The Adaptive Bilateral Control of Underwater Manipulator Teleoperation System with Uncertain Parameters and External Disturbance

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript introduces a self-adaptive bilateral control strategy for an underwater teleoperation system, effectively addressing uncertainties. The combination of reference adaptive impedance control and Radial Basis Function network-based adaptive compensation demonstrates robust force-position tracking. The inclusion of Lyapunov function analysis confirms global stability and asymptotic convergence.

The results highlight excellent performance under model uncertainties and external disturbances, showcasing the proposed adaptive control's stability, reliability, and robustness. I recommend accepting the paper in its current form, as it contributes valuable insights to underwater teleoperation systems.

Comments on the Quality of English Language

Minor English improvements are required.

Author Response

Thank you very much for all your help and looking forward to hearing from you soon. I wish to thank the reviewers for their useful comments. In the manuscript the comments for reviewer 1 are all highlighted in green.

Reviewer 1

Comment 1: The manuscript introduces a self-adaptive bilateral control strategy for an underwater teleoperation system, effectively addressing uncertainties. The combination of reference adaptive impedance control and Radial Basis Function network-based adaptive compensation demonstrates robust force-position tracking. The inclusion of Lyapunov function analysis confirms global stability and asymptotic convergence.

 

The results highlight excellent performance under model uncertainties and external disturbances, showcasing the proposed adaptive control's stability, reliability, and robustness. I recommend accepting the paper in its current form, as it contributes valuable insights to underwater teleoperation systems.

Minor English improvements are required.

Response:  Thank you for your kind feedback. I conducted a thorough review of the entire article, especially the grammar and spelling, and made careful and detailed revisions. Thanks.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The literature review can be improved

Novelty of the paper needs to be highlighted in the abstract and in the introduction

Add references of all equations used in the paper

The work needs to be compared with other control methods 

the advantage and benefits of the new method need to be highlighted. 

The boards used in the work should be justified

Why STM and not Rasberry PI or arduino

what is the type of master and slave boards?

Author Response

Thanks for your comments concerning our manuscript entitled: The adaptive bilateral control of underwater manipulator teleoperation system with uncertain parameters and external disturbance. (ID: electronics-2823700). Those comments are all valuable and very helpful for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied the comments carefully and have made correction for all the manuscript. We also have revised the manuscript according to your kind suggestion and reviewer’s detailed advice.

We appreciate the valuable feedback and suggestions. We are committed to addressing all the issues you have raised and improving the quality of our manuscript. We look forward to submitting the revised manuscript for your review and hope that our revisions meet your expectations. We sincerely hope this manuscript will be finally acceptable to be published on Electronics.

Thank you very much for all your help and looking forward to hearing from you soon. I wish to thank the reviewers for their useful comments. In the manuscript the comments for reviewer 2 are all highlighted in yellow.

Reviewer 2

Comment 1:  The literature review can be improved

Response:  Thank you for your feedback. We appreciate your suggestion regarding the literature review. I have revised and enhanced it to provide a more comprehensive and thorough analysis of the existing literature in the field.

What is more, I added three more references for the year 2023 and 2024 in the manuscript, which are expressed below:

 

Adaptive synchronization control of multimanipulator teleoperation system under constrained discrete-time network communication. 2023

Adaptive Practical Predefined-Time Control for Uncertain Teleoperation Systems With Input Saturation and Output Error Constraints. 2024

Adaptive FNN Backstepping Control for Nonlinear Bilateral Teleoperation With Asymmetric Time Delays and Uncertainties. 2023

Thanks.

Comment 2:  Novelty of the paper needs to be highlighted in the abstract and in the introduction

Response:  Thank you for your valuable feedback. We acknowledge the importance of highlighting the novelty of our paper in both the abstract and introduction sections. We emphasized the unique contributions and innovations of our work to highlight the improvement of the manuscript in these sections to better convey its significance to the readers. I have revised the manuscript to highlight the novelty. The context is expressed as below:

This paper proposes an adaptive bilateral control strategy to solve the problem of uncertainty in the motion model of the master-slave manipulator and external disturbance during the remote operation of the underwater manipulator. For the uncertainty of the model parameters and motion parameters of the master manipulator, a reference adaptive impedance control based on the nominal model is designed. The adaptive control law is employed to compensate for the model uncertainty and realize the force exerted by the operator on the master manipulator and the interaction force between the slave manipulator and the environment. For the uncertainty of the slave manipulator, the uncertain part of the model is approximated through the RBF network, and the approximation error is eliminated through the sliding mode variable structure controller and the adaptive controller, so that the position tracking error of the slave manipulator to the master manipulator is consistent, stable and bounded. And the control stability is proved by Lyayapunov function.

Thanks.

Comment 3:  Add references of all equations used in the paper.

Response:  Thank you for your kind suggestion. I have added references for all corresponding equations used in the paper to ensure proper attribution and provide readers with additional resources for further understanding except for some formulas which are derived by myself. It will enhance the transparency and credibility of our work. The example is expressed as below:

 

 

 

Thanks.

Comment 4: The work needs to be compared with other control methods

Response:  Thank you for your kind feedback. In order to illustrate the advanced advantages of the control algorithm designed in this manuscript and to evaluate our approach against existing control methods, I have added simulation comparison. The simulation comparison curves are shown in Figures 9-10, and it provided a more comprehensive understanding of its strengths and limitations. Thanks.

 

Comment 5:  the advantage and benefits of the new method need to be highlighted.

Response:  Thank you for your kind feedback. The comment is very valuable. We acknowledge the importance of highlighting the advantages and benefits of our new method. In response, I have emphasized the unique advantages and benefits of our approach in the manuscript, demonstrating its superiority over existing methods and its potential impact on the field. This will provide readers with a clear understanding of the significance and value of our work. Thanks. The context is expressed as below.

The uncertainties in the slave manipulator are compensated using an RBF network, and the tracking error is eliminated using a sliding mode variable structure controller and an adaptive controller, ensuring position tracking of the slave manipulator with respect to the master manipulator and improving the tracking performance. The asymptotic convergence performance and global stability of the tracking are proven with a Lyapunov function, guaranteeing the coordinated and consistent force-position tracking capability in the teleoperation process. The results demonstrate that the overall control system has good force-position tracking capability under internal and external disturbances, and the overall system exhibits stability and adaptability.

Comment 6:  The boards used in the work should be justified

Response:  Thank you for your comment. We have ensured that the choice of boards used in our work is thoroughly justified in the paper. This will include discussing factors such as availability, compatibility, and suitability for the specific application, providing readers with a clear rationale for our selection.  

Comment 7:   Why STM and not Rasberry PI or arduino

Response:  Thank you for your valuable comment.

We mainly use the advantages of STM 32's USART, A/D conversion, D/A conversion and PWM function. The choice of STM over Raspberry Pi or Arduino as the master and slave driver boards was based on several factors tailored to our specific requirements: Real-time performance: STM microcontrollers are known for their real-time capabilities, making them suitable for applications that require precise timing and control, which may not be achievable with Raspberry Pi or Arduino. Power consumption: STM microcontrollers typically have lower power consumption compared to Raspberry Pi, making them more suitable for battery-powered or energy-efficient applications. Cost-effectiveness: STM microcontrollers generally offer a more cost-effective solution compared to Raspberry Pi, especially for mass production or projects with budget constraints. Embedded system integration: STM microcontrollers are designed specifically for embedded systems, offering features such as on-chip peripherals and interfaces tailored for integration into various electronic systems. Development environment: The development tools and support for STM microcontrollers are well-established, providing a robust ecosystem for firmware development and debugging. Overall, the choice of STM over Raspberry Pi or Arduino was made to optimize performance, cost, and integration for our specific application needs. Thanks.

Comment 8:  what is the type of master and slave boards?

Response:  Thank you for your kind feedback. The comment is very helpful.

The type of master and slave boards used in our work are STM microcontroller development boards. Specifically, we utilized the STM32 series of microcontroller boards for both the master and slave roles. These boards offer a range of features suitable for our application, including sufficient processing power, built-in peripherals, and support for various communication protocols such as USART, A/D conversion, D/A conversion and PWM function.

The master driver board is responsible for acquiring the angle and tactile force signals through A/D conversion. It also receives the control law for the master manipulator from the master controller through the serial bus and sends the collected force and position information of the master manipulator back to the master controller through the same serial bus.

The master controller is connected to the master host computer via the internet, transmitting the master force and position signals to the master computer. It also receives the control law from the master host computer, which is then converted into PWM pulse performance and sent to the master driver board for execution.

Thanks.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

An adaptive bilateral control strategy is proposed in this paper for the teleoperation process under uncertain conditions caused by the mathematical models of the master and slave manipulators and external disturbances. The topic is interesting and novelty. But the authors need to explain how to use an RBF network in the designed controller and how to consider the friction disturbances and external uncertainties. My comments are below:  

1.      “The adaptive control law is used to compensate for the model uncertainty and realize the force exerted by the operator on the master manipulator and the interaction force between the slave manipulator and the environment. Trace matching of signals.” Please check this sentence.

2.      In section 2, it is recommended to give one figure to present the established model;

3.      Are there any assumptions for the established model?

4.      What are Fh and Fe represented for in Eq. (1)?

5.      For external tracking under external uncertainty conditions of the slave hand, an adaptive slave hand controller is designed, including RBF neural network compensator, sliding mode control and adaptive control law. Why three control laws are used in an adaptive slave hand controller?

6.      In Figure 3, did the authors use the RBF neural network in the control structure?

7.      How to consider the uncertainties in the designed controller?

8.      In figure 4, which line is the master manipulator, and which one is the slave manipulator? How to explain the accuracy of the designed controller?

9.      In Figure 5, it seems the master manipulator has better performance than the slave manipulator. Please explain the reason.

10.  In figure 9, which line is the master manipulator, and which one is the slave manipulator? The blue line is new controller. Is the new controller for the master manipulator or the slave manipulator?

11.  How to consider the disturbances and uncertainties in the experiment?

12.  It seems the results did show the capability of the controller under disturbances and uncertainties

 

 

 

Comments on the Quality of English Language

The quality of English is ok.

Author Response

Thanks for your comments concerning our manuscript entitled: The adaptive bilateral control of underwater manipulator teleoperation system with uncertain parameters and external disturbance. (ID: electronics-2823700). Those comments are all valuable and very helpful for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied the comments carefully and have made correction for all the manuscript. We also have revised the manuscript according to your kind suggestion and reviewer’s detailed advice.

We appreciate the valuable feedback and suggestions. We are committed to addressing all the issues you have raised and improving the quality of our manuscript. We look forward to submitting the revised manuscript for your review and hope that our revisions meet your expectations. We sincerely hope this manuscript will be finally acceptable to be published on Electronics.

Thank you very much for all your help and looking forward to hearing from you soon. I wish to thank the reviewers for their useful comments. In the manuscript the comments for reviewer 1 are all highlighted in blue.

Reviewer 3

Comment 1:  “The adaptive control law is used to compensate for the model uncertainty and realize the force exerted by the operator on the master manipulator and the interaction force between the slave manipulator and the environment. Trace matching of signals.” Please check this sentence.

Response:  Thank you for your kind feedback. The comment is very correct. I have checked and corrected the sentence above. Here's a revised version:

 The adaptive control law is employed to compensate for the model uncertainty and realize the force exerted by the operator on the master manipulator and the interaction force between the slave manipulator and the environment.

This revision clarifies the purpose of the adaptive control law and improves the flow of the sentence. Thanks.

Comment 2: In section 2, it is recommended to give one figure to present the established model;

Response:  Thank you for your valuable comment.

The overall control structure diagram with the master and slave established model is shown in Figure 1 in Section 3. The whole controller design is divided into the master controller and the slave controller. The structure of the master adaptive impedance control is shown in Figure 2 and the control structure diagram of the slave manipulator is shown in Figure 3 with the corresponding model. The focus of the entire system is control law design and proof. I'm worried that if I add another figure in section 2, it will cause duplication of content. Thanks.

Comment 3: Are there any assumptions for the established model?

Response:  Thank you for your kind feedback.

Yes, for the established model and easy understanding of the model, there are some assumptions in the manuscript.

In page 4, line 144, “It is assumed that Fh and Fe can be measurable with the tactile force sensor. ”

In page 4, line 145, “It is supposed that Fm (qm ) and F s (qs ) are generated from the internal joint friction.”

In page 4, under Eq.3, “Assuming that the manipulator joint is non-redundant, the Jacobian matrix Ji (qi) can be expressed as:”

In page 5, line 175, “It is assumed that the master and slave manipulators have the same linkage structure. The operator exerts force on the master manipulator, and the master manipulator moves according to the applied force.”

It is common in scientific research to make certain assumptions when establishing a model. These assumptions help simplify the model and make it more tractable for analysis. It's important to clearly state these assumptions in the paper to provide transparency and enable readers to understand the model. Thanks.

Comment 4:  What are Fh and Fe represented for in Eq. (1)?

Response:  Thank you for your kind feedback. The comment is very correct. Fh represents the force exerted by the operator on the master manipulator. Fe represents the interaction force between the slave manipulator and the environment.

I have added the sentence in the corresponding section expressed as :${F_{\rm{h}}}$ represents the force exerted by the operator on the master manipulator and ${F_{\rm{e}}}$ denotes the interaction force between the slave manipulator and the operating object. Thanks.

Comment 5: For external tracking under external uncertainty conditions of the slave hand, an adaptive slave hand controller is designed, including RBF neural network compensator, sliding mode control and adaptive control law. Why three control laws are used in an adaptive slave hand controller?

Response:  Thank you for your kind feedback. The comment is very correct.   Using three control laws in an adaptive slave hand controller allows for robust performance and enhanced adaptability in the presence of external uncertainty conditions. Here's why each control law may be included:

RBF Neural Network Compensator: Neural networks, particularly Radial Basis Function (RBF) networks, are effective at approximating nonlinear functions and modeling complex relationships in data. By incorporating an RBF neural network compensator into the controller, the system can learn and adapt to the uncertainties in the environment or system dynamics. The neural network can provide online estimation or compensation for nonlinearities, improving the controller's ability to track desired trajectories or forces.

Sliding Mode Control (SMC): Sliding mode control is known for its robustness to uncertainties and disturbances. It operates by ensuring that the system trajectory remains within a designated sliding surface, effectively mitigating the effects of disturbances and uncertainties. By including sliding mode control in the adaptive slave hand controller, the system can maintain stability and achieve accurate tracking performance even in the presence of external disturbances or model uncertainties.

Adaptive Control Law: Adaptive control laws adjust controller parameters based on real-time measurements or system states, allowing the controller to adapt to changing conditions and uncertainties. By incorporating an adaptive control law, the slave hand controller can continuously update its parameters to optimize performance and improve tracking accuracy in dynamic and uncertain environments. The adaptive control law complements the RBF neural network compensator and sliding mode control by providing additional flexibility and robustness in handling uncertain or time-varying dynamics.

Overall, the combination of these three control laws in an adaptive slave hand controller offers a synergistic approach to address various challenges associated with external uncertainty conditions. It provides robustness, adaptability, and performance optimization, ultimately enhancing the effectiveness and reliability of the slave hand control system.

Thanks.

Comment 6:  In Figure 3, did the authors use the RBF neural network in the control structure?

Response:  Thank you for your kind review. The comment is very helpful.  The RBF neural network is employed in the manuscript.  In the slave controller design section, we can conclude the position tracking performance with sliding function:

 

Where

Utilizing the RBF neural network to approximate the function f ( x ) , we can express . W is the neural network weight matrix,

ϕ ( x ) represents the basis function, and ε ∗ is the approximation error of the exact model. The estimated value of f ( x ) is given by f ( x ) =W^T ϕ ( x ) .

The uncertain term f ( x ) is estimated through the adaptive law of weights , and the estimation error is eliminated using robust control laws  with . So the RBF neural network is employed in the manuscript.

Thanks.

Comment 7:  How to consider the uncertainties in the designed controller?

Response:  Thank you for your kind suggestion.

Aiming at the problem of uncertainty in the manipulator model caused by joint friction in the master-slave manipulator, and the problem of uncertain interference in the slave manipulator caused by the complex underwater environment, in order to achieve the purpose of achieving coordinated coordination of the master-slave manipulator and displacement, a model based on uncertainty approximation is proposed. Bilateral adaptive control strategy for master-slave manipulator. Among them, an adaptive control strategy based on the expected impedance model was designed to solve the uncertainty problem caused by joint friction of the main manipulator. First, a second-order impedance model based on the master hand force and slave hand force errors was established, and then the sliding mode variables of the master hand operating space position and the impedance model reference position error were established. Based on the sliding mode variables, an adaptive model compensation control law was designed and The update law of uncertain control items is estimated to realize the tracking of the master hand force and the slave hand force. An adaptive control law based on radial basis function (RBF) neural network was designed to solve the problem of model uncertainty caused by hand joint friction and external uncertain interference. A sliding mode function based on the joint position error of the master-slave manipulator was established, and the approximation error was eliminated through the sliding mode variable structure controller, neural network controller, and robust control terms, and the position tracking of the slave hand to the master hand was gradually converged. The stability of master-slave manipulator control is proved through Lyapunov stability criterion.

Thanks.

Comment 8: 8.  In figure 4, which line is the master manipulator, and which one is the slave manipulator? How to explain the accuracy of the designed controller?

Response:  Thank you for your kind feedback. The comment is very correct.

The red line is the master manipulator force Fh, and the blue line is the slave manipulator force fe, which should track the master force. The simulation time is set to 30 s, with a 10 s application of 10 N force on the master manipulator Fh, followed by 0 N force for the remaining 20 s. I have changed the introduction text in the figure 4 which is expressed as below:

 

The slave manipulator begins to have no contact with the operating object, and Fe is 0 for a period of time. When the slave manipulator comes into contact with the operating object, the interaction force fe is applied. At this time, the slave manipulator force fe can track the force of the master manipulator Fh. It can be seen from the simulation curve that the static error of the slave manipulator tracking the force of the master manipulator Fh is 0. Thanks.

Comment 9:  9. In Figure 5, it seems the master manipulator has better performance than the slave manipulator. Please explain the reason.

Response:  Thank you for your kind feedback. The comment is very useful. This is because the master manipulator adopts an adaptive impedance control method. The desired impedance model is designed at the master manipulator end, and the master manipulator's operating space position tracks the reference position which is the  response of the desired impedance model. The slave manipulator tracks the position of the master manipulator, so the response speed is not as fast as that of the master manipulator. That is why it seems the master manipulator has better performance than the slave manipulator. Thanks.

Comment 10: 10. In figure 9, which line is the master manipulator, and which one is the slave manipulator? The blue line is new controller. Is the new controller for the master manipulator or the slave manipulator?

Response:  Thanks for your good suggestion. The comment is very valuable.

The red line with New controller x_m is the master manipulator’s trajectory, and the blue line with New controller x_s is the slave manipulator’s trajectory. m，s respectively denote the master and slave. The new controller here includes the master and slave controller. Thanks.

Comment 11: 11.  How to consider the disturbances and uncertainties in the experiment?

Response:  Thank you for your kind feedback. The comment is very good.

The disturbances is in the slave manipulator model. Since the experimental environment was not conducted in an underwater environment, the experimental process was to generate a bounded random number sequence in the math model of the manipulator to simulate the uncertain interference term.

The uncertain terms in master and slave manipulator model are the function of velocity qm and qs, and the estimation of uncertain terms is achieved through adaptive control laws. Thanks.

Comment 12: 12.  It seems the results did show the capability of the controller under disturbances and uncertainties

Response:  Thank you for your kind feedback. The comment is very correct. It appears that the results demonstrated the effectiveness of the controller in handling disturbances and uncertainties. This suggests that the controller was able to maintain stability and achieve satisfactory performance even when faced with external disturbances or uncertain conditions. This outcome underscores the robustness and adaptability of the proposed control approach, validating its capability for practical applications in real-world scenarios.

The asymptotic convergence performance and global stability of the tracking are proven using a Lyapunov function, guaranteeing the coordinated and consistent force-position tracking capability in the teleoperation process. The results demonstrate that the overall control system has good force-position tracking capability under internal and external disturbances, and the overall system exhibits stability and adaptability. Thanks.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

authors have replied all comments well. The paper can be accepted.

Author Response

Response to Reviewer 3

Thanks for your comments concerning our manuscript entitled: The adaptive bilateral control of underwater manipulator teleoperation system with uncertain parameters and external disturbance. (ID: electronics-2823700). Those comments are all valuable and very helpful for revising and improving our manuscript, as well as the important guiding significance to our researches. We have studied the comments carefully and have made correction for all the manuscript. We also have revised the manuscript according to your kind suggestion and reviewer’s detailed advice.

We appreciate the valuable feedback and suggestions. We are committed to addressing all the issues you have raised and improving the quality of our manuscript. We look forward to submitting the revised manuscript for your review and hope that our revisions meet your expectations. We sincerely hope this manuscript will be finally acceptable to be published on Electronics.

Thank you very much for all your help and looking forward to hearing from you soon. I wish to thank the reviewers for their useful comments. In the manuscript the comments for reviewer 3 are all highlighted in blue.

 

Reviewer 3

Comment 1:  Authors have replied all comments well. The paper can be accepted.

Response:  I am very happy to see that the reviewer 3 recommended this article for acceptance. That's great news! The comment is very correct. Thanks.

Author Response File: Author Response.docx