Research on Longitudinal Control of Electric Vehicle Platoons Based on Robust UKF–MPC
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper describes a Robust UKF-MPC controller for the longitudinal correction or compensation of the trajectory. It is important to highlight the novelty of this control scheme. Also, some improvements are required as follows:
Authors should include some response to fundamental research questions, such as: Why EV platooning is important? It has some broad advantages such as Environmental impact and safety due to traffic flow improvement and energy efficiency due to drag reduction. Few lines should be added in the Introduction emphasizing applications.
In the optimization problem, is their any constraint on delay?
In case of communication delay, is it possible to use 'any time control' where a precalculated local controller's command can be applied for inter-vehicle distance control?
Line 178: Feedback correction compensation looks a strange terminology. Please replace with 'Feedback control of Longitudinal platooning trajectory'
Line 257: 'Low level controller' instead of 'Lower'. There are some terminologies we can not change while making an effort to reduce similarity.
Line 277: 'PID Low level Controller' instead of lower.
Fig. 6 caption. please mention how much velocity is varied with how much delay and data loss?
Fig. 7 caption. Please mention how much acceleration is varied with how much delay and data loss in this scenario?
Fig. 8 caption. please mention how much spacing error is varied with how much delay and data loss in this scenario?
Some typos in the paper, such as:
Line 16: Use 'Feedback correction and/or compensation' instead of 'Feedback correction compensation'
Only graphical representaiton of the three robustnesss test cases is not sufficient. You should include a table with control error parameters e.g. MSE, ITAE, IAE, ISE in all simulation cases for comparison purpose.
Comments on the Quality of English Language
Some minor editing maybe required.
Author Response
Comments 1: This paper describes a Robust UKF-MPC controller for the longitudinal correction or compensation of the trajectory. It is important to highlight the novelty of this control scheme.
Response 1: Thank you very much for this comment. We highlight the innovative points and practical applications of the robust UKF-MPC controller in lines 79 to 94 on page 2, and have highlighted it in red for clarity.
Comments 2: Authors should include some response to fundamental research questions, such as: Why EV platooning is important? It has some broad advantages such as Environmental impact and safety due to traffic flow improvement and energy efficiency due to drag reduction. Few lines should be added in the Introduction emphasizing applications.
Response 2: Thank you for pointing this comment. We agree with this observation. Therefore, in the second paragraph of the introduction on the first page (lines 32 to 37), we explain the importance and advantages of platooning electric vehicles. And my changes are highlighted in red.
Comments 3: In the optimization problem, is their any constraint on delay?
Response 3: Thank you very much for this comment. We have used the robust UKF algorithm to estimate the vehicle state information under the influence of communication delay. The robust UKF algorithm can effectively deal with the noise and outliers caused by factors such as communication delay and data loss, thus improving the estimation accuracy of vehicle state information. Therefore no direct constraints are imposed on the delay in the optimization problem. We have added lines 162 to 165 on page 5 and have highlighted it in red for clarity.
Comments 4: In case of communication delay, is it possible to use 'any time control' where a precalculated local controller's command can be applied for inter-vehicle distance control?
Response 4: Thank you very much for this comment. We believe that there are some limitations of using the ‘any-time control’ approach in the presence of communication delays, such as the inability to adapt to dynamic changes, the need for large computational and storage resources, and the inability to guarantee optimal control. Therefore, we believe that real-time communication is still a key factor in ensuring the safety and stability of longitudinal control of electric vehicle formations. In the paper, we propose the robust UKF-MPC control method, which can effectively deal with the problems of communication delay and data loss, and verify its effectiveness through simulation experiments. In the future, we will continue to investigate how to further improve the reliability of the communication system and explore other robust control methods to further improve the performance of longitudinal control of electric vehicle formations.
Comments 5: Line 178: Feedback correction compensation looks a strange terminology. Please replace with 'Feedback control of Longitudinal platooning trajectory'
Response 5: Thank you very much for this comment. We agree with you on this point. We have corrected line 180 on page 6 and have highlighted it in red for clarity.
Comments 6: Line 257: 'Low level controller' instead of 'Lower'. There are some terminologies we can not change while making an effort to reduce similarity.
Response 6: Thank you very much for this comment. We agree with you on this point. We have corrected line 243 on page 8 and have highlighted it in red for clarity.
Comments 7: Line 277: 'PID Low level Controller' instead of lower.
Response 7: Thank you very much for this comment. We agree with you on this point. We have corrected line 260 on page 9 and have highlighted it in red for clarity.
Comments 8: Fig. 6 caption. please mention how much velocity is varied with how much delay and data loss?
Response 8: Thank you very much for this comment. We agree with you on this point. We have corrected the title of figure 6 on page 11, line 292, and have highlighted it in red for clarity.
Comments 9: Fig. 7 caption. Please mention how much acceleration is varied with how much delay and data loss in this scenario?
Response 9: Thank you very much for this comment. We agree with you on this point. We have corrected the title of figure 7 on page 11, line 294, and have highlighted it in red for clarity.
Comments 10: Fig. 8 caption. please mention how much spacing error is varied with how much delay and data loss in this scenario?
Response 10: Thank you very much for this comment. We agree with you on this point. We have corrected the title of figure 8 on page 12, line 296, and have highlighted it in red for clarity.
Comments 11: Some typos in the paper, such as: Line 16: Use 'Feedback correction and/or compensation' instead of 'Feedback correction compensation'
Response 11: Thank you very much for this comment. We agree with you on this point. We have corrected line 17 on page 1 and have highlighted it in red for clarity.
Comments 12: Only graphical representation of the three robustness test cases is not sufficient. You should include a table with control error parameters e.g. MSE, ITAE, IAE, ISE in all simulation cases for comparison purpose.
Response 12: Thank you very much for this comment. We have carefully considered your suggestions and made the following revisions: We have added Tables 3 and 4 to compare the performance of different controllers in different situations to further illustrate the robustness of the proposed robust UKF-MPC controller against communication interference. The details are in lines 298 to 305 on page 12 and lines 333 to 343 on page 13, and have highlighted it in red for clarity.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for Authors1. In the abstract, “It has strong robustness and stability”. There should be more actual results than a plain claim.
2. The most frequently used Abbrs in the manuscript is “UKF”. However, It was never spelled out for the first mention.
3. There are way too many equations listed in this manuscript. Please only list the crucial formula derivation/algorithm improvements of the “UKF-MPC”.
4. How does the algorithm generate the sensor noise and communication delay during simulation?
5. The conclusion looks vague as it does not include any objective results.
Author Response
Comments 1: In the abstract, “It has strong robustness and stability”. There should be more actual results than a plain claim.
Response 1: Thank you very much for this comment. We have modified the summary based on your suggestions by adding MSE and IAE to be analyzed in comparison with other controllers in order to show the advantages of the robust UKF-MPC controller more clearly. The details are in lines 20 to 23 on the first page of the manuscript, highlighted in red for clarity.
Comments 2: The most frequently used Abbrs in the manuscript is “UKF”. However, It was never spelled out for the first mention.
Response 2: Thank you very much for this comment. We explain this on the first page, lines 11 to 13, and have highlighted it in red for clarity. The full name of UKF is Unscented Kalman Filter.
Comments 3: There are way too many equations listed in this manuscript. Please only list the crucial formula derivation/algorithm improvements of the “UKF-MPC”.
Response 3: Thank you very much for this comment. We have reviewed the formulas in the paper carefully and removed some unnecessary formulas, such as auxiliary formulas and intermediate derivation steps.
Comments 4: How does the algorithm generate the sensor noise and communication delay during simulation?
Response 4: Thank you very much for this comment. We generate sensor noise and communication delays in Simulink by means of uniform random signals and variable transmission delays. We have further clarified line 272 on page 9 and highlighted it in red for clarity.
Comments 5: The conclusion looks vague as it does not include any objective results.
Response 5: Thank you very much for this comment. We have carefully considered your concerns about the vagueness of the conclusions section and have revised it to include more objective results and specific indicators. The revised conclusions now provide detailed quantitative data to support claims about robust UKF-MPC controller performance. The details are on page 13, lines 349 to 359 and are highlighted in red for clarity.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe manuscript proposed a UKF-MPC longitudinal controller, to address the issues such as random communication delays, packet loss, and external disturbances. The reviewer has the following concerns.
1. The innovation is not clear. Previous research extensively studied relative issues, but the authors didn’t compare their new methods with the current state-of-the-art methods. For example, Reference 11 dealt with the communication delay with LSTM, Reference 12 dealt with the disturbances with KF-MPC. However, the authors only claim that their approach can outperform the previous methods, but with no comparisons or evidences.
2. The objective function in Equation 36-37 need to be further clarified. The objective seems to be following the target reference trajectory. However, how did the authors generate the target trajectory? What is the physical meaning to follow the target trajectory?
3. It’s suggested to put the MPC, UKF-MPC, Robust UKF-MPC in the same figure plot, for better comparison.
4. It’s not fair to only compare the robust UKF-MPC to Mpc or ukf-mpc. Comparisons with state-of-the-art approaches need to be included. In addition, why is UKF-MPC worse than MPC in Fig. 5d? Please explain the reasons.
5. What is the meaning of the legends in Figure 3-5? Please explain it.
Comments on the Quality of English LanguageCan be improved
Author Response
Comments 1: The innovation is not clear. Previous research extensively studied relative issues, but the authors didn’t compare their new methods with the current state-of-the-art methods. For example, Reference 11 dealt with the communication delay with LSTM, Reference 12 dealt with the disturbances with KF-MPC. However, the authors only claim that their approach can outperform the previous methods, but with no comparisons or evidences.
Response 1: Thank you for your comment, we are aware of the importance of innovativeness in research and have tried to highlight this when writing the paper. Regarding the comparison with current state-of-the-art methods that you mentioned, we did face some challenges. Although we were not able to include all state-of-the-art methods in our comparison, we have conducted in-depth analyses of some of them. For example, we acknowledge the contribution of the LSTM method in reference 11, which you mentioned, to the communication delay problem, but we did not include it in the comparison due to differences in research focus and methodology.
As for the KF-MPC approach in Reference 12, we explain here the reason for not including it in the comparison. In the nonlinear problem of longitudinal control of vehicle platoon, UKF has superior performance compared to conventional KF. Therefore, in our study, we choose the classical MPC control algorithm and its improved version UKF-MPC for comparison.
The innovation of our study is to enhance the robustness of UKF by introducing Huber-M estimation to handle outliers in the observed data. This improvement effectively copes with the noise and outliers problem caused by factors such as communication delay and data loss, and significantly improves the estimation accuracy of vehicle state information. In addition, our feedback correction and compensation mechanism is able to adjust in real time according to the state estimation error, which further improves the control accuracy and system stability. We will further clarify these comparisons and innovations in the paper so that readers can better understand our research contributions.
We highlight the innovative points and practical applications of the robust UKF-MPC controller in lines 79 to 94 on page 2, and have highlighted it in red for clarity.
Comments 2: The objective function in Equation 36-37 need to be further clarified. The objective seems to be following the target reference trajectory. However, how did the authors generate the target trajectory? What is the physical meaning to follow the target trajectory?
Response 2: Thank you very much for this comment. We have elaborated on the objective function and reference trajectory as per your suggestion and have marked lines 204 to 210 on page 7 of the manuscript in red with the following changes:
- Physical significance of the objective function: We choose vehicle spacing, vehicle spacing error, relative velocity, velocity and acceleration as the objective, aiming to ensure that the vehicle travels at the desired velocity and acceleration, maintains a safe distance between vehicles, and improves the efficiency of vehicle travelling.
- How the reference trajectory is generated: We use an exponential decay function as the reference trajectory to ensure that the reference trajectory changes more smoothly as it approaches the target value.
- the physical significance of the reference trajectory: follow the reference trajectory can help the vehicle formation to achieve stability and smoothness, and to maintain a safe distance in the process of acceleration, uniform speed and deceleration.
Comments 3: It’s suggested to put the MPC, UKF-MPC, Robust UKF-MPC in the same figure plot, for better comparison.
Response 3: Thank you very much for your comment. We have considered this issue but only put the parameters of each vehicle with the same controller in the same plot in order to reflect the characteristics of vehicle platoon travelling, for comparison we have MPC, UKF-MPC and Robust UKF-MPC in the same plot in Fig. 5(d) and Fig. 8(d). To better compare the different controllers, we have added Tables 3 and 4 on page 12, lines 298 to 305, to further demonstrate the robustness of the Robust UKF-MPC controller by comparing the MSE and IAE of the different controller parameters.
Comments 4: It’s not fair to only compare the robust UKF-MPC to Mpc or ukf-mpc. Comparisons with state-of-the-art approaches need to be included. In addition, why is UKF-MPC worse than MPC in Fig. 5d? Please explain the reasons.
Response 4: Thank you very much for your comment. Due to the difficulty in obtaining the open source code of the state-of-the-art methods and matching the software environment, we chose the classical MPC control algorithm and the improved UKF-MPC algorithm for comparison.
In Fig. 5d, the reason why UKF-MPC is worse than MPC is that there is an error in the UKF state estimation, which causes the MPC algorithm to be unable to obtain accurate state information and affects the overall control accuracy. In order to solve this problem, we propose the robust UKF-MPC algorithm, which reduces the influence of outliers on state estimation by introducing Huber-M estimation, so as to improve the accuracy and robustness of state estimation. Experimental results show that the robust UKF-MPC algorithm outperforms the MPC and UKF-MPC algorithms in terms of control accuracy and stability, especially in the presence of random communication delay and packet loss. The robust UKF-MPC algorithm can effectively handle these random factors, thus ensuring the stability and safety of the fleet.
Comments 5: What is the meaning of the legends in Figure 3-5? Please explain it.
Response 5: Thank you for your question. The following is a detailed explanation of the legends in Figures 3 to 5.
Figures 3 and 4: In Figures 3(a), 3(b), 3(c), and the corresponding subfigures in Figure 4, the legends take a similar form of presentation. We take Figure 3(a) as an example for illustration. In Fig. 3(a), the title ‘MPC’ refers to the MPC controller. In the legend, ‘v_0’ represents the velocity of the leading vehicle, and ‘v_1’, ‘v_2’ and ‘v_3’ represent the velocities of the following vehicle 1, following vehicle 2 and following vehicle 3, respectively.
Figure 5: In Figure 5(a), the title ‘MPC’ also refers to the MPC controller. In the legend, ‘δd_0,1’ represents the vehicle spacing error between the leading vehicle 0 and the following vehicle 1, ‘δd_1,2’ represents the vehicle spacing error between the following vehicle 1 and the following vehicle 2, and ‘δd_2,3’ represents the vehicle spacing error between the following vehicle 2 and the following vehicle 3. In Figure 5(d), the caption ‘δd_0,1’ represents the vehicle spacing error between the leading vehicle 0 and the following vehicle 1. The legends ‘MPC’, ‘UKF-MPC’ and ‘Robust UKF-MPC’ represent three different controllers.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsKeeping in view the revised version where all queries have been addressed by the authors, I don't have further comments for this paper.
Author Response
Comments 1: Keeping in view the revised version where all queries have been addressed by the authors, I don't have further comments for this paper.
Response 1: Thank you for your comment and affirmation. We have further checked and revised the manuscript. Thank you for your support of our work.
Reviewer 3 Report
Comments and Suggestions for AuthorsPlease incorporate the responses in the rebuttal into the manuscript, to make it more readable.
Comments on the Quality of English Languageunderstandable.
Author Response
Comments 1: Please incorporate the responses in the rebuttal into the manuscript, to make it more readable.
Response 1: Thank you for your interest in our thesis and your valuable comment. We have added and modified the paper according to your suggestions and marked them in red color. We have explained how to improve the robustness of the UKF algorithm to outliers on page 5, lines 156 to 158, and modified the title of the figure on page 10, lines 290 to 301.
We believe that these changes make the paper clearer and more understandable, and make our results more reliable and convincing.
