Nonlinear Multi-Object Differential Game Simulation Model in LabVIEW

Round 1

Reviewer 1 Report

This article proposes a synthesis of a nonlinear multi-objective differential game model related to ship safety control processes in maritime collision situations. Establish a game state equation using the nonlinear dynamic equation of the target ship and the linear kinematic equation of passing ships. The model of this differential game was developed using LabVIEW software. Then, a simulation test was conducted using an example of a sailing situation, in which the target vessel passed through three encountered vessels at a safe distance under conditions of non cooperation, cooperation, and optimal non game control. The results of computer simulation are presented in the form of ship trajectories and time histories of individual game control variables.

In conclusion, this manuscript has some innovation and depth. It is suggested to make some modifications before publish it in this journal.

My comments and suggestions as follows.

1、The abstract suggests further refinement, highlighting the innovative points of the methods and conclusions adopted in the research.

2、There exist several typos in abstract, introduction and references part, please check carefully.

3、The introduction can be refined to highlight the focus and innovation of this manuscript.

4、The overall paper should be revised to increase the readability.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The article presents a methodological framework modeled on the basis of  differential game theory, for collision avoidance and safe navigation of marine vessels. Given a group of on-going sea vessels and a candidate vessel the framework formulates a set of differential equations modeling the control process and the dynamics of the system generated from the interaction of the candidate vessel with other potential targets. The differential game simulation is employed utilizing LabView and the results are demonstrated in the form of ship trajectories.

 

Chapter 2 concerns the formulation of the control process that the differential game simulation is based on. 

 

Chapter 2.2 describes the nonlinear differential equations outlining the motion dynamics with respect to vessel specific variables, changes in course, speed and rotational speed of the candidate vessel as well as the linear kinematic equations of target vessels. 

 

Chapter 2.3 deals with the state equations of the control process of the differential game system for all ships combined.

 

Remarks: 

 

• Literature review needs to be further expanded to include latest technological advancements and frameworks that deal with collision avoidance and generally routing optimization in the maritime sector. 

Relevant representative examples:

 

Kaklis, Dimitrios, et al. "Enabling digital twins in the maritime sector through the lens of AI and industry 4.0." International Journal of Information Management Data Insights 3.2 (2023): 100178.

C. Gkerekos and I. Lazakis, “A novel, data-driven heuristic framework for vessel weather routing,” Ocean Engineering, vol. 197, p. 106887, 2020.

• Notations in equation (6) need to be changed to avoid confusion, as in text x_j is described both, as the state vector of ship j, see page 5 “...where x0 is the state vector of ship 0;...”, as well as the course, angular speed, drift angle, etc, as also stated in page 5 “...where x1 =  ψ is the course…”.

 

Generally the last paragraph on page 5 needs considerable restructuring to provide the reader a clear view and understanding on the abbreviations and notations used through equations (7) - (14).

 

•  Accurate formulation of the differential game problem. Introduction & interconnection with optimal control problems. Elaborate on how and why the particular method fits the needs and requirements for the specific problem.

 

• Precise statement of the hypotheses on the interacting players (ship-j, j>0), 3) applicability (complexity) of the approach in high-traffic areas. Does the proposed approach enable entrance of new players (ships)?

 

• Availability of data for setting the dynamic equations of player- 0 (ship-0)

 

• How has the validation of the proposed method been performed? How the particular method extends beyond SOTA solutions on collision avoidance techniques currently being employed in the maritime sector.

Overall decision: 

Our decision is to accept the paper after conducting a minor revision incorporating the above mentioned comments.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

no further comments