Research on Impact of Planned Path Length and Yaw Cost on Collaborative Search of Unmanned Aerial Vehicle Swarms

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

The topic of your submission is of interest. Although this topic is investigated from several decades, I think that few readers are familiar with it. Therefore, for a comfortable reading of your paper, I have the following suggestions:

• Introduce a section/subsection clearly describing the digital pheromones for UAVs coordination;
• - line 111: It is net clear what is the payload;
• line 132: why the cell g_i has a single index; since in Fig. 2 the cells are defined as the elements of a matrix, it is more natural to have 2 indices;
• The pheromone equations must be explained  and referred;
• Eq. (3)-(6) correspond to a single UAV? Please clarify;
• Eq. (3): explain what means "k"; probably it is a time step;
• line 144, 145: what means "pheromone secreted by the grid"; please explain;
• Explain how the artificial pheromones are produced and how they are trailed;
• page 4: please provide details about the target; I missed to understand (although I have a guess) regarding the role of  it in the guidance problem; try to clearly make the difference between UAV and the target, namely clearly formulate the guidance problem; 

 

 

 

 

 

Comments on the Quality of English Language

Probably a revision by a native English speaker could be useful.

Author Response

Comments 1:[ Introduce a section/subsection clearly describing the digital pheromones for UAVs coordination.]

Response 1: Thank you for your constructive comments, which are important for readers to understand the digital pheromone mapping method. We have added a description of Equation (4) from line 168 to line 181 of the new manuscript to help readers better understand this method. We chose this approach because Section 2.2.2 is used to introduce situational information including target occurrence probability, digital pheromones, and environmental uncertainty. Adding a separate subheading for digital pheromones may affect your review experience of this manuscript.

 

Comments 2:[ - line 111: It is net clear what is the payload.]

Response 2: Thank you for pointing this out. The word 'payload' is redundant in expression, and its deletion will not affect readers' understanding. Detailed modifications have be made in line 119 of the new manuscript.

 

Comments 3:[ line 132: why the cell g_i has a single index; since in Fig. 2 the cells are defined as the elements of a matrix, it is more natural to have 2 indices.]

Response 3: Thank you for pointing out this expression error. We added an explanation in from line 136 to line 138 of the new manuscript: only two indexes were used in section 2.2.1, while one index will be used in subsequent discussions. When writing the manuscript, our original idea was to use two indexes when introducing the region partitioning method in section 2.2.1, combined with Figure 2, to help readers better understand the region partitioning method. However, in the later discussion of the manuscript, on the one hand, more indexes are needed to express other meanings (such as the situation information of the grid cell), and on the other hand, using a single index will not cause misunderstandings in the subsequent discussion. Therefore, we use a single index to uniquely represent a certain grid cell.

 

Comments 4:[ The pheromone equations must be explained and referred.]

Response 4: Your suggestion is very necessary for us. We added a citation source for the digital pheromone in line 157 of the new manuscript, and then provided explanations for the digital pheromone from line 168 to line 181. The application of digital pheromone rendering method in drone swarm task planning is very extensive, but as an academic paper, it is indeed necessary to declare the source of this method and provide readers with detailed explanations as suggested.

 

Comments 5:[ Eq. (3)-(6) correspond to a single UAV? Please clarify.]

Response 5: Thank you for pointing out this loophole. Your suggestion is necessary to dispel readers' doubts. We clarified this in lines 190 to 193 of the new manuscript.

 

Comments 6:[ Eq. (3): explain what means "k"; probably it is a time step.]

Response 6: As you guessed, 'k' represents the time step, and we have added additional clarification in line 146 of the new manuscript.

 

Comments 7:[ line 144, 145: what means "pheromone secreted by the grid"; please explain.]

Response 7: Thank you for your careful review and suggestions. This was an error in our expression, and we have corrected it in line 162 and line 163 of the new manuscript. The correct meaning should be the pheromones secreted by UAVs at the grid.

 

Comments 8:[ Explain how the artificial pheromones are produced and how they are trailed.]

Response 8: Firstly, each UAV stores its own situational information map. As information exchange with other UAVs only occurs when the UAV reaches the waypoint, before reaching the waypoint, the UAV only calculates situational information based on the information exchanged last time and its own position. This calculation includes equations (4) and (5), which update the digital pheromone;

Then, the UAV finds the grids within the detection range on the map. When calculating the digital pheromones of these grids, in addition to considering the residual pheromones from the previous moment and the pheromones propagated from other grids, the UAV will add additional pheromones, namely "secretion", to them, while grids outside the detection range do not have "secretion". After three mechanisms of secretion, volatilization, and dissemination, the pheromone has been updated. A more detailed explanation can be found on lines 168 to 181 of the new manuscript.

Finally, when selecting a new waypoint after the UAV arrives at the waypoint, the UAV makes a decision through the PSO algorithm. Each optimization calculation step of PSO uses the path grid determination algorithm (Section 3.1) to screen the grids on the candidate path, and then calculates their situational information cost, namely equations (11) to (13), which also includes the digital pheromone cost (equation (12))

We hope the above explanation is helpful for your and other readers' understanding.

 

Comments 9:[ page 4: please provide details about the target; I missed to understand (although I have a guess) regarding the role of it in the guidance problem; try to clearly make the difference between UAV and the target, namely clearly formulate the guidance problem.]

Response 9: Thank you for pointing out the shortcomings in our work. The setting of targets in simulation experiments is relatively simpler compared to UAVs. After 60 targets are uniformly generated around the task area, they traverse the task area at a speed of 20m/s along their respective directions. Their motion trajectories are straight lines parallel to the grid lines. When the target is within the detection range of the UAV and detected, it is considered captured. We have added a detailed explanation about the objectives from line 303 to line 309 of the new manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper studies the impact of path length and yaw cost on the search performance of UAV swarm in a dynamic environments. The author use a path grid to reformulate the path planning problem as a waypoint selection problem. The problem is then solved with a PSO-based multi-objective optimization. Simulation results are presented to evaluate the proposed algorithm using different performance metrics. Although the problem is interesting, but the novelty of the proposed PSO-based search scheme need to be better highlighted.

1. PSO-based waypoint planner have been explored in literature. The novelty of the proposed method need to be better highlighed and a strong motivation is needed.

2. The paper only consider simulation results, and impact of real-world scenarios, e.g., communication loss, GPS error, sensing noises, etc. hasn't been considered or dicussed in detail. The robustness of the proposed scheme to such scenarios should be analyzed.

3. What is the computation complexity of proposed algorithm? How does it scale with swarm and grid size? PSO is notrious for not scaling well. Discuss the PSO in context of other recent metaheurtistics, e.g., Ant Colony Optimization (ACO), Beetle Antennae Search (BAS), "Intelligent beetle antennae search for UAV sensing and avoidance of obstacles".

4. The multi-objective function (Eq. 20) balances path cost and yaw cost. But how are the relative weights between two objectives determined. Is it arbitrary choice by authors?

5. How were PSO parameters, e.g., inertia weight, learning coefficients, chosen in the simulations? Is there a heuristic to tune these parameters?

6. The manuscript lacks comparison with existing methods. The paper should discuss comparative analysis with well known path planning algorithms, e.g., A*.

Author Response

Comments 1:[ 1. PSO-based waypoint planner have been explored in literature. The novelty of the proposed method need to be better highlighed and a strong motivation is needed.]

Response 1: Thank you for your sincere suggestion. We use PSO algorithm for decision-making in UAVs because it has the characteristics of fewer parameters and faster computation, making it suitable for fast decision-making scenarios in multi UAV collaborative search. When there are too many selectable waypoints, the computational load of PSO algorithm will rapidly increase. Therefore, we propose to use path grid determination algorithm to replace the entire path with a small number of waypoints, achieving a significant reduction in computational load. We have provided additional explanations on lines 82 to 89 of the new manuscript.

 

Comments 2:[ 2. The paper only consider simulation results, and impact of real-world scenarios, e.g., communication loss, GPS error, sensing noises, etc. hasn't been considered or dicussed in detail. The robustness of the proposed scheme to such scenarios should be analyzed.]

Response 2: The problem you pointed out is precisely the difficulty that will be encountered in future engineering practice. In the initial manuscript, our study only considered the issue of false alarms caused by sensor noise and set the false alarm probability to 0.2 (this value will change with actual sensor performance in the future), while we did not take into account communication loss and GPS errors. Although these two factors do not hinder the implementation of UAV cluster search, they will to some extent reduce target search efficiency. Therefore, we conducted supplementary simulations, and the simulation results and analysis are presented in Section 4.3 of the manuscript.

 

Comments 3:[ 3.What is the computation complexity of proposed algorithm? How does it scale with swarm and grid size? PSO is notrious for not scaling well. Discuss the PSO in context of other recent metaheurtistics, e.g., Ant Colony Optimization (ACO), Beetle Antennae Search (BAS), "Intelligent beetle antennae search for UAV sensing and avoidance of obstacles".]

Response 3: Your question is very helpful for us to consider the significance of this research!

Firstly, the complexity of the PSO algorithm proposed in our study comes from the length of the planned path for each decision. On the one hand, as shown in Figure 5 of the initial manuscript, the longer the planned path, the more candidate waypoints (highlighted in red and blue grids) there will be, and the larger the solution space searched by the PSO algorithm. On the other hand, the longer the planned path, the more grids on the path, and the more data needs to be accumulated when calculating the path situation cost according to equations (11) to (13).

Secondly, an increase in the number of task area grids and cluster size will increase the communication burden without affecting the performance of the decision-making mechanism based on PSO algorithm. In our study, when the UAV is beyond a certain distance threshold from the waypoint, it only exchanges position information with other UAVs to prevent collision. However, when the UAV approaches the waypoint, it exchanges situational information with other UAVs and updates its intelligence. Therefore, the longer the planned path, the fewer communication and decision-making times per unit time. This is also the reason why our research discussed the impact of planned path length on communication and decision-making consumption.

Finally, as you reminded, the PSO algorithm is not as scalable as ACO and BAS. However, we believe that through our proposed information fusion mechanism and path grid determination algorithm, PSO can maintain its advantages in multi UAV collaborative search scenarios while avoiding its disadvantages. We have simplified the planning of all grids within the planned path length to a path represented by only two grids, greatly reducing computational complexity.

 

Comments 4:[ 4. The multi-objective function (Eq. 20) balances path cost and yaw cost. But how are the relative weights between two objectives determined. Is it arbitrary choice by authors?]

Response 4: Eq. 20 includes target detection probability cost, digital pheromone cost, environmental awareness cost, and yaw cost. The sum of the first three is the path situation information cost, and the expression in Eq. 20 is essentially the equal weighted sum of these four costs. In the initial manuscript, this weight was equal and unchanged. In fact, in the early stage of the search task, the weight of the path situation information cost can be increased to reduce the target search time. In the later stage of the search, the number of targets in the task area decreases, and at this time, the task area has been fully explored. In this case, this weight can be reduced to make the UAV focus more on yaw cost and reduce flight energy consumption.

 

Comments 5:[ 5. How were PSO parameters, e.g., inertia weight, learning coefficients, chosen in the simulations? Is there a heuristic to tune these parameters?]

Response 5: In this research, the values of inertia weight and learning weight were both 0.5. As the focus of this research is to test our proposed path grid determination algorithm and explore the effects of planned path length and yaw cost on collaborative search performance, we have not yet considered using heuristic methods to adjust these parameters. However, your reminder is very constructive. The PSO algorithm has many areas worth improving in terms of search performance and scalability. Our future research will focus on adaptive improvements for multi UAV collaborative search scenarios.

 

Comments 6:[ 6. The manuscript lacks comparison with existing methods. The paper should discuss comparative analysis with well known path planning algorithms, e.g., A*.]

Response 6: The question you raised is also a possible confusion for readers. In fact, in the literature cited in the manuscript, the problem of multi UAV collaborative search is to let UAVs make choices in the middle of the area adjacent to their detection range. In this study, we expanded the selection range of UAVs, not just limited to the area adjacent to UAVs. When the planned path length is small, UAVs are equivalent to only considering the surrounding area, while when the planned path length is large, UAVs take into account a larger area. This is where this study compares with other studies.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper fits the journal's scope and is written in good English. The iThenticate similarity check showed a 25% similarity index, a large portion of which comes from the reference part. In my opinion, this does not pose a problem. However, there are some fundamental issues that the authors should refer to. Thus, I recommend a major revision:

- Can the authors enlarge the decision scheme in Figure 1, e.g. by presenting it in a landscape view?

- How is the sensor's detection probability set? Were those arbitrary values, or were they obtained from past experiments or studies? How is this related to sensor type and quality?

- Please explain why the point mass model ignored the wind effect, as atmospheric conditions can significantly influence small UAV dynamics.

- The authors provided some measures of the coverage rate and search effectiveness, but what about the algorithm's robustness?

I hope those comments will help the authors improve their paper's quality.

Author Response

Comments 1:[ - Can the authors enlarge the decision scheme in Figure 1, e.g. by presenting it in a landscape view?]

Response 1: Following your suggestion, we have enlarged both sub images in Figure 1, hoping that these two images will be helpful for you and readers to understand our research work.

 

Comments 2:[ - How is the sensor's detection probability set? Were those arbitrary values, or were they obtained from past experiments or studies? How is this related to sensor type and quality?]

Response 2: The detection probability and false alarm probability are typical values selected based on the curve of false alarm probability and detection probability of the radar at a certain signal-to-noise ratio. In this study, we only use them to complete simulation research and do not represent the actual performance of the sensor.

 

Comments 3:[ - Please explain why the point mass model ignored the wind effect, as atmospheric conditions can significantly influence small UAV dynamics.]

Response 3: Your comment is about the problems we will encounter in future engineering applications. Wind can affect the flight speed and trajectory of UAVs, and further affect their energy consumption. Further exploration is needed. The current research focuses on building a UAV swarm collaborative search framework and evaluating the effectiveness of collaborative search algorithms, so we have not yet considered the impact of wind.

 

Comments 4:[ - The authors provided some measures of the coverage rate and search effectiveness, but what about the algorithm's robustness?]

Response 4: Your question is very helpful for improving our research! We conducted supplementary simulations to address the abnormal situations of GPS positioning errors and partial UAV loss. The results showed that under the influence of these two factors, the collaborative search efficiency decreased, but the search task could still be completed. The simulation results and analysis are presented in Section 4.3 of the new manuscript.

Reviewer 4 Report

Comments and Suggestions for Authors

Congratulations the paper is well-written, makes a relevant contribution to the field .

Observations - recommendations

• Observation of the clarity of the contribution and the simulated context

The paper presents an interesting and well-structured contribution, but the title and abstract do not explicitly state that the research is carried out exclusively through simulations. Although this is mentioned later in the "Simulation Experiment" section, it is recommended that the abstract or title highlight that it is a study based on simulations.

• Choice of simulation parameters – they are not explicitly justified, a brief explanation of the source of these values ​​(citations, standards, typical scenarios from practice, etc.) or a clear mention that they were chosen randomly, for demonstration purposes only, would be useful.
• Lack of model validation - The paper would be significantly improved if it included some form of validation of the proposed model. For example, a comparison with the results of similar works in the literature or a discussion of how the model could be validated in real scenarios.
• Lack of sensitivity analysis

It would be useful to include a sensitivity analysis on one or more key parameters (e.g., route length, yaw cost, number of UAVs, etc.). This would provide a more complete picture of the proposed method's robustness and increase the credibility of the results.

• Lack of justification for choosing the PSO method.
• Complete details about PSO settings

In the section on the PSO algorithm, it would be helpful to mention the concrete values ​​for specific parameters used in the simulation (number of particles, number of iterations, values ​​of learning coefficients, etc.). This information helps the reproducibility of the method

• Clarification of practical applicability

The proposed method is promising, but the paper does not contain a section dedicated to discussing possible practical implementation

• In the figures, try to see if you can adapt both the fonts and their size with the main text (or the template indications (the text in the figures seems too tiny)) – however, the text and diagrams are quite clear.

 

Author Response

Comments 1:[ The paper presents an interesting and well-structured contribution, but the title and abstract do not explicitly state that the research is carried out exclusively through simulations. Although this is mentioned later in the "Simulation Experiment" section, it is recommended that the abstract or title highlight that it is a research based on simulations.]

Response 1: Thank you for your valuable feedback. In the new manuscript, the 16th line emphasizes that our research was conducted through simulation experiments.

 

Comments 2:[ Choice of simulation parameters – they are not explicitly justified, a brief explanation of the source of these values ​​(citations, standards, typical scenarios from practice, etc.) or a clear mention that they were chosen randomly, for demonstration purposes only, would be useful.]

Response 2: This is a very constructive suggestion, explaining to readers that the source of parameter values can increase the credibility of the article.

In simulation experiments, the performance of sensors (detection distance, detection probability, false alarm probability, etc.) and UAVs (flight speed, yaw rate, etc.) come from typical values in practical scenarios. Other values (such as environmental models, PSO algorithm weights, etc.) determine the UAV's cognition and decision-making quality in the task area. Therefore, their values are determined after multiple pre simulations. We have provided additional explanations from lines 309 to 311 of the new draft.

 

Comments 3:[ Lack of model validation - The paper would be significantly improved if it included some form of validation of the proposed model. For example, a comparison with the results of similar works in the literature or a discussion of how the model could be validated in real scenarios.]

Response 3: Thank you for your reminder. We have conducted supplementary simulations to address two potential issues that may arise in engineering practice: GPS positioning error and partial UAV disconnection. The results show that these two factors will reduce the effectiveness of collaborative search, but UAV swarms can still complete the search task. The simulation results are supplemented in section 4.3 of the beginner's manuscript.

 

Comments 4:[ Lack of sensitivity analysis

It would be useful to include a sensitivity analysis on one or more key parameters (e.g., route length, yaw cost, number of UAVs, etc.). This would provide a more complete picture of the proposed method's robustness and increase the credibility of the results.]

Response 4: Your question may also be a reader's confusion. In fact, the impact of regional coverage, target search efficiency, and communication and computing resource consumption on the number of UAVs, planned path length, and yaw cost has been analyzed in Chapter 4, which can represent sensitivity.

 

Comments 5:[ Lack of justification for choosing the PSO method.]

Response 5: Thank you for your reminder. Explaining the reasons for choosing PSO algorithm can make our research more rigorous. The PSO algorithm has the advantages of fewer parameters and faster computation, but the disadvantage is that as the solution space increases, its computational complexity also increases rapidly. Therefore, we propose a path grid determination algorithm to simplify the path planning problem over a large area into a path selection problem represented by a few waypoints, reducing the computational complexity. We have provided additional explanations in lines 82 to 89 of the new manuscript.

 

Comments 6:[ Complete details about PSO settings

In the section on the PSO algorithm, it would be helpful to mention the concrete values ​​for specific parameters used in the simulation (number of particles, number of iterations, values ​​of learning coefficients, etc.). This information helps the reproducibility of the method]

Response 6: Your reminder is very necessary. In our study, the number of particles was 25, the number of iterations was 15, and the learning factor and inertia weight were both 0.5. We have provided additional explanations from lines 287 to 289 of the new manuscript.

 

Comments 7:[ Clarification of practical applicability

The proposed method is promising, but the paper does not contain a section dedicated to discussing possible practical implementation]

Response 7: Thank you for pointing out the shortcomings of our research. Your suggestions have guided us to consider the next steps of our work. The collaborative search algorithm discussed in our research is only applicable to situations where there is no no-fly zone and the shape of the task area is a regular quadrilateral, and does not consider the two limiting factors of UAV energy and communication limitations. We have provided additional explanations in lines 476 to 483 of the new manuscript.

 

Comments 8:[ In the figures, try to see if you can adapt both the fonts and their size with the main text (or the template indications (the text in the figures seems too tiny)) – however, the text and diagrams are quite clear.]

Response 8: Thank you for your reminder. We have enlarged all the images with text in the original manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In my opinion the new version of the manuscript may be recommended for publication. However I have two suggestions: - at line 157: instead of "according to Equation (4)", write "according to the following equation"; - lines 176-177: please check the sentence "The form represented."

Author Response

Comments 1:[ -at line 157: instead of "according to Equation (4)]

Response 1: Thank you for your suggestion. We have revised the relevant wording in line 157 of the latest manuscript.

 

Comments 2:[ -lines 176-177: please check the sentence "The form represented."]

Response 2: Thank you for carefully reviewing and pointing out our mistakes. The meaning of this sentence is " so the pheromone of g_i at the k+1-th time point is represented by Equation (4)". We have revised it from line 176 to line 177 in the latest manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed the comments.

Author Response

Comments 1:[ The authors have addressed the comments.]

Response 1: Thank you for your review and affirmation of this research. Your opinions and suggestions are very helpful to us.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for providing your response.

Author Response

Comments 1:[ Thank you for providing your response.]

Response 1: Thank you for your review and affirmation of this study. Your comments have helped us gain a deeper understanding of its significance.