Trajectory Control of Flexible Manipulators Using Forward and Inverse Models with Neural Networks

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a neural network approach to controlling the motion of a flexible-link robot.  The primary contribution appears to be the use of neural networks to devise essentially open-loop control of flexible robot motion, with particular regard to the management of time delays.  It is generally well-written and presents interesting findings.  However, the paper is not yet ready for publication.  In particular, the following items need to be addressed before the paper can be published:

1) Many papers have been written about motion control of flexible robots, most of which are missing from this paper.  I recommend including command shaping/input shaping approaches, as well as inverse/feedforward approaches.

2) The specific degrees of freedom available for this robot's motion are unclear from the picture in Fig. 1.  Adding some arrows showing how the joints move would be useful.  This would also clarify the statement that the two-link robot actually has three degrees of freedom.  Also, the text mentions motion in the Y and Z directions.  It would be helpful to add vectors to Fig. 1 to show these directions. 

3) The use of neural networks for inverse kinematics makes sense to me.  However, the use of the forward dynamics effectively replaces the robot with a neural network.  Was this done to simulate the robot, or was there another purpose that I did not recognize?

4) In your Results section, there seem to be two different types of results (Simulation and Experiment), done either without or with the actual robot hardware.  However, it is very difficult to ascertain which results were obtained with hardware and which were not.  Also, the text mentions the use of classical inverse kinematics (which I assume means using equations instead of neural networks), but it only mentions this when discussing the results.  This is never mentioned when describing the methods used to get these results.

5) At the beginning of the Results section, Fig. 5 results are discussed and the text states, "the inverse model struggled due to a phase shift caused by system delays."  It is not clear to me how the results of Fig. 5 lead to such a conclusion.

6) The legends to Fig. 7C (the second Fig. 7) and Fig. 8 are unclear to me, especially since there are no asterisk symbols on these plots.  Please clarify.

7) The text mentions that "future work should consider a dual-input training strategy, where both the motor input and measured output angles are used."  It would seem to me that the paper would be stronger if these new results were included prior to publication.

8) Finally, since the proposed approach appears to be open loop (as near as I can tell), I would like to see how the neural networks can be integrated into a closed-loop control framework.

I've also attached a marked-up manuscript with additional corrections and comments.

Comments for author File: Comments.pdf

Author Response

Please find attached. 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

When reviewing this article, it is difficult to find any specific errors or shortcomings.

The work was properly justified, and the research station was designed and constructed. The theoretical foundations presented are at the level of an engineering course and constitute a supplementary element. The results of the modeling and experiment were presented, and everything is correct.

In my opinion, there are two weaknesses of this article: low scientific value and lack of reference to practice.

The first aspect hard to improve without some additional work (experiments). Perhaps if the authors had attempted to analyze the sensitivity of the proposed solutions to various system variables (speed of movement, structural parameters of the object, shape of the trajectory), the work would have gained scientific significance.

The second aspect—I missed references to real-world problems of manipulation using vulnerable manipulators, as well as justification for the selection of parameters of the tested system in relation to the actual aspects of manipulation.

 

In terms of the presentation of results, I suggest changing the way they are presented (different types of graphs for practically overlapping curves).

The tables are filled with characters of different fonts and sizes. I would also unify the way numerical results are presented, as sometimes scientific notation is used and sometimes it is not, with different numbers of significant digits.

These are minor editorial weaknesses. More important are those that concern the scientific nature of the considerations and analyses presented.

 

Author Response

Please find attached.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I am rather disappointed with the revisions made to this paper.  In many cases, my concerns were not at all addressed.  In particular:

1) I still don't see any mention of alternate techniques (such as command shaping or input shaping) as applied to flexible robots, either in the text or in the reference list.

2) It is still unclear to me how the inverse dynamics are calculated.  If a rigid body model is used, then the resulting expressions would be nonlinear, not linear as the text says.  This needs further explanation.

3) I am also unsure about the proposed approach for further addressing the discrepancy of the inverse model with actual robot experiments.  Is the idea to measure actual joint torques rather than joint angles in order to improve performance?

4) The X, Y, and Z axes are not the same as joints 1, 2, and 3.  The axes are rectilinear, while the joints are rotational.  This needs correction throughout the Results section.  Also, Fig. 6c should be earlier in the text.

5) Since one claim about this work is that it allows for 3D trajectories, while only 2D trajectories are shown, I would recommend removing that statement, or else actually provide true 3D trajectories.

6) There are a number of remaining issues and corrections which I have spelled out in the attached marked-up manuscript.

Unless these issues are directly addressed in another revision, I cannot in good conscience recommend this paper for publication in its current form.

Comments for author File: Comments.pdf

Author Response

We sincerely thank the reviewer for their detailed and thoughtful comments. We acknowledge the oversights in the previous revision and have now directly addressed each of the reviewer’s concerns, including technical clarifications, text corrections, and clearer representation of coordinate systems and model structures. We hope that these substantial revisions meet the expectations for publication.

 

S.NO	REVIEWER COMMENTS	AUTHOR RESPONSE	PAGE
1.	I still don't see any mention of alternate techniques (such as command shaping or input shaping) as applied to flexible robots, either in the text or in the reference list.	we have now included a brief discussion of command shaping and input shaping in the Introduction and cited recent literature where such techniques have been applied to flexible manipulators. These methods are valuable in suppressing vibrations by pre-processing reference trajectories. However, our study focuses on neural network-based modeling as a data-driven alternative to classical model-based shaping techniques.	Page 2 And Page 20
2.	It is still unclear to me how the inverse dynamics are calculated. If a rigid body model is used, then the resulting expressions would be nonlinear, not linear as the text says. This needs further explanation.	We apologize for the misleading terminology. The reference model used in this work is not an inverse dynamics model, but rather a geometric inverse kinematics model based on rigid-body assumptions. As correctly pointed out, such models are inherently nonlinear. We have now corrected the text throughout the manuscript to remove any reference to a “linear model” and instead clearly state that the conventional method is a nonlinear inverse kinematics approach that assumes ideal, rigid links and neglects dynamic effects.	Page 9
3.	I am also unsure about the proposed approach for further addressing the discrepancy of the inverse model with actual robot experiments. Is the idea to measure actual joint torques rather than joint angles in order to improve performance?	In our current implementation, the neural network was trained using joint angle data derived from inverse kinematics. To improve performance, we plan to expand our dataset to include both measured joint torques and motor input commands, which will allow the network to learn actuation limitations and better approximate the physical behavior of the system. This plan has now been added to the Conclusion and Future Work sections	Page 19 and 20
4.	Since one claim about this work is that it allows for 3D trajectories, while only 2D trajectories are shown, I would recommend removing that statement, or else actually provide true 3D trajectories.	We acknowledge this issue. The test trajectory used in this study is constrained to the Y-Z plane. We have revised the Abstract and Introduction to clarify that only planar (2D) trajectories were evaluated, although the model architecture is capable of supporting 3D trajectory control. The original claim of demonstrated 3D motion has been removed.	Page 1 and 2
5.	should this be Joint 1?	Yes it is, have changed.	Page 3
6.	shouldn't lk output angle be replaced by motor angle in each of these schematics?	I have changed in all the schematics.	Page 8
7.	was this done using a rigid-body inverse kinematics model?	Yes and have now clearly indicated it.	Page 9
8.	I still don't know what X, Y, and Z axes are; they're not shown in the schematic of Fig. 1.	Had erroneously put two Y axis, have ammended this.	Page 12
9.	It seems that the results in Fig 6 are from applying the neural network models to the actual robot (not just the virtual case of Fig 5). This needs to be mentioned here.	Yes, this is true. We have clearly stated these.	Page 11
10.	this figure needs to come earlier	Have moved figure 6c to 6a as recommended .	Page 12
11.	the X, Y, and Z axes are not the same as the three joints	You're absolutely correct. these joints do not directly correspond to the Cartesian X, Y, and Z axes of the end-effector’s spatial motion. The confusion likely arises because Figure 8b shows motion in X, Y, Z Cartesian space, while Figure 8a shows rotational joint angles.	Page 15
12.	what model did you use for this? even a rigid body model would be nonlinear, not linear as you say here	This is true. We have acknowledged that it's a geometric, rigid-body model, which is nonlinear, but does not account for compliance, dynamics, or delays.	Page 15

 

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

While the most recent revision addresses my earlier comments, I am still disappointed by the numerous errors and oversights that are still present.  In particular:

1) It must be emphasized that the inverse kinematics equations being used are for a rigid body model.  This is not currently mentioned in section 2.2 but should be.

2) A new Figure 3 was inserted into the document, thereby throwing off the remaining figure numbers.  All figures after Figure 3 need to be renumbered.

3) Many figures still refer to "linear" inverse kinematics, even though the author's response admits that these are actually nonlinear.  All these figure legends need to be fixed.

Several additional minor corrections are indicated in the attached file.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf