Optimization of Gain Scheduled Controller for an Active Trailer Steering System Using an Evolutionary Algorithm
Round 1
Reviewer 1 Report
Dear authors,
The topic presented in your paper is interesting. However, there are some issues that should be addressed:
-The paper should contain a clear methodology section where you explain the method followed to develop the research. Please, restructure your paper including such section. Moreover, this section should present a general flowchart of the methodology to enhance reading comprehension.
-You developed a car-trailer model. Please, provide background information about the selected model: why have you chosen these parameters? Does it match any real car?...
Author Response
Reviewer 1:
Dear authors,
The topic presented in your paper is interesting. However, there are some issues that should be addressed:
-The paper should contain a clear methodology section where you explain the method followed to develop the research. Please, restructure your paper including such section. Moreover, this section should present a general flowchart of the methodology to enhance reading comprehension.
Following the above constructive comments and recommendations, Sub-section 3.3 (Optimization Model) was rewritten and extended. In the revised manuscript, the rewritten and extended sub-section was restructured as Section 4 with the heading of ‘Proposed 2-Layer Design Optimization Method’. As recommended, the design methodology is presented in the form of a general flowchart format.
-You developed a car-trailer model. Please, provide background information about the selected model: why have you chosen these parameters? Does it match any real car?...
Following the recommendation by the reviewer, the following background information about the selected car-trailer model was provided at the beginning of the first paragraph of Section 5.2 (The CarSim Car-trailer Model) of the revised manuscript:
“In this research, a car-trailer combination with a full-size car and a single axle trailer is modeled using CarSim software. The parameters of the model are close with those of the car-trailer model reported in [30], which has been validated using numerical simulations.”
Reviewer 2 Report
(1) I couldn't understand fully the originality of your paper. Figures 7 is your main proposal in the paper. However, you don't describe the detail of the system model. Your proposal seems to be only the combination of the modules developed in Matlab or CarSim. Although your paper reports the simulation results, you have to describe how your proposal is built in a practical car-trailer. For example, what's evaluation module? What's state information? What's constraint module? There are a lot of black boxes in Figure 7.
(2) The paper structure is not good. Because the contents in "Introduction", "Literature Review" and "Background" are similar description. In "Background", you show eq.(1). However, eq.(1) is an important value since the horizontal axis in Figure 7 is related with RWA. Such an equation should be indicated in theoretical sections. You have to modify the section contents.
(3) In Figures 8 and 9, you show a lot of simulation results. However, your discussion is not enough. Additionally, the error RWA is correlated largely to max deviation from ideal path. Therefore, the results in the same reaction time should be plotted in vehicle speed.
(4) In Figures 10 and 11, the results of PFOT OT is almost same as the results of RWA,Tradeoff and GS. Is it important to change the vehicle's values?
Author Response
Reviewer 2:
1) I couldn't understand fully the originality of your paper. Figures 7 is your main proposal in the paper. However, you don't describe the detail of the system model. Your proposal seems to be only the combination of the modules developed in Matlab or CarSim. Although your paper reports the simulation results, you have to describe how your proposal is built in a practical car-trailer. For example, what's evaluation module? What's state information? What's constraint module? There are a lot of black boxes in Figure 7.
The above comments/concerns are very constructive and invaluable for improving the quality of the paper. To address the aforementioned concerns, we rewrote and extended Sub-section 3.3 (The 2-Layer Optimization Model). In the revised manuscript, the rewritten and extended sub-section was restructured as Section 4 with the heading of “Proposed 2-Layer Design Optimization Method”. Actually, the proposed design optimization method is the original contribution of the manuscript. Figure 7 shows the implementation of this proposed method.
2) The paper structure is not good. Because the contents in "Introduction", "Literature Review" and "Background" are similar description. In "Background", you show eq.(1). However, eq.(1) is an important value since the horizontal axis in Figure 7 is related with RWA. Such an equation should be indicated in theoretical sections. You have to modify the section contents.
Following the above recommendation, we made corresponding revisions. To emphasize the original contribution of the manuscript, we rewrote and extended Sub-section 3.3 of Section 3 (Background). In the revised manuscript, the rewritten and extended contents were restructured as an independent section, that is, Section 4 entitled “Proposed 2-Layer Optimization Method”.
3) In Figures 8 and 9, you show a lot of simulation results. However, your discussion is not enough. Additionally, the error RWA is correlated largely to max deviation from ideal path. Therefore, the results in the same reaction time should be plotted in vehicle speed.
To respond to the above comments, in the revised manuscript a new paragraph was added and the newly added contents are provided as follows:
“Fig. 8 and 9 illustrate the Pareto-front graphs when vehicle forward speeds are 80, 90, 100, 110, and 120 km/h, while the driver’s reaction time is 0.0 and 0.1 s, respectively. Although there are minor differences among the shapes of these Pareto-front graphs, all these graphs share a common feature that the overall trade-off relationship between the design criterion of PFOT and (1-RWA) is clearly indicated. This trace-off relationship will facilitate the analysis and selection of potential compromised solutions.”
The newly added paragraph was organized as the second paragraph of Section 6.1. (GDE3 Optimal Pareto Fronts), which was Section 5.1 of the original manuscript.
As pointed out by the reviewer, the performance measure RWA is directly related to the path tracking performance as vehicle forward speed varies. Actually, Table 5 shows the impacts of vehicle forward speed and driver reaction time on the performance measure.
4) In Figures 10 and 11, the results of PFOT OT is almost same as the results of RWA,Tradeoff and GS. Is it important to change the vehicle's values?
To address the concern, we added the following contents at the end of the fourth paragraph of Section 6.1 (GDE3 Optimal Pareto Fronts):
“It should be noted that in Figs. 10 and 11, with respect to the case of passive design (without active trailer steering), the differences among the curves corresponding to the cases of PFOT, RWA, and Trade off appear not evident. This implies that compared with the passive design without ATS, the three ATS design solutions show much better performance although there exist evident differences among the three ATS designs. A close observation of Fig 10(e) indicates that among the three ATS designs, the PFOT shows the best overall trajectory-tracking performance, and the RWA exhibits the worst trajectory-tracking performance.”
Yes, some vehicle parameters, e.g., the distance between the hitch and the trailer axle, pose significant impacts on the trajectory-tracking performance. However, in this study, the parametric study is not the focus, and a typical car-trailer combination with the parameter values shown in Figs. 3 to 4 and Table 3 is selected.
Reviewer 3 Report
The authors provide an interesting step forward in the field of control of active trailers. The application of an evolutionary algorithm for the optimization of the LQR controller is new for this application even to my knowledge. The paper is well written and the main points are well addressed and discussed.
I would like to point out some suggestions for additional discussions that, in my opinion, should improve your work.
I understand the difficulty in using a software for such a complex system (car+trailer in 3D) and the impossibility for doing a validation in practice using real vehicles or models in reduced scale. However, it would be great if you can comment a bit more on the robustness of the controller that you are proposing in a more general context: what happens if, for example, the car is moving on a track with positive/negative slope? And is the control still working fine if trucks with heavy and long trails are considered?
I have a curiosity to ask you regarding the reaction times reported in Table 4 and 5. How did you choose them? They are very small (this driver model is much faster than the most reactive f1 driver).
I believe that the proposed control strategy is suited for both cases of driver of the vehicle in person and autonomous driving: could you confirm that or are any potential critical points in these two scenarios (e.g., safety maneuvers)?
Finally, I would like to point out some typos and small mistakes along the text:
Page 3, line 110-111: The sentence has a beginning, but doesn’t seem to have any end
Page 3, line 125 and 126: please use “a” instead of “an”
Page 8, figure 4: the picture is intended to have data everywhere, but there are some empty labels
Page 18: remember to fill in the Author Contribution section
Finally, I didn’t find [9] to be consistent with the text in which it is cited (page 2, section 2, line 80). Please, check if this reference can be placed somewhere else or removed.
Author Response
Reviewer 3:
The authors provide an interesting step forward in the field of control of active trailers. The application of an evolutionary algorithm for the optimization of the LQR controller is new for this application even to my knowledge. The paper is well written and the main points are well addressed and discussed.
I would like to point out some suggestions for additional discussions that, in my opinion, should improve your work.
I understand the difficulty in using a software for such a complex system (car+trailer in 3D) and the impossibility for doing a validation in practice using real vehicles or models in reduced scale. However, it would be great if you can comment a bit more on the robustness of the controller that you are proposing in a more general context: what happens if, for example, the car is moving on a track with positive/negative slope? And is the control still working fine if trucks with heavy and long trails are considered?
Essentially, the LQR-based active trailer steering (ATS) control approach proposed in the manuscript is a lateral trailer dynamic control scheme. This is reflected in the generation of the 3-DOF yaw-plane car-trailer model, in which the longitudinal motion and the associated longitudinal forces are not considered, and the vehicle forward speed is assumed to be constant. Note that the LQR controller is designed using the 3-DOF yaw-plane car-trailer model. In general, the robustness or capability of the LQR-based ATS control scheme is dependent on the cornering force of the trailer tires. Numerical simulation indicated that under low lateral accelerations, e.g., less than 0.40g, the ATS can effectively control the lateral motion of the trailer. However, at high lateral accelerations, the proposed ATS scheme may not be effective.
If the car-trailer combination with ATS is moving on a track with positive slope, due to the longitudinal load transfer, the trailer axle may gain an additional vertical load. Thus, the capability of the LQR-based ATS for trailer lateral motion control may be enhanced. In contrast, if the vehicle is traveling on a track with negative slope, the capability of the LQR-based ATS may be degraded.
It is well-known that the LQR controller is a liner control technique, and the LQR controller is designed under the assumption that the inertial and geometric parameters of the car-trailer combination are fixed. Thus, even a trailer is long and heavy, if the payload and geometric parameters are constant, the LQR-based ATS may still works fine. However, if the trailer payload varies, we may treat it in the same way as we treat the vehicle speed in this paper, and design the corresponding gain scheduling controller.
Based on the aforementioned discussion, in the conclusions of the revised manuscript, the following contents were added as the third paragraph:
“Although the proposed LQR-based gain scheduling controller (GSC) was designed for active trailer steering control for car-trailer combinations, the design method is also applicable for articulated heavy vehicles with tractor/semitrailer combinations. In the LQR-based GSC design, other uncertainties, e.g., trailer payload, may also be considered as vehicle forward speed discussed in this study. Due to the trailer tire cornering force saturation at high lateral accelerations, the proposed active trailer steering system is only effective in low lateral acceleration range, e.g., less than 0.40g.”
I have a curiosity to ask you regarding the reaction times reported in Table 4 and 5. How did you choose them? They are very small (this driver model is much faster than the most reactive f1 driver).
To address the above concern on selecting the reaction times for the built-in driver model provided in CarSim software, we added three articles by our research group (i.e., [23-25] in the revised manuscript). In [23], to achieve better path-following off-tracking (PFOT) performance of an articulated heavy vehicle during a high-speed single lane-change (SLC) maneuver, the driver model’s preview time (PT) was set to 0.6 s. With the given PT, the transport delay (i.e., reaction time (RT)) varied from 0 s with the increment of 0.02 s. Once the reaction time was a little bit higher than 0.1 s, the articulated heavy vehicle lost its lateral stability. Based on extensive numerical simulations, in the 2-dimensional coordination system (i.e., preview time versus reaction time) a Best Path Tracking Area was identified. Based on the recommended Best Path Tracking Area, one reaction time in the current research was set to 0.1s. Moreover, in [25], a double lane-change (DLC) maneuver at the speed of 110 km/h was simulated to evaluate the handling performance of a sport utility vehicle (SUV) with the PT and RT set to 0.8 and 0.15 s, respectively. It was observed that if the RT was longer than 0.17 s, the SUV lost its stability and failed the DLC test. The results reported in [25] also justify the selected reaction time of 0.1 s.
It is true that the reaction time of 0.1 s is small. As mentioned above, this small reaction time setting was to ensure better path tracking performance for the car-trailer combination. In fact, the acceptable reaction time increases with the preview time of the driver model. In [23], under the same simulated SLC maneuver, if PT was increased from 0.6 to 1.8s, the acceptable reaction time would also be increased from 0.1 to 0.5 s. However, in this case, the PFOT performance would be significantly degraded.
As for the selection of the other reaction time, i.e., 0 s, we intended to see the performance envelope of the LQR-based ATS system when an automated steering system would be applied and the driver model be used for the car front wheel steering control. It was expected that the reaction time of an automated steering system should be much shorter than human drivers.
Considering the above background for selecting the reaction times for the driver model, we added the following note at the end of the first paragraph of Section 6.1 (GDE3 Optimal Pareto Fronts):
“It should be noted that the reaction time of 0.1 s is selected following the Best Path Tracking area recommended in [23], while the reaction time of 0 s is chosen assuming that the driver model is used as an automated steering controller with negligible reaction time.”
I believe that the proposed control strategy is suited for both cases of driver of the vehicle in person and autonomous driving: could you confirm that or are any potential critical points in these two scenarios (e.g., safety maneuvers)?
As mentioned above, the two reaction time settings of the driver model correspond to two applications, i.e., human driver steering and automated steering. The performance of the LQR-based ATS scheme was evaluated using CarSim-based co-numerical simulations. Considering this fact, at the end of third paragraph of the conclusions, the following sentence was added:
“The proposed LQR-based ATS scheme is suited for both cases of autonomous driving and human driver driving.”
Finally, I would like to point out some typos and small mistakes along the text:
Page 3, line 110-111: The sentence has a beginning, but doesn’t seem to have any end
In the revised manuscript, the rest of this sentence was added:
“If the trailer is unable to follow the same path as the car, this will result in a swept path, and a wider road is required for the safe operation of the car-trailer combination.”
Page 3, line 125 and 126: please use “a” instead of “an”
In the revised manuscript, the typo was removed.
Page 8, figure 4: the picture is intended to have data everywhere, but there are some empty labels
As shown in Figure 5, for the car-trailer combination studied in the paper, the trailer has only one axle. In Figure 4, the geometric parameters of this trailer axle are defined. In CarSim software, the template trailer has two axles. Thus, another axle (i.e., rear axle) should not be defined, and the respective blocks were left empty.
Page 18: remember to fill in the Author Contribution section
In the revised manuscript, the required materials were added in the Author Contribution section.
Finally, I didn’t find [9] to be consistent with the text in which it is cited (page 2, section 2, line 80). Please, check if this reference can be placed somewhere else or removed.
We double checked the contents of this reference, and confirmed that it is not consistent with the text, in which it is cited. Thus, this reference was removed from the revised manuscript.
Round 2
Reviewer 2 Report
The modified manuscript is acceptable.
