Dynamic Modeling of the Dissipative Contact and Friction Forces of a Passive Biped-Walking Robot
Round 1
Reviewer 1 Report
The authors have addressed all the issues from the previous reviews. The content of the paper is not outstanding, but in the current form, there is not much that can be improved. There is still some space for improving the quality of the presentation.
Author Response
Dear Reviewer,
We want to show our gratitude for the time spent on improving our paper.
To facilitate the revision, we have highlighted in red the changes in the manuscript. Below is our response to your comments:
The authors have addressed all the issues from the previous reviews. The content of the paper is not outstanding, but in the current form, there is not much that can be improved. There is still some space for improving the quality of the presentation:
- We have carefully reviewed the presentation. Several images have been modified, size, colors and labels. And small changes in the wording.
- We have changed the signature of the figure 6. Modified its description in the text to make it clearer. And modified the image and its labels.
- We have made the figure 11 and 12 bigger, to facilitate its reading.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Fig. 6. The signature is wrong. Error unit (s) ?
Fig. 12. The figure is not redable -I understand it is an effect os scale.
Author Response
Dear Reviewer,
We want to show our gratitude for the time spent on improving our paper.
In this new version, we have made the modifications suggested by you.
To facilitate the revision, we have highlighted in red the changes in the manuscript. Below is our point-by-point response to your comments:
- Fig. 6. The signature is wrong. Error unit (s) ?
We have changed the signature of the figure 6. Modified its description in the text to make it clearer. And modified the image and its labels. We have clarified this: the error don’t have unit [%]. And the error is obtained comparing time periods [s]. (Line 233)
-Fig. 12. The figure is not redable -I understand it is an effect os scale.
We have made the figure 11 and 12 bigger, to facilitate its reading.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper studied the modeling and dynamics for contact problem of a passive biped-walking robot. It is well written and easy to follow. The scientific content should be solid. Before the article can be published, some points need to be addressed. The authors should further summarize the main contribution to the society. Key novelties and merits over established researches need to be clearly stressed. Make more discussions about the different contact models. Please compare and discuss in the paper the similarity and difference of the typical contact and friction model used in rotatory multi-body systems, see Energies 2019, 12(22), 4365. Figure 6 gives the error analysis and relative errors are discussed in the text. However, the errors are not directly demonstrated in the figure. The authors are advised to plot the overall error rate vs step numbers for a continuous comparison.
Author Response
Dear Reviewer,
We want to show our gratitude for the time spent on improving our paper.
In this new version, we have made the modifications suggested by you.
To facilitate the revision, we have highlighted in red the changes in the manuscript. Below is our point-by-point response to your comments:
This paper studied the modeling and dynamics for contact problem of a passive biped-walking robot. It is well written and easy to follow. The scientific content should be solid. Before the article can be published, some points need to be addressed:
-The authors should further summarize the main contribution to the society. Key novelties and merits over established researches need to be clearly stressed
The “conclusion” section has been rewritten to make the merits clearer, and the contribution to the scientific community have been added. (Line 367-392)
-Make more discussions
The “results and discussions” section has been rewritten (line 266-360) and some discussions have been summarized in the “conclusion” section. (Line 367-392)
-Please compare and discuss in the paper the similarity and difference of the typical contact and friction model used in rotatory multi-body systems, see Energies 2019, 12(22), 4365.
Without a doubt, the application of dynamics with friction is very interesting. And if there is also clearance, the dynamic study is very complicated. The dynamic / vibration analysis of rotors is a very important topic in the scientific community. We have added the comparison to the proposed reference and this text in the manuscript (line 203-212):
“Dynamic analysis with friction is a topic widely studied in the scientific community. In our model we focus on an analysis of a passive mechanism, which is very sensitive to small dynamic changes. Another interesting way to research dynamic analysis with friction would be on rotating machines with clearance. Chao Fu et Al.[34] carried out a research of the nonlinear vibrations of an uncertain system with clearance and friction. Chao define the dynamical of the rotor and stator with three critical parameters involved in the impact between the rotor and case: the clearance, the contact stiffness, and the friction coefficient. Chao Fu et Al. used the uncertainty propagation analysis method (non-intrusive).This research also suggest that small uncertainties may propagate and cause significant variabilities in the nonlinear response. This method could help for the rub-impact fault (friction and clearance) diagnosing, and can be used to investigate other general nonlinear mechanical system”
[34]Chao Fu, Dong Zhen,Yongfeng Yang, Fengshou Gu and Andrew Ballet. Effects of Bounded Uncertainties on the Dynamic Characteristics of an Overhung Rotor System with Rubbing Fault. Energies 2019, 12(22), 4365; https://doi.org/10.3390/en12224365
-Figure 6 gives the error analysis and relative errors are discussed in the text. However, the errors are not directly demonstrated in the figure.
Figure 6 and the text has been modified to facilitate its understanding. This text, with the numerical errors, has been added (line 233):
“Figure 6 shows the time period of every step of Liu's experiments compared to the time period of our model under the same initial conditions. The Error between the model and the average of the experiments of every step are: 8.02%,0.42%,1.69%,2.56%,7.69%,0.00%,4.00%.”
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The MS has been improved by the modifications as to merit publication. Just two minor spelling. Line 265: efficient ---> efficiency; Line 470: Andrew Ballet ---> Andrew Ball.
Author Response
We would like to thank you again for your review and quick response.
We have changed the two word in the manuscript:
Line 265: efficient ---> efficiency;
Andrew Ballet ---> Andrew Ball.
Regards
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Interesting work is presented in this paper. However, the presentation in this paper is not clear. Here are some comments:
Page 3, Line 119: “, denotes the relative normal contact velocity…” Something is missing in front of “denotes”. In addition, the authors need to check the equation in Line 118, the dot shall be directly on the top of Delta to represent the time derivative. It is better to place the equation in a single line and number it for later reference. Line 200/201, are there formulas to calculate K and X based on the radius of the feed and the material properties of the feet and the floor? Or, are K and X empirical constants? In most figures, labels are too small to read. The authors shall enlarge them. Line 170, “For a higher slope, the angle are increasing in every step and gaining kinematic …” I think the authors want to address “At a higher slope, the leg angle is larger ….”. The authors need to check English carefully in this paper. Line 186, “these methods have been known for more than 100 years, but their potential was not fully realized until computer became available.” I don’t agree with the authors. Euler method is the first order Rung-Kutta method. I guess the Rung-Kutta method the authors mentioned is the fourth-order classic Rung-Kutta method. If the same step size is used, the 4th order R-K method is much better than Euler’s method. Figure 10 compares the results from Euler's method. What’s the step size? If no step sizes are mentioned for ode, Euler and R-k methods, it doesn’t make any sense to compare three methods in Figure 13. is "the ode integrator scheme" the ode solver of MATLAB? if it is, it is definitely better than Euler and R-K method because it is optimized.Author Response
Dear Review1,
We would like to thank you for taking the time to review this manuscript.
Your comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied yours comments carefully and have made correction.
Below is our point-by-point response to yours reviewers' comments. We have highlighted in red our responses and changes to the manuscript to facilitate the review:
Page 3, Line 119: “, denotes the relative normal contact velocity…” Something is missing in front of “denotes”.
Right, the velocity of penetration symbol was missing. It's been added. (line 126)
In addition, the authors need to check the equation in Line 118, the dot shall be directly on the top of Delta to represent the time derivative. It is better to place the equation in a single line and number it for later reference.
Thank you for your advice. The point of the derivative was moved. It’s been corrected. We believe these failures may be due to the conversion of the file. We will pay special attention when saving so this kind of failures doesn’t happen again.
Also, we've placed the equation on a single line for better reading.
Line 200/201, are there formulas to calculate K and X based on the radius of the feed and the material properties of the feet and the floor? Or, are K and X empirical constants?
The parameters K and X are the stiffness parameter and the hysteresis damping factor respectively, which are dependent on the radius of the feet and the material properties of both the feet and floor. The radius is defined in the geometric considerations of the model, while the properties of the feet and floor are the same as the real experiment carry out by Ning Liu model [ref 31].
We've rewritten this better to make it clear on line 125
In most figures, labels are too small to read. The authors shall enlarge them.
Thank you for your advice. We've increased the size of the figures .
Line 170, “For a higher slope, the angle are increasing in every step and gaining kinematic …” I think the authors want to address “At a higher slope, the leg angle is larger ….”.
We've rewritten that sentence. Line 187
The authors need to check English carefully in this paper.
We've checked carefully the English.
Line 186, “these methods have been known for more than 100 years, but their potential was not fully realized until computer became available.” I don’t agree with the authors. Euler method is the first order Rung-Kutta method. I guess the Rung-Kutta method the authors mentioned is the fourth-order classic Rung-Kutta method. If the same step size is used, the 4th order R-K method is much better than Euler’s method.
That’s right. We compared the three most used methods, according to the literature. We have also clarified that we refer to the second-order classic Rung-Kutta, pointing out that the potential has not been "fully" achieved until modern computers. Like the MSD. Line 202
Figure 10 compares the results from Euler's method. What’s the step size? If no step sizes are mentioned for ode, Euler and R-k methods, it doesn’t make any sense to compare three methods
Figure 10 and Figure 11 are shown to compare the error propagation control (constraints violations). On Figure it can be seen that the constraints violation grows out of control with the standard method. We have increased the size of the image to appreciate more the error rate (figure 10: 10-11, figure 11: 10-13). We have also rewritten that text to make the comparison clearer. line 207
in Figure 13. is "the ode integrator scheme" the ode solver of MATLAB? if it is, it is definitely better than Euler and R-K method because it is optimized.
We compare the most popular numerical integrator methods (ODE, Euler, Runge-Kutta). When we say Ordinary Differential Equations, "ODE", we mean ode45 integrator from Matlab. The results confirm your affirmation: the fastest is ODE.
It seems trivial, but for models with contact and friction force with energy dissipation sometimes the results are not as expected. And for this research we wanted to check and compare every possible feature.
Author Response File: Author Response.pdf
Reviewer 2 Report
the paper is about the dynamic modeling of a biped walking robot.
a major weakness of the paper is that it lacks model of biped walking dynamics. this brings further problem to understand and assess the influnce of contact and friction forces. this makes difficulty to justify their simulations, without dynamic model of the system.
another weakness of the Work is that it is limited to simulation only. experimental Works are not included. it is needed to perform testing and compare experimental results with the simulations, with their prototypes.
Author Response
Dear Review2,
We would like to thank you for taking the time to review this manuscript.
Your comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied yours comments carefully and have made correction.
Below is our point-by-point response to yours reviewers' comments. We have highlighted in red our responses and changes to the manuscript to facilitate the review:
A major weakness of the paper is that it lacks model of biped walking dynamics. this brings further problem to understand and assess the influnce of contact and friction forces. this makes difficulty to justify their simulations, without dynamic model of the system.
The introduction shows a state of the art of passive dynamics. Since Mc Geer and the simplest models, more complex models of passive bipeds have been defined and developed.
Although many models have been designed, but none of them considers friction or energy dissipation. This is because being a passive system, achieving stability is not so trivial. Just to fill the gap in the lack of this kind of models, we have developed this model that does consider impact, friction and dissipative forces.
It should be noted that one of the novelties of the model is above all the application of: impact/contact detection, normal and friction force and dissipative force; in the same model. And that it works stably in a passive way. Passive models must be well defined; otherwise, a small variation can be catastrophic.
Another weakness of the Work is that it is limited to simulation only. experimental Works are not included. it is needed to perform testing and compare experimental results with the simulations, with their prototypes.
You are right, we haven't carried out any experiments, but the results of our model have been compared with the real experimental results of Ning Lui [ ref 31]. Line 139
The passive biped performed by Ning Lui, as well as the results obtained have seemed to us reliable enough to be considered. We have not found it necessary to repeat the experiment and measurements, as it has already been done in the literature. The geometrical, dynamic and material properties, including the results achieved, have been obtained and compared from these publications: [ref 17], [ref 27].
Thanks to this we have been able to verify our model, since with the same initial conditions and properties we achieved the same results and behavior.
We've rewritten this part of the manuscript to make it clearer.
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper under review is dealing with the problem of modelling the dissipative contact and friction forces during the locomotion fo the passive biped-walker.
The paper is written clearly and there are no problems with following it. However, a clear statement about the contribution made by the authors is missing. Additionally, the journal paper requires to be more specific. When stating in conclusions that the "smooth forward dynamics equations for the whole walking are presented and verified" there should be an equation in the text. But as the reader, I could not find it.
Another issue is the lack of experimental results from the real platform. The authors have tested their model in the simulation. However, there is no validation if the proposed model meets reality. Is it possible to predict how large is the reality gap between the simulation and the real experiments? The verification presented in the paper is only qualitative, not quantitive.
Next issue is related to the problem of the solvers comparison. The problem is not exactly related to the method but to the MATLAB implementation, which could not be regarded as the flawless. As the MATLAB is proprietary we as the researchers do not have access to the code and we can not tell if the coders did not make any mistake.
There are also some technical issues which mainly are related to the quality of the figures which have low resolution and are pasted using jpeg compression which introduces artefacts around the plotted lines.
Author Response
Dear Review3,
We would like to thank you for taking the time to review this manuscript.
Your comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied yours comments carefully and have made correction.
Below is our point-by-point response to yours reviewers' comments. We have highlighted in red our responses and changes to the manuscript to facilitate the review: (please, find attached the pdf )
The paper under review is dealing with the problem of modelling the dissipative contact and friction forces during the locomotion fo the passive biped-walker.
The paper is written clearly and there are no problems with following it. However, a clear statement about the contribution made by the authors is missing. Additionally, the journal paper requires to be more specific. When stating in conclusions that the "smooth forward dynamics equations for the whole walking are presented and verified" there should be an equation in the text. But as the reader, I could not find it.
We have rewritten the phrase avoiding the word “equations” in order to avoid any possible misunderstanding. With this conclusion, we want to show that the proposed model, with the previously described set of equations (friction, normal force, impact detection method, integrators and resolution method) works properly to simulate the gait of a passive biped with sliding and energy dissipation by friction force.
The main advance of this model, compared to previous works, is that friction and energy dissipation are considered. The problem of achieving stability when working with a passive system is not trivial. Just to fill the gap in the lack of this kind of models, we have developed this one that does consider impact, friction and dissipative forces.
Another issue is the lack of experimental results from the real platform. The authors have tested their model in the simulation. However, there is no validation if the proposed model meets reality. Is it possible to predict how large is the reality gap between the simulation and the real experiments? The verification presented in the paper is only qualitative, not quantitive.
You are right, we haven't carried out any experiments, but the results of our model have been compared with the real experimental results of Ning Lui [ ref 31]. Line 139
The passive biped performed by Ning Lui, as well as the results obtained have seemed to us reliable enough to be considered. We have not found it necessary to repeat the experiment and measurements, as it has already been done in the literature. The geometrical, dynamic and material properties, including the results achieved, have been obtained and compared from these publications: [ref 17], [ref 27].
Thanks to this we have been able to verify our model, since with the same initial conditions and properties we achieved the same results and behavior.
We've rewritten this part of the manuscript to make it clearer.
Next issue is related to the problem of the solvers comparison. The problem is not exactly related to the method but to the MATLAB implementation, which could not be regarded as the flawless. As the MATLAB is proprietary we as the researchers do not have access to the code and we can not tell if the coders did not make any mistake.
It is truth the fact we cannot access to the internal code of Matlab. However, we have used only matlab to solve the ordinary differential equations of motion. This equations have been written by us and then implemented on Matlab, using it as a reliable mathematical software/program. The same equations could be implemented in any other mathematical software. All the equations used are widely explained in the references (impact detection, normal force, friction, sliding, integrators… ).
For this reason, we have wanted to describe the model clearly, so that any researcher, with any mathematical software/ program, will be able to write the equations for this model (calculate the direct dynamics with methods of multibody system dynamics).
This is one of the reasons why we wanted to make a comparison of methods, integrators, etc. To show that this model, along with the combination of these equations, works properly. It should be noted that the novelty of the model is above all the implementation of impact/contact detection, normal and friction force, dissipative force…
There are also some technical issues which mainly are related to the quality of the figures which have low resolution and are pasted using jpeg compression which introduces artefacts around the plotted lines.
Thank you for your advice, we've increased the size and the quality of certain images. We will send the images in png format. We will be careful not to repeat the error in the format change.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The paper looks good to me now.
Author Response
Dear Reviewer
We want to show our gratitude for the time spent on improving our paper.
All your comments have been very helpful and have improved the quality of the paper.
We are very glad that you have accepted the paper.
Greetings
Reviewer 2 Report
this revision is not satisfying, mainly due to still lacking of dynamic models of the biped walking. this is a very major weakness. Moreover, no results of experiments are included.
Author Response
Dear Reviewer,
We want to show our gratitude for the time spent on improving our paper.
In this new version, we have made the modifications suggested by you.
We have explained better the verification of the theoretical model with the experimental one. We have rewritten the whole section (3. Verification of the model) and added some figures to improve its compression and showing the quantitative error.
In this section (3. Verification of the model) we explain the verification of the model, where we take the data from a real experiment, ref [30] and [27] (Figure 3, figure 5 and figure 6 in the manuscript). Those results have been used in many other investigations of passive bipeds so it is considered as reliable for the researchers of this field. For that reason, the authors have considered useful and interesting the use of that published experimental results as a comparison base for the model presented. Also, the explanation about the experiment has been added in this section.
We hope that the re-written section shows correctly the verification we have carried out.
Greetings
Reviewer 3 Report
The authors have not addressed the following issues:
"Another issue is the lack of experimental results from the real platform. The authors have tested their model in the simulation. However, there is no validation if the proposed model meets reality. Is it possible to predict how large is the reality gap between the simulation and the real experiments? The verification presented in the paper is only qualitative, not quantitive."
If the authors want to use the model quantitive comparison should be provided.
"There are also some technical issues which mainly are related to the quality of the figures which have low resolution and are pasted using jpeg compression which introduces artefacts around the plotted lines."
Still, most of the figures have artefacts and low quality.
Finally, in the whole paper, there are only two equations to describe the concept. In the reviewer's opinion, the equation of motion of the biped where the novel components were added are missing.
Author Response
Dear Reviewer,
We want to show our gratitude for the time spent on improving our paper.
In this new version, we have made the modifications suggested by you.
1 We have explained better the verification of the theoretical model with the experimental one. We have rewritten the whole section (3. Verification of the model) and added some figures to improve its compression and showing the quantitative error as you suggested.
We want to thank you; a quantitative comparison has allowed us to better explain the verification of the model
In this section (3. Verification of the model) we explain the verification of the model, where we take the data from a real experiment, ref [30] and [27] (Figure 3, figure 5 and figure 6 in the manuscript). Those results have been used in many other investigations of passive bipeds so it is considered as reliable for the researchers of this field. For that reason, the authors have considered useful and interesting the use of that published experimental results as a comparison base for the model presented. Also, the explanation about the experiment has been added in this section.
We hope that the re-written section shows correctly the verification we have carried out.
2 Related the quality of the images, all the figures presented in the manuscript was checked in the first review, and re-forwarded them to the journal (tiff/png format).
3 The general equations of motion for a multi-body system has been include in lines 86 to 96.
As explained in line 101, for each body, the position, velocity and acceleration is defined on local reference system, and on global reference system using Euler parameters.
We write the methodology for the model, showing only the equations of normal force and friction, and explaining how to detect the impact, and the methods to control the error, integrate, and solve the system (see reference for more detail).
The novelty of the model is the integration of the normal force (line 127), the friction force (line 156) and the detection (geometric equations) of the contact/impact in smooth way (line 144, see figure 2). The equations and the explanation how to uses this forces and impacts are included in the manuscript.
We hope these changes have improved and clarified the manuscript.
Greetings
Round 3
Reviewer 3 Report
Dear Authors,
the updates presented in terms of issue number 1 are now resolved.
However, for issue number 2 there is still missing relation between equation from line 87, 89 and those from line 127 156. Could you please improve the equations?
Author Response
Dear reviewer
We want to thank you again for your time.
- We have explained in detail equations (1) and (2).
- We have added all the explanations and equations (equations 3 to 5 ) to solve our multibody model by forward dynamics, as well as
- a better explanation of the equation that defines the penetration detection (equation 6, line 152)
To facilitate the review, we have highlighted the changes in red in the manuscript (section 2)
We have paid special attention to express it as clearly as possible
We hope that you find the reviewed paper satisfactory.
Best regards
Author Response File: Author Response.pdf
