Cost-Effective Placement of Recharging Stations in Drone Path Planning for Surveillance Missions on Large Farms

Round 1

Reviewer 1 Report

Author Response

This paper deals with the cost-effective placement of recharging stations in drone path planning. The authors propose a back-and-forth-k-opt simulated annealing approach and compare it to back-and-forth and a K-opt variant of simulated annealing. The paper is well presented and well written. The illustrations are crisp and clear. I only have a few minor points:

1. a) The important assumption that the drone can visit a recharging station only once should be stated in the introduction and problem statement.
   It would also be interesting that the authors explain in which way the problem should be reformulated in this case (not give a detailed formulation, but explain the way the formulation would change)

We have created an Assumptions section (Section 2.1). The assumption has been mentioned and explained. The formulation requires no change since this assumption was already considered in the formulation. The lack was just the fact that it was tardively stated in the original submission.

1. b) I don't understand the concept of "potential location for the recharging station" in figure 1 and later in figures 3 and 6

This has also been explained in the Assumptions section. Recharging stations cannot be installed anywhere in the farm. In fact, some locations are safe and easily accessible. These locations are potential candidates for the deployment of recharging stations. We have changed the terminology to use candidate location rather than potential location.

1. c) There is no equation 9 in the manuscript, and there is a reference problem on line 197, to equations 8 and 9, whereas equations 24 and 25 should be referred to (or equations 23 and 24, if the equations are renumbered following the missing equation 9)

A re-numbering of the affected equations has been done to solve this issue. Some equations have been added to answer the questions of other reviewers.

1. d) More details on the Python implementation would be interesting. Are the BF and KSA readily available algorithms? or were they coded by the authors as well?

Codes for Python implementation are available on GitHub. All the algorithms are written from scratch by the authors. The link to the GitHub repository has been added to the paper (see section 4.2 Simulation results and discussion) and it is also listed in the “Supplementary Materials” at the end right after the conclusions.

1. f) There is a number of typos that will be easily eliminated through a careful re-reading of the paper

The paper has been proofread again to correct typos.

Reviewer 2 Report

This paper covers an interesting topic. It describes the method of efficient placement of the drone recharging stations for large farms surveillance. The paper is very easy to read even when it contains a lot of formulas.

I have several questions.

Is there a proposed height of the drone that should be used for farm surveillance?

You analyzed different situations and influence of the weather especially wind on energy consumption.

Did you tested this algorithm in computer environmet with implemented software solution, or you tried the algorithm on actual drone in practice? 

What is the cost of introducing new algorithm to existing drone softwares?

What if there is an obsticle on the farm on calculated location for recharging station? How is this managed?

Author Response

This paper covers an interesting topic. It describes the method of efficient placement of the drone recharging stations for large farms surveillance. The paper is very easy to read even when it contains a lot of formulas.

I have several questions.

Is there a proposed height of the drone that should be used for farm surveillance?

The altitude depends on the purpose of the surveillance mission from which an overlapping between images and a minimal resolution are required.

Additional paragraphs and equations have been introduced to Section 2.2 to clarify this point in the paper.

You analyzed different situations and influence of the weather especially wind on energy consumption.

Did you tested this algorithm in computer environment with implemented software solution, or you tried the algorithm on actual drone in practice? 

We tested the algorithms using a Python-based simulation environment we have written (see also the Supplementary materials section). For papers in systems design it is common to publish simulation results first before running trials. Field trials will require additional funding and logistical complications.  

What is the cost of introducing new algorithm to existing drone softwares?

The purpose of the paper was to solve drone’s path planning and the placement problem of recharging station. Recharging station placement requires no modification to drone software. The drone path specification produced by our algorithm can be used as input to existing flight plan software.

What if there is an obstacle on the farm on calculated location for recharging station? How is this managed?

We address this in the new Assumptions section (2.1). In the paper, the drone’s altitude is 120 m, which is higher than the world’s tallest tree. For the locations of the recharging stations, we use the notion of “candidate” recharging stations to identify feasible locations for them taking into consideration exactly such problems.

Reviewer 3 Report

The paper has a good structure and is well written, but I have some concerns on assumptions, results and conclusion.

- Eq 1 limits the problem of dividing the area into cells to be based on area only not quality. In reality there is a quality dependence between height and FOV-angle.

- The density of the air is considered to be constant, is that really true? And if not true how does this affect the results and how the optimization should be formulated also with respect to Eq 1.

- Does Figure 6 a, (screen shot) add anything to the paper?

- There is no complexity analysis regarding the propose optimization methods and also comparison to some kind of exhaustive search.

- Under the assumptions in the paper what does figures 10 and 14 add?

- The assumption that the drone visit a charging station once only is unclear except in the conclusion. It is not a logical assumption, which gives the impression of a strategy of the authors to be able to publish a work with another more real assumption later – that is to maximize the number of papers of the work. If not so, the assumption needs a good motivation since synthetic assumptions decrease the novelty of the paper.

Author Response

The paper has a good structure and is well written, but I have some concerns on assumptions, results and conclusion.

- Eq 1 limits the problem of dividing the area into cells to be based on area only not quality. In reality there is a quality dependence between height and FOV-angle.

It is true! The size of cells also depends on the quality of the images that are collected. We reworked this part and we added some new equations (Eq. 2 to Eq. 4). But as you can see in reference [22], the altitude (120m) used for monitoring sorghum growth is the same we adopted in the paper. We also provided a justification for such a choice in the paper.

- The density of the air is considered to be constant, is that really true? And if not true how does this affect the results and how the optimization should be formulated also with respect to Eq 1.

We address this issue in our new “Assumptions” section (Section 2.1).  Our assumption of atmospheric conditions being constant imply that the density of air is also constant, except for possible variations due to altitude (see https://www.omnicalculator.com/physics/air-density). As far as altitude, a 100 m variation in altitude produces only about a 1% variation in air density, which is a negligible effect. The density value we used (1.225 kg/m3) corresponds to a temperature of 15°C.

- Does Figure 6 a, (screen shot) add anything to the paper?

It was just to present the part of the interface that shows the current values of the parameters during simulation. This subfigure has been removed.

- There is no complexity analysis regarding the propose optimization methods and also comparison to some kind of exhaustive search.

We added a new section to the paper 2.5 Complexity analysis of the problem.

Since we are dealing with large farms, an exhaustive search strategy is impossible to implement due to the factorial time complexity of the problem. If we reduce the size of the instances, the drone will need no recharging station since the area to cover is not large. So, there is no need to compare the proposed algorithms with an exhaustive search strategy.

Since BFKSA and KSA are stochastic approaches, they have no fixed complexity. The algorithms are run until a stopping criterion set by the user is met.

- Under the assumptions in the paper what does figures 10 and 14 add?

Energy consumption is a key constraint in drone path planning. Figures 10 and 14 compare the energy consumption of the different approaches and show that the energy consumption of BFKSA is remarkably close to that of BF which is known to be energy effective.

- The assumption that the drone visit a charging station once only is unclear except in the conclusion. It is not a logical assumption, which gives the impression of a strategy of the authors to be able to publish a work with another more real assumption later – that is to maximize the number of papers of the work. If not so, the assumption needs a good motivation since synthetic assumptions decrease the novelty of the paper.

We have added an explanation for this assumption in the paper, as follows (See Section 2.1)

After recharging the drone, the recharging station must recharge itself using another energy source, such as solar panels. Since it takes time, we consider that recharging stations can be visited only once per mission to reduce the overall completion time of the mission.

Round 2

Reviewer 3 Report

The revision of the paper has improved on may Points, but I still have one major concern regarding the research design:

• Last assumption 125-127, is still very syntetic. It is syntetic since the number of charging stations is used as cost, but the cost of adding charging station would be much higher than increasing the capacity of one station. The paper needs to incorporate this or to have a convinsing motiviation of this assumption.

Some details regarding the added text:

• Last sentence, lindes 163-164, do not add understanding of the description.
• Example in lines 307-311 do not add understanding of the description.

Author Response

The revision of the paper has improved on may Points, but I still have one major concern regarding the research design:

    Last assumption 125-127, is still very syntetic. It is syntetic since the number of charging stations is used as cost, but the cost of adding charging station would be much higher than increasing the capacity of one station. The paper needs to incorporate this or to have a convinsing motiviation of this assumption.

Current charging stations are using grid power to recharge drones. But farms are usually located in remote areas where having a grid power can be too difficult. That is why we thought about a solar-based charging station. The accumulated energy of the solar system depends on the season. As a precaution we consider that the drone can visit the charging station only once, just to be sure that the mission can be completed. In addition, even if we consider that the charging station has an unlimited energy capacity, the area that can be surveyed is limited to a radius of half the possible travelling distance of the drone when it is fully charged, since it will do a run trip, with the possibility of revisiting some areas several times. Consequently, this can drastically increase the completion time of the mission. It is true, we put a focus on the cost, but the travelling time should be reasonable. Another important point is the fact that if the charging is slow, even if there is increased battery capacity eventually the capacity will run out. So, there is an advantage to equalizing the load on all charging stations.

However, your suggestion of increasing the capacity of the solar-based charging station is interesting. But unfortunately, this amounts to completely rewrite the paper, rethink a new approach and redo the simulation. Simulation has taken several months to be completed. It is not a simple matter. We are deeply sorry, but this cannot be addressed.

Some details regarding the added text:

    Last sentence, lindes 163-164, do not add understanding of the description.

We agree with you and the last sentence has been removed.

    Example in lines 307-311 do not add understanding of the description.

We found this point important for other reviewers and to better justify the use of metaheuristics.

Round 3

Reviewer 3 Report

Thanks for a good reply, however I'm not totally convinced – so I leave the decision to the editor take the decision.