Balance Control of a Quadruped Robot Based on Foot Fall Adjustment

Round 1

Reviewer 1 Report

Dear Authors, thank you for your paper.

Here follow some suggestions to improve it before pubblication:

1) in equations 4 and 5 they appear some fixed coefficients; it is not clear how they were selected; a discussion about this poit could be youseful. What if different values were selected?

2) in lines 158-159 you write that "the diagonal legs need to land at the same time to improve the flight rate"; it is not clear if and how you plan to control the difference between the two landing time, you only explain how you use this difference to control the landing attitude. You should better explain this point

3) In line 280 you set the friction coefficient of the robot to 0.5. Is this the friction coefficient between feet and surface? Why do you assume 0.5? What if it is lower?

4) It is necessary to specify the main size of the robot (length and width of the platfonrm, length of the links of the legs) in order to understand what does a 40 mm step involve

5) in figure 10 and 12 you propose a comparison of roll and pitch with and without the proposed strategy. It would be more effective to compare on the same graph the same data with and without your strategy, i.e: fig 10a end 12a Pitch, with and without strategy, 10b and 12b Roll with and without strategy. Use larger characters in the pictures

Line 310-311, you write "The oscillation 310 center of roll angle and pitch angle converges to 0, and the oscillation amplitude of pitch 311 angle decreases. It is not clear where does the reader see this

 

Line 320: you should explain if the force is applied as a step or with a ramp and if it is mantained until the end of the simulation or if it falls down to zero after a while

 

Author Response

Cover letter

Dear Editor-in-Chief,

Thanks to the reviewers for the thoughtful and thorough review. Your comments are helpful to us in revising our paper. We have revised and resubmitted our manuscript entitled “Balance Control of A Quadruped Robot Based on Foot Fall Adjustment” (applsci-1536708). We have made changes to our manuscript in accordance with the reviewers′ comments. The revised portion has been marked in highlight in the revised paper. Hopefully we have addressed all of your concerns. 

We confirm that this manuscript has not been published elsewhere and is not under consideration by another journal. All authors have approved the manuscript and agree with its submission to Applied Sciences.

The authors declare that there are no competing interests regarding the publication of this paper. There is no conflict of interest with any of the suggested reviewers.

Please let me know of your decision at your earliest convenience.

Best regards,

Wenkai Sun

Response to reviewers

Manuscript ID: applsci-1536708

January 19, 2022

Thanks to the reviewers for the thoughtful and thorough review. Point-by-point responses to the reviewers’ comments are stated below in texts with dark red color. Hopefully we have addressed all of your concerns.

 Reviewer #1:

1. In equations 4 and 5 they appear some fixed coefficients; it is not clear how they were selected; a discussion about this point could be useful. What if different values were selected?

Response: Your kind assistance on our manuscript is very much appreciated.We assumed that the trajectory curve is a cubic spline, the step length and step height of the foot target trajectory are S and H, respectively. The initial position of the foot end is (-20,0,0), the unit is mm, the speed at the beginning and end are 0, and the movement period is T. According to these conditions, the foot trajectory curve of quadruped robot is realized. If there are any other modifications we could make, we would like very much to modify them and we really appreciate your help.

2. In lines 158-159 you write that "the diagonal legs need to land at the same time to improve the flight rate"; it is not clear if and how you plan to control the difference between the two landing time, you only explain how you use this difference to control the landing attitude. You should better explain this point

Response: Thanks very much for your suggestion. We use the flight rate as a condition to determine whether the robot has reached steady state. To show this more clearly, we add the flow chart of strategy adjustment.

3. In line 280 you set the friction coefficient of the robot to 0.5. Is this the friction coefficient between feet and surface? Why do you assume 0.5? What if it is lower?

Response: Thanks very much for your suggestion. 0.5 is the friction coefficient between feet and surface. To make the experiment more universal, we adopted the default physical parameters in the Webots simulation environment, and we added a description of this point to the paper.

4. It is necessary to specify the main size of the robot (length and width of the platfonrm, length of the links of the legs) in order to understand what does a 40 mm step involve.

Response: Thanks for your helpful suggestions and we totally agree with your comments.We add the description table of the physical parameters of the robot in the simulation environment.

5. In figure 10 and 12 you propose a comparison of roll and pitch with and without the proposed strategy. It would be more effective to compare on the same graph the same data with and without your strategy, i.e: fig 10a end 12a Pitch, with and without strategy, 10b and 12b Roll with and without strategy. Use larger characters in the pictures Line 310-311, you write "The oscillation 310 center of roll angle and pitch angle converges to 0, and the oscillation amplitude of pitch 311 angle decreases. It is not clear where does the reader see this?Line 320: you should explain if the force is applied as a step or with a ramp and if it is mantained until the end of the simulation or if it falls down to zero after a while

Response: Thanks for your helpful suggestions and we totally agree with your comments. We conducted the experiment again and modified the comparison data according to your suggestion. To make it clearer, we changed the units of radians to angles. At the same time, we do a more rigorous description and analysis of the experimental results.We changed the description of impact from force to impulse.

 

 

Reviewer 2 Report

This paper proposed a balance control method using foot fall adjustment for a quadruped robot doing diagonal gait. The authors defined and used the flight rate as an index to estimate the stability during the diagonal gait. When determining the flight rate, they used the time difference between the landing time of the two diagonal legs. Also, they developed their balance control method that increase the flight rate and lead to the stability improvement. For evaluating the method, the Webot simulation software was used for the simulations of ground walking and lateral impact. The results of the two simulations show that the stability of the quadruped robot can be improved by applying the balance control method. However, there are several recommendations to improve the readibility of the paper.

1) It would be better to use a name for the quadruped robot instead of using the experssion of our robot in the caption of Fig. 1.

2) Fig. 3 needs more explanations. For example, the explanations about what are the diagonal leg and the virtual leg in Fig. 3 and how they can be equal are necessary.

3) In Fig. 5, the symbols of W, w' and w'' can be shown in an additional figure by using the different view of the robot.

4) I' and I'' in line 167 do not appear in following sentences or paragraphs. They may be typos.

5) In the captions of the four cases of Fig. 6, there are typos that are "In (a)".

6) In line 186, it looks like that "legs rise from air to ground" has a typo.

7) More explanations for how the body shift and shake in line 197~199 is needed. For example, the explanations for what is the body motions of shift and shake can be provided.

8) When determining d2 and d1 in Equation (12) and (13), how the half of phi can be used needs additional explanations because the angle phi seems not symetrical with respect to the center line.

9) Additional representation of using a flow chart for gait adjustment strategy can be helpful.

10) Additional explanation about the quadruped J in line 261 is necessary because J is not used in following equations.

11) In Section 4 about simulation, the word 'experiment' is used several times. It is recommended to use the word 'simulation' instead of 'experiment' because experiments are conducted by using acutal hardware. (In lines of 270, 277, 284, 286, 289, 314, 318, 342, and 346)

12) In line 280, the friction coefficient is used, which needs more explanations. For example, where the friction is assumed to occur can be explained.

13) If the step length and height used in line 289 are S and H in Equation 4 and 5, it would be better to mention that they are the same.

14) Figures used in Fig. 10 and 11 need more descriptions because the differences between the figures are not apparent. The use of the time stamp of figures may be helpful for better understanding. Also, using degree for the unit of the angles would be better because degree unit are usually more intuitive. Additionaly, overlaying the results of using the adjustment strategy or not would be better for comparing the results. For example, (a) can show the results of roll angles with and without the adjustment strategy.

15) When flat ground walking, the robot starts in the air 3 cm away from the ground, which seems to be longer than the total length of the leg (17.75 = L1 + L2 + L3). Does the robot start to fall in the beginning of the flat ground walking?

16) It looks like that the length of leg used in simulations are presented in the paper. The other dimensions of the robot used in simulations, such as the length, width, thickness of trunk, weight of the robot, should be also presented.

Author Response

Cover letter

Dear Editor-in-Chief,

Thanks to the reviewers for the thoughtful and thorough review. Your comments are helpful to us in revising our paper. We have revised and resubmitted our manuscript entitled “Balance Control of A Quadruped Robot Based on Foot Fall Adjustment” (applsci-1536708). We have made changes to our manuscript in accordance with the reviewers′ comments. The revised portion has been marked in highlight in the revised paper. Hopefully we have addressed all of your concerns. 

We confirm that this manuscript has not been published elsewhere and is not under consideration by another journal. All authors have approved the manuscript and agree with its submission to Applied Sciences.

The authors declare that there are no competing interests regarding the publication of this paper. There is no conflict of interest with any of the suggested reviewers.

Please let me know of your decision at your earliest convenience.

Best regards,

Wenkai Sun

Response to reviewers

Manuscript ID: applsci-1536708

January 19, 2022

Thanks to the reviewers for the thoughtful and thorough review. Point-by-point responses to the reviewers’ comments are stated below in texts with dark red color. Hopefully we have addressed all of your concerns.

 Reviewer #2:

1. It would be better to use a name for the quadruped robot instead of using the experssion of our robot in the caption of Fig. 1.

Response: Thanks very much for your suggestion. We feel sorry for our inappropriate expression. As the reviewer suggested, we have revised the description here.

2. Fig. 3 needs more explanations. For example, the explanations about what are the diagonal leg and the virtual leg in Fig. 3 and how they can be equal are necessary.

Response: Thanks very much for your careful reading. We feel sorry for our inappropriate expression. We describe the principle of this part in more detail and add references.

3. In Fig. 5, the symbols of W, w' and w'' can be shown in an additional figure by using the different view of the robot.

Response: Thanks very much for your suggestion. We added another view of the robot to the paper.

4. I' and I'' in line 167 do not appear in following sentences or paragraphs. They may be typos.

Response: Thanks for your careful review. We feel sorry for our typos. We have made corrections in the article.

5. In the captions of the four cases of Fig. 6, there are typos that are "In (a)".

Response: Thanks for your careful review. We feel sorry for our typos. We have made corrections in the article.

6. In line 186, it looks like that "legs rise from air to ground" has a typo.

Response: Thanks for your careful review. We feel sorry for our typos. We have made corrections in the article.

7. More explanations for how the body shift and shake in line 197~199 is needed. For example, the explanations for what is the body motions of shift and shake can be provided.

Response: Thanks very much for your careful reading. We feel sorry for our inappropriate expression. We have rewritten the expression of this part and add references.

8. When determining d2 and d1 in Equation (12) and (13), how the half of phi can be used needs additional explanations because the angle phi seems not symetrical with respect to the center line.

Response: Thanks for your careful review. We feel sorry for our inappropriate expression. We have made corrections of the expression in the article.

9. Additional representation of using a flow chart for gait adjustment strategy can be helpful.

Response: Thanks for your helpful suggestions and we totally agree with your comments.We added a flow chart of gait adjustment to the paper

10. Additional explanation about the quadruped J in line 261 is necessary because J is not used in following equations.

Response: Thanks for your careful review. We feel sorry for our typos. We have deleted J in the paper

11. In Section 4 about simulation, the word 'experiment' is used several times. It is recommended to use the word 'simulation' instead of 'experiment' because experiments are conducted by using acutal hardware. (In lines of 270, 277, 284, 286, 289, 314, 318, 342, and 346).

Response: Thanks for your careful review. We feel sorry for our inappropriate expression. We have made corrections of the expression in the article.

12. In line 280, the friction coefficient is used, which needs more explanations. For example, where the friction is assumed to occur can be explained.

Response: Thanks very much for your suggestion. The coefficient of friction is between the foot and surface. To make the experiment more universal, we adopted the default physical parameters in the Webots simulation environment, and we added a description of this point to the paper.

13. If the step length and height used in line 289 are S and H in Equation 4 and 5, it would be better to mention that they are the same.

Response: Thanks very much for your suggestion. We have added the expression of this point in the article.

14. Figures used in Fig. 10 and 11 need more descriptions because the differences between the figures are not apparent. The use of the time stamp of figures may be helpful for better understanding. Also, using degree for the unit of the angles would be better because degree unit are usually more intuitive. Additionaly, overlaying the results of using the adjustment strategy or not would be better for comparing the results. For example, (a) can show the results of roll angles with and without the adjustment strategy.

Response: Thanks for your helpful suggestions and we totally agree with your comments. We conducted the experiment again and modified the comparison data according to your suggestion. We also changed the units of radians to angles. At the same time, we revised the description and analysis of the experimental results.

15. When flat ground walking, the robot starts in the air 3 cm away from the ground, which seems to be longer than the total length of the leg (17.75 = L1 + L2 + L3). Does the robot start to fall in the beginning of the flat ground walking?

Response: Thanks for your careful review. We feel sorry for our typos. We made a mistake with the units in the manuscript, which we have corrected in the article.

16. It looks like that the length of leg used in simulations are presented in the paper. The other dimensions of the robot used in simulations, such as the length, width, thickness of trunk, weight of the robot, should be also presented.

Response: Thanks for your helpful suggestions and we totally agree with your comments.We add the description table of the physical parameters of the robot in the simulation environment.

 

Round 2

Reviewer 1 Report

The authors improved the paper according to comments to version 1. The work is now ready for publication