A Model Predictive Control Method for Vehicle Drifting Motions with Measurable Errors
Round 1
Reviewer 1 Report
please refere the attaches.
Comments for author File: 
Comments.pdf
Author Response
Thank you for your important suggestions. Please see the attachment
Author Response File: Author Response.pdf
Reviewer 2 Report
The authors present a model predictive control method for vehicle drifting motions with measurable errors. Below are some of the main concerns.
I. General comments on the motivation of this work
1. The authors stated that “However, the expert-based methods need so much operational data of drivers to retrain the controller if replacing different vehicles that it is very difficult for most research institutes and universities.” This is partially true for expert-based methods based on NNs. There are many other “expert-based” methods that do not suffer this major drawback, see for instance, the following recent fuzzy vehicle control results and many other related references.
https://ieeexplore.ieee.org/document/7963822
https://ieeexplore.ieee.org/abstract/document/9204811
Please provide a suitable discussion on this point to better motivate the presented work.
2. In my opinion, most of the references are not really appropriate and/or out of date to motivate proposed work, for instance the statements on the numerical complexity of LPV and/or T-S fuzzy control or MPC control approaches for real-time vehicle control are not reasonable. The authors should refer to the recent surveys on these control methods, for instance the following ones and related references, for recent advances on this topic.
https://www.sciencedirect.com/science/article/pii/S0888327021003265
https://ieeexplore.ieee.org/document/6402735
3. The contribution of the paper is not clear compared to the existing methods, especially with respect to the previous work of the same authors. It must be emphasized.
II. Technical comments
4. Suitable references must be given for the vehicle modeling part.
5. The state-space vehicle model in page 6 is not given in a reasonable way because it’s a linear model while equations (1)-(4) are nonlinear. Further development is required.
6. The real-time computational burden of the proposed MPC control must be discussed.
7. How to guarantee the validity of expression (21), especially the existence of the inverse matrix?
8. For the tests, the vehicle speed is too low and almost not varying. Can we have more convincing test scenarios?
9. We can see the response time of the closed-loop system is about 6 seconds, which is too much large for vehicle control. Moreover, the responses are very oscillatory, which can lead to issues on security and comfort. Please discuss in detail these point.
III. Other comments
10. The graphic presentation of the obtained control results must be improved.
11. There are too many typos. The English must be further improved for a better readability.
Author Response
Thank you very much for your important suggestions. Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
This paper proposed a vehicle drifting control method based on the vehicle dynamics model and MPC theory. The topic is interesting for unmanned vehicles. However, several issues need to be solved.
- The contribution is confusing. The vehicle dynamics model, the Unitire model, and MPC are commonly used in the vehicle control field. Please clarify the contribution of this paper.
- There is no field experiment. It is insufficient to validate the proposed method.
- The language should be polished. There are several spelling and grammatical errors in the paper, that authors should revised them carefully.
Author Response
Thank you very much for your important suggestions.
Point 1. The contribution is confusing. The vehicle dynamics model, the UniTire model, and MPC are commonly used in the vehicle control field. Please clarify the contribution of this paper.
Response 1. There are some new descriptions of the contribution in the last paragraph in Section 1.
Point 2. There is no field experiment. It is insufficient to validate the proposed method.
Response 2. Thank you very much for your suggestions. The MPC method is widely used and has an excellent performance in the automatic drive as the reference [14] shown. The simulation model in this paper approaches the practical vehicle and the vehicle dynamics model equations are extensively used, whose performance in vehicle drifting control is verified in the published paper [16]. And the feasibility of automatic drifting control is also verified in references [1-13] and [15-16]. Thus, the proposed method can be validated.
Point 3. The language should be polished. There are several spelling and grammatical errors in the paper, the authors should revise them carefully.
Response 3. Thank you for your suggestions. The language has been checked and errors have been modified in the revision.
Reviewer 4 Report
Interesting paper analyzing the mechanism of motion of a drifting vehicle.
During the reading, the following questions / comments came to my mind:
- Why are not all eqasions numbered?
- Not all variables were explained, e.g. eqasion 4, KΦ, CΦ. Please verify the article in this respect.
- Why is not all aerodynamic forces in the vehicle dynamics model taken into account? How does such a simplification affect the obtained results?
- What are the possibilities of continuing the research and using the obtained results?
Author Response
Thank you very much for your important suggestions.
Point 1. Why are not all equations numbered?
Response 1. Thank you for your suggestions. All equations are numbered.
Point 2. Not all variables were explained. Please verify the article in this respect.
Response 2. Thank you for your suggestions. All variables are explained.
Point 3. Why is not all aerodynamics forces in the vehicle model taken into account? How does such a simplification affect the obtained results?
Response 3. In this paper, the vehicle moves forward with the positive longitudinal velocity, and the other aerodynamics forces have less influence on the vehicle than the forward direction. The simplification has very little effect on the obtained results.
Point 4. What are the possibilities of continuing the research and using the obtained results?
Response 4. Combined with the published paper [16], vehicle drifting control can improve vehicle dynamics performance with existing results. The vehicle drifting control study will be combined with automatic driving including obstacle avoidance to improve driving safety.
Round 2
Reviewer 1 Report
I have no further suggestions, good luck.
Author Response
Thank you very much for your review.
Reviewer 2 Report
- I partially agree with the response of Point 5. The authors must specify in the paper that the state-space matrices are obtained by a linearization.
- I don’t agree with the response of Point 9. I understand that the vehicle is under some limit working conditions. However, having a time response of more than 6 seconds would be too dangerous from practical viewpoint. Moreover, the responses are very oscillatory, especially the steering angle, which can lead to serious issues on safety and comfort issues. This point must be revised.
Author Response
Thank you very much for your suggestions. Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The revised paper has reached the standard level for WEVJ. Therefore this paper is suitable for publishing.
Author Response
Thank you very much for your review.
Round 3
Reviewer 2 Report
The manuscript has been appropriately revised.
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
The manuscript considers a model of vehicle dynamics and discusses the construction of the optimal vehicle drifting control based on the analysis of the corresponding linearized system. The results are confirmed by the performed numerical simulation.
The content of this manuscript is a small addition to paper [13] written by a part of the authors. In particular, the model, Section 2 and the first part of Section 3 in this manuscript overlap substantially with those from [13]. A relatively new result for this model is contained in the second part of Section 3. However, from a theoretical point of view, this result is basic and rather trivial and cannot be regarded as a scientific achievement worthy of publication.
Author Response
Thank you very much for your important suggestion.
We have checked the English language and style.
The vehicle dynamics model is the essential basis of the drifting study. This paper proposes a different method MPC from paper [13] to realize drifting motions by considering measurable errors, because the Robust method in paper [13] is computationally complex based on the dynamics model which is indicated in line 72 in this paper. Although there are the T-S fuzzy model and the LPV method to reduce the computational complexity of the Robust controller, there are too many variable parameters in the controller model in this paper and paper [13] that these methods are not applicable. This paper designs the controller based on the MPC theory with measurable errors.
Thank you very much for your important suggestion again.
Reviewer 2 Report
line 98 Lateral and not "lateraling"
line 161 gray dashed lines and "not gray broken lines"
line 164 Combining Equation (11) and Equation (4) instead of "Combined with the Equation (4)"
line 178 "affine approximation" not clear meaning
line 179 is an equation, not write inside the text
line 196 is an equation, not write inside the text
line 200 is an equation, not write inside the text
General: There are some problem in the number of figure after the (10) are in two lines and also in the position of the text (not in the middle of the pages)
Why have been considered low speed to evaluate the drift? Clearify. How it is possible to extend the use of the model for high speed?
Extend the conclusions
The authors contribution is not indicated.
Author Response
Thank you very much for your important suggestions. We have added this information as your suggestions. And English language and style have been checked.
Point 1: line 98 Lateral and not "lateraling"
Response 1: Thank you very much for your important suggestion. The word “lateraling” is a clerical error and has been changed to “lateral”.
Point 2: line 161 gray dashed lines and "not gray broken lines"
Response 2: Thank you very much for your important suggestion. The term “gray broken lines” has been changed to “gray dashed lines”.
Point 3: line 164 Combining Equation (11) and Equation (4) instead of "Combined with the Equation (4)"
Response 3: Thank you very much for your important suggestion. "Combining Equation (11) and Equation (4)" has taken the place of "Combined with the Equation (4)".
Point 4: line 178 "affine approximation" not clear meaning
Response 4: The phrase "affine approximation" is the linearized method of tire forces as shown in Figure 4. To facilitate the understanding, the explaining is in line 181 in the revision.
Point 5: line 179 is an equation, not write inside the text
Response 5: Thank you very much for your important suggestion. The TYDEX longitudinal slip ratio is widely known, and the equation has been deleted in the revision.
Point 6: line 196 is an equation, not write inside the text
Response 6: Thank you very much for your important suggestion. The expression in line 196 in the first draft is a matrix and has been deleted in the revision, whose complete description is shown in Equation (15).
Point 7: line 200 is an equation, not write inside the text
Response 7: Equations in line 200 in the first draft are explanations of matrix elements that don't appear and are not described at present, so equations in line 200 in the first draft are retained.
Point 8: General: There are some problem in the number of figure after the (10) are in two lines and also in the position of the text (not in the middle of the pages)
Response 8: The number of figures after the (10) are in two lines because explanations are too long and positions reference the template.
Point 9: Why have been considered low speed to evaluate the drift? Clearify. How it is possible to extend the use of the model for high speed?
Response 9: Thank you very much for your important suggestion. A new simulation is included in the revision to suggest the controller can realize a higher speed drifting motion than the first draft. The new target is randomly chosen to achieve a circular of radius 20m which is the maximum in Figure 5.
Point 10: Extend the conclusions
Response 10: Thank you very much for your important suggestion. There are some minor changes in the conclusion.
Point 11: The authors contribution is not indicated.
Response 11: Thank you very much for your important suggestion. "Author Contributions" has been indicated in the revision.
Round 2
Reviewer 1 Report
The manuscript contains only an incremental step in the authors’ research. The theoretical results are rather trivial.
