Rapid Construction of Aerocapture Attainability Sets Using Sequential Convex Programming
Round 1
Reviewer 1 Report
This is a very interesting paper about how to estimate aerocapture attainability sets. Besides, the simulation example of aerocapture on Mars is well selected.
The following points should be considered:
You should improve the quality of your figures, particularly, figure 5.
You mention that "the path constraints in the simulation are Q'max=105 W/cm2, nmax=4.5gM and qmax=10KN/m2". How do you select such values?
Your technique should be compared with respect to another previous methods. If this is the first time that an algorithm (as yours) is proposed to solve the current problem, then this should be clearly mentioned in the paper.
How could you guarantee the convergence of your algorithm? You should devote some words to this point.
You claim that "Because of the relatively low computational cost, the proposed algorithm can potentially be used onboard to rapidly assess the aerocapture attainability set." However, how do you estimate the computational cost and computation time?
Author Response
Thank you very much for valuable and helpful comments, as well as the important guiding significance to our research. The main corrections in the paper and our responses are elaborated below:
Point1: You should improve the quality of your figures, particularly, figure 5.
Response 1: Figure 5 has been replaced with a higher definition figure in the paper.
Point 2: You mention that "the path constraints in the simulation are Q'max=105W/cm2, nmax=4.5gM and qmax=10KN/m2". How do you select such values?
Response 2: The path constraint upper bound usually depends on the corresponding endurance of the spacecraft. For a low lift-to-drag ratio spacecraft, the heat rating constraint is generally between 30-300 W/cm2, and the maximum overload peak value does not exceed 20 gM. The path constraint boundary values used in this paper refer to the design values of most existing Mars rovers. In order to enhance the credibility, corresponding supplementary explanations are added to the paper, and the Reference is given.
Point 3: Your technique should be compared with respect to another previous methods. If this is the first time that an algorithm (as yours) is proposed to solve the current problem, then this should be clearly mentioned in the paper.
Response 3: The research in this paper is the first time that the calculation method of the aerocapture attainability sets is given, so no comparative simulation results are given. Sorry for the lack of a clear explanation in the paper, we have added a corresponding explanation for this.
Point 4: How could you guarantee the convergence of your algorithm? You should devote some words to this point.
Response 4: Aiming at the convergence of the method proposed in this paper, it is mainly improved in three aspects. First, the dynamic model reduces the state quantity by one dimension through the substitution of independent variables, thereby reducing the complexity of the problem. Secondly, the groove-shape initial trajectory is given for the solution of boundary points for the first time calculation, which increases the feasibility of the problem. Finally, when solving other boundary points, the initial value is given by the optimal solution of the previous solution. This adjacency idea greatly improves the sensitivity of the initial value. This paper adds corresponding explanations at the end of Sec. 4.
Point 5: You claim that "Because of the relatively low computational cost, the proposed algorithm can potentially be used onboard to rapidly assess the aerocapture attainability set." However, how do you estimate the computational cost and computation time?
Response 5: Sorry for not giving a detailed description of computational efficiency. In this paper, all computations will be performed by MATLAB-R2018a on a desktop with Intel i7-4790K CPU @4.00GHz. Note that, in the aforementioned computing environment, it takes a total of 7.47 s to calculate the envelope of the attainability set in Fig. 7. Specifically, a total of 57 extreme values of points are calculated, and the average calculation time per extreme value is about 0.131 s. That is, it takes only about a hundred milliseconds. At the same time, in the process of solving all extreme values, the successive approximation is generally completed between 4~7 steps, and the calculation time of each step is about 0.02~0.03 s, which is equivalent to the time of solving a convex subproblem. The statistical results of the calculation time demonstrate the high efficiency of the proposed method, and it also verifies the feasibility of the method to determine the aerocapture attainability set onboard for aerocapture mission. We supplement the corresponding explanatory notes in Subsec. 5.1.
Reviewer 2 Report
This is in general an interesting paper, and its subject is consistent with the scope of the Journal. In my opinion, the paper can be accepted in the presented form.
Author Response
Point: This is in general an interesting paper, and its subject is consistent with the scope of the Journal. In my opinion, the paper can be accepted in the presented form.
Response: Thank you very much for acknowledging our work.
Reviewer 3 Report
The article quit specifical, but it was interesting to read. The research done logical and looking fine. I have just two suggestions:
- Extend introduction part and more dipper indificate actuality.
- Check gramatic mistakes.
Author Response
Thank you very much for your comments, as well as the recognition of our research. My coauthors and I take your feedback seriously, and we have thought carefully about the suggestions. The main corrections are given below:
Point1: Extend introduction part and more dipper indificate actuality.
Response 1: Thank you very much for your suggestion to improve the depth of the Introduction. The introduction summarize the articles that are representative of aerocapture and reachable domain of the spacecraft. According to your kind suggestion, we set up the introduction succinctly, so as to summarize the research situation of this problem more systematically.
Point2: Check gramatic mistakes.
Response 2: We are very sorry for some grammatical errors in this paper. We have revised the whole manuscript carefully and tried to avoid any grammar or syntax error. We believe that the language is now acceptable.
Reviewer 4 Report
Please, find my comments on the pdf file.
Comments for author File: 
Comments.pdf
Author Response
Thank you very much for your comments, as well as the recognition of our research. My coauthors and I take your feedback seriously, and we have thought carefully about the suggestions. The main corrections are given below:
Point1: Abstract. The text “To capture a vehicle from a hyperbolic orbit to a target mission orbit, aerocapture is more efficient in fuel consumption than traditional propulsive orbital maneuvers. Due to the limited control ability of the vehicle during the atmospheric flight, there exists an aerocapture attainability set, which is a key to assess the feasibility of performing an aerocapture orbit maneuver and to assist the design of a permissible target mission orbit." can be deleted without lost the information of the abstract. Moreover, at the end of the abstract a synthesis of conclusions is missing. Please insert a text for synthesis of conclusions.
Response 1: Thank you very much for your suggestion on the structure of the Abstract. We have removed redundant text upon recommandation, and added conclusion at the end of the Abstract.
Point2: Inconsistency of mathematical notation. Is strange the mathematical notation, for instance on page 3 (line 85) the authors write \. . . as x(t) = [r; V; g]T ; where . . . " and on page 3 (lines 88-90) write…The notation is incompatible, since “r” and “r” are different, “V” and “V” are different, etc. Please unify the notation, for instance in the case the coherent notation for the system is given by…
Response 2: Thank you very much for pointing out these confusing errors, we have corrected them in detail.
Point3: Quality of figures. The resolution of Figures 5 and 8 is poor.
Response 3: Figure 5 and 8 have been replaced with higher definition figures in the paper.
Point4: Future work. exp At the conclusions section the possible future work is missing. Please include a new paragraph with a extensive discussion of lines for future research.
Response 4: Thank you very much for your suggestion, we have supplemented the conclusion with an outlook for future work.
