Continuous body robot robust sliding mode control method based on nonlinear extended state observer

Abstract

The invention discloses a robust sliding mode control method for a continuum robot based on a nonlinear extended state observer, and belongs to the technical field of robot control. Aiming at the problem that the continuum robot suffers from model uncertainty and external unknown interference in the operation process, the method comprises the following steps: firstly, establishing a Lagrange dynamical model of the continuum robot, and uniformly regarding the uncertain factors as comprehensive disturbance terms; secondly, designing a nonlinear extended state observer (NESO) to observe and estimate the system state and the comprehensive disturbance in real time; then, a sliding mode controller is designed based on an estimation error of the observer, and a saturation function (sat function) is adopted to construct an approaching law to weaken buffeting. According to the method, the consistency bounded property of signals of the closed-loop system is proved through the Lyapunov stability theory. Simulation results show that the method has good robustness and tracking performance when processing complex disturbances and faults.

Description

Technical Field

[0001] This invention belongs to the field of medical robot technology, specifically relating to a robust trajectory tracking control method for a continuum robot for intracavitary surgery. It is particularly suitable for motion control of continuum surgical robots with parameter uncertainties and external environmental influences in complex and restricted environments such as minimally invasive surgery and natural cavity intervention. Background Technology

[0002] With the increasing demand for minimally invasive surgery in modern medicine, traditional rigid surgical robots are gradually revealing limitations in terms of space occupation, flexibility, and safety. Continuum surgical robots (CSRs), due to their continuous flexible structure, can mimic the natural deformation of biological limbs, exhibiting excellent compliance and spatial manipulation capabilities, providing novel solutions for neurosurgery, otolaryngology, and cardiovascular interventional procedures. However, continuum robots lack discrete rigid connection points and face complex tissue environments during surgery, posing significant challenges to their accurate modeling and control. Existing technologies regarding the modeling and control of continuum robots mainly suffer from the following problems:

[0003] (1) It is difficult to balance modeling accuracy and computational efficiency. Existing geometric modeling methods (such as constant curvature models) are simple in structure and fast in solution, but their accuracy is severely limited under load or multi-segment coupling conditions; while methods based on continuum mechanics (such as Cosserat rod theory) are highly accurate, but involve solving complex nonlinear differential equations, resulting in extremely high computational costs, which makes it difficult to meet the millisecond-level real-time control requirements of surgical robots.

[0004] (2) Insufficient robustness and adaptability of the control system. Continuum robots have strong nonlinear and strongly coupled dynamic characteristics. Existing control strategies often rely on simplified kinematic models, ignoring factors such as material nonlinearity, rope friction, and external load disturbances. When the robot comes into contact with human tissue or the environment changes dynamically, existing linear control strategies are difficult to cope with effectively, leading to a decrease in trajectory tracking accuracy and even safety hazards.

[0005] (3) Weak ability to handle multi-source disturbances. There are many uncertainties in actual surgery, including actuator failure and external environmental disturbances. Although some existing robust control or adaptive control can suppress disturbances to a certain extent, they still lack a fast observation and compensation mechanism when facing complex nonlinear coupled disturbances.

[0006] In summary, establishing a control framework that can guarantee both real-time computation and model accuracy, and effectively addressing the disturbance rejection problem under strong nonlinear coupling, is a key technical issue that urgently needs to be solved for the clinical application of continuum surgical robots. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a sliding mode control method for a continuum robot based on a nonlinear extended state observer. This method utilizes a nonlinear extended observer to estimate the system's overall disturbance and fault information in real time, and incorporates this information into the sliding mode control law for compensation. Simultaneously, a saturated function is used to design a reaching law to suppress chattering, thereby effectively reducing the impact of uncertainties on system stability.

[0008] The core idea of ​​this invention is as follows: A dynamic model based on the Lagrange equation is constructed for a continuum robot, and model uncertainties and external environmental disturbances are uniformly summarized into a lumped disturbance term. A nonlinear extended state observer (NESO) is introduced to perform real-time observation and high-precision estimation of the system state and the aforementioned lumped disturbances, thereby achieving proactive compensation for unknown dynamics and faults. Based on this, a sliding mode controller is designed, utilizing the saturation function (sat) to optimize the reaching law to suppress high-frequency chattering and improve control quality. Finally, based on Lyapunov stability theory, the convergence of the closed-loop system is proved, ensuring that the robot can still achieve accurate and stable tracking of the desired trajectory under multi-source disturbance coupling conditions, and that all error signals remain consistently bounded.

[0009] Firstly, this invention provides a robust sliding mode control architecture for continuum robots based on NESO. Specifically, it includes:

[0010] (1) Construct a dynamic model of the continuum robot.

[0011] Considering the robot's physical parameters, and applying the Euler-Lagrange equations, the dynamic model of the continuum surgical robot is derived as follows:

[0012]

[0013] Where q = [q1 q2] Τ Let M(q) be the joint angle and M(q) be the inertia matrix. Let G(q) be the Coriolis force-centrifugal force matrix, G(q) be the gravity term, B(q) be the Jacobian matrix, u be the control input, and d be the external disturbance. The influence of uncertainties on the model is considered, and reasonable compensation is implemented in the control system design. The model uncertainties are as follows:

[0014]

[0015] The interference terms can be written in the following form:

[0016]

[0017] The dynamic model of the continuum robot can then be rewritten as follows:

[0018]

[0019] Subsequently, by introducing model uncertainty, the dynamic model is transformed into the following form:

[0020]

[0021] Rewrite the system in state-space form:

[0022]

[0023] b(q) = M0 -1 B0

[0024] Where x1 and x2 are the position and velocity state variables, respectively, and -M0 -1 (x)w represents the combined perturbation to be observed.

[0025] (2) Design a nonlinear extended state observer (NESO)

[0026] Systems are often affected by uncertainties such as external disturbances and modeling errors. In order to effectively compensate for these unknown disturbances in the controller and improve the control accuracy and robustness of the system, a nonlinear extended state observer is designed to estimate the comprehensive disturbances of the system in real time.

[0027] Define the state variables for the system as: x1 = q, and -M0 -1 If (x)w is considered as the new state x3(t), then

[0028]

[0029] The above equation can be used to construct a nonlinear extended state observer:

[0030]

[0031] Where z1(t), z2(t), z3(t) are state estimates, e1(t) = z1(t) - x1(t) is the observation error, a1, a2, a3 are the observer gains, and fal(.) is a nonlinear function.

[0032]

[0033] This compensation mechanism can achieve real-time tracking of unknown disturbances by extending the state observer without relying on a precise actuator model, ensuring that the actual input remains sufficiently effective. This module is an important component of the controller structure of this invention.

[0034] (3) Design an anti-chattering sliding mode controller based on saturation function.

[0035] The sliding surface is designed as

[0036]

[0037] Where, e = qq d For the position tracking error, q d Let λ be the desired trajectory and λ be the sliding surface parameter.

[0038] Design a sliding mode reaching law. To mitigate chattering in traditional sliding mode control, a saturation function is used instead of the sign function, and the reaching law is designed as follows:

[0039]

[0040] Where k is the control gain. The saturation function is used to reduce chattering; the final control law u includes equivalent control, switching control, and observer compensation terms, and its form satisfies:

[0041]

[0042] The unknown faults and disturbances in the system are offset by z3(t).

[0043] (4) System stability analysis

[0044] Here we quote a lemma: Suppose there exists a continuous positive definite function V(x) > 0, whose derivative satisfies

[0045] If c1 and c2 are both positive constants, then the solution x(t) of the system is uniformly bounded.

[0046] The design is based on Lyapunov functions as follows:

[0047]

[0048] Define the estimation error:

[0049] e1=z1-x1, e2=z2-x2, e3=z3-x3

[0050] Substitute the observer's estimation:

[0051]

[0052] Differentiating with respect to V1, we get

[0053]

[0054] Eliminating cross terms using inequalities for any ε > 0, we have

[0055]

[0056] The fal term exists based on its properties, so we will discuss it in different cases.

[0057] When |e1|>l

[0058] - 22 fal(e1(t),j1,l1)- 33 fal(e1(t),j1,l1)≤-a2|2||1| j -a3|e3||1| j

[0059] At the same time, for any r > 0, we have

[0060]

[0061] Substitute

[0062]

[0063] When |e1|≤l

[0064]

[0065] Similarly, we can obtain

[0066]

[0067] In summary

[0068]

[0069] The final result can be summarized into the following two cases.

[0070]

[0071] Desirable

[0072]

[0073] Substituting the above constraints, we can obtain

[0074]

[0075] Right now Substitute arrive Zhongde

[0076]

[0077] There are also

[0078]

[0079] but

[0080]

[0081] Substitute b(q)u into The expression yields

[0082]

[0083] Right now

[0084]

[0085] Where Δ = x3(t) - z3(t), its upper bound is known to be ζ, that is, ||Δ||≤ζ.

[0086]

[0087] Furthermore, Cauchy's inequality leads to...

[0088]

[0089] Substituting, we can obtain

[0090]

[0091] Given n=2 degrees of freedom, we obtain the following formula:

[0092]

[0093] It can be known

[0094]

[0095] Right now

[0096]

[0097] a1 = min{k1,k2,k3}, Multiply both sides of the above equation Integrating over the interval [0,t], we get:

[0098]

[0099] It can be concluded that

[0100]

[0101] Based on the above equation and the definition of uniformly bounded, we can conclude that errors e1, e2, e3, and s are all uniformly bounded. Therefore, all signals in the closed-loop system of this continuum robot are uniformly bounded, and the system is stable in closed loop.

[0102] Secondly, the present invention provides an electronic device;

[0103] An electronic device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps described above for robust sliding mode control of a continuum robot based on a nonlinear extended state observer.

[0104] Thirdly, the present invention provides a computer-readable storage medium;

[0105] A computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the above-described robust synovial control method for a continuum surgical robot oriented towards model uncertainty and external environmental disturbances.

[0106] Fourthly, the present invention provides a computer program product;

[0107] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of the aforementioned robust synovial control method for a continuum surgical robot oriented towards model uncertainty and external environmental disturbances.

[0108] Compared with the prior art, the beneficial effects of the present invention are:

[0109] To address the challenges of accurately establishing dynamic models for continuum robots and their susceptibility to multi-source disturbances (such as unmodeled friction, tissue contact forces, and parameter uncertainties) during operation, this invention introduces a Nonlinear Extended State Observer (NESO). Unlike traditional control methods that rely on precise models, this invention uniformly defines model uncertainties and external environmental disturbances as "lumped disturbances," utilizing NESO for real-time observation and estimation. This mechanism enables the control system to proactively compensate for various unknown disturbances without relying on precise mathematical models, significantly enhancing the system's robustness in complex surgical environments.

[0110] To address the chattering phenomenon (i.e., high-frequency switching of control signals) commonly found in traditional sliding mode control, this invention employs a saturation function (sat function) instead of the traditional sign function in the sliding mode reaching law design. This improvement significantly smooths the control input signal while ensuring the reachability of the sliding surface and the speed of error convergence. It effectively avoids actuator wear or flexible cable fatigue caused by high-frequency oscillations, extends the robot's lifespan, and better meets the stringent requirements for motion smoothness in medical surgery.

[0111] To address the potential impact of disturbances on actuators, this invention utilizes real-time state reconstruction by an observer to quickly identify dynamic deviations caused by faults and automatically adjust control inputs. Combined with the low sensitivity of sliding mode control to parameter changes, this method ensures that the robot maintains high-precision trajectory tracking capabilities even in the event of actuator failure or sudden load changes, achieving fault-tolerant control of the system.

[0112] This invention provides a rigorous mathematical derivation and proof of a closed-loop control system based on Lyapunov stability theory. Theoretical analysis shows that under the proposed control law, the system's trajectory tracking error, observer estimation error, and all closed-loop signals are uniformly and ultimately bounded. This theoretical completeness provides a reliable safety guarantee for the practical application of continuum robots in high-safety-requirement scenarios such as minimally invasive surgery. Attached Figure Description

[0113] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0114] Figure 1 The joint 1 trajectory tracking and trajectory tracking error curve provided for the example of the present invention;

[0115] Figure 2 Joint 2 trajectory tracking and trajectory tracking error curves are provided for examples of the present invention;

[0116] Figure 3 Positioning and its error curves are provided for examples of the present invention;

[0117] Figure 4 The disturbance estimation curve provided for the example of the present invention;

[0118] Figure 5 Output a torque chattering comparison curve for an example of this invention;

[0119] Figure 6 This is a curve comparing the control effects of examples of the present invention. Detailed Implementation

[0120] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0121] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0122] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0123] Example 1

[0124] (1) Experimental objective:

[0125] This experiment aims to verify the effectiveness of a sliding mode control (SMC) scheme based on a nonlinear extended state observer (NESO) in the control of a continuous robot (CR). Specific objectives are as follows:

[0126] Verify disturbance rejection and fault tolerance capabilities: Verify whether the proposed control strategy can maintain the robustness of the system when facing dynamic uncertainties and unknown external disturbances.

[0127] Evaluation of observer performance: Test whether the nonlinear extended state observer (NESO) can estimate unknown actuator faults and uncertain dynamic terms of a continuum robot in real time and accurately, thereby achieving compensation for the overall disturbance.

[0128] Verify the accuracy and stability of trajectory tracking: Through simulation experiments, verify whether the system can achieve high-precision tracking of the desired trajectory (position and velocity) under complex interference conditions.

[0129] Suppressing chattering: Verify whether the approach law designed with the introduction of the saturation function can effectively reduce the high-frequency chattering phenomenon in traditional sliding mode control.

[0130] (2) Experimental system setup:

[0131] A numerical simulation platform for a two-degree-of-freedom continuum robot was built using the MATLAB programming environment. The core architecture of the platform consists of a robot dynamics model module, a nonlinear extended state observer (NESO) module, a sliding mode control (SMC) module, and a signal acquisition module. Unlike conventional ODE solvers, this experiment employs a high-precision fixed-step numerical integration method to directly iteratively solve the Lagrange dynamic equations, ensuring computational stability and real-time simulation under strong nonlinearity and high-frequency disturbances. The control module integrates a sliding mode control law based on a saturation function to suppress system chattering; the observation module deploys the NESO algorithm to reconstruct the total disturbance of the system (including unmodeled dynamics and external disturbances) in real time through error feedback. A built-in time-varying disturbance generator can suddenly apply sinusoidal / cosine external torques at specified time points; the data acquisition module is responsible for recording joint positions, velocities, tracking errors, control torques, and disturbance observations at high frequency, constructing a complete closed-loop verification environment.

[0132] (3) Experimental Implementation Procedure

[0133] 1. Simulation Platform Initialization: Start the MATLAB simulation script, load the physical parameters of the continuum robot and convert them to standard units. Initialize the system state variables (including joint angles and angular velocities) and the internal state of the NESO observer, and set the initial position deviation to verify the convergence capability of the controller.

[0134] 2. Control Algorithm Deployment: The proposed NESO-based disturbance rejection sliding mode control strategy is integrated into the simulation main loop. First, an NESO observer is constructed, with its input set as the system state error and its output as a real-time estimate of the unknown combined disturbance. Second, an integral sliding surface is defined, and a saturation function is used to replace the traditional sign function to weaken high-frequency chattering. The disturbance estimate output by NESO is then introduced into the control law for feedforward compensation, forming a composite control logic of "observation-compensation-feedback".

[0135] 3. Disturbance and Fault Configuration: Write disturbance injection logic in the simulation code. Set the simulation to apply time-varying sine and cosine disturbance torques to the two joints respectively at t=5s, superimposed with constant deviation, to simulate sudden environmental contact forces and model parameter perturbations during robot operation.

[0136] 4. Target trajectory setting: Construct the desired sinusoidal trajectory, set specific amplitude and frequency, so that the robot end effector can perform continuous and smooth reciprocating motion in the workspace, and comprehensively test the transient response and steady-state accuracy of the system under dynamic tracking tasks.

[0137] 5. Simulation Execution and Data Acquisition: The main simulation loop is executed, and the system updates its state step by step according to the dynamic equations. During this process, NESO corrects the disturbance estimate in real time, and the controller dynamically adjusts the output torque. The recording module synchronously saves the actual joint trajectory, velocity response, sliding surface convergence curve, and disturbance observation error. The effectiveness of the proposed algorithm in disturbance rejection and vibration reduction is verified by comparing the graphs.

[0138] (4) Experimental Results

[0139] The experimental results are shown in the figure below:

[0140] Figure 1 The joint 1 trajectory tracking and trajectory tracking error curve provided for the example of the present invention;

[0141] Figure 2 Joint 2 trajectory tracking and trajectory tracking error curves are provided for examples of the present invention;

[0142] Figure 3 Positioning and its error curves are provided for examples of the present invention;

[0143] Figure 4 The disturbance estimation curve provided for the example of the present invention;

[0144] Figure 5 Output a torque chattering comparison curve for an example of this invention;

[0145] Figure 6 This is a curve comparing the control effects of examples of the present invention.

[0146] Example 2

[0147] Embodiment 2 of the present invention provides an electronic device, including a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, they complete the steps of the above-described sliding mode control method for a continuum robot based on a nonlinear extended state observer.

[0148] Example 3

[0149] Embodiment 3 of the present invention provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the above-described sliding mode control method for a continuum robot based on a nonlinear extended state observer.

[0150] Example 4

[0151] Embodiment 4 of the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the above-described sliding mode control method for a continuum robot based on a nonlinear extended state observer.

[0152] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The functional device specified in one or more boxes.

[0153] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0154] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0155] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0156] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A robust sliding mode control method for a continuum surgical robot based on a nonlinear extended state observer, characterized in that, Includes the following steps: Step 1: Establish a dynamic model of the continuum robot. Considering parameter uncertainties and external disturbances, the model is transformed into a state-space equation containing a comprehensive disturbance term. Step 2: Construct a nonlinear extended state observer, select system state variables, and expand the comprehensive disturbance term into new state variables. Use the nonlinear extended state observer to estimate the system state and comprehensive disturbance value of the continuum robot in real time. Step 3: Define the position tracking error and design the sliding surface; Step 4: Design a sliding mode control law based on a saturation function. Introduce the comprehensive disturbance estimate obtained in Step 2 into the control law for compensation. Combine the sliding surface designed in Step 3 to calculate the control input and drive the continuous robot motion.

2. The method according to claim 1, characterized in that, In step S1, the dynamic model of the continuum robot is established based on the Lagrange equation, and its form is: Where q is the joint angle, and M(q) is the inertia matrix. Let G(q) be the Coriolis force-centrifugal force matrix, G(q) be the gravity term, B(q) be the Jacobian matrix, u be the control input, and d be the external disturbance. The system dynamics model can be expanded as follows: The known term is M0(q). G0(q), B0(q), the total interference terms can be written in the following form: Rewrite the system in state-space form: Where x1 and x2 are the position and velocity state variables, respectively, and -M0 -1 w represents the combined perturbation to be observed.

3. The method according to claim 1, characterized in that, In step S2, the design of the nonlinear extended state observer includes: defining -M0 -1 w represents the extended state, and the nonlinear extended observer is designed as follows: Where z1(t), z2(t), z3(t) are state estimates, e1(t) = z1(t) - x1(t) is the observation error, a1, a2, a3 are the observer gains, and fal(.) is a nonlinear function.

4. The method according to claim 1, characterized in that, In step S3, the sliding surface s is designed as follows: Where e = qq d For the position tracking error, q d Let λ be the desired trajectory and λ be the sliding surface parameter.

5. The method according to claim 1, characterized in that, In step S4, the sliding mode control law is designed using a saturation reaching law: Where k is the control gain. The saturation function is used to reduce chattering; the final control law u includes equivalent control, switching control, and observer compensation terms, and its form satisfies: The unknown faults and disturbances in the system are offset by z3(t).

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the robust synovial control method for a continuum surgical robot oriented towards parameter uncertainty and external disturbances as described in any one of claims 1-5.

7. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When executed by a processor, the computer program / instructions implement the steps of the robust synovial method for a continuum surgical robot as described in any one of claims 1-5.

8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the robust control method for a continuum surgical robot oriented towards parameter uncertainty and external disturbances as described in any one of claims 1-5.

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