R-DFS: A Coverage Path Planning Approach Based on Region Optimal Decomposition

Round 1

Reviewer 1 Report

The paper provides a coverage path planning method based on the optimal decomposition of regions, through images taken from Google Earth, images on which a search for optimal subregions of travel is performed by means of a Genetic Algorithm, with the aim of minimizing the number of turns to be completed by a UAV.

The contribution seems to be poor, although the Genetic Algorithm may present a good alternative to complete the problem. Nevertheless, the paper presents several weaknesses throughout its description. On the other hand, the abstract mentions that images are taken from Google Earth, however, the paper also mentions the way to obtain aerial images by means of a UAV.

Below are some details about the reading.

In line 57, 110 the concept of smooth path is mentioned, however this concept has not been worked on, the authors have a erroneous concept about the meaning of Smooth Path.

The reading in the introduction is not continuous, there is no connection between phrases, so in general the section should be rewritten.

Figure 2, labels are not visible

Text repeated in several places throughout the paper. Repeated explanations, same variables are used and terms are changed.

Line 170, 178, revise explanations.

Figure 3, labels are not visible

Figure 4, labels are not visible

Figure 4 does not correspond to equation 2.

Equation 3, term (W, w, V ??)

Line 239-240, definition Vi, Vi-1, Vi+1 is not correct.

Lines 355, reference is given to an image that does not correspond.

Figure 18d, the labels are not visible, also the results of this image are not explained.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents a coverage path planning approach based on an optimal decomposition of concave polygons. The authors present some preliminary results with different work area shapes but don't present a benchmark of performance with respect to the detail of the state-of-art methods in the introduction. 

I've read your paper with great interest, although some points should be reviewed to ensure that the article achieves the expected quality to be approved:

• It doesn't make sense to start the Abstract with "While" Please improve the sentence.
• The first time that you refer to UAV, use capital letters.
• Line 81, remove space in the sentence.
• Line 115, can you explain what do you mean by "severe areas"? A concave polygon?
• Good work in the definition of the paper contribution related to the state-of-the-art.
• Increase the size of figure 4. Even with 150% of PDF, it wasn't easy to read the symbols.
• The legend of figure 5, must be on the same page.
• Explain with the equations, how to obtain the V1 ... V4 of figure 6b
• Equation 3, doesn't have the symbol V, so correct the sentence in line 215
• Figure 8, doesn't explain the covering path planning. Maybe remove the flow chart and replace it with an algorithm with the required equations.
• Improve the sentence of lines 255 and 256. How do you obtain the 10 convex polygons? Manually? Why 10?
• Improve section 3.2, including a figure with the algorithm, and remove the steps.
• Improve sentence from lines 294 and 295. Too many "accessed"
• Lines 304  - 326. Including a figure with the algorithm, and remove the steps.
• Line 377. Missing the "." 
• In line 387, include a reference to paper about the center of gravity, otherwise, you need to explain with more detail equation 6.
• Line 397, the genetic algorithm method is based on some previous work? If so, please include a reference.
• Improve the sentence from line 413. Suggestion: Start by saying that D represents the Euclidean distance.
• Line 450. The figure reference is not correct (Figure 19?)
• Line 463: Please explain the genetic algorithm parameters. Why inn=24, GnMax=100 ...? Improve this section with more details about the parameters? Did you perform preliminary tests with different values? What is the impact of using other parameters? 
• The results present in chapter 5, must be compared with a method detail in the state of the art, otherwise is not possible to evaluate the improvement by following your proposed approach. The cooperation should be detail in table 5.
• What is the computational cost of your method went compare to other approaches?
• Conclusions are well detailed, especially the problem related to the replanning problem in case of strong wind, and also the problem of tuning the genetic algorithm parameters to improve the final result.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

This is a very thorough, complete, well-organized, and well-documented study.  I have highlighted some English issues. In particular, there are many issues concerning singular and plural forms.  The content is excellent, and excellently presented. Please note in Eq. 6 the matrices should be not be in brackets but with vertical bars, to show they are determinants (or you may use "det() to indicate.  It would probably be a good idea also to clarify that this formula works only for convex polygons, and the vertices must be specified in consecutive order. 

Comments for author File: Comments.pdf

Author Response

Point 1: Please note in Eq. 6 the matrices should be not be in brackets but with vertical bars, to show they are determinants (or you may use "det() to indicate.  It would probably be a good idea also to clarify that this formula works only for convex polygons, and the vertices must be specified in consecutive order.

 

 

Response 1: Thank you very much for your comments. Thank you for your reminder, we have modified the relevant formula

 

Action 1: Please see the attachment.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

This paper deals with a very important topic in Multirotor unmanned aerial vehicle, it introduces a coverage path planning method based on region optimal decomposition (ROD) in three approaches. First, obtaining the remote sensing map of a port from Google Earth image, and a concave polygon area of the port is divided into several subregions by the method of region optimal decomposition. Second, the optimal combination for each subregion is determined by an improved depth-first search (DFS) algorithm. Finally, the traversal order for all subregions is determined by a genetic algorithm. The whole approach is applied to the path planning of an Unmanned aerial vehicle (UAV) in a port area and the experimental results are compared with a common coverage path based on the minimum width method. The experimental results show that the adopted approach is particularly suitable for irregular areas such as wharf yards. But the paper did not consider the influence of wind disturbance on path planning. Also, other important constraints are not taken into account such as the impact of wind disturbance on path planning.

Generally, the paper quality is good, it is very well organized and the obtained results are well presented. Other comments and remarks:

1. The abstract section needs to be reformulated. It does not clearly describe the paper idea and the transition between some sentences is not well done. In general, the abstract should represent the entirety of your article – introduction, methodology, results, and conclusions.

 

2. The Introduction section is well written, but it is too long and the main contributions of this article should be more highlighted to distinguish it from the existing works.

 

3. The simulation part can be more enhanced by comparisons between your work and other work results in form of numerical or plot presentations. And you should show if your proposed method can contribute to improving the energy efficiency, the Cost, and the Coverage time of Unmanned aerial vehicle for a complete Coverage Path Planning Approach Based on Region Optimal Decomposition. And justify why you have chosen GA and not other existing methods in the literature.
4. You have mentioned that the experiment shows that the R-DFS can reduce the number of turns by 4.34%, and shorten the non-operating distance by about 29.91% in the process of UAV coverage path planning, but is preferable to show experimentally how this reduces the number of turns can improve the energy efficiency, the Cost and the Coverage time.

 

5. More interpretation and justification are needed in the Simulation and analysis, the obtained results in Table 4 are not well commented on and justified. You can more justify the big difference between. You can more justify the big difference between before and after region decomposition, by justifying why the number of turns, the length of the working path, and the length of the non-working path are significantly reduced. And clearly show how your approach can contribute to effectively reduce the number of subregions compared to other methods.

 

6. You should improve the quality of figure 21 for a future comparison by other authors because the label values do not clearly show that the length of the non-working path in the decomposed polygon area is significantly reduced.

 

7. There are few mistakes in the English language. The writing quality should be improved further to avoid typos and editing errors. Some sentences are not well structured (you should use commas) and others their meaning is not well clear. For example, use “experiment results" instead of “experiments results”. Please check the language carefully by reading the paper many times.

 

8. You should add more references, especially in the Introduction section and in the mathematical expression.

Author Response

Point 1: The abstract section needs to be reformulated. It does not clearly describe the paper idea and the transition between some sentences is not well done. In general, the abstract should represent the entirety of your article – introduction, methodology, results, and conclusions.

 

Response 1: Thank you very much for your comments. We have rewritten the abstract.

 

Action 1:

Abstract: The coverage path planning (CPP) in concave polygon area is likely to generate more non-working path, the research in this paper introduces a CPP method based on the region optimal decomposition (ROD). First, obtaining the remote sensing map of port from the Google Earth image, and the map of port area is divided by the method of ROD. Second, combining the subregions by the improved depth-first-search (DFS) algorithm. Finally, the traversal order for all subregions is determined by the genetic algorithm. The whole approach is applied to the path planning of an unmanned aerial vehicle (UAV) in the port area. The experiment shows that the R-DFS can reduce the number of turns by 4.34%, and shorten the non-working distance by about 29.91% in the coverage path of UAV. Overall, the method of R-DFS provides a sound solution for the coverage path planning and operations of UAV.

 

 

Point 2: The Introduction section is well written, but it is too long and the main contributions of this article should be more highlighted to distinguish it from the existing works.

 

Response 2: Thank you very much for your comments. We have rewritten the introduction.

 

Action 2:

Multi-rotor unmanned aerial vehicle (UAV) has the advantages of small size, high reliability and hovering [1], and has been widely used in many fields of production, life and safety. Such as agricultural plant protection [2], film and television shooting [3], structure detection [4] and river inspection [5]. Path planning is an optimization problem when a UAV has to carry out various tasks. According to UAV's movement characteristics and tasks to perform, path planning tasks can be divided into two categories. The first one is the usual path planning problem from point to point [6], the main purpose is to find a collision-free path from the starting point to the endpoint. The second one is the coverage path planning(CPP) [7], in which the main purpose is to search all areas except obstacles in the working area, such as sweeping robots, industrial detection robots, agricultural robots [8,9,10].

Due to the complex environment of wharf yard, a full coverage inspection of a given region is usually required. As the manual inspection is often time-consuming, and the cost of helicopter inspection is too high, a good option is to use the camera-equipped UAV to conduct the coverage inspection on the port area.

Search direction and motion form are the two main factors affecting the coverage path planning. First, the search direction of the coverage path planning has a greater impact on the energy consumption. In the coverage path, the minimum number of turns is generally used as the basis for selecting the search direction. Current methods that can be applied to determine the convex polygon's minimum width are mainly the rotary caliper method [11] and vertex perpendicular method [12]. The rotating calipers method can quickly obtain the minimum width of the convex polygon area and the process of the vertex perpendicular method is simpler. Second, the forms of motion can be divided into spiral motion [13, 14], random motion and back-and-forth motion [15]. The spiral pattern is only suitable for use in convex polygon areas, the random pattern will generate more non-working distance. Therefore, the back-and-forth path is usually used as the coverage path.

When the back-and-forth path is used as the coverage path, more non-working paths will be generated, resulting in waste of time and energy. Therefore, the method of region optimal decomposition (ROD) needs to be applied to complex concave polygonal areas. According to the way of free space decomposition, coverage path planning algorithms can be categorized into cell decomposition algorithm [16,17,18,19,20] and grid algorithm [21,22,23,24]. The algorithm based on a cell decomposition divides an original area into some smaller areas, and then cover the cell area through some simple motion. The cell decomposition method simple and easy to implement. The grid-based method applies a uniform grid set to represent the given area [25]. But this method is only suitable for search areas with regular shapes.

So far it appears that most of the covering algorithms are applied to convex polygons, while for concave polygons, the general approach is to convert a concave polygon into multiple convex polygons. For example, the concave polygon can be decomposed into multiple convex polygons through the "top-down" trapezoidal decomposition, but it will deviate from the optimal and lead to excessive decomposition [26]. A specific convex decomposition method that occurs at the point where the inner angle between the two edges of the target polygon exceeds 180 degrees has been introduced [27], but the intersection of edge extension lines generated many smaller subregions. A Voronoi based path generation algorithm under the condition that the UAV flight distance is limited has been developed but this cannot fully cover the extensive search areas [28], but the path generated by this algorithm is not smooth enough and has a large turning angle compared with the back-and-forth motion.

When dividing a search area, a necessary constraint is to determine the partition area's traversal and search order. For instance, the bottom of the bridge can be divided according to the risk level in order to found a path that can cover the most dangerous area using a genetic algorithm, but that method is only applied to a few severe areas [29]. The Pattern Search (PS), the Genetic Algorithm (GA) and the Particle Swarm Optimization (PSO) performance comparisons have been studied for convex and non-convex polygon areas. The findings show that PS performs much better than the two others, but the study and PS is mostly suitable for polygons with small coverages and does not consider overlap rations [30]. A discrete particle swarm optimization algorithm took into account the coverage and obstacle constraints by transforming the search problem into a Travelling Salesman Problem, this shortening the algorithm planning time. However, there is no detailed description of the camera layout and view feature acquisition [31].

Given the many limitations that appear from the above related work, and particularly the non-straightforward consideration of concave regions and optimization of a full coverage path algorithm, the research presented in this paper takes an irregular concave polygon area as the wharf yard as the research object of study. First, an improved depth first search method optimizes a concave polygon area's segmentation in order to minimize the number of subregions and reduce the subregions to be merged. Secondly, the minimum width method determines the best scanning direction of each subregions. Third, the UAV's coverage path width is determined by the flight height and camera parameters of the UAV. Finally, a genetic algorithm determines the UAV's traversal order in all subregions after segmentation.

Our contributions are summarized as follows.

 A method capable of completely decomposing concave polygon region into convex polygon subregions.

 Improving the depth-first search algorithm and applied it to the merging of port subregions.

 Center of gravity of convex polygon subregions for characteristic points of TSP problem.

The rest of the paper is organized as follows. Section 2 introduces the principles behind the coverage path planning of a convex polygon region. Section 3 develops the coverage path planning of concave polygon regions. Section 4 describes the traversal ordering principles and scanning ordering of each region. Finally, Section 5 presents the simulation results while Section 6 concludes the paper and draws some conclusions.

 

 

Point 3: The simulation part can be more enhanced by comparisons between your work and other work results in form of numerical or plot presentations. And you should show if your proposed method can contribute to improving the energy efficiency, the Cost, and the Coverage time of Unmanned aerial vehicle for a complete Coverage Path Planning Approach Based on Region Optimal Decomposition. And justify why you have chosen GA and not other existing methods in the literature.

 

Response 3: Thank you very much for your comments. This article mainly takes the effective working path length and the number of turns as the measurement standard of the path planning results, and does not consider the energy correlation for the time being. Thank you very much for your new ideas. In addition, since we have relatively few sub-regions, we generally only need a few iterations to solve the TSP problem, so it is not meaningful to compare other algorithms with genetic algorithms, but thank you very much for your suggestions.

 

 

 

 

Point 4: You have mentioned that the experiment shows that the R-DFS can reduce the number of turns by 4.34%, and shorten the non-operating distance by about 29.91% in the process of UAV coverage path planning, but is preferable to show experimentally how this reduces the number of turns can improve the energy efficiency, the Cost and the Coverage time.

Response 4: Thank you very much for your comments. At present, our research is mainly based on theoretical analysis, and then through computer simulation. Future research will increase the relevant content of the experimental part, thank you very much for your suggestions.

 

 

 

Point 5: You should improve the quality of figure 21 for a future comparison by other authors because the label values do not clearly show that the length of the non-working path in the decomposed polygon area is significantly reduced.

 

Response 5: Thank you very much for your comments. We have redrawn Figure 21.

Action 5:

	(a)
	(b)
	(c)
	(d)
	(e)

Figure 21. Coverage path of five regions before and after decomposition. (a) Path comparison of Scenario A; (b) Path comparison of Scenario B; (c) Path comparison of Scenario C; (d) Path comparison of Scenario D; (e) Path comparison of Scenario E.

 

 

Point 7: There are few mistakes in the English language. The writing quality should be improved further to avoid typos and editing errors. Some sentences are not well structured (you should use commas) and others their meaning is not well clear. For example, use “experiment results" instead of “experiments results”. Please check the language carefully by reading the paper many times.

 

Response 7: Thank you very much for your comments. We have revised the grammatical problems in the text

 

Action 7:

The “As compared with a ground mobile robot, the working environment of an aerial the UAV has some specific peculiarities.” is changed to “Compared with a ground mobile robot, the working environment of the UAV has some specific peculiarities.”

The “Imaging range of UAV aerial photography”is changed to “ Top view of UAV aerial photography.”

The “Overlap of coverage area in the horizontal and vertical direction.” is changed to “Overlap of coverage area.”

The “The search for the direction of UAV needs to be determined after the UAV coverage width is determined. Different search directions and then will generate different turns and search turning times will be generated by the coverage path planning,” is changed to“The search direction of UAV needs to be determined after the coverage width is determined. Different search directions will generate different turns and search times”.

 

 

 

Point 8: You should add more references, especially in the Introduction section and in the mathematical expression.

 

Response 8: Thank you very much for your comments. We have added some references.

 

Action 8:

Add“11. Cabreira, T.; Brisolara, L.; Ferreira Jr., P. R. Survey on Coverage Path Planning with Unmanned Aerial Vehicles. Drones 2019, 3, 4.”

Add“27. Han, G.; Zhou, Z.; Zhang, T.; Wang, H.; Liu, L.; Peng, Y.; Guizani, M. Ant-Colony-Based Complete-Coverage Path-Planning Algorithm for Underwater Gliders in Ocean Areas With Thermoclines. IEEE Transactions on Vehicular Technology 2020, 69, 8959–8971.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

A Complete Coverage Path Planning Approach Based on Region Optimal Decomposition

The paper does not have a correct presentation, it needs more work.

In the abstract it is ensured the obtaining of the remote sensing map of the port from an image taken by Google Earth, and the development of the methodology together with a genetic algorithm determines the order of travel a navigable path by a UAV.

General remarks.

Figures 3, 4, 6, 9, 15, the lettering in the figure is too small and cannot be read well.

Figures 17, 18, 19, 21, the size of the lettering on the axes is too small, neither the numbers nor the units of measurement can be read.

Figure 18d, not explained.

In general the font size in all figures should be standardized to a legible size. Figures have different font sizes and different fonts.

The use of a UAV is repeatedly mentioned, however, the specifications of the UAV, its characteristics, kinematic/dynamic model, etc., are not detailed.

The use of a Sony A6000 camera is described, however, there is no detailed description of its characteristics, at least in one citation.

Section 2.2 details the determination of the width of the coverage path through photographs taken by a camera located on a UAV at a certain altitude, however, this theory is not applied in a later section of the paper.

The language must be improved.

Author Response

Please check the attachment. Thanks.

Author Response File: Author Response.docx

Reviewer 2 Report

Dear authors,

Thanks for accepting the comments and proceed with the article improvement. 

Author Response

Please see the attachment.

Author Response File: Author Response.docx