Dead zone adaptive compensation control system and method for wire-driven continuum robot

Abstract

The application discloses a dead zone self-adaptive compensation control system and method of a wire-driven continuum robot, and comprises the following steps: a first model module is used to establish a standard dynamic model of a continuum robot; a dead zone function module is used to establish a dead zone function for the drive dead zone of the wire-driven continuum robot; a second model module is used to establish an uncertain error model based on the standard dynamic model; a neural network compensator comprises two introduced RBF neural networks; one of the RBF neural networks is used to estimate the proposed uncertain error model; the other RBF neural network is used for dead zone compensation of a system feedforward channel to approximate the established dead zone function; and an adaptive compensation module is used to update the established model and dead zone function in an adaptive manner to improve the control accuracy of the continuum robot; the method has the beneficial effect of compensating for the influence of the drive dead zone on the control system.

Description

Technical Field

[0001] This invention relates to the field of continuum robot technology, and more specifically to a dead-zone adaptive compensation control system and method for a line-driven continuum robot. Background Technology

[0002] Continuum robots are a new type of robot inspired by biomimetic structures. Composed of elastic materials, these robots can undergo continuous deformation and large-scale transformations, exhibiting advantages such as high structural compliance and flexibility. Continuum robots can overcome the shortcomings of traditional rigid robots in coping with complex environments, and are therefore widely used in industries such as industrial search and rescue, equipment maintenance, aerospace, and medicine, becoming a hot topic in the development of next-generation robots.

[0003] Compared to traditional rigid-body robots, continuum robots possess high flexibility and compliance, but this also significantly increases their structural complexity. The models of continuum robots involve complex factors, and their dynamic models exhibit strong nonlinearity and high coupling, inevitably leading to modeling errors. Furthermore, continuum robots are subject to numerous external disturbances in practical applications. These disturbances and errors severely impact the control accuracy of the continuum robot under dynamic models and may even affect the stability of the entire system. Therefore, traditional robot control methods are ill-suited for handling the control problems of continuum robots.

[0004] Continuous robots using linear drives suffer from a driving dead zone. The non-differentiable nonlinear nature of this dead zone makes compensation extremely difficult, increasing the complexity of the transmission system control. However, if the dead zone cannot be eliminated, in addition to causing output errors, it can lead to limit cycle oscillations in the high-precision control system of the continuous robot, reducing performance and even causing instability. Summary of the Invention

[0005] To address the technical deficiencies in the prior art, the purpose of this invention is to provide a dead-zone adaptive compensation control system and method for a line-driven continuum robot, thereby overcoming the shortcomings of the prior art, such as the existence of driving dead zones and inaccurate modeling affecting the control system.

[0006] To achieve the above objectives, in a first aspect, embodiments of the present invention provide a dead-zone adaptive compensation control system for a line-driven continuum robot, applied to a controller, comprising:

[0007] The first model module is used to establish a standard dynamic model of a continuum robot based on Euler's Bernoulli beam theorem and the constant curvature assumption;

[0008] The dead zone function module is used to establish the dead zone function for the drive dead zone of a line-driven continuum robot.

[0009] The second model module is used to establish an uncertainty error model based on the standard dynamic model.

[0010] A neural network compensator comprising two introduced RBF neural networks; one RBF neural network is used to estimate the proposed uncertainty error model; the other RBF neural network is used for dead-zone compensation of the system feedforward channel to approximate the established dead-zone function.

[0011] An adaptive compensation module is used to update the established model and dead zone function in an adaptive manner to improve the control accuracy of the continuum robot; wherein the model includes the standard dynamic model and the uncertainty error model.

[0012] As a preferred embodiment of this application, the adaptive approach specifically includes:

[0013] Design the adaptive rate of the neural network;

[0014] Based on the acquired error signal, establish the error function;

[0015] The error function is fed into the adaptive rate of the neural network for compensation and update, thereby updating the established model and dead zone function.

[0016] In a second aspect, embodiments of the present invention also provide a dead-zone adaptive compensation control method for a line-driven continuum robot, applied to the dead-zone adaptive compensation control system of the line-driven continuum robot described in the first aspect, the method comprising:

[0017] Based on Euler's Bernoulli beam theorem and the assumption of constant curvature, a standard dynamic model of a continuum robot is established.

[0018] Establish a dead-zone function for the driving dead zone of a line-driven continuum robot;

[0019] An uncertainty error model is established based on the aforementioned standard dynamic model;

[0020] Two RBF neural networks are introduced; one RBF neural network is used to estimate the proposed uncertainty error model; the other RBF neural network is used for dead zone compensation of the system feedforward channel to approximate the established dead zone function.

[0021] An adaptive approach is used to update the established model and dead zone function to improve the control accuracy of the continuum robot; wherein the model includes the standard dynamic model and the uncertainty error model.

[0022] The dead-zone adaptive compensation control system and method for a line-driven continuum robot implementing the embodiments of the present invention have the following advantages:

[0023] By utilizing the excellent fitting performance of neural networks to compensate for the driving dead zone, modeling error, and unknown uncertainties, the influence of the driving dead zone on the control system is effectively mitigated. Furthermore, considering the factors of modeling error and external interference, the system is updated adaptively, which also reduces the accuracy requirements of the mathematical model of the continuum robot. It also has the advantages of high control accuracy, fast response speed, and strong robustness. Attached Figure Description

[0024] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below.

[0025] Figure 1 This is a schematic diagram of the dead zone adaptive compensation control system for a line-driven continuum robot provided in an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of the structure of a continuum robot provided in an embodiment of the present invention;

[0027] Figure 3 A coordinate diagram for modeling a continuum robot provided in an embodiment of the present invention;

[0028] Figure 4 A signal transmission diagram of a system provided in an embodiment of the present invention;

[0029] Figure 5 This is a flowchart illustrating a dead-zone adaptive compensation control method for a line-driven continuum robot provided in an embodiment of the present invention. Detailed Implementation

[0030] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention.

[0031] Throughout this specification, references to "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination.

[0032] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0033] Please refer to Figures 1 to 4 As shown, the dead-zone adaptive compensation control system for a line-driven continuum robot provided in this embodiment of the invention is applied to a controller and includes:

[0034] The first model module is used to establish a standard dynamic model of a continuum robot based on Euler's Bernoulli beam theorem and the constant curvature assumption;

[0035] The dead zone function module is used to establish the dead zone function for the drive dead zone of a line-driven continuum robot.

[0036] The second model module is used to establish an uncertainty error model based on the standard dynamic model.

[0037] A neural network compensator comprising two introduced RBF neural networks; one RBF neural network is used to estimate the proposed uncertainty error model; the other RBF neural network is used for dead-zone compensation of the system feedforward channel to approximate the established dead-zone function.

[0038] An adaptive compensation module is used to update the established model and dead zone function in an adaptive manner to improve the control accuracy of the continuum robot; wherein the model includes the standard dynamic model and the uncertainty error model.

[0039] In this embodiment, the continuum robot structure is referenced. Figure 2 It consists of a spacer disk 3, an elastic drive line 5, and an elastic main body 1; the spacer disk at the end of the continuous robot is called the end spacer disk 4, the spacer disk closest to the motor is called the base spacer disk 2, the spacer disk 3 is fixed on the elastic main body 1, and the elastic drive line 5 is fixed on the end spacer disk 4 and passes through the small hole of the spacer disk 3 to connect to the motor so as to drive the continuous robot to move as a whole.

[0040] The process of establishing the standard dynamic model is as follows:

[0041] 1) Establish the coordinate system of the continuum robot.

[0042] like Figure 3 A coordinate system is established as shown, with the base disk coordinate system connected to the base spacer disk. The X-axis points from the center to the first-stage trunk, the Z-axis is perpendicular to the disk, and the Y-axis is established according to the "right-hand rule." By rotating the base disk coordinate system around the Z-axis, let the rotation angle be γ, the length of the continuum robot trunk be L, and s be the cross-sectional area of ​​the drive line and the trunk. The continuum robot will bend perpendicular to the XOY plane at a bending angle of β.

[0043] 2) Perform energy analysis and calculate the dynamic model of the continuum robot.

[0044] Based on Euler's Bernoulli beam theorem and the assumption of constant curvature, the position of any point P on the main body of the continuum robot can be expressed as:

[0045]

[0046] The kinetic and gravitational potential energy of the continuum robot can be obtained from the above formula. The elastic potential energy of the continuum robot can be given by the Bernoulli formula for rigid bodies:

[0047]

[0048] Combining the above equation, by analyzing the kinetic and potential energy of the continuum robot, and using the Euler-Lagrange equations, the dynamic equations of the continuum robot in the form of second-order partial differential equations can be obtained. After simplification, the standard dynamic model of the continuum robot is finally obtained as follows:

[0049]

[0050] Where q represents the position vector of the continuum robot. The velocity vector represents the velocity vector of the continuum robot. The acceleration vector representing the continuum robot. Let be the system's inertia matrix. N(q) is the matrix related to the Coriolis centripetal force of the system, and G(q) is the matrix related to gravity and elastic force.

[0051] Then, the dead zone of the linearly driven continuum robot is described. The dead zone phenomenon can be represented as:

[0052]

[0053] Where u is the input control signal, i.e., the control input before entering the dead zone, g(u) and h(u) are two smooth nonlinear functions, ψ is the output of the control signal after the dead zone, and d +With d - The dead zone parameter is defined in the above equation, and the dead zone description function covers various cases of driving dead zone.

[0054] Since g(u) and h(u) are two smooth nonlinear functions, the dead zone description function has an inverse:

[0055]

[0056] Where Ψ is the output of the controller in the system, the basis of this scheme for establishing the neural network compensator of the RBF network is to use the inverse of the dead zone of the neural network fitting to compensate through feedforward, that is:

[0057] D(D -1 (Ψ))=Ψ

[0058] The system flowchart of this invention is as follows: Figure 4 The transmission is performed as shown.

[0059] Establish an uncertainty error model for the continuum robot system.

[0060] Assuming a continuum robot has an accurate nominal model, and the controller is modified based on this nominal model, let the nominal model of the continuum robot be:

[0061]

[0062] Where d represents external disturbance. Based on the actual model of the continuum robot, the uncertainty error model of the continuum robot system can be obtained as follows:

[0063]

[0064] ΔM=MM e ,ΔV=VV e ,ΔN=NN e ,ΔG=GG e

[0065] Where d represents external disturbance, e represents error signal, and q represents the position vector of the continuum robot. The velocity vector M represents the velocity vector of the continuum robot. The same meaning refers to the system's inertia matrix, V and N and N(q) have the same meaning; they are matrices related to the Coriolis centripetal force of the system. G and G(q) have the same meaning; they are matrices related to gravity and elastic force. Similarly, M... e In the nominal model The meaning is the same in the nominal model. With V e The same meaning, N e With N in the nominal model e(q)q has the same meaning, G e G in the nominal model e (q) has the same meaning (it should be noted that: the uncertain model includes uncertainty caused by modeling error and external disturbance); then the uncertain model is introduced into the neural network compensator for fitting compensation.

[0066] Design a neural network compensator for a continuum robot.

[0067] The adaptive neural network compensator designed in this invention includes two RBF neural networks. The first RBF network is used to estimate the uncertainty model error model of the continuum robot system proposed in the third step, and the other RBF network is used for the "dead zone" compensation of the system's feedforward channel.

[0068] According to the design, the controller drive dead-time input is:

[0069]

[0070] The inverse of a dead-zone element can be represented in the following equivalent form:

[0071] D -1 (Ψ)=Ψ+Ψ NN

[0072] Among them Ψ NN Represented as:

[0073]

[0074] Based on the universal approximation property of RBF neural networks, we can obtain:

[0075] D(u)=W T ·Φ(u)+Δ(u)

[0076] Ψ NN +ξ(*)=W i T ·Φ i (Ψ)+Δ i (Ψ)

[0077] Where Δ(u), Δ i (Ψ) is the modeling error of the neural network, and W and W i , are the ideal weights, Φ(u) and Φ i (Ψ) is the output of the radial basis function, which is defined as:

[0078]

[0079] Where s is the input vector of the RBF neural network, h i ∈R 2 ,b i≥0, where represents the center vector of the i neurons and the basis width vector of the Gaussian function, respectively. The continuous function E is the activation function, usually chosen as a Gaussian function, with E(c) = exp(-c) and ||*|| representing the Euclidean norm.

[0080] definition and To estimate the weights of the ideal RBF network, the corresponding steps are estimated using two RBF neural networks:

[0081]

[0082]

[0083] definition The weight estimation error of the RBF neural network.

[0084] Depend on Figure 4 It is clear that the ultimate goal is to make the controller's output ψ as consistent as possible with the dead-zone-compensated input Ψ of the continuum robot. Through mathematical calculations, the mathematical relationship between the control input Ψ and the control output ψ driving the dead zone can be obtained, and the controller can be designed accordingly:

[0085] The controller here refers to the controller that drives the output of the continuous robot control system.

[0086]

[0087] Here, Ω(t) represents the model mismatch term, which is derived from Lyapunov theory and other mathematical theorems on stability. The purpose of introducing the model mismatch term here is to theoretically prove that the controller designed by this scheme is strictly stable, and that the set neural network weights and other parameters are uniformly bounded.

[0088] It should be noted that the adaptive approach specifically includes:

[0089] Design the adaptive rate of the neural network;

[0090] Based on the acquired error signal, establish the error function;

[0091] The error function is fed into the adaptive rate of the neural network for compensation and update, thereby updating the established model and dead zone function.

[0092] Specifically, the error signal is:

[0093]

[0094] Where, q d The desired attitude trajectory is set.

[0095] Define the error function as:

[0096]

[0097] Where Λ = Λ T >0.

[0098] The design adaptive rate of the neural network is:

[0099]

[0100] Where S and T are artificially selected positive definite constant symmetric matrices, K1 and K2 are positive constants, and r is the error function; W and W i , are the ideal weights, Φ(u) and Φ i (Ψ) is the output of the radial basis function. and For estimating the weights of an ideal RBF network, for The derivative of F, abbreviated as F-norm, is a matrix norm; for example, the Frobenius norm of matrix A is defined as the sum of the squares of the absolute values ​​of all elements of matrix A.

[0101] The above technical solution utilizes the excellent fitting performance of neural networks to compensate for drive dead zones, modeling errors, and interference from unknown and uncertain errors. It effectively mitigates the impact of drive dead zones on the control system and considers the factors of modeling errors and external disturbances. By updating the model adaptively, it also reduces the accuracy requirements of the mathematical model for the continuum robot. Furthermore, it offers advantages such as high control accuracy, fast response speed, and strong robustness.

[0102] Reference Figure 5 As shown, this embodiment of the invention also provides a dead-zone adaptive compensation control method for a line-driven continuum robot, applied to the dead-zone adaptive compensation control system of the line-driven continuum robot described above. The method includes:

[0103] S101, based on Euler's Bernoulli beam theorem and the assumption of constant curvature, establishes a standard dynamic model of a continuum robot;

[0104] S102, establish the dead zone function for the drive dead zone of the line-driven continuum robot;

[0105] S103, Establish an uncertainty error model based on the standard dynamic model;

[0106] S104, introduce two RBF neural networks; one RBF neural network is used to estimate the proposed uncertainty error model; the other RBF neural network is used for dead zone compensation of the system feedforward channel to approximate the established dead zone function;

[0107] S105, the established model and dead zone function are updated in an adaptive manner to improve the control accuracy of the continuum robot; wherein, the model includes the standard dynamic model and the uncertainty error model.

[0108] Specifically, the adaptive approach includes:

[0109] Design the adaptive rate of the neural network;

[0110] Based on the acquired error signal, establish the error function;

[0111] The error function is fed into the adaptive rate of the neural network for compensation and update, thereby updating the established model and dead zone function.

[0112] It should be noted that the specific implementation steps and beneficial effects in the method embodiments can be referred to the description of the aforementioned system embodiments, and will not be repeated here.

[0113] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0114] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0115] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A dead-zone adaptive compensation control system for a linearly driven continuum robot, applied to a controller, characterized in that, include: The first model module is used to establish a standard dynamic model of a continuum robot based on Euler's Bernoulli beam theorem and the constant curvature assumption; The dead zone function module is used to establish the dead zone function for the drive dead zone of a line-driven continuum robot. The second model module is used to establish an uncertainty error model based on the standard dynamic model. A neural network compensator comprising two introduced RBF neural networks; one RBF neural network is used to estimate the proposed uncertainty error model; the other RBF neural network is used for dead-zone compensation of the system feedforward channel to approximate the established dead-zone function. An adaptive compensation module is used to update the established model and dead zone function in an adaptive manner to improve the control accuracy of the continuum robot; wherein, the model includes the standard dynamic model and the uncertainty error model; The uncertainty error model is designed as follows: ； in, Due to external interference, For error signals, This represents the position vector of the continuum robot. The velocity vector represents the velocity vector of the continuum robot. and The same meaning refers to the system's inertia matrix. and , and The meaning is the same; it is a matrix related to the Coriolis centripetal force of the system. and Both matrices have the same meaning and are related to gravity and elastic force.

2. The dead-zone adaptive compensation control system for a line-driven continuum robot as described in claim 1, characterized in that, The adaptive approach specifically includes: Design the adaptive rate of the neural network; Based on the acquired error signal, establish the error function; The error function is fed into the adaptive rate of the neural network for compensation and update, thereby updating the established model and dead zone function.

3. The dead-zone adaptive compensation control system for a line-driven continuum robot as described in claim 1, characterized in that, The dead-time function can be expressed as: in, It is the input control signal, that is, the control input before entering the dead zone. and They are two smooth nonlinear functions. To control the output of the signal after the dead zone, and This refers to the dead zone parameter.

4. The dead-zone adaptive compensation control system for a line-driven continuum robot as described in claim 3, characterized in that, The standard dynamic model is designed as follows: in, This represents the position vector of the continuum robot. The velocity vector represents the velocity vector of the continuum robot. The acceleration vector representing the continuum robot. Let be the system's inertia matrix. and The matrix is ​​related to the Coriolis centripetal force of the system. This is a matrix related to gravity and elastic force.

5. The dead-zone adaptive compensation control system for a line-driven continuum robot as described in claim 4, characterized in that, The introduced RBF neural network algorithm is designed as follows: After approximation, the resulting fitted function is: in, Indicates the inverse of the dead zone. For the controller output, It is the modeling error of the neural network. and , is the ideal weight. and It is the output of the radial basis function.

6. A dead-zone adaptive compensation control method for a linearly driven continuum robot, characterized in that, The dead-zone adaptive compensation control system for the linearly driven continuum robot according to claim 1, the method comprising: Based on Euler's Bernoulli beam theorem and the assumption of constant curvature, a standard dynamic model of a continuum robot is established. Establish a dead-zone function for the driving dead zone of a line-driven continuum robot; An uncertainty error model is established based on the aforementioned standard dynamic model; Two RBF neural networks are introduced; one RBF neural network is used to estimate the proposed uncertainty error model; the other RBF neural network is used for dead zone compensation of the system feedforward channel to approximate the established dead zone function. An adaptive approach is used to update the established model and dead zone function to improve the control accuracy of the continuum robot; wherein the model includes the standard dynamic model and the uncertainty error model.

7. The dead-zone adaptive compensation control method for a line-driven continuum robot as described in claim 6, characterized in that, The adaptive approach specifically includes: Design the adaptive rate of the neural network; Based on the acquired error signal, establish the error function; The error function is fed into the adaptive rate of the neural network for compensation and update, thereby updating the established model and dead zone function.

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