Continuous body robot control system and method for fractional order equivalent input disturbance estimation

Abstract

The invention relates to the related technical field of continuum robot control, and provides a continuum robot control system and method based on fractional order equivalent input disturbance estimation, and the system comprises a feedback linearization module which is used for obtaining a kinetic model of a continuum robot and carrying out the linearization processing of the kinetic model; the fractional order equivalent input disturbance estimator is used for acquiring the linearized control input and evaluating and inhibiting the influence of external disturbance on the continuum robot according to the linearized control input; and the fractional order feedback controller is used for generating control input of the kinetic model after linearization, linearization processing can be carried out on the kinetic model of the continuum robot, the design of a control system is simplified through decoupling, and the controllability of a complex system is greatly improved. Due to the introduction of the fractional order feedback controller, the system has a more flexible response characteristic in a frequency domain, and the dynamic performance and the control precision of the system can be effectively improved.

Description

Technical Field

[0001] The present application relates to the technical field related to continuum robot control, and in particular to a continuum robot control system and method based on fractional-order equivalent input disturbance estimation. Background Art

[0002] Continuum Robots are a new type of robot. Different from traditional rigid joint robots, the structure of continuum robots is closer to flexible continuum. Its flexibility and deformation ability enable it to perform tasks in complex and restricted spaces. The advantage of continuum robots is that they can adapt to various shapes and environments with their unlimited degrees of freedom. They have been widely used in the fields of medicine, aerospace, underground exploration and ocean exploration.

[0003] However, due to the flexibility and continuous deformation characteristics of the continuum robot, the modeling is complicated. Conventional rigid body dynamics models are difficult to fully and accurately describe the continuum robot, which leads to deviations and uncertainties in the dynamics model. Even if the model is established, there may be some unconsidered dynamic effects, making it difficult to achieve precise control of the continuum robot. Summary of the invention

[0004] In view of this, it is necessary to provide a continuum robot control system and method based on fractional-order equivalent input disturbance estimation, which can overcome at least one of the above defects.

[0005] In a first aspect, an embodiment of the present application provides a continuum robot control system based on fractional-order equivalent input disturbance estimation, which is applied to control a continuum robot, and the system includes:

[0006] A feedback linearization module, used for obtaining a dynamic model of the continuum robot and performing linearization processing on the dynamic model;

[0007] A fractional-order equivalent input disturbance estimator, used to obtain the linearized control input, and to evaluate and suppress the influence of external disturbance on the continuum robot according to the linearized control input;

[0008] A fractional-order feedback controller is used to generate a control input of the linearized dynamic model. The control input of the fractional-order feedback controller is:

[0009]

[0010] Where v is the control input, q d is the target state that the continuum robot should reach, q is the current actual state of the continuum robot, The second derivative of qd represents the desired acceleration, Kp is the proportional gain function, K d is the differential gain parameter, Q d The μ-order derivative of is the μ-order derivative of q, μ is the order of fractional differential, μ∈(0,2).

[0011] According to one embodiment of the present application, the dynamic model of the continuum robot is:

[0012]

[0013] Where M(q) is the inertia matrix, is the Coriolis force and centrifugal force matrix, is the joint velocity, Kq is the rigid torque term, τ is the control input torque, and d is the external disturbance term;

[0014] The linearization expression of the feedback linearization module is:

[0015]

[0016] Among them, v is the virtual control input;

[0017] The feedback linearization module is also used to decouple the dynamic model to obtain a decoupled linear system, and obtain a state space expression according to the decoupled linear system;

[0018] The linear system expression after decoupling is:

[0019]

[0020] in, and They represent the angular accelerations of the two decoupled systems, v1 and v2 represent the two independent parts of the virtual control input, and d e1 and e2 are two decoupled equivalent disturbance terms respectively;

[0021] The state space expression is:

[0022]

[0023] Where x is the state variable vector, is the derivative of the state variable, A is the system matrix, B is the input matrix, v1 is the linearized control input, Bd e1 is the disturbance term influence matrix, y is the output variable, and C is the output matrix.

[0024] According to one embodiment of the present application, the system further includes:

[0025] A state observer, configured to evaluate unmeasured state variables of the continuum robot in real time and feed the evaluation results back to the fractional-order feedback controller;

[0026] The fractional-order feedback controller is also used to adjust the control input of the continuum robot according to the unmeasured state variable to improve the control accuracy and dynamic performance of the continuum robot.

[0027] According to one embodiment of the present application, the equation of the state observer is:

[0028]

[0029] Among them, yδ=y+δ, δ is the measurement noise, L is the gain matrix of the state observer, v 1f is the input of the state observer, is the state vector of the state observer, is the estimated output of the state observer.

[0030] According to one embodiment of the present application, the state observer is used to perform disturbance evaluation based on the error between the output and the estimated output, and the formula for the disturbance evaluation is:

[0031]

[0032] in, is the pseudo-inverse matrix of B.

[0033] According to one embodiment of the present application, the fractional-order feedback controller includes:

[0034] A low-pass filter is used to filter high-frequency noise to retain low-frequency disturbances. The expression of the low-pass filter is:

[0035]

[0036] Wherein, F(s) is the expression of the low-pass filter, T is the time constant, α is the order of the low-pass filter, and α∈(0,2).

[0037] According to one embodiment of the present application, the expression of the fractional-order feedback controller is:

[0038] C(s)=K p +K d s μ

[0039] Among them, K p is the proportional gain, K d is the differential gain, and s is the Laplace transform variable.

[0040] According to one embodiment of the present application, the control input of the continuum robot is:

[0041]

[0042] in, is the disturbance estimate.

[0043] According to an embodiment of the present application, the adjustment of the fractional-order feedback controller is based on frequency domain indicators, and the frequency domain indicators include gain margin, phase margin, bandwidth and resonance peak.

[0044] In a second aspect, an embodiment of the present application provides a continuum robot control method based on fractional-order equivalent input disturbance estimation, which is applied to the continuum robot control system based on fractional-order equivalent input disturbance estimation as described in the first aspect, and the method includes:

[0045] Acquire a dynamic model of the continuum robot, and perform linearization processing on the dynamic model to obtain a linearized control input of the continuum robot;

[0046] Acquire the linearized control input, and evaluate and suppress the influence of external disturbance on the continuum robot according to the linearized control input;

[0047] The linearized control input of the continuum robot is controlled, and the control input of the fractional-order feedback controller is:

[0048]

[0049] Where v is the control input, q d is the target state that the continuum robot should reach, q is the current actual state of the continuum robot, Q d The second derivative of represents the desired acceleration, K p is the proportional gain function, K d is the differential gain parameter, Q d The μ-order derivative of is the μ-order derivative of q, μ is the order of fractional differential, μ∈(0,2).

[0050] The continuum robot control system and method based on fractional-order equivalent input disturbance estimation provided in the embodiments of the present application, through the combination of a fractional-order feedback controller and a disturbance estimator, show superior performance when processing complex dynamic systems, especially in the face of nonlinear and multi-disturbance environments, and bring improvements in control accuracy, dynamic performance, anti-interference, frequency domain regulation and state observation, etc., and are suitable for continuum robot control. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A schematic block diagram of a continuum robot control system based on fractional-order equivalent input disturbance estimation provided in one embodiment of the present application.

[0052] Figure 2 A schematic diagram of simulation results of a continuum robot control system of different orders based on fractional-order equivalent input disturbance estimation provided in one embodiment of the present application.

[0053] Figure 3 A schematic diagram showing a comparison of simulation results of the control effects of different controllers provided in one embodiment of the present application.

[0054] Figure 4 A schematic flow chart of a continuum robot control method based on fractional-order equivalent input disturbance estimation provided in one embodiment of the present application.

[0055] Figure 5 A schematic diagram of an electronic device provided in one embodiment of the present application.

[0056] Main component symbol description Continuum robot control system based on fractional-order equivalent input disturbance estimation 10

[0057] Fractional Order Feedback Controller 110

[0058] Feedback linearization module 120

[0059] State Observer 130

[0060] Fractional Order Equivalent Input Perturbation Estimator 140

[0061] Electronic devices 20

[0062] Processor 21

[0063] Memory 22

[0064] Steps S100-S300 DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0066] It should be noted that, in the embodiments of the present application, "at least one" refers to one or more, and "more" refers to two or more. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art in the present application. The terms used in the specification of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application.

[0067] It should be noted that, in the embodiments of the present application, words such as "first" and "second" are only used for the purpose of distinguishing descriptions, and cannot be understood as indicating or implying relative importance, nor can they be understood as indicating or implying order. Features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a concrete way.

[0068] Based on the implementations in this application, all other implementations obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0069] Continuum Robots are a new type of robot. Different from traditional rigid joint robots, the structure of continuum robots is closer to flexible continuum. Its flexibility and deformation ability enable it to perform tasks in complex and restricted spaces. The advantage of continuum robots is that they can adapt to various shapes and environments with their unlimited degrees of freedom. They have been widely used in the fields of medicine, aerospace, underground exploration and ocean exploration.

[0070] However, due to the flexibility and continuous deformation characteristics of the continuum robot, the modeling is complicated. Conventional rigid body dynamics models are difficult to fully and accurately describe the continuum robot, which leads to deviations and uncertainties in the dynamics model. Even if the model is established, there may be some unconsidered dynamic effects, making it difficult to achieve precise control of the continuum robot.

[0071] The continuum robot control system and method based on fractional-order equivalent input disturbance estimation provided in the embodiments of the present application, through the combination of a fractional-order feedback controller and a disturbance estimator, show superior performance when processing complex dynamic systems, especially in the face of nonlinear and multi-disturbance environments, and bring improvements in control accuracy, dynamic performance, anti-interference, frequency domain regulation and state observation, etc., and are suitable for continuum robot control.

[0072] Figure 1 is a block diagram of a continuum robot control system based on fractional-order equivalent input disturbance estimation provided by an embodiment of the present application. Figure 1 As shown, the continuum robot control system 10 based on fractional-order equivalent input disturbance estimation includes the following parts: a fractional-order feedback controller 110 , a feedback linearization module 120 , a state observer 130 , and a fractional-order equivalent input disturbance estimator 140 .

[0073] In the embodiment of the present application, the feedback linearization module 120 is used to obtain the dynamic model of the continuum robot and perform linearization processing on the dynamic model.

[0074] Specifically, the dynamic model of the continuum robot is:

[0075]

[0076] Where M(q) is the inertia matrix, is the Coriolis force and centrifugal force matrix, is the joint velocity, Kq is the rigid torque term, τ is the control input torque, and d is the external disturbance term.

[0077] It is understandable that due to the flexibility and continuous deformation characteristics of the continuum robot, modeling is complex. Conventional rigid body dynamics models are difficult to fully and accurately describe the continuum robot, which leads to deviations and uncertainties in the dynamics model. Therefore, the dynamics model of the continuum robot provided in the embodiment of the present application is based on the Lagrangian dynamics model, with external disturbances and uncertainties added.

[0078] In the embodiment of the present application, the linearization expression of the feedback linearization module 120 is:

[0079]

[0080] Among them, v is the virtual control input.

[0081] It is understandable that the dynamic model of the continuum robot is nonlinear in itself, and it is relatively complex to directly control such a system, especially when the robot has a high degree of freedom. In order to simplify the control design, a feedback linearization module 120 is used to convert the nonlinear model into a linear model by introducing a virtual control input. Through the linearized expression, the complex dynamic system can be regarded as a simple input-output relationship, which is convenient for using conventional linear control methods. The complex nonlinear problem is simplified to a linear problem that can be handled.

[0082] In the embodiment of the present application, the feedback linearization module 120 is also used to decouple the dynamic model to obtain a decoupled linear system, and obtain a state space expression according to the decoupled linear system.

[0083] Specifically, the decoupled linear system expression is:

[0084]

[0085] in, and They represent the angular accelerations of the two decoupled systems, v1 and v2 represent the two independent parts of the virtual control input, and d e1 and e2 are two decoupled equivalent disturbance terms respectively.

[0086] It is understandable that in complex dynamic systems, multiple degrees of freedom may have mutually coupled dynamic effects. The purpose of decoupling is to separate the various motion axes or parts of the system so that each axis can be controlled independently. and Represent two independent decoupled subsystems. The control inputs v1 and v2 control the two degrees of freedom of the system respectively, and the disturbance term d e1 and e2 This means that the two decoupled systems are affected by external disturbances separately. The significance of the decoupling step is that it separates the multiple dynamic effects of the system, so that each subsystem can be designed with a separate controller without considering the interference of other degrees of freedom. This significantly simplifies the difficulty of controller design and improves the controllability and accuracy of the system.

[0087] In the embodiment of the present application, the state space expression is:

[0088]

[0089] Where x is the state variable vector, is the derivative of the state variable, A is the system matrix, B is the input matrix, v1 is the linearized control input, Bd e1 is the disturbance term influence matrix, y is the output variable, and C is the output matrix.

[0090] It is understandable that in control theory, state-space expressions are a form of unified representation of the relationship between system states (such as position, velocity, etc.) and inputs and outputs. State-space expressions allow the dynamic behavior of the system to be expressed in a unified framework, making it easy to use modern control theory to analyze and design controllers. The state-space form is particularly suitable for dealing with multiple-input, multiple-output (MIMO) systems, improving the systematicity and robustness of the design.

[0091] In the embodiment of the present application, the state observer 130 is used to evaluate the unmeasured state variables of the continuum robot in real time, and feed the evaluation results back to the fractional-order equivalent input disturbance estimator 140.

[0092] It is understandable that in actual operation of the continuum robot, there may be some state variables that cannot be directly measured by sensors, such as the velocity or angular acceleration of certain joints. Therefore, it is necessary to estimate these unmeasured state variables through the state observer 130. By evaluating these states in real time, the state observer 130 can provide more comprehensive information to the control system, thereby ensuring more precise control.

[0093] In the embodiment of the present application, the equation of the state observer 130 is:

[0094]

[0095] Among them, y δ =y+δ, δ is the measurement noise, L is the gain matrix of the state observer 130, v 1f is the input of the state observer 130, is the state vector of the state observer 130, is the estimated output of the state observer 130.

[0096] Understandably, It is a feedback term that performs correction based on the measurement error, that is, the difference between the true output and the estimated output. Through this correction term, the state observer 130 can gradually correct its estimate to make it closer to the actual system state.

[0097] It is understandable that in the actual measurement process, the output collected by the sensor is often affected by the measurement noise. Therefore, the state observer 130 needs to take into account the noise effect, that is, the true measurement value, so that it can still work effectively in a noisy environment. The state observer 130 filters and corrects the noise through the gain matrix to ensure that the system can maintain an accurate estimate of the state variables in the presence of noise. This is very important for improving the robustness and reliability of the system in actual complex environments.

[0098] It is understandable that the gain matrix is ​​a key parameter in the state observer 130, which determines the strength of the state observer 130 to correct the measurement error. In an embodiment of the present application, the gain matrix is ​​designed by configuring the poles of the control system to ensure that the state observer 130 can quickly and accurately track the system state. In other embodiments, an optimization algorithm can also be used to configure the gain matrix, which is not limited by the present application. By reasonably selecting the value of the gain matrix, the state observer 130 can suppress the influence of high-frequency noise while maintaining the estimation accuracy. Appropriate gain matrix design can significantly improve the dynamic response speed of the observer, ensuring that the system can still provide reliable state estimates when changing rapidly.

[0099] In the embodiment of the present application, the estimated output is the system output estimated by the state observer 130, which is used to compare with the actual measured value to calculate the error and perform feedback correction. This process helps the system to continuously correct its state estimate, making the state estimate gradually more accurate. This feedback mechanism ensures that even if the system state changes are complex and immeasurable, the state observer 130 can still adjust and correct the error between the estimated output and the actual measured value, thereby improving the prediction accuracy of the unmeasured state.

[0100] It is understandable that the state observer 130 provided in the embodiment of the present application is adjusted by error feedback. By correcting the measurement error in real time, the state observer 130 can gradually approach the real state, thereby improving the accuracy of the estimation. In addition, the state observer 130 uses the known model of the system for prediction, so that the internal state of the system can be estimated even when the state is not measured.

[0101] In the embodiment of the present application, the state observer 130 is used to perform disturbance evaluation according to the error between the output and the estimated output. The formula for disturbance evaluation is:

[0102]

[0103] in, is the pseudo-inverse matrix of B.

[0104] It is understandable that the role of the disturbance assessment formula is to infer the size and impact of external disturbances through the error between the system output and the estimated output. The state observer can estimate the external disturbances to the system by observing the difference between the actual state and the estimated state, combined with the control input. The disturbance assessment process can help the system identify and compensate for the impact of the external environment on the robot control, making the system anti-disturbance capable and enhancing its robustness in complex environments.

[0105] Understandably, is the pseudo-inverse matrix of B. Since in some cases the matrix B may be singular and cannot be directly inverted, this problem is solved in the form of a pseudo-inverse matrix, so that the system can handle more state variables. The use of the pseudo-inverse matrix ensures that even if the system matrix B is not invertible, it can be solved by mathematical methods, thereby achieving the evaluation and processing of disturbances.

[0106] It can be understood that, through the disturbance evaluation formula, the state observer 130 can effectively identify and compensate for the impact of external disturbances. Disturbance estimation not only relies on the error between the system output and the estimated output, but also combines the correction of the pseudo-inverse matrix and the control input to ensure that the system has strong anti-disturbance ability in complex environments.

[0107] In the embodiment of the present application, the fractional-order equivalent input disturbance estimator 140 is used to obtain the linearized control input, and evaluate and suppress the influence of the external disturbance on the continuum robot according to the linearized control input.

[0108] It is understandable that the fractional-order equivalent input disturbance estimator 140 first obtains the linearized control input (i.e., virtual control input). By analyzing these inputs and the state feedback of the system, the fractional-order equivalent input disturbance estimator 140 can evaluate the external disturbance to the system. This evaluation is based on the characteristics of fractional-order differentials, and the disturbance is identified by capturing small changes in the system response. It is understandable that the key to evaluating external disturbances is to identify the external interference (such as friction, collision force, random noise in the environment, etc.) to which the continuum robot is subjected during operation. Through this evaluation, the system can dynamically detect the impact of external factors on the robot's motion control.

[0109] It is understandable that after evaluating the external disturbance, the fractional-order equivalent input disturbance estimator 140 suppresses these disturbances by adjusting the control input. Through the fractional-order feedback control strategy, the fractional-order equivalent input disturbance estimator 140 compensates the control input and offsets the impact of the external disturbance, so that the system can continue to operate according to the expected trajectory and state. The key to suppressing external disturbances is to ensure that the robot can still operate stably under disturbance. This suppression capability greatly enhances the adaptability and robustness of the continuum robot in complex environments, enabling it to cope with various external uncertainties and maintain precise control of the system.

[0110] It is understandable that the fractional-order equivalent input disturbance estimator 140 uses fractional-order differentials to adjust the control system. Fractional-order differentials have more flexible dynamic response characteristics than integer-order control and can respond to external disturbances in multiple frequency domains. Therefore, the fractional-order equivalent input disturbance estimator 140 can capture the details of the disturbance more accurately and suppress the disturbance over a wider frequency range. It is understandable that fractional-order control has significant advantages in dealing with complex and nonlinear systems. Compared with traditional integer-order controllers, the fractional-order feedback controller 110 exhibits better filtering effects when dealing with high-frequency disturbances and can adapt to more types of disturbances.

[0111] It is understandable that the fractional-order equivalent input disturbance estimator 140 works together with the feedback linearization module, the feedback linearization module transforms the complex nonlinear system into a linear system, and the disturbance estimator performs disturbance evaluation and suppression based on the linearized control input. This synergy enables the system to handle complex external disturbances under a simplified control framework.

[0112] In the embodiment of the present application, the fractional-order feedback controller 110 is used to generate the control input of the linearized dynamic model. The control input of the fractional-order feedback controller 110 is:

[0113]

[0114] It can be understood that v is a control input signal, which is a control input generated by the fractional-order feedback controller 110 and is ultimately used to drive the continuum robot to perform the desired motion. d is the desired joint position (or desired state), i.e., the target state that the continuum robot should reach. q is the actual joint position (or actual state), i.e., the current actual state of the continuum robot. Q d The second derivative of K, that is, the second derivative of the desired joint position, represents the desired acceleration. p K is the proportional gain function, which is used for proportional adjustment of the control system and determines the degree of error amplification between the desired position and the actual position. d It is the differential gain parameter, which is used for differential adjustment of the control system and determines the adjustment of the error between the desired speed and the actual speed. Q d The μ-order derivative of represents the fractional-order differential of the desired state and is used to reflect the changing trend of the desired motion. is the μ-order derivative of q, which represents the fractional differential of the actual state and is used to reflect the changing trend of the actual motion. μ is the order of the fractional differential, μ∈(0,2), which represents the order of the system differential feedback controller and can more flexibly adjust the dynamic response of the system.

[0115] In the embodiment of the present application, the fractional-order feedback controller 110 includes a low-pass filter, which is used to filter high-frequency noise to retain low-frequency disturbances. The expression of the low-pass filter is:

[0116]

[0117] Wherein, F(s) is the expression of the low-pass filter, T is the time constant, α is the order of the low-pass filter, and α∈(0,2).

[0118] It is understandable that the main function of the low-pass filter is to make the control system have better anti-interference ability to high-frequency disturbances and reduce the impact of high-frequency noise on the system. In the control of continuum robots, excessive noise may cause the control system to be unstable. The low-pass filter suppresses these high-frequency components to ensure that the system can run more smoothly.

[0119] In the embodiment of the present application, the expression of the fractional-order feedback controller 110 is:

[0120] C(s)=K p +K d s μ

[0121] Among them, K p is the proportional gain, K d is the differential gain, and s is the Laplace transform variable.

[0122] It can be understood that the fractional order feedback controller 110 can adjust the system response more flexibly than the traditional integer order controller. The proportional gain controls the strength of the system response, and the differential gain is used to adjust the system response to the changing speed. Through the fractional order differential, the system can be flexibly adjusted within different frequency ranges, so that the controller exhibits better dynamic performance and response sensitivity when processing complex systems.

[0123] In the embodiment of the present application, the control input of the continuum robot is:

[0124]

[0125] in, is the disturbance estimate.

[0126] It can be understood that the control input formula combines the fractional-order control strategy with the disturbance estimation. By using the fractional-order derivative, the system can more accurately capture the difference between the target state and the current state and adjust according to this information. In addition, the introduction of the disturbance estimation value allows the system to effectively respond to external disturbances and compensate, thereby ensuring that the continuum robot can still operate stably in complex environments.

[0127] In the embodiment of the present application, the fractional-order feedback controller 110 is also used to adjust the control input of the continuum robot according to the unmeasured state variables to improve the control accuracy and dynamic performance of the continuum robot.

[0128] It can be understood that, through the design of the fractional-order feedback controller 110, the system can handle unmeasured state variables, such as position, speed, etc. The state observer 130 will provide estimated values ​​of these unmeasured variables, and the fractional-order feedback controller 110 will adjust the control input in real time according to these estimated values ​​to ensure that the control system can achieve higher accuracy and dynamic performance. This adaptive adjustment enables the continuum robot to have higher stability and response speed in a dynamic environment.

[0129] In the embodiment of the present application, the adjustment of the fractional-order feedback controller 100 is based on frequency domain indicators, which include gain margin, phase margin, bandwidth and resonance peak.

[0130] It is understandable that frequency domain indicators determine the performance of the control system. Gain margin and phase margin are used to evaluate the stability of the system, bandwidth determines the speed of system response, and resonance peak reflects the sensitivity of the system to external disturbances. By adjusting these frequency domain indicators when designing the controller, the system can show the best control effect at different frequencies, so that the robot can achieve a high level in terms of fast response, anti-interference and accuracy.

[0131] In the embodiment of the present application, the robot is controlled to achieve the desired motion trajectory by adjusting the error between the desired position and the actual position, as well as the feedback of their velocity and acceleration. The introduction of the fractional-order differential controller enables the system to have higher flexibility in adjusting dynamic tracking and disturbance suppression capabilities.

[0132] Please also read Figure 2 , Figure 2 It is a schematic diagram of simulation results of continuum robot control systems of different orders based on fractional-order equivalent input disturbance estimation provided in an embodiment of the present application.

[0133] In the embodiment of the present application, during the simulation process, a periodic disturbance with a maximum frequency of 3πrad / s is added at the 3rd second, and a ramp disturbance is added at the 10th second. Figure 3 As shown in Figure 1, the higher the order α of the low-pass filter, the stronger its ability to suppress periodic disturbances. When α>1, the output caused by ramp disturbances can be completely suppressed. When α≤1, the output caused by ramp disturbances can also be suppressed to a certain extent.

[0134] Please also read Figure 3 , Figure 3 It is a schematic diagram comparing simulation results of the control effects of different controllers provided in the embodiments of the present application.

[0135] In an embodiment of the present application, the continuum robot control system 10 based on fractional-order equivalent input disturbance estimation provided in the embodiment of the present application is compared with the simulation results of control using a disturbance observer and control using an extended state observer. It can be found that the control effect of the present application is significantly better than control using an extended state observer and control using a disturbance observer.

[0136] Figure 4 FIG. 1 is a flow chart of a continuum robot control method based on fractional-order equivalent input disturbance estimation provided by an embodiment of the present application. Figure 4 As shown, the continuum robot control method based on fractional-order equivalent input disturbance estimation includes at least the following steps: S100: obtaining the dynamic model of the continuum robot, and linearizing the dynamic model to obtain the linearized control input of the continuum robot; S200: obtaining the linearized control input, and evaluating and suppressing the influence of external disturbances on the continuum robot according to the linearized control input; S300: controlling the linearized control input of the continuum robot.

[0137] S100: Acquire a dynamic model of the continuum robot, and perform linearization processing on the dynamic model to obtain a linearized control input of the continuum robot.

[0138] In step S100 of the embodiment of the present application, the continuum robot control system 10 based on fractional-order equivalent input disturbance estimation is used to obtain the dynamic model of the continuum robot and linearize the dynamic model to obtain the linearized control input of the continuum robot. For specific acquisition and processing methods, please refer to Figures 1 to 3 And the corresponding description will not be repeated here.

[0139] S200: Obtain a linearized control input, and evaluate and suppress the influence of external disturbances on the continuum robot according to the linearized control input.

[0140] In step S200 of the embodiment of the present application, the continuum robot control system 10 based on fractional-order equivalent input disturbance estimation is used to obtain the linearized control input, and evaluate and suppress the influence of external disturbance on the continuum robot according to the linearized control input. For specific acquisition and evaluation methods, please refer to Figures 1 to 3 And the corresponding description will not be repeated here.

[0141] S300: Control the linearized control input of the continuum robot.

[0142] In step S300 of the embodiment of the present application, the continuum robot control system 10 based on fractional-order equivalent input disturbance estimation is used to control the linearized control input of the continuum robot. The control input of the fractional-order feedback controller is:

[0143]

[0144] Among them, v is the control input, qd is the target state that the continuum robot should reach, and q is the current actual state of the continuum robot. The second derivative of qd represents the desired acceleration, K p is the proportional gain function, K d is the differential gain parameter, Q d The μ-order derivative of is the μ-order derivative of q, μ is the order of fractional differential, μ∈(0,2).

[0145] Please refer to the specific acquisition and processing methods. Figures 1 to 3 And the corresponding description will not be repeated here.

[0146] Figure 5 This is an electronic device 20 provided in an embodiment of the present application. Figure 5 As shown, the electronic device 20 includes at least the following parts: a processor 21 and a memory 22 .

[0147] In the embodiment of the present application, the memory 22 is used to store instructions executable by the processor 21, and the processor 21 is configured to implement the following when executing the instructions: Figure 1 The continuum robot controller design method based on nonlinear dynamic model is shown.

[0148] In an embodiment of the present application, a computer-readable storage medium includes instructions, and the instructions instruct a device to execute the continuum robot control method for fractional-order equivalent input disturbance estimation as in the second aspect. For example, the instructions instruct the device to execute Figure 2 A continuum robot control method based on fractional-order equivalent input disturbance estimation is shown.

[0149] The program operating in the electronic device 20 involved in one embodiment of the present application may be a program (a program that enables a computer to function) that controls a central processing unit (CPU) and the like to realize the functions of the above-mentioned embodiment involved in one scheme of the present invention. Then, the information processed by these devices is temporarily stored in a random access memory (RAM) during its processing, and then stored in various ROMs such as a read-only memory (Flash ROM) and a hard disk drive (HDD), and is read, modified, and written by the CPU as needed.

[0150] It should be noted that part of the electronic device 20 of the above embodiment may be implemented by a computer. In this case, a program for implementing the control function may be recorded in a computer-readable recording medium and implemented by reading the program recorded in the recording medium into a computer system and executing it.

[0151] It should be noted that the "computer system" mentioned here refers to a computer system built into the electronic device 20, and adopts a computer system including hardware such as an OS and peripheral devices. In addition, "computer-readable recording medium" refers to removable media such as a floppy disk, a magneto-optical disk, a ROM, a CD-ROM, and a storage device such as a hard disk built into the computer system.

[0152] Furthermore, "computer-readable recording media" may include: media that dynamically store programs for a short period of time, such as communication lines when sending programs via networks such as the Internet or communication lines such as telephone lines; and media that store programs for a fixed period of time, such as volatile memories inside computer systems that serve as servers or clients in this case. In addition, the above-mentioned program may be a program for realizing a part of the above-mentioned functions, or a program that can realize the above-mentioned functions by combining with a program already recorded in a computer system.

[0153] In addition, the electronic device 20 in the above-mentioned embodiment can also be implemented as a collection (device group) composed of multiple devices. Each device constituting the device group can have a part or all of the functions or functional blocks of the electronic device 20 in the above-mentioned embodiment. As a device group, it is sufficient to have all the functions or functional blocks of the electronic device 20.

[0154] In the embodiment of the present application, the electronic device 20 may be a continuum robot.

[0155] The continuum robot control system 10 and method based on fractional-order equivalent input disturbance estimation provided in the embodiment of the present application can linearize the dynamic model of the continuum robot through the use of a feedback linearization module, and simplify the design of the control system by decoupling, thereby greatly improving the controllability of the complex system. The introduction of the fractional-order feedback controller 110 enables the system to have more flexible response characteristics in the frequency domain, which can effectively improve the dynamic performance and control accuracy of the system, and can also perform adaptive adjustments to external disturbances of different frequencies, thereby ensuring the stability and robustness of the system.

[0156] Secondly, the system can evaluate and compensate for external disturbances in real time and process unmeasured state variables by combining the fractional-order equivalent input disturbance estimator 140 with the state observer 130. This design not only improves the robot's anti-interference ability in complex environments, but also enhances the adaptability of control inputs, ensuring high-precision operation of the system in dynamic environments. In addition, the application of low-pass filters effectively reduces the impact of high-frequency noise, further improving the control stability and reliability of the system. While improving the performance of the continuum robot control system, the present application also has strong practicality and adaptability.

[0157] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A continuum robot control system based on fractional-order equivalent input disturbance estimation, applied to control a continuum robot, characterized in that: The system comprises: A feedback linearization module, used for obtaining a dynamic model of the continuum robot and performing linearization processing on the dynamic model; A fractional-order equivalent input disturbance estimator, used to obtain the linearized control input, and to evaluate and suppress the influence of external disturbance on the continuum robot according to the linearized control input; A fractional-order feedback controller is used to generate a control input of the linearized dynamic model. The control input of the fractional-order feedback controller is: Where v is the control input, q d is the target state that the continuum robot should reach, q is the current actual state of the continuum robot, Q d The second derivative of represents the desired acceleration, K p is the proportional gain function, K d is the differential gain parameter, Q d The μ-order derivative of is the μ-order derivative of q, μ is the order of fractional differential, μ∈(0,2).

2. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 1, characterized in that: The dynamic model of the continuum robot is: Where M(q) is the inertia matrix, is the Coriolis force and centrifugal force matrix, is the joint velocity, Kq is the rigid torque term, τ is the control input torque, and d is the external disturbance term; The linearization expression of the feedback linearization module is: Among them, v is the virtual control input; The feedback linearization module is also used to decouple the dynamic model to obtain a decoupled linear system, and obtain a state space expression according to the decoupled linear system; The linear system expression after decoupling is: in, and They represent the angular accelerations of the two decoupled systems, v1 and v2 represent the two independent parts of the virtual control input, and d e1 and e2 are two decoupled equivalent disturbance terms respectively; The state space expression is: Where x is the state variable vector, is the derivative of the state variable, A is the system matrix, B is the input matrix, v1 is the linearized control input, Bd e1 is the disturbance term influence matrix, y is the output variable, and C is the output matrix.

3. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 2, characterized in that: The system further comprises: A state observer, configured to evaluate unmeasured state variables of the continuum robot in real time and feed the evaluation results back to the fractional-order feedback controller; The fractional-order feedback controller is also used to adjust the control input of the continuum robot according to the unmeasured state variable to improve the control accuracy and dynamic performance of the continuum robot.

4. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 3, characterized in that: The equation of the state observer is: Among them, y δ =y+δ, δ is the measurement noise, L is the gain matrix of the state observer, v 1f is the input of the state observer, is the state vector of the state observer, is the estimated output of the state observer.

5. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 4, characterized in that: The state observer is used to perform disturbance evaluation according to the error between the output and the estimated output. The formula for the disturbance evaluation is: in, is the pseudo-inverse matrix of B.

6. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 5, characterized in that: The fractional-order feedback controller comprises: A low-pass filter is used to filter high-frequency noise to retain low-frequency disturbances. The expression of the low-pass filter is: Wherein, F(s) is the expression of the low-pass filter, T is the time constant, α is the order of the low-pass filter, and α∈(0,2).

7. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 6, characterized in that: The expression of the fractional-order feedback controller is: C(s)=K p +k d s μ Among them, K p is the proportional gain, K d is the differential gain, and s is the Laplace transform variable.

8. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 7, characterized in that: The control input of the continuum robot is: in, is the disturbance estimate.

9. The continuum robot control system based on fractional-order equivalent input disturbance estimation according to claim 3, characterized in that: The adjustment of the fractional-order feedback controller is based on frequency domain indicators, which include gain margin, phase margin, bandwidth and resonance peak.

10. A continuum robot control method based on fractional-order equivalent input disturbance estimation, characterized in that: Applied to a continuum robot control system based on fractional-order equivalent input disturbance estimation as claimed in any one of claims 1 to 9, the method comprising: Acquire a dynamic model of the continuum robot, and perform linearization processing on the dynamic model to obtain a linearized control input of the continuum robot; Acquire the linearized control input, and evaluate and suppress the influence of external disturbance on the continuum robot according to the linearized control input; The linearized control input of the continuum robot is controlled, and the control input of the fractional-order feedback controller is: Where v is the control input, q d is the target state that the continuum robot should reach, q is the current actual state of the continuum robot, Q d The second derivative of represents the desired acceleration, K p is the proportional gain function, K d is the differential gain parameter, Q d The μ-order derivative of is the μ-order derivative of q, μ is the order of fractional differential, μ∈(0,2).

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