Adaptive Virtual Impedance Control of a Mobile Multi-Robot System
Round 1
Reviewer 1 Report
The paper is related to the modeling and control of mobile multi-robot systems. The history of authors in robotics is worth to be mentioned.
The paper is appreciated and its revision is advised using these comments:
1) A careful editing must be done. Please check and polish. For example, you should take care to the formulation. You should replace 'stability' with
'movement stability' all over the paper because the stability analysis is not done.
2) You should show in the introduction which are the new ideas of this paper with respect to the literature in the field. The motivation of your approach
should also be given.
3) You are advised to refine, in Section 1, the analysis of the literature in the field. The papers are correctly presented but you could be more specific.
4) The objectives of control are not presented.
5) The authors use various models in Section 2. How are these models next used in the design?
6) Please specify how did you compute the parameters of the controllers.
7) In the context of the comments 5) and 6), you are encouraged to emphasize the following few ideas that actually produce good results in control related to robotics: A novel auto-adapted path-planning method for a shape-shifting robot (IJICC 2011), Cascade control for telerobotic systems serving space medicine (IFAC PV 2011).
8) The number of references for a journal paper is low. The comment 6) helps.
I expect positive responses to all these comments, reflected in the revised version of the paper. It has potential to be appreciated by the audience of this
journal.
Author Response
Please see the attachment.
Response to Reviewer 1 Comments
The paper is related to the modeling and control of mobile multi-robot systems. The history of authors in robotics is worth to be mentioned.
The paper is appreciated and its revision is advised using these comments:
1) A careful editing must be done. Please check and polish. For example, you should take care to the formulation. You should replace 'stability' with
'movement stability' all over the paper because the stability analysis is not done.
The authors thank the reviewer for the remark and have made the suggested changes throughout.
2) You should show in the introduction which are the new ideas of this paper with respect to the literature in the field. The motivation of your approach
should also be given.
The authors enriched the introduction with previous work and edited the introduction to include a clear objective of the research work.
3) You are advised to refine, in Section 1, the analysis of the literature in the field. The papers are correctly presented but you could be more specific.
The authors agree with the reviewer and have done this.
4) The objectives of control are not presented.
5) The authors use various models in Section 2. How are these models next used in the design?
The authors agree with the reviewer and all variables in the mentioned equations as well as the rest of the manuscript have been explained. The authors also used one of the most widespread conventions for denoting scalars and matrices: scalars are denoted by italic non-bold font, and vectors/matrices are denoted by non-italic bold font. This clarifies comments 4) and 5)
6) Please specify how did you compute the parameters of the controllers.
The simulation parameters have been added to the manuscript so that the results can be reproduced by fellow researchers. This can be found on page 12 and 15.
7) In the context of the comments 5) and 6), you are encouraged to emphasize the following few ideas that actually produce good results in control related to robotics: A novel auto-adapted path-planning method for a shape-shifting robot (IJICC 2011), Cascade control for telerobotic systems serving space medicine (IFAC PV 2011).
The authors thank the reviewer for the comment and have inserted these methods in section 7 and find the work of real value.
8) The number of references for a journal paper is low. The comment 6) helps.
The reference list has also been enlarged with recent relevant work.
I expect positive responses to all these comments, reflected in the revised version of the paper. It has potential to be appreciated by the audience of this
journal.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This manuscript addresses a path planning methodology for multiple mobile robots that uses two layered hierarchy.
The topic is very important and is being addressed by several authors. This paper lacks this connection (a related work or state of the art section, even if brief).
Lines 142-152: there are several papers available in literature that addresses "path planning based on potential field". this topic could be improved and include some references.
Figure 11: please clarify: when does the mobile robot see the red obstacle? at what distance?
Figure 14: The A* makes it path planning just once? Or is continuously re-planning? It should be interesting to compare this last solution with the obtained results.
Figure 17: for multiple robots, why don't authors use a multiple layer A* planning? There are several works available at the state of the art.
Equations 2 to 5, there are some variables unexplained.
It is mainly well written, and some typos are pointed:
Line 15, 16: This paper proposed
Line 37: feedback [1] A repulsive… (missing dot)
Line 45: [2] should be before dot
Author Response
Please see the attachment.
Response to Reviewer 2 Comments
This manuscript addresses a path planning methodology for multiple mobile robots that uses two layered hierarchy.
The topic is very important and is being addressed by several authors. This paper lacks this connection (a related work or state of the art section, even if brief).
The authors thank the reviewer for the remark and have enriched the introduction with previous work and edited the introduction to include a clear objective of the research work.
Lines 142-152: there are several papers available in literature that addresses "path planning based on potential field". this topic could be improved and include some references.
The authors agree with the reviewer. Multiple navigation algorithms, such as the potential field method have been added to the manuscript. The reference list has also been enlarged with recent relevant work.
Figure 11: please clarify: when does the mobile robot see the red obstacle? at what distance?
The simulation parameters have been added to the manuscript so that the results can be reproduced by fellow researchers. For clarity, the robot detects the red obstacle at 2m (size of sensing envelope) but only starts avoiding it when it enters the security zone (1m). These two parameters are represented with R and S respectively
Figure 14: The A* makes it path planning just once? Or is continuously re-planning? It should be interesting to compare this last solution with the obtained results.
The A* path planner is only used at the start of navigation, thus there is no re-planning of the desired path. Instead, the robot recovers to the planned path after avoiding dynamic obstacles before proceeding to the goal. The authors do agree with reviewer in regard to testing an auto-adapted path planner, and this is included in Section 7.
Figure 17: for multiple robots, why don't authors use a multiple layer A* planning? There are several works available at the state of the art.
The authors agree with the reviewer to a certain extend. The paper mainly focuses on the improvement of the virtual impedance control method. However, a variety of global path planners can be used with the system and the on-going research will consider the suggested method as it can provide several advantages.
Equations 2 to 5, there are some variables unexplained.
The authors agree with the reviewer and all variables in the mentioned equations as well as the rest of the manuscript have explained. The authors also used one of the most widespread conventions for denoting scalars and matrices: scalars are denoted by italic non-bold font, and vectors/matrices are denoted by non-italic bold font.
It is mainly well written, and some typos are pointed:
Line 15, 16: This paper proposed
Line 37: feedback [1] A repulsive… (missing dot)
Line 45: [2] should be before dot
The authors thank the reviewer for all comments made and took all of them into consideration during the revising of the manuscript. A careful grammar edit was done on the revised manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper presents a multi-robot trajectory tracking algorithm based on impedance control, which avoids obstacles and local minima, by adaptively tuning the impedance gains.
Many aspects of the paper need to be greatly improved. These are:
1) English revision is required. The authors use "clustered" many times, but it seems that they want to use "cluttered" instead. In addition to this, there are many other grammar mistakes or typos, please go through the paper and revise all of them.
2) The introduction is too short, and it contains almost no citations to previous work. The reference list in the end seems insufficient. The introduction should be a bit longer, and especially, it should provide a clear portrait of this research field. This is a well researched problem that has a large body of literature available, so the introduction should be enriched with this body of literature, and the proposed work should be contrasted with this body of literature in order to highlight the novelty, contribution and value of it.
3) Many equations are difficult to follow because the authors did not distinguish between scalar variables and matrix or vector variables. Please, follow one of the most widespread conventions for denoting scalars and matrices: scalars should be denoted by italic non-bold font, and vectors/matrices should be denoted by non-italic bold font.
4) In addition to this, many of the variables or parameters appearing in the equations are not defined in the text. The meaning of some of them can be inferred from figures or by common sense, but to avoid confusion, the authors should explicitly define the meaning of every variable or parameter appearing in their equations. Thus, I recommend that the authors go throughout the manuscript and make a list of all variables and parameters appearing, making sure that they all are clearly defined, either in a table at the beginning of the paper, or by defining these variables the first time they appear in the manuscript.
5) Equation (6): should it be dji > Lblock, instead of "less than" (<)?
6) Equations (4) and (5): should it be plus (+) Dijmobiles and plus (+) Dijobstacles, instead of minus (-)? Coherence with (2) and with the rest of the equations tells me that it should be plus (+).
7) Moreover, why include the velocity of Sj in equation (5)? Aren't obstacles supposed to be static in this paper? If not, then they can be treated like mobile obstacles using equation (4).
8) As I remarked previously, please make sure to define all variables and parameters appearing in all equations, and that these equations match the figures. For example: Figure 4 (which should be made bigger, to clearly see it) has angle theta, whereas equations (7) to (10) include greek angle phi instead of theta (moreover, this does not seem to be the greek symbol phi, but it looks more like the standard symbol for diameters).
9) Also, I cannot understand equations (7) to (10). What are "traj" and "pose"?? They seem to mean "trajectory" and "pose", but they are used as scalars for computing the orientation and velocity in equations (7) and (9), which makes little sense. Please clarify this.
10) Lines 201 to 203 are not completely accurate. They state that integration of equation (18) yields speed, whereas a second integration yields "acceleration" (do you mean position??). Actually, equation (18) is a state equation, i.e., a first-order differential matrix equation, so it only needs to be integrated once in order to find both velocity and position simultaneously.
11) Section 6 needs many improvements. For example, this section does not provide enough data to guarantee that the research can be reproduced. The authors should provide the values of all tuning parameters that they used as input data for obtaining the shown experiments and simulations. What are the numeric values of the tuning parameters of the adaptation algorithm of section 5? What are the numeric parameters of the reference model of section 4? What are the masses of the robots? And what are the initial values of the impedance gains K and D? And how do these impedances evolve over time during the experiments? The analysis of section 6 needs to be enriched with all this information, to guarantee that the presented research is reproducible.
12) Section 6 has several figures with subfigures (a, b, c, d...) showing the results of the presented method. Please, when explaining these figures in the text, make explicit reference to these subfigures as you explain the results. Otherwise, it becomes more difficult to follow the explanations.
13) The quality of all figures should be improved, especially those of the results section (otherwise, they look too pixelated and it gives the impression that these trajectories are drawn using powerpoint, instead of using Matlab graphs). For the Matlab figures, it would be better if you remove the outer part of the Windows interface, and you only paste the XY chart instead. You can do this easily as follows: Edit -> Copy Figure, then you go to your preferred image edition software (Powerpoint, Paint...) and paste it.
14) Please, can you provide a video with the recording of the animation of the simulations in Matlab? This can be provided as supplementary material when submitting the paper. It would be useful to see the experiments of Figures 11, 14, 17 in motion.
15) Finally, the conclusions section must be improved. The authors should discuss in more detail their findings in this section (only a few lines are used for discussing their findings in the conclusions). And the future work should be more elaborated and more related to the presented work (how will the presented work evolve in future research?). For example: is it really necessary to mention the COVID-19 pandemic in the future work section? Regarding lines 487-501, they repeat too many times the same words and ideas: adding a manipulator to the mobile robot will surely pose new challenges due to the need to accurately grasp objects (what I mean is that these lines 487-501 can be greatly summarized and polished). And the ideas suggested in the last paragraph seem a bit too forced: why mention the use of brain-computer interfaces to control a set of mobile robots? This has little to do with the topic of this paper (automatic planning the motion of a set of robots so that they do not collide with the environment or with each other while following desired trajectories).
Please do not misinterpret me: I am not saying that these ideas mentioned in the future work are bad, I just think that they are a bit too far from the work presented in this manuscript. The future work should point out research lines that are more immediately related to what was presented in this manuscript (autonomous trajectory planning and control), to remain more focused on the topic.
Author Response
Please see the attachment.
Response to Reviewer 3 Comments
This paper presents a multi-robot trajectory tracking algorithm based on impedance control, which avoids obstacles and local minima, by adaptively tuning the impedance gains.
Many aspects of the paper need to be greatly improved. These are:
1) English revision is required. The authors use "clustered" many times, but it seems that they want to use "cluttered" instead. In addition to this, there are many other grammar mistakes or typos, please go through the paper and revise all of them.
The authors agree that the word “clustered” was used incorrectly and have made changes. Further grammar checks have been done as well.
2) The introduction is too short, and it contains almost no citations to previous work. The reference list in the end seems insufficient. The introduction should be a bit longer, and especially, it should provide a clear portrait of this research field. This is a well researched problem that has a large body of literature available, so the introduction should be enriched with this body of literature, and the proposed work should be contrasted with this body of literature in order to highlight the novelty, contribution and value of it.
The authors enriched the introduction with previous work. The reference list has also been enlarged with recent relevant work.
3) Many equations are difficult to follow because the authors did not distinguish between scalar variables and matrix or vector variables. Please, follow one of the most widespread conventions for denoting scalars and matrices: scalars should be denoted by italic non-bold font, and vectors/matrices should be denoted by non-italic bold font.
All scalars and vectors/matrices are denoted according to the suggested method.
4) In addition to this, many of the variables or parameters appearing in the equations are not defined in the text. The meaning of some of them can be inferred from figures or by common sense, but to avoid confusion, the authors should explicitly define the meaning of every variable or parameter appearing in their equations. Thus, I recommend that the authors go throughout the manuscript and make a list of all variables and parameters appearing, making sure that they all are clearly defined, either in a table at the beginning of the paper, or by defining these variables the first time they appear in the manuscript.
The authors inserted explanations of all variables in text as they appear in the manuscript.
5) Equation (6): should it be dji > Lblock, instead of "less than" (<)?
The authors thank the reviewer. It is a typo and was fixed.
6) Equations (4) and (5): should it be plus (+) Dijmobiles and plus (+) Dijobstacles, instead of minus (-)? Coherence with (2) and with the rest of the equations tells me that it should be plus (+).
The authors agree with the review to a certain extend. The sign will not be a problem as the coefficients are obtained by optimization. However, in order to keep the right meaning, regarding the physical meaning when it comes to obstacles (fixed or mobile) avoidance, the sign is changed to +.
7) Moreover, why include the velocity of Sj in equation (5)? Aren't obstacles supposed to be static in this paper? If not, then they can be treated like mobile obstacles using equation (4).
The authors agree with the reviewer. The equations are deduced directly from the damping forces in general case based on the interaction of 2 objects in the virtual field. When implemented the dSj/dt=0. For clarity, this is removed.
8) As I remarked previously, please make sure to define all variables and parameters appearing in all equations, and that these equations match the figures. For example: Figure 4 (which should be made bigger, to clearly see it) has angle theta, whereas equations (7) to (10) include greek angle phi instead of theta (moreover, this does not seem to be the greek symbol phi, but it looks more like the standard symbol for diameters).
The authors agree with the reviewer and reworked the entire section as there were indeed fundamental errors.
9) Also, I cannot understand equations (7) to (10). What are "traj" and "pose"?? They seem to mean "trajectory" and "pose", but they are used as scalars for computing the orientation and velocity in equations (7) and (9), which makes little sense. Please clarify this.
These equations were incorrectly used and have been removed. Correct kinematic equations have been inserted with relevant references.
10) Lines 201 to 203 are not completely accurate. They state that integration of equation (18) yields speed, whereas a second integration yields "acceleration" (do you mean position??). Actually, equation (18) is a state equation, i.e., a first-order differential matrix equation, so it only needs to be integrated once in order to find both velocity and position simultaneously.
The authors thank the reviewer for the remark. It is typo and is was corrected. Indeed, the integration of the state space equation (18 in old paper, equation 17 in revised paper) yields to speed and the position.
11) Section 6 needs many improvements. For example, this section does not provide enough data to guarantee that the research can be reproduced. The authors should provide the values of all tuning parameters that they used as input data for obtaining the shown experiments and simulations. What are the numeric values of the tuning parameters of the adaptation algorithm of section 5? What are the numeric parameters of the reference model of section 4? What are the masses of the robots? And what are the initial values of the impedance gains K and D? And how do these impedances evolve over time during the experiments? The analysis of section 6 needs to be enriched with all this information, to guarantee that the presented research is reproducible.
The simulation parameters have been added to the manuscript so that the results can be reproduced by fellow researchers.
12) Section 6 has several figures with subfigures (a, b, c, d...) showing the results of the presented method. Please, when explaining these figures in the text, make explicit reference to these subfigures as you explain the results. Otherwise, it becomes more difficult to follow the explanations.
Noted, these errors have been corrected.
13) The quality of all figures should be improved, especially those of the results section (otherwise, they look too pixelated and it gives the impression that these trajectories are drawn using powerpoint, instead of using Matlab graphs). For the Matlab figures, it would be better if you remove the outer part of the Windows interface, and you only paste the XY chart instead. You can do this easily as follows: Edit -> Copy Figure, then you go to your preferred image edition software (Powerpoint, Paint...) and paste it.
The authors thank the reviewer for this comment, Mr. Engelbrecht has improved the quality of the figures, using the suggested method
14) Please, can you provide a video with the recording of the animation of the simulations in Matlab? This can be provided as supplementary material when submitting the paper. It would be useful to see the experiments of Figures 11, 14, 17 in motion.
Mr. Engelbrecht will record the motion videos and upload as soon as possible.
15) Finally, the conclusions section must be improved. The authors should discuss in more detail their findings in this section (only a few lines are used for discussing their findings in the conclusions). And the future work should be more elaborated and more related to the presented work (how will the presented work evolve in future research?). For example: is it really necessary to mention the COVID-19 pandemic in the future work section? Regarding lines 487-501, they repeat too many times the same words and ideas: adding a manipulator to the mobile robot will surely pose new challenges due to the need to accurately grasp objects (what I mean is that these lines 487-501 can be greatly summarized and polished). And the ideas suggested in the last paragraph seem a bit too forced: why mention the use of brain-computer interfaces to control a set of mobile robots? This has little to do with the topic of this paper (automatic planning the motion of a set of robots so that they do not collide with the environment or with each other while following desired trajectories).
The authors agree and edited the mentioned paragraphs. Neural networks form part of our on-going research, this is the reason why it is included. However, the BCI section was removed as it does not synergise well with the work of the paper.
Please do not misinterpret me: I am not saying that these ideas mentioned in the future work are bad, I just think that they are a bit too far from the work presented in this manuscript. The future work should point out research lines that are more immediately related to what was presented in this manuscript (autonomous trajectory planning and control), to remain more focused on the topic.
The authors thank the reviewer for all comments made and took all of them into consideration during the revising of the manuscript.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors did a great job in the revision of this very good manuscript. Their efforts are appreciated.
The responses to my comments are well documented and supported by relevant information.
Moreover, all these responses are reflected in the improvement of the manuscript. Therefore, the revised manuscript is correct and technically sound.
I especially appreciate the validation. This revised manuscript contains a sound theory and an illustrative validation, which accompanies and also supports the theoretical claims.
Concluding, I agree again with the publication of this manuscript. This manuscript will certainly continue authors' other past well-acknowledged manuscripts in the growing field of the manuscript.
I estimate that the manuscript will have a high impact for the readers of this highly ranked journal.
Author Response
The authors would once again like to thank the reviewer for the comments.
