Game Control Methods Comparison when Avoiding Collisions with Multiple Objects Using Radar Remote Sensing

Round 1

Reviewer 1 Report

This paper formulates the concept of games in the field of process control theory in marine sciences and reviews the literature on the possible applications of games.

The paper throughly explained the process control theory with mathematical equations.

The authors should consider to perform some statistical evaluation of the proposed method.

Overall paper is well written and organised, however there are many typos and grammatical mistakes need to be corrected. 

Author Response

Response to Reviewer 1 Comments

Point 1: The authors should consider to perform some statistical evaluation of the proposed method.

Response 1: This research proposal is included in section 6, in the form of:

“The article deals with the deterministic approach to the problems of games and their application to control multiple moving objects. In the next works one can consider elements of the theory of stochastic games and the possibilities of their application. Statistical evaluation of the proposed methods would also be important by simulation testing of typical navigation scenarios, for example on the ARPA simulator.”

Point 2:  Overall paper is well written and organised, however there are many typos and grammatical mistakes need to be corrected. 

Response 2: The text has been checked by MDPI English Editing for correct use of grammar and common technical terms and edited to a level suitable for reporting research in a scholarly journal, confirmed by a certificate ID-18620.

Author Response File: Author Response.pdf

Reviewer 2 Report

[COMMENTS]

This is a review paper about application of game control theory for collision avoidance in marine navigation under different scenarios. Simulation results have been presented considering the COLREG rules and object's dynamics.

This is an important problem and the problem itself has been formulated well. This is a very active area of research and recently several practical algorithms have been proposed with promising results. Although the author has touched upon various aspects of the problem, discussion of many recent works has unfortunately not been included. The scope of the final comparative simulation is narrow. This paper needs to be revised and some suggestions are given below:

1. Author should cite COLREG website (IMO) and documentation:
https://ecolregs.com/index.php?option=com_k2&view=item&layout=item&id=51&Itemid=383&lang=en

It is better to cite the following book which closely relates to the problem:

A. Cockcroft J. Lameijer, "A Guide to the Collision Avoidance Rules", Butterworth-Heinemann Publication; 7 edition (January 5, 2012), ISBN-10: 0080971709

2. In Eq.1, i = 1,2,...,N. But, x1, ..., xi ..., xn is used. It should be xN. Please check.

3. Same goes for Eq.2, please check.

4. Below Eq.2, integral payment?, final payment? Are these standard math terminologies?

5. Good seamanship has several requirements comprising of evasive manoeuvre, smooth manoeuvre, course changes, speed changes, etc. in practical maritime navigation. In recent years research has focused more on multi-objective optimization approaches which addresses such factors. Particularly, path smoothness is a practical case as abrupt and sharp manoeuvres are sometimes infeasible due to the kinematic constraints. Recent works addressing these issues must be included:

L. Hu et al., "A Multiobjective Optimization Approach for COLREGs-Compliant Path Planning of Autonomous Surface Vehicles Verified on Networked Bridge Simulators," in IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 3, pp. 1167-1179, March 2020, doi: 10.1109/TITS.2019.2902927.

S. Campbell, W. Naeem, "A Rule-based Heuristic Method for COLREGS-compliant Collision Avoidance for an Unmanned Surface Vehicle",
IFAC Proceedings Volumes, Volume 45, Issue 27, 2012, Pages 386-391, https://doi.org/10.3182/20120919-3-IT-2046.00066.

An extensive review of path smoothing algorithms given in the following paper should also be cited:

Ravankar, A.; Ravankar, A.A.; Kobayashi, Y.; Hoshino, Y.; Peng, C.-C. Path Smoothing Techniques in Robot Navigation: State-of-the-Art, Current and Future Challenges. Sensors 2018, 18, 3170.

6. In SI units, nm is the abbreviation of nanometers. The abbreviation of Nautical mile is: M, NM, or nmi. M is used by IHO, NM by ICAO, and nmi by engineers. Although some people use nm, nm is a non-standard abbreviation.

7. Page 5, paragraph below Eq.6, parameter description can be summarized in a table. This is difficult to read and comprehend.

8. Hr: drive screw reference stroke, Ftj thurst force .... etc. these parameters are never used in this paper. Why use variables for them? This paper has a huge number of variables which are often never used anywhere.

9. Eq.8, rightarrow --> min. What does this mean.

10. Below Eq.8, rjf (jf should be sub-scripted as in Eq.8). Similarly, epsilon_f. There are many similar inconsistencies throughout the paper. Please correct.

11. Fig.4. Is this author's own simulation result? Please describe what is to be seen here?

12. Fig.10, 11 Please provide captions of the figures on left and right.

13. Fig.10, Fig.11 the start, and final locations of the object must be marked.

14. Overall, as a reader, the reviewer found it difficult to read this paper. Particularly, all the equations have been poorly formulated. The variables used in the paper are either too tiny to be seen without zooming, or are aligned improperly. There are abrupt font changes in the equations. The variables are declared but seldom used anywhere. These can be corrected by proof-reading the paper well. Using Latex is also recommended. The problem of collision avoidance defined in COLREG should be explained in a point-wise manner. The proposed solutions should also be listed in a point-wise manner. Next, the focus should be determined and the review should follow smoothly. Since this is a review paper, novel contributions were not considered in the review. However, this review work should help the readers in this area in a comprehensive way. Author should strive to make the paper as readable and comprehensive as possible. The quality of figures used in this paper is also poor.

15. There are grammatical mistakes, but they were ignored while reviewing the paper.

Author Response

Response to Reviewer 2 Comments

Point 1: Author should cite COLREG website (IMO) and documentation:
https://ecolregs.com/index.php?option=com_k2&view=item&layout=item&id=51&Itemid=383&lang=en
It is better to cite the following book which closely relates to the problem:
A. Cockcroft J. Lameijer, "A Guide to the Collision Avoidance Rules", Butterworth-Heinemann Publication; 7 edition (January 5, 2012), ISBN-10: 0080971709

Response 1: The proposed items were cited in section 4.1.1 and included in References as items 58 and 59:

58. Cockcroft, C.; Lameijer, J. A guide to the collision avoidance rules; Butterworth-Heinemann Publication: Oxford, UK, 2012; ISBN 978-0-080-97170-4.
59. https://ecolregs.com/index.php?option=com_k2&view=item&layout=item&id=51&Itemid=383&lang=en

Point 2:  In Eq.1, i = 1,2,...,N. But, x1, ..., xi ..., xn is used. It should be xN. Please check.

Response 2: In equation (1) x_n was corrected to x_N:

Point 3: Same goes for Eq.2, please check.

Response 3: In equation (2) it is correctly as x_N:

Point 4: Below Eq.2, integral payment?, final payment? Are these standard math terminologies?

Response 4: In mathematics, the game is usually depicted using a payoff matrix representing players, their strategies and payoff assigned to these strategies, therefore the sentence below formula (2) has been corrected to:

“where f_oj is the integral payoff; f is the final payoff.”

Point 5: Good seamanship has several requirements comprising of evasive manoeuvre, smooth manoeuvre, course changes, speed changes, etc. in practical maritime navigation. In recent years research has focused more on multi-objective optimization approaches which addresses such factors. Particularly, path smoothness is a practical case as abrupt and sharp manoeuvres are sometimes infeasible due to the kinematic constraints. Recent works addressing these issues must be included:

10. Hu et al., "A Multiobjective Optimization Approach for COLREGs-Compliant Path Planning of Autonomous Surface Vehicles Verified on Networked Bridge Simulators," in IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 3, pp. 1167-1179, March 2020, doi: 10.1109/TITS.2019.2902927.
11. Campbell, W. Naeem, "A Rule-based Heuristic Method for COLREGS-compliant Collision Avoidance for an Unmanned Surface Vehicle",
    IFAC Proceedings Volumes, Volume 45, Issue 27, 2012, Pages 386-391, https://doi.org/10.3182/20120919-3-IT-2046.00066.

An extensive review of path smoothing algorithms given in the following paper should also be cited:

Ravankar, A.; Ravankar, A.A.; Kobayashi, Y.; Hoshino, Y.; Peng, C.-C. Path Smoothing Techniques in Robot Navigation: State-of-the-Art, Current and Future Challenges. Sensors 2018, 18, 3170.

Response 5: I included the issue of path smoothness in section 6 as:

“However, the designated set-up trajectories consist of consecutive maneuvers, major course changes, the smoothness of the calculated object path is important, which the works of Hu et al. [61], Campbell et al. [62], and in particular Ravankar et al. [63] are devoted to.”

and I added three proposed items in References as:

61. Hu, L.; Naeem,W.; Rajabally, E.; Watson, G.; Mills, T.; Bhuiyan, Z.; Raeburn, C. Salter, I.;Pekcan, C. A multi-objective optimization approach for COLREGs-compliant path planning of autonomous surface vehicles verified on networked bridge simulators. IEEE Transactions on Intelligent Transportation Systems 2020. 21(3), 1167-1179, doi:10.1109/TITS.2019.2902927.
62. Campbell, S.; Naeem, W. A rule-based heuristic method for COLREGs-compliant collision avoidance for an unmanned surface vehicle. IFAC Proceedings Volumes 2012, 45(27), 386-391, doi:10.3182/20120919-3-IT-2046.00066.
63. Ravankar, A.; Ravankar, A.A.; Kobayashi, Y.; Hoshino, Y.; Peng, C.C. Path smoothing techniques in robot navigation: state-of-art, current and future challenges. Sensors 2018, 18, 3170, doi:10.3390/s18093170.

Point 6:  In SI units, nm is the abbreviation of nanometers. The abbreviation of Nautical mile is: M, NM, or nmi. M is used by IHO, NM by ICAO, and nmi by engineers. Although some people use nm, nm is a non-standard abbreviation.

Response 6: I have corrected the manuscript, abbreviation nautical mile unit, throughout nmi.

Point 7: Page 5, paragraph below Eq.6, parameter description can be summarized in a table. This is difficult to read and comprehend.

Response 7: The description of the parameters of equation (6) is given in Table 1:

Variable	Means	Mark
	own object state 0 - dimensional vector
x0,1	own object course	
x0,2	angular speed of the own object of return
x0,3	own object speed	V
x0,4	own object drift angle	β
x0,5	own object main drive screw rotational speed	n
x0,6	own object main drive propeller pitch	H
	j-th object state j - dimensional vector
xj,1	distance to the j-th object	Dj
xj,2	bearing to the j-th object	Nj
xj,3	course of the j-th object	j
xj,4	speed of the j-th object	Vj
	own object control 0 - dimensional vector
u0,1	own object rudder deflection reference angle	αr
u0,2	own object main propeller reference rotational speed	nr
u0,3	own object main drive screw reference stroke	Hr
	j-th object control j - dimensional vector
uj,1	angular speed of the j-th object of return
uj,2	thrust force of the propeller of the j-th object	Ftj

Point 8: Hr: drive screw reference stroke, Ftj thurst force .... etc. these parameters are never used in this paper. Why use variables for them? This paper has a huge number of variables which are often never used anywhere.

Response 8: The basic model of differential game is a generalized model of the described control process and contains measurable and non-measurable variables. We can measure all variables on our object, but not all variables of the meet object. Therefore, variables such as H_r,  and F_tj are only found in the generalized base model. And for the synthesis of practical control algorithms we will have to simplify this generalized model and find the surrogate models presented in section 4 to use only measurable quantities.

Point 9:  Eq.8, rightarrow --> min. What does this mean.

Response 9: Equation (8) has been corrected to:

Point 10:  Below Eq.8, rjf (jf should be sub-scripted as in Eq.8). Similarly, epsilon_f. There are many similar inconsistencies throughout the paper. Please correct.

Response 10: I have made corrections throughout the manuscript text regarding sub-scripted:

“of collision r_jf and descent _f of the own object from the set route”

Point 11:  Fig.4. Is this author's own simulation result? Please describe what is to be seen here?

Response 11: The Conclusions were removed for points.:

“On the example of a container ship with a load capacity of 15,000 DWT, the state equations (6) were modeled in MATLAB software, obtaining a computer simulator of controlling own object in situations of passing by with many objects encountered. In this way, it becomes possible to both laboratory study of various possible states of the anti-collision process and testing practical algorithms for safe control of the object.

Figure 4 illustrates the nature and extent of changes in state and control variables during simulation of the basic model of the game control process during an anti-collision maneuver with a change of course.”

Point 12:   Fig.10, 11 Please provide captions of the figures on left and right.

Response 12: The captions under figures 10, 11, 12 from left to right have been corrected.

Point 13:  Fig.10, Fig.11 the start, and final locations of the object must be marked.

Response 13: The figures 7, 8, 10 and 11 marked the start and end points of the own object's trajectories.

Point 14:  Overall, as a reader, the reviewer found it difficult to read this paper. Particularly, all the equations have been poorly formulated. The variables used in the paper are either too tiny to be seen without zooming, or are aligned improperly. There are abrupt font changes in the equations. The variables are declared but seldom used anywhere. These can be corrected by proof-reading the paper well. Using Latex is also recommended. The problem of collision avoidance defined in COLREG should be explained in a point-wise manner. The proposed solutions should also be listed in a point-wise manner. Next, the focus should be determined and the review should follow smoothly. Since this is a review paper, novel contributions were not considered in the review. However, this review work should help the readers in this area in a comprehensive way. Author should strive to make the paper as readable and comprehensive as possible. The quality of figures used in this paper is also poor.

Response 14: Equation formatting has been improved and variables have been aligned. Figures have been graphically corrected to improve their quality. In section 4.1.1, points are added to the rules of COLREGs consideration:

“Each particular type of the situation involving the approach of the ships is assigned the logical variable value equal to one or zero:

A – encounter of the ship from bow or from any other direction,

B – approaching or moving away of the ship,

C – passing the ship astern or ahead,

D – approaching of the ship from the bow or from the stern,

E – approaching of the ship from the starboard or port side.

By minimizing logical function L_j by using a method of the Karnaugh's Tables the following is obtained:

                                                                  (14)

Point 15:  There are grammatical mistakes, but they were ignored while reviewing the paper.

Response 15: The text has been checked by MDPI English Editing for correct use of grammar and common technical terms and edited to a level suitable for reporting research in a scholarly journal, confirmed by a certificate ID-18620.

Author Response File: Author Response.pdf

Reviewer 3 Report

The introduction section needs to be reworked. Indicate in more detail for each source of literature a review. the author made an enlargement of the literature review.

The research topic is quite relevant. 

add more modern sources references.

Mathematical models need to be reworked. A lot of simplified models.

Author Response

Response to Reviewer 3 Comments

Point 1: The introduction section needs to be reworked. Indicate in more detail for each source of literature a review. the author made an enlargement of the literature review.

Response 1: The introduction has been redrafted. On the other hand, the literature review concerned the applications of game theory in various fields, but the least concerned the control of moving objects. Literature analysis was focused on the subject of the article, i.e. the game control of multiple moving objects.

Point 2:  Add more modern sources references.

Response 2: The following 5 items have been added to the manuscript text and the References section: 58, 59, 61, 62 and 63.

Point 3: Mathematical models need to be reworked. A lot of simplified models.

Response 3: The essence of the article was to present a very complex general model of differential game, and then show what are the possibilities of its simplification. As a result, two surrogate models of positional and matrix games were received. Further simplification leads to non-game models, and this would go beyond the topic of the article.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Editor,

Author has revised the paper well. It can be accepted and send for proof-reading.

Best Regards,

Reviewer