Fractional order equivalent input disturbance estimation for continuous-time robot control systems and methods

Abstract

The application relates to the technical field of continuum robot control, and provides a continuum robot control system and method based on fractional order equivalent input disturbance estimation. The system comprises a feedback linearization module, which is used for acquiring a dynamic model of the continuum robot and performing linearization processing on the dynamic model; a fractional order equivalent input disturbance estimator, which is used for acquiring a linearized control input, evaluating and inhibiting the influence of external disturbance on the continuum robot according to the linearized control input; and a fractional order feedback controller, which is used for generating a control input of the linearized dynamic model, can perform linearization processing on the dynamic model of the continuum robot, and greatly improves the controllability of a complex system by decoupling and simplifying the design of a control system. The introduction of the fractional order feedback controller enables the system to have more flexible response characteristics in the frequency domain, and can effectively improve the dynamic performance and control precision of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of continuum robot control, and particularly relates to a continuum robot control system and method based on fractional order equivalent input disturbance estimation. BACKGROUND

[0002] A continuum robot is a new type of robot. Unlike traditional rigid-joint robots, a continuum robot has a structure closer to a flexible continuum. Its flexibility and deformation capability enable it to perform tasks in complex and confined spaces. The advantage of a continuum robot is that it can adapt to various shapes and environments using its infinite degrees of freedom, and has been widely used in medical, aerospace, underground exploration, and ocean exploration fields.

[0003] However, due to the flexibility and continuous deformation characteristics of the continuum robot, modeling is complex. The conventional rigid-body dynamics model is difficult to completely and accurately describe the continuum robot, which leads to bias and uncertainty of the dynamics model. Even if the model is established, there may be some dynamic effects that are not considered, making it difficult to achieve precise control of the continuum robot. SUMMARY

[0004] Therefore, it is necessary to provide a continuum robot control system and method based on fractional order equivalent input disturbance estimation, which can at least overcome 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, applied to control a continuum robot, the system comprising:

[0006] a feedback linearization module, configured to obtain a dynamics model of the continuum robot, and perform linearization processing on the dynamics model;

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

[0008] a fractional order feedback controller, configured to generate a control input of the linearized dynamics model, the control input of the fractional order feedback controller being:

[0009]

[0010] wherein v is the control input, q d is a target state that the continuum robot should reach, q is an actual state of the continuum robot, is a second-order derivative of qd representing the expected acceleration, and Kp Kp is a proportional gain function, d Kd is a derivative gain parameter, is the μth derivative of q, d is the μth derivative of q, is the μth derivative of q, μ is the order of fractional derivative, μ∈(0, 2).

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

[0012]

[0013] wherein M(q) is an inertia matrix, C(q, q) is a Coriolis force and centrifugal moment matrix, q is joint velocity, Kq is a rigid moment term, τ is a control input moment, d is an external disturbance term;

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

[0015]

[0016] wherein v is a virtual control input;

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

[0018] The expression of the decoupled linear system is:

[0019]

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

[0021] The state space expression is:

[0022]

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

[0024] According to an embodiment of the present application, the system further comprises:

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

[0026] The fractional order feedback controller is further configured 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.

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

[0028]

[0029] where y = y + d, d is measurement noise, L is a gain matrix of the state observer, v 1f is an input of the state observer, is a state vector of the state observer, is an estimated output of the state observer.

[0030] According to an embodiment of the present application, the state observer is configured to perform disturbance evaluation according to the error between the output and the estimated output, and the formula of the disturbance evaluation is:

[0031]

[0032] where is a pseudo-inverse matrix of B.

[0033] According to an embodiment of the present application, the fractional order feedback controller comprises:

[0034] a low-pass filter configured to filter high-frequency noise to retain low-frequency disturbance, and the expression of the low-pass filter is:

[0035]

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

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

[0038] C(s) = K p + K d s μ

[0039] where K p is a proportional gain, K d is a derivative gain, and s is a Laplace transform variable.

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

[0041]

[0042] wherein, is a disturbance estimation value.

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

[0044] In a second aspect, the embodiments of the present application provide a continuum robot control method based on fractional order equivalent input disturbance estimation, applied to the continuum robot control system based on fractional order equivalent input disturbance estimation as described in the first aspect, and the method comprises:

[0045] obtaining a dynamics model of the continuum robot, performing linearization processing on the dynamics model to obtain a linearized control input of the continuum robot;

[0046] obtaining the linearized control input, and evaluating and suppressing the influence of external disturbance on the continuum robot according to the linearized control input;

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

[0048]

[0049] wherein, v is a control input, q d is a target state that the continuum robot should reach, q is a current actual state of the continuum robot, is a second-order derivative of q d , indicating an expected acceleration, K p is a proportional gain function, K d is a derivative gain parameter, is a μ-order derivative of q d , is a μ-order derivative of q, and μ is an order of fractional derivative, μ∈(0, 2).

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

[0051] Figure 1 A block diagram of a continuous body robot control system based on fractional order equivalent input disturbance estimation is provided for an embodiment of the present application.

[0052] Figure 2 A simulation result diagram of a continuous body robot control system based on fractional order equivalent input disturbance estimation of different orders is provided for an embodiment of the present application.

[0053] Figure 3 A simulation result comparison diagram of control effects of different controllers is provided for an embodiment of the present application.

[0054] Figure 4 A flowchart of a continuous body robot control method based on fractional order equivalent input disturbance estimation is provided for an embodiment of the present application.

[0055] Figure 5 An electronic device diagram is provided for an embodiment of the present application.

[0056] Main element symbol explanation Continuous body robot control system 10 based on fractional order equivalent input disturbance estimation

[0057] Fractional order feedback controller 110

[0058] Feedback linearization module 120

[0059] State observer 130

[0060] Fractional order equivalent input disturbance estimator 140

[0061] Electronic device 20

[0062] Processor 21

[0063] Memory 22

[0064] Steps S100-S300 DETAILED DESCRIPTION

[0065] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not constitute a conflict.

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

[0067] It should be noted that in the embodiments of the present application, the terms "first", "second", etc. are used only for the purpose of distinguishing description, and cannot be understood as indicating or implying relative importance, nor can it be understood as indicating or implying order. The features limited by "first", "second" can explicitly or implicitly include one or more of the features. In the description of the embodiments of the present application, the terms "exemplary" or "for example" are used to represent as an example, illustration or description. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. Rather, the use of "exemplary" or "for example" is intended to present the relevant concept in a specific manner.

[0068] Based on the embodiments in the present application, all other embodiments obtained by a person skilled in the art without creative labor are within the scope of protection of the present application.

[0069] Continuum robots are a new type of robot, unlike 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 using their infinite degrees of freedom, and have been widely used in medical, aerospace, underground exploration and ocean exploration fields.

[0070] However, due to the flexibility and continuous deformation characteristics of continuum robots, modeling is complex. The conventional rigid body dynamics model is difficult to completely and accurately describe the continuum robot, which leads to the deviation and uncertainty of the dynamics model. Even if the model is established, there may be some dynamic effects that are not considered, 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 by the embodiments of the present application, through the combination of fractional order feedback controller and disturbance estimator, show more superior performance when dealing with complex dynamic systems, especially in the face of nonlinear, multi-disturbance environment, in control accuracy, dynamic performance, anti-interference, frequency domain regulation and state observation, etc. It brings improvement, and is suitable for continuum robot control.

[0072] Figure 1 is a block diagram schematic view of a continuum robot control system based on fractional order equivalent input disturbance estimation provided by an embodiment of the present application. As shown in Figure 1 the continuum robot control system based on fractional order equivalent input disturbance estimation 10 comprises 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 configured to obtain a dynamics model of the continuum robot, and perform linearization processing on the dynamics model.

[0074] Specifically, the dynamics model of the continuum robot is as follows:

[0075]

[0076] wherein M(q) is an inertia matrix, C(q, q) is a Coriolis and centrifugal force matrix, q is a joint velocity, Kq is a rigid force moment term, τ is a control input moment, and d is an external disturbance term.

[0077] It can be understood that due to the flexibility and continuous deformation characteristics of the continuum robot, the modeling is complex. The conventional rigid body dynamics model is difficult to completely and accurately describe the continuum robot, which leads to the deviation and uncertainty of the dynamics model. Therefore, the dynamics model of the continuum robot provided by the embodiment of the present application is based on the Lagrange dynamics model, and the external disturbance and uncertainty are added.

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

[0079]

[0080] wherein v is a virtual control input.

[0081] It can be understood that the dynamics model of the continuum robot itself is nonlinear, 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, the feedback linearization module 120 is used to convert the nonlinear model into a linear model by introducing a virtual control input. Through the linearization expression, the complex dynamics 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 embodiments of the present application, the feedback linearization module 120 is further configured 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 as follows:

[0084]

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

[0086] It can be understood that in a complex dynamic system, multiple degrees of freedom can have mutual coupling dynamic effects. The purpose of decoupling is to separate each axis or part of the system, so that each axis can be controlled independently. and represent two independent decoupled subsystems. The control inputs v1 and v2 control two degrees of freedom of the system respectively, and the disturbance terms d e1 and d e2 represent the influences of external disturbances on the two decoupled systems respectively. The significance of the decoupling step is to separate the multiple dynamic effects of the system, so that each subsystem can be designed independently without considering the interference of other degrees of freedom. This significantly simplifies the design difficulty of the controller and improves the controllability and accuracy of the system.

[0087] In the embodiments of the present application, the state space expression is as follows:

[0088]

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

[0090] It can be understood that in control theory, the state space expression is a form of expressing the system state (such as position, speed, etc.) and the input and output in unison. The state space expression enables the dynamic behavior of the system to be expressed in a unified framework, which can facilitate the use of modern control theory to analyze and design controllers. The state space form is particularly suitable for processing multiple input, multiple output (MIMO) systems, and improves the systematicness and robustness of the design.

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

[0092] It can be understood that in actual operation, some state variables of the continuum robot may not be directly measured by sensors, such as the speed or angular acceleration of some 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 for the control system, thereby ensuring more accurate control.

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

[0094]

[0095] where 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] It can be understood that, is a feedback term based on the measurement error, i.e., the difference between the true output and the estimated output. Through this correction term, the state observer 130 can gradually correct its estimated value to make it closer to the actual system state.

[0097] It can be understood that in actual measurement, the output collected by the sensor is often affected by measurement noise. Therefore, the state observer 130 needs to consider the influence of noise, i.e., the true measurement value, so as to still work effectively in a noisy environment. The state observer 130 corrects and filters the noise through the gain matrix, ensuring that the system can maintain accurate estimation 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 can be understood that the gain matrix is a key parameter in the state observer 130, which determines the strength of the state observer 130 in correcting the measurement error. In the embodiments of the present application, the gain matrix is designed by configuring the pole 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 in 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. Proper gain matrix design can significantly improve the dynamic response speed of the observer, ensuring that the system can still provide reliable state estimation when changing rapidly.

[0099] In the embodiments 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 measurement value to calculate the error and perform feedback correction. This process helps the system to continuously correct its state estimation, so that the state estimation gradually tends to be accurate. This feedback mechanism ensures that even if the system state changes are complex and unmeasurable, the state observer 130 can still adjust and correct through the error between the estimated output and the true measurement value, thereby improving the prediction accuracy of the unmeasured state.

[0100] It can be understood that the state observer 130 provided in the embodiments of the present application adjusts through error feedback. Through real-time correction of measurement error, the state observer 130 can gradually approach the true 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 also be estimated in the case of unmeasured state.

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

[0102]

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

[0104] It can be understood that the role of the disturbance evaluation formula is to infer the size and influence of external disturbance through the error between the system output and the estimated output. The state observer can estimate the external disturbance suffered by the system by observing the difference between the actual state and the estimated state, combined with the control input. The disturbance evaluation process can help the system to identify and compensate for the influence of the external environment on the robot control, so that the system has anti-disturbance ability and enhances its robustness in complex environment.

[0105] It can be understood that, is the pseudo-inverse matrix of B. Since matrix B may be singular in some cases and cannot be directly inverted, this problem is solved by the form of pseudo-inverse matrix, so that the system can handle more state variables. The use of pseudo-inverse matrix ensures that even if the system matrix B is not reversible, it can be solved by mathematical method, and then the evaluation and processing of the disturbance are realized.

[0106] It can be understood that through the disturbance evaluation formula, the state observer 130 can effectively identify and compensate the influence of external disturbance. The disturbance estimation not only depends 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, ensuring that the system has strong anti-disturbance ability in complex environment.

[0107] In the embodiment of the present application, the fractional equivalent input disturbance estimator 140 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.

[0108] It can be understood that the fractional 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 equivalent input disturbance estimator 140 can evaluate the external disturbance suffered by the system. This evaluation is based on the characteristics of fractional differentiation, which identifies disturbances by capturing small changes in the system response. It can be understood that the key to evaluating external disturbance is to identify the external interference (such as friction, collision force, random noise in the environment, etc.) suffered by the continuum robot during operation. Through this evaluation, the system can dynamically detect the influence of external factors on the motion control of the robot.

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

[0110] It can be understood that the fractional order equivalent input disturbance estimator 140 adjusts the control system in the manner of fractional order differentiation. Fractional order differentiation has 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 more accurately capture the details of the disturbance and suppress the disturbance in a wider frequency range. It can be understood that fractional order control has significant advantages in dealing with complex and nonlinear systems. Compared with the traditional integer order controller, the fractional order feedback controller 110 shows better filtering effect when dealing with high frequency disturbances, and can adapt to more types of disturbances.

[0111] It can be understood that the fractional order equivalent input disturbance estimator 140 works together with the feedback linearization module, and the feedback linearization module converts the complex nonlinear system into a linear system, and the disturbance estimator evaluates and suppresses the disturbance based on the linearized control input. This cooperation enables the system to deal with 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, and 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 the control input generated by the fractional order feedback controller 110 and is finally used to drive the continuum robot to perform the expected motion. d is the desired joint position (or the desired state), that is, the target state that the continuum robot should reach. q is the actual joint position (or the actual state), that is, the current actual state of the continuum robot. is the second order derivative of q d , that is, the second order derivative of the desired joint position, indicating the desired acceleration. p is a proportional gain function, which is used for proportional adjustment of the control system and determines the amplification degree of the error between the desired position and the actual position. d is a derivative gain parameter, which is used for derivative adjustment of the control system and determines the adjustment of the error between the desired speed and the actual speed. is the μth order derivative of q d , indicating the fractional order derivative of the desired state, which is used to reflect the change trend of the desired motion. is the μth order derivative of q, indicating the fractional order derivative of the actual state, which is used to reflect the change trend of the actual motion. μ is the order of the fractional order derivative, μ ∈ (0, 2), indicating the order of the system differential feedback controller, which can more flexibly adjust the dynamic response of the system.

[0115] In the embodiments of the present application, the fractional order feedback controller 110 includes a low-pass filter for filtering high-frequency noise to retain low-frequency disturbances, and 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, and a is the order of the low-pass filter, and a e (0, 2).

[0118] It can be understood that the main role of the low-pass filter is to make the control system have better anti-interference ability to high-frequency disturbances, and reduce the influence of high-frequency noise on the system. In the control of continuum robots, too high noise may cause the control system to be unstable, and the low-pass filter can ensure that the system can run more smoothly by suppressing these high-frequency components.

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

[0120] C(s) = K p + K d s μ

[0121] wherein K p is the proportional gain, K d is the derivative gain, and s is the Laplace transform variable.

[0122] It can be understood that the fractional order feedback controller 110 can more flexibly adjust the system response compared to the traditional integer order controller. The proportional gain controls the strength of the system response, and the derivative gain is used to adjust the response of the system to the change speed. Through fractional order differentiation, the system can flexibly adjust in different frequency ranges, so that the controller shows better dynamic performance and response sensitivity when dealing with complex systems.

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

[0124]

[0125] wherein, is the disturbance estimation value.

[0126] It can be understood that the control input formula combines the fractional order control strategy with the disturbance estimation. Through the use of 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 cope with external disturbances and make compensation, so as to ensure that the continuum robot can still run stably in a complex environment.

[0127] In the embodiments of the present application, the fractional order feedback controller 110 is further configured to adjust the control input of the continuum robot according to the unmeasured state variables, so as 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 process unmeasured state variables such as position and speed. The state observer 130 provides the estimated values of these unmeasured variables, and the fractional order feedback controller 110 adjusts the control input in real time according to the estimated values, so as to ensure that the control system can achieve higher accuracy and dynamic performance. This adaptive adjustment makes the continuum robot have higher stability and response speed in a dynamic environment.

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

[0130] It can be understood that the frequency domain indicators determine the performance of the control system. The gain margin and the phase margin are used to evaluate the stability of the system, the bandwidth determines the speed of the system response, and the resonance peak value reflects the sensitivity of the system to external disturbances. By adjusting these frequency domain indicators when designing the controller, the system can exhibit the best control effect at different frequencies, so that the robot can achieve a high level in terms of fast response, disturbance rejection and accuracy.

[0131] In the embodiments of the present application, the robot is controlled to reach the expected motion trajectory by adjusting the error between the expected position and the actual position, as well as the feedback of their speed and acceleration. The introduction of the fractional order differential controller makes the system have higher flexibility when adjusting the dynamic tracking and disturbance suppression capability.

[0132] Please refer to Figure 2 , Figure 2 which are simulation result diagrams of the continuum robot control systems based on fractional order equivalent input disturbance estimation of different orders provided by the embodiments of the present application.

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

[0134] Please refer to Figure 3 , Figure 3 which are simulation result comparison diagrams of the control effects of different controllers provided by the embodiments of the present application.

[0135] In the embodiment of the present application, the control effect of the continuum robot control system 10 based on the fractional order equivalent input disturbance estimation provided in the embodiment of the present application is obviously better than that of the control using the extended state observer and the control using the disturbance observer, by comparing the simulation results of the control using the disturbance observer and the control using the extended state observer.

[0136] Figure 4 is a flowchart of a continuum robot control method based on fractional order equivalent input disturbance estimation provided in an embodiment of the present application. As shown in Figure 4 The continuum robot control method based on fractional order equivalent input disturbance estimation at least includes the following steps: S100: obtaining a dynamics model of a continuum robot, performing linearization processing on the dynamics model to obtain a linearized control input of the continuum robot; S200: obtaining the linearized control input, and evaluating and suppressing the influence of external disturbance on the continuum robot according to the linearized control input; and S300: controlling the linearized control input of the continuum robot.

[0137] S100: obtaining a dynamics model of a continuum robot, performing linearization processing on the dynamics 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 a dynamics model of a continuum robot, perform linearization processing on the dynamics model to obtain a linearized control input of the continuum robot. For specific obtaining and processing methods, please refer to Figures 1 to 3 and the corresponding description thereof, which are not repeated here.

[0139] S200: obtaining the linearized control input, and evaluating and suppressing the influence of external disturbance 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 obtaining and evaluation methods, please refer to Figures 1 to 3 and the corresponding description thereof, which are not repeated here.

[0141] S300: controlling 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 the 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] where v is the control input, q d is the target state that the continuum robot should reach, q is the actual state of the continuum robot, is the second derivative of q d representing the desired acceleration, K p is the proportional gain function, K d is the derivative gain parameter, is the mu-th derivative of q, d is the mu-th derivative of q, and mu is the order of the fractional derivative, mu e (0, 2).

[0145] The specific acquisition and processing manner can be known from Figures 1 to 3 and the corresponding description, which will not be repeated here.

[0146] Figure 5 The electronic device 20 is provided by an embodiment of the present application. As shown in Figure 5 , the electronic device 20 at least includes 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 the executable instructions of the processor 21, and the processor 21 is configured to execute the instructions to implement the method for designing a continuum robot controller based on a nonlinear dynamic model as shown in Figure 1 .

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

[0149] ​The program that operates in the electronic device 20 according to an embodiment of the present application can be a program (a program that causes a computer to function) that controls a central processing unit (CPU) or the like to realize the functions of the above-described embodiments according to one aspect of the present application. Then, the information processed by these devices is temporarily stored in a random access memory (RAM) while it is processed, and thereafter, is stored in various ROMs such as a read only memory (Flash ROM), a hard disk drive (HDD), and the like, and is read out, corrected, and written by the CPU as necessary.

[0150] Note that a part of the electronic device 20 according to the above-described embodiments can also be realized by a computer. In this case, a program for realizing the control function can be recorded in a computer-readable recording medium, and the realization can be achieved by reading the program recorded in the recording medium into a computer system and executing it.

[0151] Note that the "computer system" referred to here means a computer system built in the electronic device 20, and a computer system including an OS, a peripheral device, and the like. Further, the "computer-readable recording medium" means a removable medium such as a flexible disk, a magneto-optical disk, a ROM, a CD-ROM, and the like, a storage device such as a hard disk built in the computer system.

[0152] Further, the "computer-readable recording medium" can include a medium that dynamically stores a program for a short time, such as a communication line in the case of transmitting a program via a network such as the Internet or a communication line such as a telephone line, and a medium that stores a program for a fixed time, such as a volatile memory inside a computer system that is a server or a client in this case. Further, the above-described program can be a program for realizing a part of the above-described functions, and can also be a program that can realize the above-described functions by being combined with a program already recorded in the computer system.

[0153] Further, the electronic device 20 according to the above-described embodiments can also be realized as an assembly (a device group) constituted by a plurality of devices. Each device constituting the device group can have a part or all of each function or each functional block of the electronic device 20 according to the above-described embodiments. As the device group, all of each function or each functional block of the electronic device 20 can be possessed.

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

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

[0156] Secondly, the system can real-time evaluate and compensate external disturbances and process unmeasured state variables through the combination of the fractional equivalent input disturbance estimator 140 and the state observer 130. This design not only improves the anti-interference ability of the robot in a complex environment, but also enhances the adaptability of the control input, ensuring high-precision operation of the system in a dynamic environment. In addition, the application of the low-pass filter effectively reduces the influence of high-frequency noise, further improving the control stability and reliability of the system. The present application not only improves the performance of the continuum robot control system, but also has strong practicality and adaptability.

[0157] Those skilled in the art will readily understand that the above description is only the preferred embodiments of the present application, and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A continuous body robot control system based on fractional order equivalent input disturbance estimation applied to control a continuous body robot, characterized by, The system comprises: a feedback linearization module, configured to obtain a disturbance estimation dynamics model of the continuum robot, and linearize the disturbance estimation dynamics model; a fractional equivalent input disturbance estimator, configured to obtain a control input of the linearized disturbance estimation dynamics model, and estimate and suppress the influence of external disturbance on the continuum robot according to the linearized control input; a fractional feedback controller, configured to generate a control input of the linearized disturbance estimation dynamics model, and the control input of the fractional feedback controller is: ； wherein, is a control input to the linearized dynamics model, is a target state that the continuum robot should reach, is the current actual state of the continuum robot, is a second derivative of is a proportional gain function, is a derivative gain parameter, is a first derivative of is a second derivative of is a third derivative of is a fourth derivative of is a fifth derivative of is an order of fractional derivative, ; The dynamics model of the continuum robot is: ； wherein, is the inertia matrix, is the Coriolis and centrifugal force matrix, is the joint velocity, is the rigid body moment term, is the control input moment, is the external disturbance term; The linearization expression of the feedback linearization module is: ； wherein, is the control input to the linearized dynamics model; The feedback linearization module is further configured to decouple the disturbance estimation dynamics model to obtain a decoupled linear system, and obtain a state space expression according to the decoupled linear system; The expression of the decoupled linear system is: ； wherein, and respectively represent the angular accelerations of the two decoupled systems, and respectively represent the two independent parts of the virtual control input, and are respectively the two decoupled equivalent disturbance terms; The state space expression is: ； wherein, is a state variable vector, is a derivative of the state variable, is a system matrix, is an input matrix, is a linearized control input, is a disturbance term influence matrix, is an output variable, is an output matrix.

2. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 1, wherein, The system further comprises: a state observer, configured to estimate an unmeasured state variable of the continuum robot in real time, and feed back the estimation result to the fractional feedback controller; The fractional feedback controller is further configured to adjust the control input of the continuum robot according to the unmeasured state variable, so as to improve the control accuracy and dynamic performance of the continuum robot.

3. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 2, wherein, The equation of the state observer is: ； wherein, , L is a gain matrix of the state observer, is an input of the state observer, is a state vector of the state observer, is an estimated output of the state observer.

4. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 3, wherein, The state observer is configured to perform disturbance estimation according to the error between the output and the estimated output, and the formula of the disturbance estimation is: ； wherein is the pseudo-inverse matrix of 5. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 4, wherein, The fractional feedback controller comprises: a low-pass filter, configured to filter high-frequency noise to retain low-frequency disturbance, and the expression of the low-pass filter is: ； wherein is an expression of a low-pass filter, is a time constant, is an order of the low-pass filter, and .

6. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 5, wherein, The expression of the fractional feedback controller is: ； wherein is a proportional gain, is a derivative gain, is a Laplace transform variable.

7. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 6, wherein, The control input of the continuum robot is: ； wherein, is a disturbance estimate.

8. The continuous body robot control system based on fractional order equivalent input disturbance estimation of claim 2, wherein, The adjustment of the fractional feedback controller is based on a frequency domain index, and the frequency domain index comprises a gain margin, a phase margin, a bandwidth, and a resonance peak value.

9. A control method for a continuum robot based on fractional-order equivalent input perturbation estimation, characterized in that, The method is applied to the continuum robot control system based on the fractional equivalent input disturbance estimation according to any one of claims 1 to 8, and the method comprises: obtaining a disturbance estimation dynamics model of the continuum robot, linearizing the disturbance estimation dynamics model, and obtaining a control input of the linearized disturbance estimation dynamics model of the continuum robot; obtaining a control input of the linearized disturbance estimation dynamics model, and estimating and suppressing the influence of external disturbance on the continuum robot according to the linearized control input; controlling the linearized control input of the continuum robot, and the control input of the fractional feedback controller is: ； wherein, is a control input to the linearized dynamics model, is a target state that the continuum robot should reach, is the current actual state of the continuum robot, is a second derivative of is a proportional gain function, is a derivative gain parameter, is a first derivative of is a second derivative of is a third derivative of is a fourth derivative of is a fractional order derivative of is an order of the fractional derivative, .

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