Design and Implementation of an Energy-Efficient Vehicle Platoon Control Algorithm Using Prescribed Performance and Extremum Seeking Control

Round 1

Reviewer 1 Report

This paper proposed an algorithm employing extremum-seeking control integrated with the prescribed performance control technique to find the optimal inter-vehicular distance. Overall, the problem formulation is reasonable, the method is well-designed and the verification is sufficient for the validation of the approach. The quality of this paper is good enough and meets the caliber of the journal. I just have some minor suggestions to improve the paper.

- The figures in the paper are blue and I recommend improving them and elaborating more on the captions to let the readers understand the figures better.

- Figure 9 spent a lot of space but it is not informative.

- Please detail the experiment hardware setup not just software including Matlab and also the computation consumption of the algorithms.

- There is a statement saying that “This property is proved in [3], [17].” Could you please give a little more brief introduction on this? This statement is not very clear to me.

- From the paper, I can see the algorithm only considers the longitudinal platoon and assume the state of the vehicle can be obtained directly, however, the speed, position, and orientation of the vehicle can not be measured directly. In that sense, could you please discuss the effects from the uncertainties of the state estimation such as in the works: autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; automated vehicle sideslip angle estimation considering signal measurement characteristic; imu-based automated vehicle body sideslip angle and attitude estimation aided by gnss using parallel adaptive kalman filters; improved vehicle localization using on-board sensors and vehicle lateral velocity; estimation on imu yaw misalignment by fusing information of automotive onboard sensors. As the control performance relies on the estimated speed, position and orientation a lot. So please discuss these works in the paper and share the insights of the robustness of the algorithms in the paper.

 

- In the real application, there are system delays from different modules such as the perception in the works (automated driving systems data acquisition and processing platform; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning), and communication delay in strategic and tactical decision-making for cooperative vehicle platooning with organized behavior on multi-lane highways. How is the performance of the work in this paper against the system time delay? Please discuss the time delay issue regarding the works mentioned above and clarify the robustness of the approach in the paper. 

Author Response

This paper proposed an algorithm employing extremum-seeking control integrated with the prescribed performance control technique to find the optimal inter-vehicular distance. Overall, the problem formulation is reasonable, the method is well-designed and the verification is sufficient for the validation of the approach. The quality of this paper is good enough and meets the caliber of the journal. I just have some minor suggestions to improve the paper.

Q1. The figures in the paper are blue and I recommend improving them and elaborating more on the captions to let the readers understand the figures better.

A1. First of all the authors would like to thank the reviewer for all his/her comments. Concerning the above thanks for commenting on the readability of the figures. For that reason, we have reorganized the captions and adjusted the figures according to the journal’s format.

Q2. Figure 9 spent a lot of space but it is not informative.

A2. We agree with the reviewer. Thus, figure 9 has been removed and the data with the discussion are placed now in the same section as plain text.

Q3. Please detail the experiment hardware setup not just software including Matlab and also the computation consumption of the algorithms.

A3. Thanks for the comment. Hardware specifications that concern the simulation are now added at the beginning of the simulation results and discussion. Moreover, computation consumption for all cases is also added as an element of comparison.

Q4. There is a statement saying that “This property is proved in [3], [17].” Could you please give a little more brief introduction on this? This statement is not very clear to me.

A4. Indeed, the statement is not so clear, for that reason further explanation is now provided in the revised version.

Q5. From the paper, I can see the algorithm only considers the longitudinal platoon and assume the state of the vehicle can be obtained directly, however, the speed, position, and orientation of the vehicle can not be measured directly. In that sense, could you please discuss the effects from the uncertainties of the state estimation such as in the works: autonomous vehicle kinematics and dynamics synthesis for sideslip angle estimation based on consensus kalman filter; automated vehicle sideslip angle estimation considering signal measurement characteristic; imu-based automated vehicle body sideslip angle and attitude estimation aided by gnss using parallel adaptive kalman filters; improved vehicle localization using on-board sensors and vehicle lateral velocity; estimation on imu yaw misalignment by fusing information of automotive onboard sensors. As the control performance relies on the estimated speed, position and orientation a lot. So please discuss these works in the paper and share the insights of the robustness of the algorithms in the paper.

A5. Thank you for the comment. Indeed, the works that the reviewer proposes seem to solve many problems especially when concerning model uncertainties. Since our focus was to develop a control scheme, we considered an ideal model without leakage and without uncertainty when measuring the state. For that reason, we added further discussion of how our work could be improved in the future citing these valuable researches.

Q6. In the real application, there are system delays from different modules such as the perception in the works (automated driving systems data acquisition and processing platform; yolov5-tassel: detecting tassels in rgb uav imagery with improved yolov5 based on transfer learning), and communication delay in strategic and tactical decision-making for cooperative vehicle platooning with organized behavior on multi-lane highways. How is the performance of the work in this paper against the system time delay? Please discuss the time delay issue regarding the works mentioned above and clarify the robustness of the approach in the paper.

A6. Once again thank you for the insightful information. As in question 5, since our objective is only the control design process, we consider no delays in our ideal system. It is obvious that the worse the estimation is, ESC will be slower and may not converge to the optimal distance, so the PPC part of the algorithm will operate with a bigger position error. Future research can also take into consideration the system delays problem, for that reason we added this issue in the future works with the citation you provided.

Reviewer 2 Report

See attached file

Comments for author File: Comments.pdf

Author Response

The paper proposes an ESC approach to reduce drag of a vehicle platoon. The work is quite good, albeit incremental. It draws on previous work by the team and adds some standard ESC methods to adapt the inter-vehicle distance. It is a bit naive in places, but seems to have been conducted systematically.

The paper could do with a lot of improvement. Mostly this is fairly minor and could be done quite easily. Appropriate discussion and comment could alleviate the other shortcomings and make this a decent paper and a worthy addition to the subject.

 

Q1. Introduction – well written & clear, motivates the problem and reviews the literature. The potential impact of the paper is discussed just before the lit review, usually it would be after the contribution. Otherwise a good introduction.

A1. First of all, the authors would like to thank the reviewer for all his/her constructive comments. Concerning the above to keep the coherence of the text and to further clarify the introduction a sub-tittle is added to point out the motivation and contribution’s part.

 

Q2. Problem Formulation – mostly clear, but with numerous minor typos (see below).

There seems to be a notation discrepancy, d is defined as the inter-vehicular distance (line 143), and the optimal vehicle gap (distance) is defined as ∆_i−1,i (line 154) [Krstic denotes the optimal parameter by θ^∗].  Given that C_d(d) is assumed time-invariant (Fig. 4), then the optimal gap must be constant. But in Figure 1 it seems that ∆i-1,i is varying? This should be clarified. Furthermore, the fonts and notation in Figure 1 should match that of the text.

In addition, on line 174 , “... the desired distance ∆_col < ∆_i−1,i < ∆_con, ...” it seems that the definition of ∆_i−1,i has changed?

A2. Thanks for indicating. In the revised version, we corrected the issue. More specifically, the optimal gap is now redefined as ∆^*_i−1,i   to show that indeed is a constant value and in our case the distance which the drag coefficient function has its minimum. In the ESC analysis it is now clarified that ∆^*_{i−1,i   =} θ_i^*  to comply with Krstic’s analysis. Therefore, ∆_i−1,i is a varying variable to correctly state that ESC controller exports throughout the control process different distances (transient-state) before reaching the optimal one. Lastly, figure 1 has been re-captioned providing a more detailed explanation. Lastly, d is the real inter-vehicular distance, d = p_i-1-p_i, while ∆_i−1,i  is also the desired distance that PPC controller expects as an input.

 

Q3. Extremum Seeking with Prescribed Performance Control – fairly clear, but again with a number of minor typos/errors. In particular: Figure 2 shows α as both the control function and the magnitude of the sinusoidal perturbation. In the text, both are denoted by a_i. This must be clarified. Furthermore, the various variables in eqs (14) – (17) are not defined, and no explicit citation is provided for the ESC architecture or theory.

 

A3.  The authors agree with the comment. After the revision, figure 2 has been readjusted to distinguish the two different, previously defined, α variables. Furthermore, all definitions are now given, and further information is cited for the ESC theory which is mostly based on Krstic’s work.

 

Q4. Simulation Results and Discussion – the weakest part of the paper:

 

Q4-a. A simulation time of 800 sec is fine to ensure long term stability, but only the transients of the plots should be shown. The quality of the solution depends very much on the transient behaviour, and this cannot be assessed from the plots in the paper. This is the biggest weakness of the paper. The transient responses must be shown and the quality of the solutions discussed. From what can be seen, the transients are quite oscillatory, and this will enormously affect the practicality of the system for crewed vehicles. It is of less concern for future uncrewed [‘uncrewed’ is often regarded as a more modern term than ‘unmanned’], freight vehicles. In particular, the transient accelerations should be plotted since this has a major impact on the comfort of the passengers.

Note that if the accelerations are too high, this does not necessarily invalidate the work, it just needs discussion and inclusion in further work studies, and the impact of the work in the paper would be limited to future uncrewed vehicles.

A4-a. Thanks for the comment. In the revised version we added a zoomed plot inside the distances’ graph (figure 5) to demonstrate the transient state where further discussion is made. Although the note about the practicality of the system especially for crewed vehicles can be truly a matter, since our work is not experimentally tested, we cannot extract safe results about ‘practical’ issues. The transient state is indeed oscillatory (yet observing the zoomed plots the oscillations are not as “tough” as expected by the original plot) which is a common issue when adopting extremum seeking techniques.

 

Q4-b. The plots should include units

A4-b. Thanks for pointing out. All plot units are now shown and corrected.

 

Q4-c. Figure 4 is piecewise linear - this is unlike the actual drag function, which will be continuously varying with d (as well as time-varying because the drag will depend on side-winds, cornering, effect of nearby structures and overtaking vehicles etc). In ref [15], for example, spline fitting is performed to smooth the function. Does the piecewise linear nature of the function have any effect on the convergence and convergence rate of the ESC? This needs some discussion and inclusion in further work.

A4-c  The authors totally agree with the comment. Adopting a piecewise linear drag function is far from reality and that piecewise nature also violates the conditions for the ESC design as Equation (18) depicts. Moreover, the values are extracted from experimental data point. For that reason, in the revised version we re-simulated the system adopting now drag functions conducting spline fitting in the data, as you correctly stated that ref [15] also does. Eventually, the computation time has been improved and the system is now performing better. Once again, thank you for the indication.

 

Q4-d. I am also curious whether the sinusoidal variation of the i = 0 vehicle helps or hinders the convergence of the scheme? Possibly it has no effect?

A4-d. The sinusoidal velocity profile that the leading vehicle has, was chosen in such way to make the problem closer to a real driving scenario and prove the effectiveness of the algorithm (instead of choosing a smoother velocity function or a constant velocity). The convergence of the scheme is not affected from that selection at all.

 

Q4-e. “The leading vehicle is set to follow a continuously differentiable velocity profile as” - this is confusing. Surely there is an i = 0 vehicle (the leader) that is following this profile? Vehicle 1 follows the lead i = 0 vehicle. This needs clarifying.

A4-e. Thanks for the indication. The platoon setup with the leading vehicle is further explained in the simulation results and discussion part.

 

Q4-f. How dependent on the conditions and platoon configuration is the tuning? This has an obvious impact on the practicality of the scheme

A4-f. Fortunately, the robustness of the Prescribed Performance Control methodology allows the augmented ESC system operate as expected since the tracking performance with time-varying reference inter-vehicular distances is guaranteed a priori without requiring exhaustive tuning of the controller’s gains (the performance functions are selected according to the performance specifications and the gains are selected positive). Since the control performance is decoupled by the ESC output (i.e., no matter what is the output of the ESC module the prescribed performance controller guarantees accurate tracking) the only necessary tuning concerns the ESC parameters, which has been explained in details [7].

 

Q4-g. A collision distance of 0.3 m seems very small (especially because C_d is undefined below about 2.5 m in Fig 4)— it is only 30 cm which does not seem safe to me.

A4-g. The authors agree with the observation. Indeed, 30cm is not a safe distance and since the adopted drag profiles indicate that distances below 2.5m can create complex aerodynamics the collision distance value is reselected at 2.5m after the revision. The change of that value does not seem to highly affect the control process nor the tuning of the algorithm nor the energy results.

 

Q4-h. The comparison between the proposed ESCWAO scheme and the PPC scheme is unfair, simply because the PPC scheme sets desired distance ∆_i−1,i = 8 for all i, which is very far from the minimal drag values from Fig. 4 (line 322). Unless I have misunderstood, I think the comparison is worthless, because the result is obvious, and should hence be removed. A more interesting comparison would be between ESC and ESCWAO, but if this has not already been conducted, could be suggested for further work.

A4-h. The comparison was made to prove the efficiency of the algorithm. Indeed, selecting ∆_i−1,i = 8m  for the PPC part is not near the optimal value (not so far) but the real system does not know the aerodynamic profile thus if we select the optimal value as predefined for the plain PPC algorithm the energy consumption will probably be less than in the ESCWAO, since the system will operate under the lowest aerodynamics from the beginning. In a real scenario there is no chance to predefine the optimal distance since it cannot be calculated. Moreover, and most importantly, in the plain PPC algorithm the transient state of the system is minor compared to the transient state of the PPC with ESCWAO and as stated in your previous comment there are high oscillations in the transient state in the proposed scheme. The comparison proves that even if the transient state has oscillations and the system may require more energy, in the end the result is still more efficient. Otherwise, the proposed algorithm would have no practical use.

An extensive comparison between the ESC and ESCWAO is given in the cited work [19] as numbered in the revised version, for that reason higher analysis concerning the matter is not required in our work since the results are similar. However, the authors agree that basic ESC comparison should somehow find a useful place in the work and for that reason ESC with PPC comparison is added in the energy bar results to further demonstrate the energy efficiency.

 

Q5. Conclusions – these are rather thin and lack insight. I think that the work is a long way from being ready for experimental validation. Gradient disturbances, wind and turbulence effects as well as uncertainty in the model (for the observer) should all be investigated first in extensive simulation tests. Altitude, humidity and temperature affect ρ, and the drag is linearly dependent on ρ, so these variables are much less important than the others. Some other issues for inclusion in further work and discussion are given in the comments for Simulation Results and Discussion.

A5. Thanks for the comment. Indeed, the work is far from experimental validation and our intention was to highlight the matter, however in the text is not clearly stated. We expanded the conclusions and explained the above issues.

 

Q6. Various typos etc:

 

• line 71: “ Less studies can be found for ESC when concerning platoons systems, since the idea is still at early stages.” −→ “Fewer studies can be found for ESC when concerning platoon systems, since the idea is still at an early ”
• line 135 “The dynamics of a platoon with N vehicles is given by:” −→ “The dynamics of a platoon with N vehicles is given by:” i.e. “N” should be in italics. Also line 210 (extended) and
• line 154, 173 and elsewhere “ i=1,...,N” in italics −→ “i = 1, . . . , N ”
• line 158: Make sure figure reference “fig.(1)” corresponds with MDPI house style (https://www.mdpi.com/authors/layout):

Any figures, tables, supplementary information, etc., must be cited in the main text of the document, e.g.,

“The data are shown in Table 3.” “This case is depicted in Figure 3d.”

Do not abbreviate Table and Figure to Tab. or Fig. The cited object should usually appear shortly after the citation and at the end of a paragraph. The final

position of objects in the published PDF file is determined by the MDPI production team and may change between proofreading and publication.

• lines 178 : “diag” is an operator so should be upright text

 

• line 179 : ditto for “ln” (see eqns (13) and (14) in ref [5] (also lines 188, 189, 194 )
• line 196, eq (13): L_i and H_i are not
• line 195 eq (12) : ditto for “max” and “exp”. Also for the max operator, should it be max(·, ·) (the parentheses have been omitted)?
• line 210 (extended) eq (17) “for” should not be italicized

 

• line 219: “l” should be italicized “l”
• eq (81) the operator indicated by a small circle ◦ is not defined
• eq (19) “exp” should not be italicized
• line 258: “...and maintain it in a ..” −→ “...and maintain it at a point...”
• line 268: “MATLAB” should be upper case

 

• References — should be consistently presented, e.g. [8] vs. [14].

 

• References — doi information is missing for many of the references

 

• Ref [7]:“Ariyur, ; Krstic, M. Real-time optimization by extremum-seeking control: Ariyur/extremum seeking; John Wiley & Sons: Nashville,TN, 2003. ” TN, 2003” — remove “Ariyur/extremum seeking”
• Ref [17] : does not need full address, just city & state (“Warrendale, PA”)

 

• Ref[18]: “Bhattacharjee, ; Subbarao, K. Extremum seeking control with attenuated steady- state oscillations. Automatica (Oxf.) 2021, 125, 109432.” — remove “(Oxf.)

 

A6. Thanks for the detailed indications. All typos are fixed after the revision.

Reviewer 3 Report

The authors developed an algorithm to find the optimal inter-vehicular distance for minimizing the energy consumption of the vehicles during the platooning situation. The proposed control algorithm allows the platoon to seek and track the optimal inter-vehicular distance in order to achieve the minimum aerodynamic drag. The paper is well written and the organization of the paper is good. The results have been given and discussed sufficiently. The physical meaning of the results have been discussed very well.  There are some minor points to revise for increasing the readability of the paper. The issues and important points are listed below.

 1. The abstract was written very well.

 2. The author should improve the literature review section and they should add some more studies about the subject. Other parts are very well and the authors gave the main idea, main motivation and goals successfully.

 3. In Eq 2, which shows the drag force equation, the authors should use vri instead of vr. Author should check this equation. Either equation 2 should be generalized to each vehicle, or the vri equation in Line 44 should be customized for a single vehicle.

 4. Check the format of the figure caption according to journal format.

 5. The conclusion section needs to improve. The author should add some important results of this study and the main contribution of this study to the literature.

Author Response

The authors developed an algorithm to find the optimal inter-vehicular distance for minimizing the energy consumption of the vehicles during the platooning situation. The proposed control algorithm allows the platoon to seek and track the optimal inter-vehicular distance in order to achieve the minimum aerodynamic drag. The paper is well written and the organization of the paper is good. The results have been given and discussed sufficiently. The physical meaning of the results has been discussed very well.  There are some minor points to revise for increasing the readability of the paper. The issues and important points are listed below.

Q1. The abstract was written very well.

A1. Firstly, the authors would like to thank the reviewer for all his/her comments.

Q2. The author should improve the literature review section and they should add some more studies about the subject. Other parts are very well and the authors gave the main idea, main motivation and goals successfully.

A2. Thanks for the indication. Further works are added both in the literature review and in the introduction to clarify the importance of our work.

Q3. In Eq 2, which shows the drag force equation, the authors should use vri instead of vr. Author should check this equation. Either equation 2 should be generalized to each vehicle, or the vri equation in Line 44 should be customized for a single vehicle.

A3. The authors agree with the comment. After the revision, all equations are generalized to each vehicle, adapting the ‘i’ index wherever is necessary or missing.

Q4. Check the format of the figure caption according to journal format.

A4. Thanks for the comment. In the revised version, we have now readjusted the figures according to the journal’s format.

Q5. The conclusion section needs to improve. The author should add some important results of this study and the main contribution of this study to the literature.

A5. Thanks for the indication, therefore conclusion section is enriched after the revision to further clarify the results and the contribution with respect to the related literature.

Round 2

Reviewer 2 Report

Paper is much improved and worthy of publication. Comparison is still of limited value, because the final integration time of 800 s is entirely arbitrary and its choice will affect the results. No matter, discerning readers will spot that immediately, and it does not affect the scientific integrity of the paper. 

Overall a good addition to the literature.