Smooth and Robust Path-Tracking Control for Automated Vehicles: From Theory to Real-World Applications

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, a robust path tracking controller based on Dubins paths is proposed, focusing on the key challenges (dead time compensation, path discontinuity handling, parameter tuning) from theory to practical applications. The study is validated by realizing double-shift line conditions on a real vehicle, demonstrating good tracking performance and smooth steering control. Some comments are as follows.

1. Controller sensitivity to vehicle parameters (e.g., mass, tire friction) should be discussed.

2. Lack of quantitative comparison with classical methods (e.g., MPC, LQR). It is recommended to compare tracking error, computational efficiency and steering smoothness in the same test scenario.

3. In Section 3.3, it is mentioned that positioning errors lead to 0.15m front-axis errors, but the specific effect on the controller is not analyzed.

4. Conclusion should emphasize the novel contributions.

5. Some of the literature is old.

Author Response

Comments 1: Controller sensitivity to vehicle parameters (e.g., mass, tire friction) should be discussed.
Response 1: added section 2.3 "Inherent characteristics"

Comments 2: Lack of quantitative comparison with classical methods (e.g., MPC, LQR). It is recommended to compare tracking error, computational efficiency and steering smoothness in the same test scenario.
Response 2: added subsection 2.4 "Comparison to state of the art controllers" where 2 sota controllers are compared to the proposed one in simulation, in the double-lane-change scenario that is used for the real-vehicle tests

Comments 3: In Section 3.3, it is mentioned that positioning errors lead to 0.15m front-axis errors, but the specific effect on the controller is not analyzed.
Response 3: described the effect more clearly in section 3.3 "Positioning system"

Comments 4: Conclusion should emphasize the novel contributions.
Response 4: a dedicated subsection is added to the conclusion

Comments 5: Some of the literature is old.
Response 5: the introduction section is rewritten completely. it now includes a more extended literature review and better emphasizes the contribution of the paper

Reviewer 2 Report

Comments and Suggestions for Authors

I congratulate the author on the article. However, some revisions are necessary for its publication.

The article frequently cites previous studies ([9], [16]), but it should be more clearly emphasized how the current study addresses the gap in the literature. The authors should highlight the innovative aspects (e.g., the look-ahead approach, dead-time compensation).

The equations are quite dense, but some sections (especially equations 3–7 in Chapter 2) may be difficult for the reader to understand. A more intuitive explanation or simplified example would be helpful.

The experiments were conducted on a Ford Mondeo, but more information (weather conditions, speed ranges, road surface conditions) is needed to ensure repeatability. Only a double lane change maneuver was tested. Different scenarios (e.g., winding roads, longer driving periods) were not tested; this limitation deserves discussion.

Some challenges (measurement error, sensor delay, model differences) were mentioned in the study, but these limitations deserve a more comprehensive discussion. For example, the impact of errors in GNSS/INS integration in different scenarios could be discussed.

More recent application-focused studies (industrial applications between 2023 and 2025) could be added.

Author Response

Comments 1: The article frequently cites previous studies ([9], [16]), but it should be more clearly emphasized how the current study addresses the gap in the literature. The authors should highlight the innovative aspects (e.g., the look-ahead approach, dead-time compensation).
Response 1: the introduction section is rewritten completely to better emphasize the contribution of the paper.

Comments 2: The equations are quite dense, but some sections (especially equations 3–7 in Chapter 2) may be difficult for the reader to understand. A more intuitive explanation or simplified example would be helpful.
Response 2: there was a confusion with delta_f and delta_l that is now corrected. also, the section is extended with some explanations

Comments 3: The experiments were conducted on a Ford Mondeo, but more information (weather conditions, speed ranges, road surface conditions) is needed to ensure repeatability. Only a double lane change maneuver was tested. Different scenarios (e.g., winding roads, longer driving periods) were not tested; this limitation deserves discussion.
Response 3: added weather and road surface information to section "Real test conditions". the limitations of only this one maneuver are discussed in the section "outlook"

Comments 4: Some challenges (measurement error, sensor delay, model differences) were mentioned in the study, but these limitations deserve a more comprehensive discussion. For example, the impact of errors in GNSS/INS integration in different scenarios could be discussed.
Response 4: the effects of positioning/heading errors are described more clearly in section 3.3 "Positioning system". however, the paper is indeed missing a more extensive evaluation of these and other disturbance effects, which is now hightlighted in the "outlook" section

Comments 5: More recent application-focused studies (industrial applications between 2023 and 2025) could be added.
Response 5: the introduction section now includes a more extended literature review

Reviewer 3 Report

Comments and Suggestions for Authors

This paper describes a variable structure path-tracking control approach, which is based on the geometrically optimal solution of a Dubins car, and offers a promising solution to this challenge. The controller generates an n-smooth and differentially bounded steering angle and, with n+1 parameters, can be tuned towards performance, robustness, or low magnitude of the steering angle derivatives.

Strengths of this paper: The paper describes a new trend in Path-Tracking Control for Automated Vehicles. In addition, some simulation and experimental results are shown to evaluate it.

Weaknesses of the paper: The paper would benefit from improved organization to enhance its overall structure and logical flow. Additionally, the literature review should be expanded and strengthened to provide a more comprehensive overview of related work and better contextualize the study.

The following points should be considered:

1-The literature review is not well-written and lacks relevant information, as well as an analysis of the drawbacks of previous research. As a result, the rationale and methodology behind the proposed algorithm are unclear and may confuse the reader.

2-The authors did not provide a dedicated conclusion section. Instead, they included a subsection titled Discussion and Conclusion within Section 5. However, this subsection does not sufficiently serve as a proper conclusion, nor does it clearly highlight the significance and contributions of the work.

3-In Figure 14, the title of the y-axis is missing.

4-In. Figures 5, 7, 11, 13, and 14 each contain multiple subfigures. The authors should provide separate titles or labels for each subfigure to improve clarity and help readers understand the content more easily.

5-The abstract should include a summary of the key results, such as the mean error, to provide a clearer understanding for readers.
6-The results presented in the paper should be compared with previous work in the field to better highlight the novelty, performance, and significance of the proposed approach.

7-A flowchart for the algorithm should be added.

Author Response

Comments 0: The paper would benefit from improved organization to enhance its overall structure and logical flow. Additionally, the literature review should be expanded and strengthened to provide a more comprehensive overview of related work and better contextualize the study.
Response 0: restructured the introduction and extended the literature review. the introduction now includes an overview of the paper organization. also I added structure (subsections) to chapter 2 

Comments 1: The literature review is not well-written and lacks relevant information, as well as an analysis of the drawbacks of previous research. As a result, the rationale and methodology behind the proposed algorithm are unclear and may confuse the reader.
Response 1: the introduction section is rewritten completely. it now includes a more extended literature review and better emphasizes the contribution of the paper. in section 2, subsection 2.4 "Comparison to state of the art controllers" has been added

Comments 2: The authors did not provide a dedicated conclusion section. Instead, they included a subsection titled Discussion and Conclusion within Section 5. However, this subsection does not sufficiently serve as a proper conclusion, nor does it clearly highlight the significance and contributions of the work.
Response 2: the conclusion is now a dedicated section, including contributions of the work

Comments 3: In Figure 14, the title of the y-axis is missing.
Response 3: added axis title

Comments 4: In. Figures 5, 7, 11, 13, and 14 each contain multiple subfigures. The authors should provide separate titles or labels for each subfigure to improve clarity and help readers understand the content more easily.
Response 4: for saving space, multiple axis are put in a single figure. To still improve clarity, the captions are extended with more details

Comments 4: The abstract should include a summary of the key results, such as the mean error, to provide a clearer understanding for readers.
Response 5: added summary and quantities of the test results, including the maximum tracking error

Comments 6: The results presented in the paper should be compared with previous work in the field to better highlight the novelty, performance, and significance of the proposed approach.
Response 6: added subsection 2.4 "Comparison to state of the art controllers" where 2 sota controllers are compared to the proposed one in simulation, in the double-lane-change scenario that is used for the real-vehicle tests

Comments 7: A flowchart for the algorithm should be added.
Response 7: added a flowchart and described it in section 4.3 "Summary of adaptions"

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The paper is accepted in its present form.