
[0049] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.
[0050] The embodiments of the present invention provide a method and device for kinematic identification of a robot arm based on enhanced adaptive parameters.
[0051] Please refer to Figure 1 , Figure 1 : is a flow chart of a method for kinematic identification of a robotic arm based on enhanced adaptive parameters in an embodiment of the present invention, which specifically includes the following steps: The first step is to establish the kinematic model of the robot arm based on the standard DH parameter method.
[0052] The mathematical expression of the kinematic model of the robot arm is as follows:
[0053] in, Indicates the position and posture information of the end of the robot. is the degrees of freedom of the task space; is the positive kinematic function; q represents the joint vector of the robot arm, and N is the degree of freedom in the joint space; The forward kinematics function is obtained by multiplying the transformation matrices of adjacent joints of the robot arm in sequence. The mathematical form of is as follows:
[0054] Where n is the ordinal number of the joint; d is the offset of the connecting rod; is the connecting rod torsion angle; a is the connecting rod length. Multiply the transformation matrix of the coordinate system established by each joint , the total transformation matrix of the manipulator's end coordinate system relative to the base coordinate system is obtained, which is the forward kinematics equation of the manipulator.
[0055] In the second step, the kinematic model of the robot arm is linearized and split into the product of constant unknown parameters and the regression matrix.
[0056] The Jacobian matrix is calculated by partial differential of the kinematic model of the robot arm, and the calculation formula is:
[0057] in, Indicates the speed of the end effector of the robot arm; is the Jacobian matrix of the robot, is the parameter vector; represents the joint velocity; The end motion of the manipulator actuator is linearly affected by the joint angle. The above equation is linearized to separate the product of the regression matrix and the constant variable. The mathematical expression is as follows:
[0058] in, represents the separated regression matrix; Represents the constant parameter vector in the separated kinematic parameters.
[0059] The third step is to filter the product and introduce an auxiliary matrix to construct an intermediate variable containing the estimation error, specifically: Step 1: In order to reduce the impact of noise on the system and improve the accuracy of the estimation process, a low-pass linear filter is used to filter the product of the regression matrix and the constant variable. The mathematical expression is as follows:
[0060] in, and Respectively represent the velocity and regression matrix of the end effector of the robot arm after filtering. The filtered waveform satisfies the following mathematical form:
[0061] Among them, k>0 is the transfer parameter; , They represent the regression matrix and velocity of the end effector of the robot arm respectively; From the mathematical form of the waveform, the relationship between the speed and position of the end effector of the robot arm is as follows:
[0062] Step 2: Introduce an auxiliary matrix to define the intermediate variable containing error information. The specific mathematical expression of the definition is as follows:
[0063] in, is the auxiliary matrix, is the auxiliary vector, , They are , The derivative of; v represents the forgetting factor of the filter matrix, and satisfies v>0; P is the intermediate variable, is the estimated value of the constant parameter vector; The definition of the auxiliary matrix is differentiated and solved as follows:
[0064] Combined with the definition of the auxiliary matrix, we can get T=D , and then we can conclude that the intermediate variable P contains estimation errors, which can be expressed mathematically as:
[0065] in, Estimation error of the constant parameter vector.
[0066] The fourth step is to convert the estimation error into a transformation error by introducing an inverse matrix and designing a predefined boundary based on the PPF function.
[0067] The error transformation converts the estimation error into a transformed error and the rate of change of the transformed error.
[0068] Among them, the rate of change of the transformation error is expressed as a function, which can be simply expressed as follows:
[0069] in, is the transformation error; is the error transformation function, which is a monotonically increasing bounded function. The inverse function of the error transformation function can be obtained.
[0070] in, is an intermediate variable.
[0071] The transformation error and the rate of change of the transformation error satisfy the following properties:
[0072] in, is a constant greater than 0.
[0073] The mathematical expression of the predefined boundaries is as follows:
[0074] in, is a constant greater than 0; ; represents the time-dependent transient estimation error; is the PPF function, which is a designed monotonically decreasing function, in order to ensure the estimation The transient and steady-state convergence performance of the error within predefined boundaries is mathematically expressed as follows:
[0075] in, > >0; l>0 is a priori selected constant.
[0076] The following bounds can be used to predefine the transient estimation error convergence (e.g., overshoot and convergence rate). Note that the PPF function and boundary conditions in this paper are designed for constant parameters. With this bound, the estimation error The transient performance can be adjusted by ,l, and to specify quantitatively and formulate a priori.
[0077] S5. Design an adaptive parameter estimation rate by combining the intermediate variables with the transformation error and the convergence performance of the estimation error within the predefined bounds.
[0078] The condition for the convergence of the estimation error within the predefined boundary is that Z and S(Z) are bounded, where S(Z) is a bounded function and the boundedness of Z is maintained.
[0079] When the estimation error converges, when the regression matrix R satisfies the PE condition, it can be concluded that the matrix D is a positive definite matrix and is reversible. However, it is not easy to calculate the inverse matrix online, so we introduce a matrix as follows:
[0080] Solving the above equation for differentials yields
[0081] From the above formula, we can see that under the initial conditions In this case, the matrix Q approaches the inverse of D, and Q is introduced as the inverse matrix of matrix D. At this time, for matrices D and Q, D(t)Q(t)=I−M(t) holds, where I is the identity matrix, is the residual matrix, representing the initial conditions and converges to zero with the exponential t→∞.
[0082] After introducing the transformation error, the constraint equation can be written as
[0083] Since S(Z) is strictly increasing, the inverse function of S(Z) is expressed as:
[0084] Can get , and then get the intermediate vector The expression is:
[0085] Considering the constant unknown parameters , whose adaptive update law can be used as a “virtual control input” to converge the transformation error Z.
[0086] In order to keep Z bounded, an adaptive law is given according to the dynamics of Z, and the derivative of Z is:
[0087] in, is a diagonal matrix with For the boundary, and is a non-zero matrix.
[0088] The mathematical expression of the designed adaptive estimation rate is:
[0089] in, represents the adaptive estimate of the parameter; is the learning gain matrix.
[0090] Next we use the Lyapunov function to prove its stability. Considering , we have
[0091] The Lyapunov function is defined as , then its time derivative is:
[0092] By choosing the appropriate gain , the above inequality can be simplified to
[0093] in, is a normal number, from which we can conclude that Z is convergent and tends to zero. The proof is complete.
[0094] In the sixth step, the adaptive parameter estimator is enhanced with a preset convergence performance to achieve the kinematic identification of the manipulator within the predefined boundaries.
[0095] To verify the effectiveness of the algorithm, we conducted simulations on a 6-DOF PUMA560 robot and experiments on a 6-DOF MyCobot280 robot. The corresponding link parameters are as follows: Figure 2As shown. Where a2=0.4, a3=0.02, d2=0.15, d4=0.43, d6=0.056. Assuming these parameters are unknown, they will be estimated using the adaptive update law. During the kinematic estimation process, the manipulator operates in the position control module to make the velocity of each joint stable and bounded.
[0096] PUMA560 is commanded to track the reference trajectory , where a1=a4=a5=a6=1,a2=a3=0.5. The estimated parameter vector is , the initial values of the estimated parameters are set to The other initial conditions are set as q1(0)=q2(0)=q3(0)=q4(0)=q5(0)=q6(0)=0, A1=A2=E, k=1, l=0.001. The PPF function is selected as .
[0097] The experimental results are as follows Figure 3 As shown, from Figure 3 From the simulation results, it can be seen that the unknown joint parameter error tends to stabilize and converge after 10 seconds. Under the preset performance boundary, the parameter estimation error converges quickly and tends to 0. The error order of magnitude is one ten-thousandth, indicating that the proposed method has good estimation effects in both transient and steady-state conditions.
[0098] In order to further verify the feasibility and advantages of the proposed method, MyCobot280 six-degree-of-freedom robot was used as the experimental object. The DH parameters of the MyCobot280 robot are as follows: Figure 4 As shown. Figure 5 As shown in the figure, given a joint signal of a circular trajectory, the offline reference signal q is taken for the manipulator to estimate, and the result is as follows Figure 6 As shown in Figure 2, the proposed estimation method converges after 10 seconds, and the estimated parameter results obtained by the experiment are: ,The estimation error is within 0.1mm of the standard parameter estimation error given by the MyCobot280 system, which verifies the accuracy and efficiency of the proposed estimation method.
[0099] See also Figure 7 , Figure 7 40 is a schematic diagram of the working of the hardware device of an embodiment of the present invention, wherein the hardware device specifically comprises: a computer device 401, a processor 402 and a storage medium 403.
[0100] A computer device 401: The computer device 401 implements the robotic arm kinematics identification method based on enhanced adaptive parameters.
[0101] Processor 402: The processor 402 loads and executes the instructions and data in the storage medium 403 to implement the robotic arm kinematics identification method based on enhanced adaptive parameters.
[0102] Storage medium 403: The storage medium 403 stores instructions and data; the storage medium 403 is used to implement the robotic arm kinematics identification method based on enhanced adaptive parameters.
[0103] The beneficial effects of the present invention are as follows: the present invention simplifies the identification algorithm and improves the parameter estimation convergence rate by obtaining the error information of parameter estimation by constructing an auxiliary matrix, integrates PPF into the APE framework to design an adaptive parameter estimation rate, effectively overcomes the uncertainty of system model parameters caused by changes in measurement methods and environmental parameters, predetermines the transient estimation error performance of the robot arm parameter estimation, and greatly improves the convergence speed.
[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A kinematic identification method of a robotic arm based on enhanced adaptive parameters, characterized in that: The specific steps include: S1. Establish the kinematic model of the robot arm based on the standard DH parameter method; S2, linearize the kinematic model of the robot arm and split it into the product of constant unknown parameters and regression matrix; S3, filtering the product equation, introducing an auxiliary matrix to construct an intermediate variable containing the estimation error; S4, converting the estimation error into a transformation error, by introducing an inverse matrix, and designing a predefined boundary based on the PPF function; S5, designing an adaptive parameter estimation rate in combination with the preset convergence performance of the intermediate variable and the transformation error and the estimation error within the predefined bounds; S6. Enhance the adaptive parameter estimator with preset convergence performance to achieve kinematic identification of the robot arm within predefined boundaries.
2. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 1, characterized in that: The mathematical expression of the kinematic model of the robotic arm is as follows: in, Indicates the position and posture information of the end of the robot. is the degrees of freedom of the task space; is the positive kinematic function; q represents the joint vector of the robot arm, and N is the degree of freedom in the joint space; The forward kinematics function is obtained by multiplying the transformation matrices of adjacent joints of the robot arm in sequence. The mathematical form of is as follows: Where n is the ordinal number of the joint; d is the offset of the connecting rod; is the connecting rod torsion angle; a is the connecting rod length.
3. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 1, characterized in that: The Jacobian matrix is calculated by partial differential of the kinematic model of the robot arm, and the calculation formula is: in, Indicates the speed of the end effector of the robot arm; is the Jacobian matrix of the robot, is the parameter vector; represents the joint velocity; Linearize the above equation and separate the product of the regression matrix and the constant variable. The mathematical expression is as follows: in, represents the separated regression matrix; Represents the constant parameter vector in the separated kinematic parameters.
4. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 1, characterized in that: Step S3 is specifically as follows: S31. Use a low-pass linear filter to filter the product of the regression matrix and the constant variable. The mathematical expression is as follows: in, and Respectively represent the velocity and regression matrix of the end effector of the robot arm after filtering. The filtered waveform satisfies the following mathematical form: Among them, k>0 is the transfer parameter; , They represent the regression matrix and velocity of the end effector of the robot arm respectively; From the mathematical form of the waveform, the relationship between the speed and position of the end effector of the robot arm is as follows: S32. An auxiliary matrix is introduced to define an intermediate variable containing error information. The specific mathematical expression of the definition is as follows: in, is the auxiliary matrix, is the auxiliary vector, , They are , The derivative of; v represents the forgetting factor of the filter matrix, and satisfies v>0; P is the intermediate variable, is the estimated value of the constant parameter vector; The definition of the auxiliary matrix is differentiated and solved, and combined with the definition, it is concluded that the intermediate variable P contains the estimation error, which can be expressed mathematically as follows: in, Estimation error of the constant parameter vector.
5. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 1, characterized in that: The error conversion converts the estimation error into a transformation error and a rate of change of the transformation error; The rate of change of the transformation error is expressed as a function, which can be simply expressed as follows: in, is the transformation error; is the error transformation function, which is a monotonically increasing bounded function. The inverse function of the error transformation function can be obtained. in, is an intermediate variable.
6. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 5, characterized in that: The transformation error and the rate of change of the transformation error satisfy the following properties: in, is a constant greater than 0.
7. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 6, characterized in that: The mathematical expression of the predefined boundary is as follows: in, is a constant greater than 0; ; represents the time-dependent transient estimation error; is the PPF function, is the designed monotonically decreasing function, and its mathematical expression is as follows: in, > >0; l >0 is a priori chosen constant.
8. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 7, characterized in that: The conditions for the convergence of the estimation error within the predefined boundary are: maintaining the boundedness of Z; Introducing a matrix as follows: At the initial condition , the matrix Q approaches the inverse of D, and Q is introduced as the inverse matrix of matrix D. At this time, for matrices D and Q, D(t)Q(t)=I−M(t) holds, where I is the identity matrix, is the residual matrix, representing the initial conditions The influence of , and converges to zero with the exponential t→∞; After introducing the transformation error, the constraint equation is expressed as: The inverse function of S(Z) is expressed as: get , and then get the intermediate vector The expression is: In order to maintain the boundedness of Z, Z is differentiable, and the derivative of Z is: in, is a diagonal matrix with For the boundary, and is a non-zero matrix.
9. A method for kinematic identification of a robotic arm based on enhanced adaptive parameters as claimed in claim 1, characterized in that: The mathematical expression of the adaptive estimation rate of the design is: in, represents the adaptive estimate of the parameter; is the learning gain matrix.
10. A computer device, characterized in that: include: Processor and storage medium; the processor loads and executes instructions and data in the storage medium to implement a robotic arm kinematics identification method based on enhanced adaptive parameters as described in any one of claims 1 to 9.