Flexible mechanical arm fractional order modeling method based on combined multi-information gradient

Abstract

The invention discloses a fractional order modeling method of a flexible mechanical arm based on a combined multi-information gradient, which comprises the following steps: a fractional order dynamic model of the flexible mechanical arm is constructed through a fractional viscous element, and input data and output data of the fractional order dynamic model are voltage data and a rotation angle respectively; converting the fractional order dynamical model into a multi-information fractional order dynamical model, and constructing a multi-information fractional order joint gradient according to the multi-information fractional order dynamical model; constructing an error model according to the multi-information fractional order dynamical model, and constructing a fractional order recursive iteration model and a model parameter recursive iteration model according to the error model and the multi-information fractional order joint gradient; and carrying out joint interactive iteration solution on the model parameter recursive iteration model and the fractional order recursive iteration model to obtain a model parameter and fractional order identification result.

Description

Technical Field

[0001] The present invention belongs to the technical field of system modeling and parameter identification, and mainly relates to a fractional order modeling method of a flexible manipulator based on joint multi-information gradients. Background Art

[0002] Fractional calculus has a history of more than 300 years. Compared with integer calculus, the fractional-order model established using fractional-order calculus can more accurately characterize the dynamic changes of actual physical systems, such as relaxation and creep of viscoelastic materials, temperature diffusion, virus transmission, battery energy estimation, and optoelectronic system trajectory tracking.

[0003] With the continuous breakthroughs in robot application technology, robotic arms are widely used in various automated production lines such as machinery, chemical industry, electronics, logistics, etc. Flexible robotic arms have the characteristics of high flexibility, strong adaptability to complex environments, and safe human-computer interaction, and have received extensive attention and research from scholars and institutions at home and abroad. Flexible robotic arms can be divided into one-degree-of-freedom, two-degree-of-freedom, three-degree-of-freedom and multi-degree-of-freedom flexible robotic arms according to the degree of freedom, and can be divided into rod-flexible and joint-flexible robotic arms according to the position of the flexible material. Compared with the huge size and load-bearing capacity of rigid robotic arms, flexible robotic arms are smaller in size and use lighter and cheaper manufacturing materials, which enables flexible robotic arms to have higher operating speeds and larger working spaces. Flexible robotic arms can have larger working volumes in the same size area.

[0004] The rotating flexible robotic arm studied in the present invention is a one-degree-of-freedom flexible system with single input and single output. The existing system model is established on the basis of ignoring flexible vibration. However, such model cannot accurately describe the change process of the rotation angle of the flexible robotic arm and the dynamic characteristics of the system, which leads to deviation in the rotation angle of the robotic arm and cannot accurately locate and acquire the target. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a fractional-order modeling method for a flexible manipulator based on a joint multi-information gradient to solve the problems existing in the above-mentioned prior art. A fractional-order dynamic model of the flexible manipulator is constructed, and a fractional-order multi-information joint gradient descent algorithm is used to synchronously identify unknown fractional orders and model parameters to solve the problem that the existing integer-order model of the rotating flexible manipulator cannot accurately characterize the changing process of the rotation angle and the dynamic characteristics of the system, and the fractional-order parameter estimation method cannot accurately and synchronously identify the model parameters and fractional orders of the flexible manipulator. The constructed flexible manipulator model can be used as a control model for controlling the manipulator to effectively control the manipulator, laying the foundation for the design of advanced controllers and providing a prerequisite for achieving accurate positioning and accurate acquisition of targets.

[0006] To achieve the above object, the present invention provides a fractional order modeling method for a flexible manipulator based on joint multi-innovation gradients, comprising:

[0007] A fractional-order dynamic model of a flexible manipulator is constructed by using a fractional viscosity element, wherein input data and output data of the fractional-order dynamic model of the flexible manipulator are driving voltage and rotation angle respectively;

[0008] Converting the fractional-order dynamics model into a multi-innovation fractional-order dynamics model, and constructing a multi-innovation fractional-order joint gradient according to the multi-innovation fractional-order dynamics model;

[0009] An error model is constructed according to the multi-innovation fractional-order dynamics model, and a fractional-order recursive iterative model and a model parameter recursive iterative model are constructed according to the error model and the multi-innovation fractional-order joint gradient;

[0010] The model parameter recursive iterative model and the fractional order recursive iterative model are jointly interactively solved to obtain model parameter and fractional order identification results; the model parameters and fractional order identification results are substituted into the fractional order dynamic model, and the flexible robotic arm is controlled by the fractional order dynamic model after substitution.

[0011] Optionally, the fractional order kinetic model is:

[0012]

[0013] Where k represents the current moment, y(k) is the rotation angle of the flexible robotic arm, and u(k) is the input voltage of the flexible robotic arm. and are two fractional viscous components, representing the fractional rotation angles at the past k-1 and k-2 moments, is the fractional order, a1, a2, b0 are model parameters.

[0014] Optionally, the generation process of the multi-innovation fractional-order dynamics model includes:

[0015]

[0016] Where Y(p,k) is the output data multi-innovation matrix, Y(p,k)=[y(k),y(k-1),…,y(k-p+1)] T , where p is the length of the multi-innovation, and the superscript T represents the matrix transpose.

[0017] = is the multi-innovation matrix transformed by the fractional-order viscous element and the input data,

[0018]

[0019] θ is the model parameter matrix, θ = [a1, a2, b0].

[0020] Optionally, the multi-innovation fractional-order joint gradient is:

[0021]

[0022] Among them, J1(θ), denote the joint gradient of model parameters and fractional order respectively, and Fractional order and the estimated value of the model parameter matrix θ, and N is the final moment of a single joint iteration.

[0023] Optionally, the error model is:

[0024]

[0025] Among them, e(p,k) is the error value, θ(k-1) represents the model parameter matrix at time k-1, represents the estimated value of the fractional order at time k.

[0026] Optionally, the fractional order recursive iterative model is:

[0027]

[0028] in, represents the estimated value of the model parameter matrix at time k, is the fractional gradient, α is the order of the fractional gradient, μ is the step size factor of the fractional multi-innovation gradient, Γ(·) is the gamma function, are the estimated values ​​of a1, a2, and b0 respectively, ε represents the constant term, and diag represents the diagonal matrix.

[0029] Optionally, the model parameter recursive iteration model is:

[0030]

[0031] Among them, μ1 represents the gradient step factor, represents the partial derivative matrix, represents the fractional order at time k.

[0032] Optionally, the joint interactive iterative solution process includes:

[0033] Acquire input data and output data, and perform iterative joint interaction on the model parameter recursive iterative model and the fractional order recursive iterative model according to the input data and the output data until the number of interactions is reached, thereby obtaining model parameter and fractional order identification results;

[0034] In the joint interaction, the model parameter recursive iterative model is iteratively solved to obtain updated model parameters, and the updated model parameters are brought into the fractional order recursive iterative model for iterative solution to obtain the updated fractional order, completing one joint interaction, and the next joint interaction is carried out based on the recursive iterative model with the updated fractional order model parameters.

[0035] Optionally, after obtaining the model parameters and fractional-order identification results, the following steps are also included:

[0036] The model parameters and the fractional-order identification results are brought into the fractional-order dynamics model to obtain the current driving voltage, and the current driving voltage is calculated by the introduced fractional-order dynamics model to generate the current rotation angle of the flexible manipulator.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] 1. The present invention combines two fractional-order gradients and utilizes the two gradients to interactively identify model parameters and fractional orders, thereby being able to synchronously estimate unknown fractional orders and model parameters of the flexible manipulator.

[0039] 2. The joint fractional-order gradient of the present invention combines the multi-innovation theory and uses the data of the current moment and the past moment to synchronously estimate the model parameters of the flexible manipulator, so that the constructed model is more accurate.

[0040] 3. The flexible robotic arm model established by the present invention has high precision and can accurately describe the dynamic characteristics of the robotic arm. The model can provide a theoretical basis for the simulation and application of advanced control technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0042] Figure 1 is a flow chart of a flexible manipulator fractional-order modeling method based on joint gradient according to an embodiment of the present invention;

[0043] Figure 2 It is a process of joint interactive identification of unknown parameters and fractional orders of a rotating flexible manipulator according to an embodiment of the present invention;

[0044] Figure 3 is a comparison diagram of the fractional order model and the integer order model established in the embodiment of the present invention;

[0045] Figure 4 1 is an ITAE diagram of an actual system and a fractional-order model with different joint orders according to an embodiment of the present invention;

[0046] Figure 5 3 are ITAE diagrams of an actual system and a fractional-order model with different multi-innovation lengths according to an embodiment of the present invention. DETAILED DESCRIPTION

[0047] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0048] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0049] The present invention relates to a method for fractional-order modeling of a flexible manipulator based on a joint multi-information gradient, comprising the following steps: first, a fractional-order dynamic model of the input voltage and output rotation angle of the flexible manipulator is constructed using a fractional-order viscous element. Secondly, real input and output data are collected to construct a joint gradient criterion function of unknown fractional orders and model parameters. Then, a method for identifying a fractional-order model of a rotating flexible manipulator based on a fractional-order multi-information joint gradient is designed. Through the joint interactive iteration of the two gradients, the unknown parameters and fractional orders of the model can be accurately and synchronously estimated. The flexible manipulator model established by the present invention has high precision and can accurately describe the dynamic characteristics of the manipulator. The model can provide a theoretical basis for the simulation and application of advanced control technology.

[0050] The present invention provides a fractional-order modeling method for a flexible robotic arm based on a joint multi-innovation gradient. A fractional-order model of the flexible robotic arm is established using fractional-order viscoelastic elements, and the unknown parameters and fractional orders of the model are estimated in combination with a fractional-order multi-innovation joint gradient descent algorithm, thereby achieving an accurate description of the dynamic characteristics of a rotating flexible robotic arm.

[0051] In order to achieve the above object, the technical solution of the present invention is:

[0052] Step 1: Use fractional-order viscous elements to construct a fractional-order dynamic model of the flexible robotic arm's input voltage data and output rotation angle.

[0053] Step 2: Collect the real data of input voltage data and output rotation angle, and construct the joint gradient of unknown fractional order and model parameters.

[0054] Step 3: Design a fractional-order model identification method for a rotating flexible robotic arm based on fractional-order multi-information joint gradient.

[0055] Step 4: Use the fractional-order multi-innovation gradient descent method to estimate the model parameters, then bring the parameters into the fractional-order multi-innovation gradient descent method of the model order, identify the fractional order, and then bring the fractional order back to the gradient descent algorithm of the model parameters to continue identifying the model parameters, and repeat the joint interaction back and forth in sequence.

[0056] Step 5: Set the number of joint interactions. If the number of joint interactions is less than the set value, return to step 4 to continue the interaction. When the number of joint interactions is equal to the set value, output the identified fractional-order model parameters and order of the rotating flexible manipulator.

[0057] Step 6: The constructed fractional-order model of the flexible robotic arm can be used to design a high-precision rotation control system, which can accurately control the rotation angle of the robotic arm and achieve accurate positioning and acquisition of the target.

[0058] like Figure 1 As shown, the above technical solution of the present invention is described in detail:

[0059] Step 1: Use fractional-order viscous elements to construct a fractional-order dynamic model of the flexible robot arm's input voltage and output rotation angle.

[0060] The fractional-order dynamics model is based on the fractional-order viscous element, which expands the integer-order physical quantity to the fractional order. For a one-degree-of-freedom rotating flexible manipulator, two fractional-order elements can be used to describe the dynamic change of the rotation angle, namely

[0061]

[0062] Where k represents the current moment, y(k) is the output rotation angle of the rotating flexible robotic arm, and u(k) is the input voltage data of the rotating flexible robotic arm. and are two fractional-order viscous components, representing the fractional-order rotation angles at the past k-1 and k-2 moments, is the fractional order, a1, a2, b0 are different model parameters.

[0063] Step 2: Collect input data and output data, and construct a joint gradient criterion function of unknown fractional orders and model parameters.

[0064] The data acquisition system of the rotating flexible robotic arm was built using Matlab / Simulink, and the input data and output data were obtained through the Quarc acquisition module. The input data was the driving voltage. The input driving voltage of the present invention was 1V, the output was the rotation angle, the acquisition period was 5s, the sampling interval was 0.004s, and the data length was 1250.

[0065] Multi-innovation is to combine the output data of the current moment and the output data of the past moment into a multi-innovation matrix, and use the multi-innovation matrix to estimate the unknown parameters. Compared with the traditional iterative method, multi-innovation uses a larger amount of data, so the identification result is more accurate. According to the multi-innovation theory, the rotation angle of the rotating flexible manipulator, that is, the output data, is converted into the form of a multi-innovation matrix, and the output data multi-innovation matrix Y(p,k):

[0066] Y(p,k)=[y(k),y(k-1),…,y(k-p+1)] T (2)

[0067] Where p is the length of the multi-innovation.

[0068] Similarly, the fractional-order viscous element and the input voltage are converted into a multi-innovation matrix.

[0069]

[0070] Rewrite the unknown parameters into matrix form, the unknown model parameter matrix θ:

[0071] θ=[a1,a2,b0] (4)

[0072] Then the fractional-order dynamic model of the rotating flexible manipulator can be rewritten as

[0073]

[0074] In formula (5), there are unknown fractional orders And the unknown model parameter matrix θ, therefore, in order to identify the accurate model parameters, a multi-innovation fractional-order joint gradient is established:

[0075]

[0076] Among them, J1(θ), denote the joint gradient of model parameters and fractional order respectively, and Fractional order and the estimated values ​​of the model parameters θ, and N is the final moment of a single joint iteration.

[0077] Step 3: Design a rotating flexible robotic arm model identification method based on fractional-order multi-information joint gradient descent.

[0078] A fractional-order multi-innovation gradient descent algorithm with unknown parameters θ is designed to define the dynamic change process of the rotation angle of the rotating flexible manipulator and the error of the identification model. The error model is:

[0079]

[0080] Among them, e(p,k) is the error value, θ(k-1) represents the model parameter matrix at time k-1, Represents the estimated value of the fractional order at time N.

[0081] By taking the partial derivative of J1(θ) in formula (6) and then recursively iterating it in combination with formula (7), we can obtain the fractional-order recursive iterative model:

[0082]

[0083] in is the fractional gradient, α is the order of the fractional gradient, μ is the step size factor of the fractional multi-innovation gradient, Γ(·) is the gamma function, are the estimated values ​​of a1 and a2 respectively. k-1 and k-2 in brackets represent the corresponding k-1 and k-2 moments. ε=0.001 represents the constant term, and diag represents the diagonal matrix.

[0084] For the formula By finding the partial derivative and then performing recursive iteration based on formula (7), we can obtain the model parameter recursive iteration model:

[0085]

[0086] Among them, μ1 represents the gradient step factor, represents the partial derivative matrix, represents the fractional order at time k.

[0087] Step 4: When performing joint gradient identification, first initialize Set the multi-innovation length p=5 and the fractional gradient order α=1.5.

[0088] Secondly, the unknown parameters of the rotating flexible manipulator model are identified using formula (8). By gradually iterating 1250 observation data, the identification parameters at the final moment after the first joint iteration can be obtained.

[0089] Then, Substitute it into formula (9) and use formula (9) to identify the unknown fractional order of the rotating flexible manipulator model. Iterate 1250 times to get the updated

[0090] Finally, update the Substitute into formula (8) and perform joint interaction to achieve joint iteration of fractional order and model parameters. The joint interactive identification process of unknown parameters and fractional order of rotating flexible manipulator is as follows: Figure 2 shown.

[0091] Step 5: Formulas (8) and (9) are iterated 1250 times each, which is regarded as one joint interaction. The number of joint interactions is set to 3. If the number of interactions is less than 3, return to step 4 for joint interaction. When the third interaction is completed, the identification result is output. and And ITAE (time and absolute value integral of error) is used as the performance index to evaluate the model accuracy, and the results of different joint interactions are recorded in Table 1. Table 1 shows the estimation results of model parameters and fractional orders under different numbers of joint interactions.

[0092] Table 1

[0093]

[0094] Substituting the third joint identification result, i.e. the final model parameters and the fractional-order identification result, into formula (1), we can obtain the fractional-order model of the rotating flexible manipulator:

[0095] y(k)=0.4314Δ 1.19 y(k-1)+0.7621Δ 1.19 y(k-2)-0.2547u(k) (10)

[0096] Step 6: Collect the input voltage u(t) data of the rotating flexible manipulator, input the input voltage data into the fractional-order model of the rotating flexible manipulator shown in formula (10), output the rotation angle of the flexible manipulator, and obtain the dynamic change process of the manipulator's rotation angle. This model can be used to design a high-precision rotation control system. By comparing the rotation angle with the set angle, the error of the rotation angle can be obtained. Combining the error feedback principle with the dynamic characteristics of the rotation angle, the input voltage of the manipulator can be controlled, and the rotation angle of the manipulator can be accurately controlled to achieve the target grasping or precision processing.

[0097] The comparison results of the fractional order model established in the embodiment of the present invention and the dynamic change process of the rotation angle of the flexible manipulator are as follows: Figure 3 As shown. Figure 3 It can be seen that the fractional order model established by the present invention can more accurately characterize the dynamic change process of the rotation angle of the flexible manipulator compared with the traditional integer order model. As the number of joint interactions increases, ITAE gradually decreases, and the model fits the real data better. Figure 4 Therefore, the effectiveness of the present invention is verified.

[0098] In addition, the influence of different multi-innovation lengths on the identification results is verified. Figure 5It can be seen from the figure that with the increase of the multi-new information length, ITAE gradually decreases and the identification accuracy gradually increases. Therefore, the feasibility of the method proposed in the present invention in the identification of the rotating flexible manipulator system is further verified.

[0099] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A fractional-order modeling method for a flexible manipulator based on joint multi-innovation gradients, characterized in that: include: A fractional-order dynamic model of a flexible manipulator is constructed by using a fractional viscosity element, wherein input data and output data of the fractional-order dynamic model of the flexible manipulator are driving voltage and rotation angle respectively; Converting the fractional-order dynamics model into a multi-innovation fractional-order dynamics model, and constructing a multi-innovation fractional-order joint gradient according to the multi-innovation fractional-order dynamics model; An error model is constructed according to the multi-innovation fractional-order dynamics model, and a fractional-order recursive iterative model and a model parameter recursive iterative model are constructed according to the error model and the multi-innovation fractional-order joint gradient; The model parameter recursive iterative model and the fractional order recursive iterative model are jointly solved interactively to obtain the model parameter and fractional order identification results; The model parameters and the fractional-order identification results are substituted into the fractional-order dynamics model, and the flexible manipulator is controlled by the substituted fractional-order dynamics model.

2. The method according to claim 1, characterized in that The fractional order kinetic model is: Where k represents the current moment, y(k) is the rotation angle of the flexible robotic arm, and u(k) is the input voltage of the flexible robotic arm. and are two fractional viscous components, representing the fractional rotation angles at the past k-1 and k-2 moments, is the fractional order, a1, a2, b0 are model parameters.

3. The method according to claim 2, characterized in that The generation process of the multi-innovation fractional-order dynamics model includes: Where Y(p,k) is the output data multi-innovation matrix, Y(p,k)=[y(k),y(k-1),…,y(k-p+1)] T , where p is the length of the multi-innovation, and the superscript T represents the matrix transpose. = is the multi-innovation matrix transformed by the fractional-order viscous element and the input data, θ is the model parameter matrix, θ = [a1, a2, b0].

4. The method according to claim 3, characterized in that The multi-innovation fractional-order joint gradient is: Among them, J1(θ), denote the joint gradient of model parameters and fractional order respectively, and Fractional order and the estimated value of the model parameter matrix θ, and N is the final moment of a single joint iteration.

5. The method according to claim 4, characterized in that The error model is: Among them, e(p,k) is the error value, θ(k-1) represents the model parameter matrix at time k-1, represents the estimated value of the fractional order at time k.

6. The method according to claim 5, characterized in that The fractional order recursive iterative model is: in, represents the estimated value of the model parameter matrix at time k, is the fractional gradient, α is the order of the fractional gradient, μ is the step size factor of the fractional multi-innovation gradient, Γ(·) is the gamma function, are the estimated values ​​of a1, a2, and b0 respectively, ε represents the constant term, and diag represents the diagonal matrix.

7. The method according to claim 6, characterized in that The model parameter recursive iteration model is: Among them, μ1 represents the gradient step factor, represents the partial derivative matrix, represents the fractional order at time k.

8. The method according to claim 1, characterized in that: The joint interactive iterative solution process includes: Acquire input data and output data, and perform iterative joint interaction on the model parameter recursive iterative model and the fractional order recursive iterative model according to the input data and the output data until the number of interactions is reached, thereby obtaining model parameter and fractional order identification results; In the joint interaction, the model parameter recursive iterative model is iteratively solved to obtain updated model parameters, and the updated model parameters are brought into the fractional order recursive iterative model for iterative solution to obtain the updated fractional order, completing one joint interaction, and the next joint interaction is carried out based on the recursive iterative model with the updated fractional order model parameters.

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