Risk-Aware Lane Change and Trajectory Planning for Connected Autonomous Vehicles Based on a Potential Field Model
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThank you very much for this excellent work. In my view the approach for complex modeling lane behavior and trajectory planning based on potential field theory and integrating the motion state of the vehicle, equipped with connectivity capabilities, with real-time data from surrounding vehicles to develop a comprehensive risk potential field model is novel. The measures to reduce computational complexity and increase efficiency of the algorithm as well as the developed minimum safe distance model to further optimize trajectories are highly appreciated, the 3 scenarios type simulation analysis and interesting results are esteemed. The paper is well written and structured; please check the heading 3.4.2 and provide the definition of what you mean by "cost" here and enlarge some figures, notably fig. 3, 7, 12, before publication.
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Reviewer 2 Report
Comments and Suggestions for AuthorsThe subject matter of the paper is up-to-date, and the manuscript has been carefully prepared. However, it might seem that the initial sections are slightly too long. I believe they could be shortened without losing clarity, both in terms of text and mathematical equations (many of which are similar to each other). Conversely, it would be advisable to expand the description of the procedure for finding the family of trajectories in the section concerning the simulation studies.
Below, I list specific comments:
1. Model (1) appears to describe a general concept but includes specific parameter values. Are these chosen parameters optimal, and how do they influence the solutions reported in this work?
2. Where does proposition (3) come from? Additionally, it seems that the exponential function \exp(-\sigma v) could be factored out before the square root. This would better highlight the scaling of the length |b_m| by velocity.
3. How should the ratio b_m/|b_m| be interpreted? Can b_m be negative? Is this related to equation (17)?
4. The relationships (7) and (8) partially stem from formulas (3) and (4), but they should be derived or cited from the literature more clearly. Additionally, (7) and (8) could be reduced to a single formula – it would suffice to indicate that certain terms have indices FV or TV, respectively.
5. I believe the derivations of polynomial forms in section 3.2 could be significantly shortened. In particular, equations (28) and (29) can be removed, and a general form of the result for variables ddd and sss could be presented. Referencing similar formulas (30) and (31) is unnecessary.
6. In section 3.4, the authors refer to “sampled trajectory points”. Previously, the description was given in the continuous domain. I think it would be worthwhile to briefly comment on why a discrete space is necessary at the optimisation stage. It could be assumed that this results from the lack of closed-form mathematical formulas for determining the properties of polynomial trajectories.
7. The results shown in Fig. 14 should reference the indicators defined in section 3.4.2. The terms ‘total loss’ and ‘risk values’ are not precise.
8. Where is the indicator defined by (46) used? In equation (43), J_{\text{dev}}^i does not appear. The adopted numbering convention suggests that subsequent components of (43) are being discussed here.
9. Given the numerical computations and discrete representation of the trajectories, the question arises about the sensitivity of the algorithm to discretisation parameters. The presented results are shown for constant parameter values. Were the reported results compared to more accurate solutions obtained with a smaller discretisation step?
10. The computational procedure has not been explained in detail. There is less detail here, especially compared to the earlier, more comprehensive points. I think it would be valuable to explain how the trajectories were generated in the initial stage of finding solutions. Were deterministic methods (e.g., searching on a regular grid) used, or were probabilistic methods and random sampling employed?
11. The paper does not mention computational efficiency. What are the computation times for the scenarios presented? Is it feasible to implement the algorithms in real-time using more efficient tools (e.g., low-level programming languages, parallel computing)?
Comments on the Quality of English Languagea) Line 161: The statement is unclear. What would be a reasonable assumption to suggest that the curvature of the road is not high?
b) The function exp in formulas (15) and (16) should be written in a standard font (not italicised).
c) Line 590: There is a reference to formula (43), which has not been previously defined.
Author Response
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Reviewer 3 Report
Comments and Suggestions for AuthorsTopics related to autonomous transport are very relevant and important for its improvement.
The problem is revealed in detail in the Introduction. Most of the mentioned sources are quite new and reveal the current situation in the subject under consideration. The methodology is described in detail in Section 2, illustrated with figures. Lane change trajectory planning is presented in Section 3. Information is presented in a coherent and logical manner. Section 4 presents simulation analysis. To fully validate the real-time performance and effectiveness of the proposed trajectory planning algorithm, the algorithm was programmed using Python, and simulations were performed on a three-lane curved road. Different scenarios are considered, which are described in a sufficiently understandable manner. The conclusions reflect the results of the conducted research. In my opinion, the conclusions could be more detailed.
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Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe current version of the manuscript has been revised properly, which has improved its readability. However, I have noticed the need for clarification of the notation used in the article.
1. I believe that the term b, explained under equation (2), does not describe a distance but rather a vector. Therefore, it would be important to explicitly state that b belongs to \mathbb{R}^2. This is significant and affects the interpretation. Additionally, the meaning of the symbol ∣⋅∣ should be explicitly defined. Typically, the symbol ∥⋅∥ is used to denote the norm of a vector x\in\mathbb{R}^n.
2. In equation (4), U_v is described as a "potential field." However, a potential field is scalar, and here it would be more appropriate to refer to it as a vector field, since v\in \mathbb{R}^2. In any case, this point should be briefly commented on.
There are also errors in the references to the literature in the manuscript. Instead of [number], there is a [?]. I assume this is a technical issue.
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