Round 1

Reviewer 1 Report

1. A Survey of existing literature is not sufficient. It would useful to include in section 2 of the paper some discussion on other possible real applications of the obtained results.
2. The authors did not explain the difference between the work in reference [18] and the work in this paper.
3. The contribution is not indicated. The author highlighted the conclusion at the end of section 2, not a contribution. The contribution has to be stated in points.
4. What is the research object in this paper?
5. The authors should give more information about the kinematic and dynamic of a 2-DOF elastic robot arm system in section 3.
6. Why the sliding surface is described by two equations (Eq. (3) and Eq. (4)).
7. The proposed switching element in the control law of the STSMC (Super-Twisting Sliding Mode Controller), represented by equation (*), was not explained. I recommend a more detailed discussion about it.
8. The local asymptotic stability is the goal of this study. Why the authors did not address the global asymptotic stability.
9. The design analysis is good, but the choice of design parameters is still a challenging problem. If not possible to perform one of the modern techniques in tuning these design parameters, I suggest referring to some of them.
10. The comparison of the proposed controller with the PID controller is not fair. The efficiency of the proposed controller will be more evaluated if a comparison was set with other control techniques mentioned before for the same robot with the proposed approach.
11. There is no quantitative evaluation of the simulated results. The authors have to give numerical tables which report the quantitative comparison. The numerical comparison has to be conducted in terms of transient dynamic and chattering reduction.
12. The robustness of the controller shall be checked at least with two disturbances signals not only one to prove the efficiency of the controller.
13. The RMSR (Root Mean Square Error) has to be used for evaluation and comparison.
14. The authors tried to increase the results by using different types of inputs.
15. A deep discussion is required in simulated results.
16. The study did not address the practical verification of simulated results. Despite it being mentioned in future work, the work is still weak unless it is experimentally implemented.
17. The conclusion is descriptive. It is void of quantitative and numerical improvement and comparison. The description contents of the conclusion have to be omitted and the conclusion has to be revised.

Author Response

List of changes in journal paper

The authors would like to thank the reviewers for constructive feedback on our journal paper " A Novel Adaptive Sliding Mode Controller for a 2-DOF Elastic" by Hua Minh Tuan, Filippo Sanfilippo and Nguyen Vinh Hao, submitted to the Special Issue "Intelligent Technologies and Robotics" in MDPI Robotics. As described in details below, we have made changes to the paper in accordance with the suggestions from each reviewer.

Reviewer 1

Comment from reviewer:

1. A Survey of existing literature is not sufficient. It would useful to include in section 2 of the paper some discussion on other possible real applications of the obtained results.

Our response and resulting change in the paper:

Thank you for your suggestion. A paragraph is added to section 2 to discuss the possible real applications:

“Elastic actuators and elastic robots are applied in various applications, which are summarised in Table 1. In [6], NASA Valkyrie [7], a humanoid robot with series elastic actuators, is applied for the deployment in improvised explosive devices (IEDs) Response. In [8], a series-elastic actuated snake robot is proposed, which is capable to navigate in pipe bends and junctions. Elastic actuators are also adopted in rehabilitation robots [9–11].”

Comment from reviewer:

2. The authors did not explain the difference between the work in reference [18] and the work in this paper.

Our response and resulting change in the paper:

Thank you for giving us the opportunity to clarify this point. Compared to the work in reference [​​18] (of the submitted manuscript), we extend our research by presenting a more extensive simulation and experiments section in this paper. Moreover, we also make a comparison with the conventional sliding mode controller to show the effectiveness of the proposed algorithm. This is now highlighted in the revised manuscript. The following sentence has been added in the Introduction Section:

“In this paper, we extend our research by presenting more simulation experiments. We also make a comparison with the conventional sliding mode controller to show the effectiveness of the proposed algorithm.”

Comment from reviewer:

3. The contribution is not indicated. The author highlighted the conclusion at the end of section 2, not a contribution. The contribution has to be stated in points.

Our response and resulting change in the paper:

Thank you for your comment. The contribution is now stated in points in section 1, as it follows:

“To address these challenges, the following contributions are presented in this study:

- An adaptive control mechanism is proposed to deal with the controlling task of a 2-DOF elastic robot arm. The control mechanism has two loops. The outer loop is an adaptive sliding mode controller (ASMC) to deal with uncertainties and disturbances on the load side of the robot arm. The output of this loop is the desired angular position of the motors. The inner loop consists of the model reference adaptive controllers (MRAC) to stabilise the motor side of the robot arm;

- Extensive simulation experiments and a comparison with the conventional sliding mode controller are conducted to demonstrate the effectiveness of the proposed controller.”

Comment from reviewer:

4. What is the research object in this paper?

Our response and resulting change in the paper:

Thank you for your question. The research object of this paper is to introduce a novel adaptive sliding mode controller for a 2-DOF elastic robotic arm. In the revised manuscript this is now clearly stated in section 1, as mentioned in the previous comments.

Comment from reviewer:

5. The authors should give more information about the kinematic and dynamic of a 2-DOF elastic robot arm system in section 3.

Our response and resulting change in the paper:

Thank you for your comment. The following paragraphs and a table are added to Section 3 to provide more details about the kinematics and dynamics of the elastic robot:

"Based on this diagram, the Denavit-Hartenberg (DH) parameters are shown on Table 1, where d is the offset along the z-axis to the common normal, θ is the angle about the z-axis, from the old x-axis to new x-axis, a is the length of the common normal, and α is the angle about common normal, from old z-axis to new z-axis."

"Equation 1 has the form of a typical robotic dynamic model. The difference is that instead of the motor torque, the load side is controlled by an elastic force Ks (θ −q). This elastic force is created from the motor torque by creating a deviation between motor (θ) and load (q) angular positions. This is shown in equation 2."

Comment from reviewer:

6. Why the sliding surface is described by two equations (Eq. (3) and Eq. (4)).

Our response and resulting change in the paper:

Thank you for giving us the opportunity to clarify this point. In sliding mode control, there are 2 phases of operation: the sliding phase and the reaching phase. The sliding surface is determined with the PID form so that, in the sliding phase (σ=0), the error always slides to 0. In the equation (3), the time-derivative of the sliding surface is presented. In the reaching phase (σ≠0), a control input has to be proposed to ensure that the sliding surface will be 0 in limited time. This control input appears in equation (4).

Comment from reviewer:

7. The proposed switching element in the control law of the STSMC (Super-Twisting Sliding Mode Controller), represented by equation (*), was not explained. I recommend a more detailed discussion about it.

Our response and resulting change in the paper:

Thank you for your comment. The following paragraph is added to section 4 to give more information about the Super-Twisting Sliding Mode Controller:

“where U is a positive constant to be chosen sufficiently large to assure good tracking performance. The term  ̇u2 = −1.1Utanh(σ) describes the leakage of the “super-twisting” second-order sliding controller [40]. In addition, the tanh(σ) is used instead of sign(σ) because it creates a smoother control signal.”

Comment from reviewer:

8. The local asymptotic stability is the goal of this study. Why the authors did not address the global asymptotic stability.

Our response and resulting change in the paper:

Thank you for pointing out this challenge. In this paper, we do not prove the global stability of the two combined algorithms. However, through extensive simulations, we have tested the global performance of the proposed combined controller. In future work, we are planning to prove the local asymptotic stability. This is now highlighted in the Conclusion Section:

“Furthermore, we will also address and prove local and global asymptotic stability.”

Comment from reviewer:

9. The design analysis is good, but the choice of design parameters is still a challenging problem. If not possible to perform one of the modern techniques in tuning these design parameters, I suggest referring to some of them.

Our response and resulting change in the paper:

Thank you very much for your comment. The following paragraphs are added to give more details on the modern techniques of tuning the design parameters:

“There are four parameters needed to be tuned in the proposed approach, namely Kp , Ki , α and U. A discussion of the effect of these parameters and how to tune them is presented here. Kp and Ki constitute the sliding surface and affect the convergence of the error. Generally, Kp has a role as the proportional gain of a traditional PID controller [43]. Choosing an appropriate value of Kp would make the system stable [43]. If the value of Kp is too large, the system may be destabilised, and if the value of Kp is too small, the system may converge sluggishly [43]. The integral gain Ki affects the rates of error integration. In addition, Kp and Ki have to be chosen such that the characteristic polynomials

s2 + Kp1 s + Ki1 = 0

s2 + Kp2 s + Ki2 = 0

with s is the variable in the frequency domain, are strictly Hurwitz [31–33]. There are many methods adopted to choose the parameters for the sliding surface. In this paper, the trial-and-error method is used. Besides, alternative methods are also applied in the literature, e.g. Ziegler-Nichols method [44], particle swarm optimisation [44], evolutionary algorithms [45], etc.

 

The parameter α could be chosen such that the assumption A2 (that is B(q)−1 α −I ≈ 0) is satisfied. In practice, the values in matrix B(q)−1 can be obtained from the design or measured. In addition, the angular load positions q have to be operated in a predefined range. Therefore, we can easily estimate the range of matrix B(q)−1 and use that to choose the values in α. The value of parameter U is chosen by trial-and-error. The larger the value of U is, the better the tracking performance is. However, if the value of U is too large, it could destabilise the system.”

Comment from reviewer:

10. The comparison of the proposed controller with the PID controller is not fair. The efficiency of the proposed controller will be more evaluated if a comparison was set with other control techniques mentioned before for the same robot with the proposed approach.
11. There is no quantitative evaluation of the simulated results. The authors have to give numerical tables which report the quantitative comparison. The numerical comparison has to be conducted in terms of transient dynamic and chattering reduction.
12. The robustness of the controller shall be checked at least with two disturbances signals not only one to prove the efficiency of the controller.
13. The RMSR (Root Mean Square Error) has to be used for evaluation and comparison.

Our response and resulting change in the paper:

Thank you for giving us the opportunity to highlight the efficiency of the proposed controller and to improve the Simulation Section. In the revised manuscript, the following changes have been implemented:

• New simulations with the conventional sliding mode controller are implemented to compare this former algorithm with the proposed approach.
• A new simulation with step input to evaluate the transient dynamics and the chattering is presented.
• Simulation experiments with the sine wave and square wave disturbances are now added in the Simulation Section.
• Three more tables reporting the RMS error and the total variance of the control signal are considered in the simulation experiments.

Comment from reviewer:

14. The authors tried to increase the results by using different types of inputs.

Our response and resulting change in the paper:

Thank you very much for your comment.

Comment from reviewer:

15. A deep discussion is required in simulated results.

Our response and resulting change in the paper:

Thank you very much for your comment. The new results have been scrupulously discussed in the revised Simulations Section. 

Comment from reviewer:

16. The study did not address the practical verification of simulated results. Despite it being mentioned in future work, the work is still weak unless it is experimentally implemented.

Our response and resulting change in the paper:

Thank you for giving us the opportunity to clarify this point. We have recently developed a 2-DOF robot arm with elastic joints in our Frontier journal. As a future work, we will test the proposed approach on this physical robot. The following text has been added in the Conclusion Section:

“In the future, the proposed method should be implemented on a real elastic robotic arm. In our previous work [29], a physical 2-DOF robot arm with elastic joints was introduced. We will carry out further empirical experiments on this prototype to demonstrate the effectiveness of the proposed algorithm.”

Comment from reviewer:

17. The conclusion is descriptive. It is void of quantitative and numerical improvement and comparison. The description contents of the conclusion have to be omitted and the conclusion has to be revised.

Our response and resulting change in the paper:

The Conclusions section has been revised by highlighting the performance of the proposed controller, describing the improvement in the settling time, RMS error, and mentioning all the numbers that we obtained in the Simulation Section.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is well organized and reports a new adaptive (sliding mode) control framework for flexible mechanisms.  Although the article contains some interesting information, some major modifications are required as:

 

• Abstract section:

What are the main achievements of this work?

Report some numerical results from the simulation.

 

• Introduction and related work sections:

Why authors believe that sliding mode controller is rather better than other adaptive control approaches?

In the related work, explain other control methods on compliant mechanisms and cite following papers:

Guan, Ping, Xiang-Jie Liu, and Ji-Zhen Liu. "Adaptive fuzzy sliding mode control for flexible satellite." Engineering Applications of Artificial Intelligence 18.4 (2005): 451-459.

Barjuei, Erfan Shojaei, et al. "Robust control of three-dimensional compliant mechanisms." Journal of Dynamic Systems, Measurement, and Control 138.10 (2016): 101009.

Thieffry, Maxime, et al. "Control design for soft robots based on reduced-order model." IEEE Robotics and Automation Letters 4.1 (2018): 25-32.

 

• Modeling and control design sections:

How the gravity and deformation factors are taken into account?

How the stability of the control approach is guaranteed?

 

• Simulation section:

What are the gain and weigh of the proposed control approach and the PID controller?

 

• Conclusion section:

Again, what is the main contribution of this work?

Which problem has been addressed and how did you solve it?

What are the challenging of this work?

Author Response

List of changes in journal paper

The authors would like to thank the reviewers for constructive feedback on our journal paper " A Novel Adaptive Sliding Mode Controller for a 2-DOF Elastic" by Hua Minh Tuan, Filippo Sanfilippo and Nguyen Vinh Hao, submitted to the Special Issue "Intelligent Technologies and Robotics" in MDPI Robotics. As described in details below, we have made changes to the paper in accordance with the suggestions from each reviewer.

Reviewer 2

Comment from reviewer:

Abstract section:

What are the main achievements of this work?

 

Report some numerical results from the simulation.

Our response and resulting change in the paper:

Thanks for giving us an opportunity to clarify this. The main achievements of this work and the numerical results from the simulation are now mentioned in the Abstract Section as below:

“In this work, the control of a 2-DOF robot arm with elastic actuators is addressed by proposing a two-loop adaptive controller. For the outer control loop, an adaptive sliding mode controller (ASMC) is adopted to deal with uncertainties and disturbance on the load side of the robot arm. For the inner loops, model reference adaptive controllers (MRAC) are utilised to handle the uncertainties on the motors side of the robot arm. To show the effectiveness of the proposed controller, extensive simulation experiments and a comparison with the conventional sliding mode controller (SMC) are carried out. As a result, the ASMC has a 50.35% lower average RMS error than the SMC controller, and a shorter settling time (5% criterion) (0.44 seconds compared to 2.11 seconds).”

Comment from reviewer:

Introduction and related work sections:

Why authors believe that sliding mode controller is rather better than other adaptive control approaches?

Our response and resulting change in the paper:

Thanks for your comment. The adaptive sliding mode controller is chosen because of two reasons. First of all, the sliding mode algorithm is considered because it has the ability to exhibit stability against parameter variations, unmodelled dynamics and external disturbances. It can excellently deal with the nonlinearities of the robot arm mathematical model. However, in a dynamic environment with disturbances and uncertainties, the conventional sliding mode controller is not sufficient. Therefore, an adaption mechanism is added to enhance the algorithm. In sum, the first reason for choosing the adaptive sliding mode controller is the ability to deal with nonlinearities, and the second reason is the ability to deal with disturbances and uncertainties.

Comment from reviewer:

In the related work, explain other control methods on compliant mechanisms and cite following papers:

 

Guan, Ping, Xiang-Jie Liu, and Ji-Zhen Liu. "Adaptive fuzzy sliding mode control for flexible satellite." Engineering Applications of Artificial Intelligence 18.4 (2005): 451-459.

 

Barjuei, Erfan Shojaei, et al. "Robust control of three-dimensional compliant mechanisms." Journal of Dynamic Systems, Measurement, and Control 138.10 (2016): 101009.

 

Thieffry, Maxime, et al. "Control design for soft robots based on reduced-order model." IEEE Robotics and Automation Letters 4.1 (2018): 25-32.

Our response and resulting change in the paper:

Thanks for your comment. The papers are cited in the revised manuscript in the Related Research Work Section.

Comment from reviewer:

How the gravity and deformation factors are taken into account?

Our response and resulting change in the paper:

Thanks for giving us an opportunity to clarify this. The gravity and deformation factors are considered in the estimated matrices A(q,̇q), B(q). If there is any change in these parameters, the adaption scheme will be in charge of adjusting the controller appropriately.

Comment from reviewer:

How the stability of the control approach is guaranteed?

Our response and resulting change in the paper:

Thank you for giving us the opportunity to clarify this point. In this work, we have highlighted the efficacy of the proposed controller through extensive simulations. However, we did not prove the global stability of the proposed control approach. While recognising the importance of this aspect, we will consider this as a task for future work. This is now clearly stated in the Conclusion section.

Comment from reviewer:

Simulation section:

What are the gain and weigh of the proposed control approach and the PID controller?

Our response and resulting change in the paper:

Thanks for your comment. In the revised manuscript, the PID controller for comparison is replaced by the conventional sliding mode controller. A table is also added (Table 4) to show the control parameters of the ASMC.

Comment from reviewer:

Conclusion section:

Again, what is the main contribution of this work?

 

Which problem has been addressed and how did you solve it?

 

What are the challenging of this work?

Our response and resulting change in the paper:

Thanks for your comment. The main contribution of this work is introducing a two-loop controller for controlling a 2-DOF robot arm with elastic actuators. The problem that has been addressed is stabilising the system when disturbances and uncertainties are present. The main challenge of this work is the trade-off between the tracking performance and the chattering phenomenon. The following paragraph is added to the Conclusion Section to clarify this:

“We introduced a two-loop controller in this work. To deal with uncertainties and interference on the load side of the robot arm, an adaptive sliding mode controller (ASMC) is proposed in the outer loop. Model reference adaptive controllers (MRAC) are adopted for each joint in the inner loop to address uncertainty on the robot arm’s motor side. The usefulness of the presented ASMC algorithm in stabilising the system in the presence of uncertainties and disturbances is proved through detailed simulated studies. Accordingly, the ASMC has a 50.35% lower average RMS error than the SMC controller. It also has a shorter settling time (5% criterion) (0.44 seconds compared to 2.11 seconds). However, this improvement comes at the expense of an increase in the total variance of the control signal.”

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

All my comments have been addressed—no further comments

Reviewer 2 Report

The article has been modified a lot and it can be accepted for publication.