An Accelerated Dual Fast Marching Tree Applied to Emergency Geometric Trajectory Generation

Round 1

Reviewer 1 Report

The paper discusses the problem of aircrafts’ emergency trajectories generation, which in general seems to be an important issue to be analysed. It is a pity, however, that the authors do not take into account weather conditions and aircrafts’ failures influencing the possible trajectory selection. In my opinion, these are two very important factors and should not be missed. What advantage can give a super quickly computed trajectory (within 10 or even 5 seconds) if it is not possible to use it due to the weather or a damage to aircratf’s systems?

In my opinion the begging of the paper (till page 8-9) should be significantly rewritten to be clear and complete. Chapter no 1 in first line. The authors mention “two main issues” (line 30), then point out some of them are not addressed, some are but these division is not clear. Firstly, I suggest to shorten the placed descriptions to the necessary ones, strictly related with the paper’s topic. Secondly, I suggest to define precisely the aim of the paper and assumptions/restrictions made. Moreover, the authors did not check whether their solution is innovative and what research have been conducted during the last 3-5 years in this field. State-of-the-art part is completely missing. From the 22 literature positions only one (!) is dated 2019, the rest is older than 3-5 years. So thirdly, I suggest to conduct a systematic state-of-the-art analysis to place it in the paper and then define what type of research is missing in the aircrafts’ emergency trajectories generation problem. Mayby the problem You analyse have already been solved…

I cannot agree with some statements made by authors in this first part of the paper. For example, line 10 – what do You mean that “the pilots have no help to safe the aircraft”? Then, what do You mean in lines 78-79 “the landing site is known”? Of course it is, each aircraft has its destination, but in case of an emergency (considered in the paper) the initial destination may not be possible to reach. Line 141, methods You mention are based on data from 2011. That’s 11 years. Is this statement still actual? Please, carefully read the beginning of Your paper (chapters 1 and 2) and significantly change it.

Figure captions should have the source added. Tables as well. Is this Your own work? Or is it based on someone’s other work? Please, add.

Please also check the passive form in Your paper, e.g. line 175. Verify the edition of the paper (e.g. lines 342, 170).

I find the second part of Your paper much better than the initial one. Chapters 3 and 4 are quite ok. In chapters 5 and 6 please underline Your achievements. It will be much easier when You precisely indicate the aim and restrictions, as suggested before. So address this part once again after correcting the beginning.

I believe, there is still some work to be done before further processing of the paper. Try not to extend its volume (it is already quite long) but to rewrite it in a way showing the most important elements for this research.

Author Response

Dear reviewer,

Thank you for your feedback on our paper.

Please find our answers below:

The paper discusses the problem of aircrafts’ emergency trajectories generation, which in general seems to be an important issue to be analysed. It is a pity, however, that the authors do not take into account weather conditions and aircrafts’ failures influencing the possible trajectory selection. In my opinion, these are two very important factors and should not be missed. What advantage can give a super quickly computed trajectory (within 10 or even 5 seconds) if it is not possible to use it due to the weather or a damage to aircratf’s systems?

This paper focuses on the computing time of the emergency trajectory generation. We did not take into account the weather or the impact of an eventual failure. However, we take into account the curvature radius and the descent angle. These values could be computed by another algorithm and then integrated into our algorithm. Therefore, these values are considered known. Some sentences have been added to the paper to precise this hypothesis.

In my opinion the begging of the paper (till page 8-9) should be significantly rewritten to be clear and complete. Chapter no 1 in first line. The authors mention “two main issues” (line 30), then point out some of them are not addressed, some are but these division is not clear. Firstly, I suggest to shorten the placed descriptions to the necessary ones, strictly related with the paper’s topic. Secondly, I suggest to define precisely the aim of the paper and assumptions/restrictions made. Moreover, the authors did not check whether their solution is innovative and what research have been conducted during the last 3-5 years in this field. State-of-the-art part is completely missing. From the 22 literature positions only one (!) is dated 2019, the rest is older than 3-5 years. So thirdly, I suggest to conduct a systematic state-of-the-art analysis to place it in the paper and then define what type of research is missing in the aircrafts’ emergency trajectories generation problem. Mayby the problem You analyse have already been solved…

The two first parts were rewritten to show clearly the main subject of the paper and the hypotheses. Firstly, we precise that the main contribution of this paper is on the computing time of the algorithm. Some sentences have been deleted and replaced by new sentences to explain the goal of our works. Concerning the state of the art, we added 4 other papers on emergency trajectory generation, old (2006) and very recent (2022) papers. Finally, we explain that the previous works are very interesting but the computing time is not mentioned or is a lit bit high. That is why we propose this work.

I cannot agree with some statements made by authors in this first part of the paper. For example, line 10 – what do You mean that “the pilots have no help to safe the aircraft”? Then, what do You mean in lines 78-79 “the landing site is known”? Of course it is, each aircraft has its destination, but in case of an emergency (considered in the paper) the initial destination may not be possible to reach. Line 141, methods You mention are based on data from 2011. That’s 11 years. Is this statement still actual? Please, carefully read the beginning of Your paper (chapters 1 and 2) and significantly change it.

We changed the first sentence of the paper by: "the pilot does not have a tool to help him in this kind of extremely critical situation".  Then, the emergency landing site is considered known because determined by another algorithm that takes into account the altitude data around the aircraft position. The methods presented Line 141 are still used. We added a reference to a paper published in 2021.

Figure captions should have the source added. Tables as well. Is this Your own work? Or is it based on someone’s other work? Please, add.

We added the source of the figures and the tables.

Please also check the passive form in Your paper, e.g. line 175. Verify the edition of the paper (e.g. lines 342, 170).

Several sentences have been modified.

I find the second part of Your paper much better than the initial one. Chapters 3 and 4 are quite ok. In chapters 5 and 6 please underline Your achievements. It will be much easier when You precisely indicate the aim and restrictions, as suggested before. So address this part once again after correcting the beginning.

We added a few sentences to remind the issues of the paper in Chapters 5 and 6

 

 

 

Reviewer 2 Report

The paper purpose is interesting, but I have quite a few concerns related to it:

• I find the state of the art partial, focusing in methods based on exploratory search of solutions, while many other approaches may also be found in the literature for similar problems.
• The results section is very limited, with either one extremely simple problem or an example os application in a city area, but in a case where, apparently, obstacles are irrelevant.
• There is much effort devoted to describe well known solutions (in te state of the art sections, the anexes, ...), and not so much to your actual innovations.
• There is little effort devoted to compare it with other solutions, and to describe the parametrization of the algorithm, which results on reduced reproducibility.

Finally, I have a concern with some of the results. I do not understand how you lead to average computing times which are always multiple of 100 ms (see table 2). Is it a constraint in your algorithm? Are you limiting it somehow?

 

Author Response

Dear reviewer,

Thank you for your feedback on our paper.

Please find our answers below:

I find the state of the art partial, focusing in methods based on exploratory search of solutions, while many other approaches may also be found in the literature for similar problems.

We added new references to papers published several years ago (2006) and more recently (2022).

The results section is very limited, with either one extremely simple problem or an example os application in a city area, but in a case where, apparently, obstacles are irrelevant.

The subject of this paper is to have a very efficient algorithm. Firstly, we tested our algorithm on simple cases. These first tests were to show the impact of our improvements on the computing time. The results show that our method reduces the computing of the trajectory generation. Then we tested our algorithm on a real case, in Grenoble in France. This test shows that we can take into account the aeronautical constraints (curvature radius, descent angle). The computed trajectory avoids obstacles (mountains in this example) and the computing time is acceptable. Few sentences have been added to explain more this part.

There is much effort devoted to describe well known solutions (in te state of the art sections, the anexes, ...), and not so much to your actual innovations.

New sentences and a new figure have been added in the paper to explain the proposed algorithm.

There is little effort devoted to compare it with other solutions, and to describe the parametrization of the algorithm, which results on reduced reproducibility.

In the state of art, we added some sentences to explain more in detail our choice of method. Reasons why we do not test Dijkstra, A*, Bellman, RRT or PRM. The input data set is considered to be known, determined by another algorithm taking into the terrain, the weather, and the failure. This explanation is added to the paper.

Finally, I have a concern with some of the results. I do not understand how you lead to average computing times which are always multiple of 100 ms (see table 2). Is it a constraint in your algorithm? Are you limiting it somehow?

We have chosen to round our results in order to facilitate the reading of the paper, but if it is necessary, we can put the exact values.

Reviewer 3 Report

The paper presents an interesting approach to constructing fast and safe emergency landing trajectories for the aviation domain. Although the work is sound, there are some issues that need to be addressed by the authors:

1) The classic route-finding algorithms (Dijkstra, Bellman-Ford, A*) are included but never tested within the experimental work; this is a significant item to include (well-studied optimality) or rejected with proper justification.

2) As the authors note, their proposed approach takes into account only heading and descend constraints. However, the main issue in emergency situations is degraded performance and local weather (especially winds), which must be included for proper treatment of the task at hand.

3) The proposed algorithm uses a random sampling scheme in two phases; this is clearly sub-optimal, since the pilot or the aircraft itself has a specific flight envelope to fly through, i.e., a general direction based on altitude, speed, weight, performance, nearest airport, etc. Thus, the sampling should be randomized only around this general path, instead of blindly towards improper or invalid envelope parameters. If the authors actually do this, it is not clearly described in the text.

4) The authors employ a simplification of the general problem, stating that "Without loss of generality, this paper presents the free space checker in 2D." This is somewhat misleading, as for the most part of any emergency landing the vertical constraints are very few (e.g. mountains) to none, appearing only in the terminal phase right before landing (tall buildings). If the target is to address the very low altitude situations, then the airplanes are well within standard takeoff aborting procedures, with specific exit trajectories from the airport (avoid traffic).

5) The experimental protocol is unclear; specific dataset size, properties, number of test runs, performance metrics and analytical results should be included in the experimental work.

 

Author Response

Dear reviewer,

Thank you for your feedback on our paper

Please find our answers below:

The classic route-finding algorithms (Dijkstra, Bellman-Ford, A*) are included but never tested within the experimental work; this is a significant item to include (well-studied optimality) or rejected with proper justification.

The following sentence has been added: "These classical algorithms assume the existence of a graph. A simple way to construct this graph would be to use a grid. However, the trajectory obtained would be very dependent on the accuracy of the grid. More recently, new graph-based algorithms more efficient have been proposed. These algorithms generate a graph to find a path between two points. Moreover, some versions of these methods are asymptotically optimal."

As the authors note, their proposed approach takes into account only heading and descend constraints. However, the main issue in emergency situations is degraded performance and local weather (especially winds), which must be included for proper treatment of the task at hand.

This paper focuses on the computing time of the emergency trajectory generation. We did not take into account the weather or the impact of an eventual failure. However, we take into account the curvature radius and the descent angle. These values could be computed by another algorithm and then integrated into our algorithm. Therefore, these values are considered known. Some sentences have been added to the paper (mainly in the introduction) to clarify these hypotheses.

The proposed algorithm uses a random sampling scheme in two phases; this is clearly sub-optimal, since the pilot or the aircraft itself has a specific flight envelope to fly through, i.e., a general direction based on altitude, speed, weight, performance, nearest airport, etc. Thus, the sampling should be randomized only around this general path, instead of blindly towards improper or invalid envelope parameters. If the authors actually do this, it is not clearly described in the text.

We agree with you, the proposed solution is sub-optimal. However, it is not the goal of the problem. We want to rapidly generate a trajectory. Our method is composed of two phases, a first one is to determine an approximate trajectory from the emergency position to the landing site. Then a new sampling is generated around this first solution to refine it. A sentence has been added to explain more.

The authors employ a simplification of the general problem, stating that "Without loss of generality, this paper presents the free space checker in 2D." This is somewhat misleading, as for the most part of any emergency landing the vertical constraints are very few (e.g. mountains) to none, appearing only in the terminal phase right before landing (tall buildings). If the target is to address the very low altitude situations, then the airplanes are well within standard takeoff aborting procedures, with specific exit trajectories from the airport (avoid traffic).

The free space checker is presented in 2D in the paper, to facilitate understanding of the readers because the procedure is the same in 3D, the only difference is the data structure (2D = Quadtree, 3D = Octree). However, in our case, the free space checker is in 3D. A sentence has been added to clarify this.

The experimental protocol is unclear; specific dataset size, properties, number of test runs, performance metrics, and analytical results should be included in the experimental work.

During the study, we tested a dozen simple scenarios. These scenarios were created to show the efficiency of our algorithm. We compared our algorithm with the original FMT. The results (Table 1) show that for the same error, the computing time is lower with our algorithm. Some sentences have been added or replaced to explain the first tests procedure.  The second test is to show that we can consider the aeronautical constraints (curvature radius and descent angle). This case is around Grenoble in France with big mountain obstacles. The results show that the trajectory is smooth and avoids obstacles. Moreover, the computing time is acceptable. Some sentences have been added to clarify this.

 

 

Round 2

Reviewer 1 Report

I have noticed the changes made in Chapters 1 and 2. I am sorry, but I still don’t find them satisfactory. First of all the authors still didn’t carry out the state-of-the-art research. In my opinion, it should be placed around line 77 and contain an extensive overview of publications not older than 3 years. Out of 30 positions in chapter References only 4 - no 9, 15, 16 and 24 are dated 2021, 2019 and 2022. I clearly paid attention to this issue in my previous review! In my opinion, the paper should contain a systematic state-of-the-art analysis and then a definition what type of research is missing in the aircrafts’ emergency trajectories generation problem. Maybe the problem You analyse have already been solved by someone else…

The authors didn’t pay attention also to the next remark I gave – figures and tables captions. I repeat that I believe their origin should be clearly marked. Figures: 1-3, 7, 10-25, as well as Table 2, which mean almost ALL still have unknown origins. Although authors ensure in the cover letter, they added them. I see an incompatibility here!

If line 10 writes: the pilot does not have a tool…, as I understand the pilot is singular, so the next sentence cannot start with “their decisions…”, which is plural.

Lines 53-56 and 84-89 are a repetition. Please, find one adequate spot in Your paper to place this (important) information once.

Last but not least… line 518. Have You reached Your goal? I asked You before to underline Your achievements at the end of the paper. It will be much easier when You precisely indicate the aim of the paper and restrictions. In this second review I keep my previous remark.

Please, read Your paper once again in order to smooth it out.

Author Response

Dear reviewer,

Thank you for your second feedback on the paper.

Here are our responses to your comments:

I have noticed the changes made in Chapters 1 and 2. I am sorry, but I still don’t find them satisfactory. First of all the authors still didn’t carry out the state-of-the-art research. In my opinion, it should be placed around line 77 and contain an extensive overview of publications not older than 3 years. Out of 30 positions in chapter References only 4 - no 9, 15, 16 and 24 are dated 2021, 2019 and 2022. I clearly paid attention to this issue in my previous review! In my opinion, the paper should contain a systematic state-of-the-art analysis and then a definition what type of research is missing in the aircrafts’ emergency trajectories generation problem. Maybe the problem You analyse have already been solved by someone else…

The first two parts have been modified again. In the introduction, the part about the bank angle and descent angles has been moved to the mathematical modeling part to better explain the constraints. Concerning the state of the art part, it has been significantly modified. This part is composed of four different parts. The first one is about emergency trajectory design, in this part, we explain the main works focused on the impact of eventual failure and the computed time is not mentioned. The second part is about recent fast methods of trajectory generation. The third part is about Graph-based path planning algorithms. One of these methods is used in the proposed algorithm. However, PRM and RRTparts have been reduced. The final part is about Dubins curve.

The authors didn’t pay attention also to the next remark I gave – figures and tables captions. I repeat that I believe their origin should be clearly marked. Figures: 1-3, 7, 10-25, as well as Table 2, which mean almost ALL still have unknown origins. Although authors ensure in the cover letter, they added them. I see an incompatibility here!

We are sorry,  we forgot to put the origin on some figures. But we also forgot to mention to you that most of the images were made by us.

If line 10 writes: the pilot does not have a tool…, as I understand the pilot is singular, so the next sentence cannot start with “their decisions…”, which is plural.

The error is corrected.

Lines 53-56 and 84-89 are a repetition. Please, find one adequate spot in Your paper to place this (important) information once.

We deleted some sentences to avoid repetition.

Last but not least… line 518. Have You reached Your goal? I asked You before to underline Your achievements at the end of the paper. It will be much easier when You precisely indicate the aim of the paper and restrictions. In this second review I keep my previous remark.

A paragraph has been added to explain that our method meets its objectives of being quick and adaptable. Moreover, the proposed method can be integrated into a global system composed of independent modules. 

 

Reviewer 2 Report

My concerns on the paper hace not been addressed at all in this review:

1. I still find the state of the art partial, focusing in planning methods based on exploratory search of solutions, while many other approaches may also be found in the literature for similar problems. This is an extremely wide area, discussion on other approaches must be included.
2. You added no results in this review. The results section is again very limited, with either one extremely simple problem with only one obstacle or an example os application in a city area, but in a case where, apparently, obstacles are not clearly relevant. It is not posible to assess this solution taking into account your figures, it is not clear if the aircraft is very high or not, etc.
3. There is much effort devoted to describe well known solutions (in the state of the art sections, the anexes, ...), and not so much to your actual innovations. You should more clearly state what is yours and what is others. For instance, discussion on RRT vs RRT* is misleading, as it is not yours, and comparisons between approaches in the literature are not so relevant. What is important is that you clearly show with results the improvements over other solutions. Again, including all Dubins curves descriptions, which are not yours, is misleading. Please focus on your contribution.
4. There is little effort devoted to compare it with other solutions, as I previously discussed.
5. Finally, please provide the times in milliseconds without rounding. This is again very misleading.

Author Response

Dear reviewer,

Thank you for your second feedback on the paper.

We are sorry that we did not understand your requests. We hope you will be satisfied with our changes. 

Here are our responses to your comments:

I still find the state of the art partial, focusing in planning methods based on exploratory search of solutions, while many other approaches may also be found in the literature for similar problems. This is an extremely wide area, discussion on other approaches must be included.

We have reorganized and completed our state-of-the-art. The first part focuses on the generation of emergency trajectories. We point out that previous work focuses on the impact of the failure and not the computation time. The second part presents recent papers on fast trajectory generation. The third deals with generation of trajectory using graphs. One of these methods is used in the proposed algorithm.

You added no results in this review. The results section is again very limited, with either one extremely simple problem with only one obstacle or an example os application in a city area, but in a case where, apparently, obstacles are not clearly relevant. It is not posible to assess this solution taking into account your figures, it is not clear if the aircraft is very high or not, etc.

Firstly, we added a new test scenario, more complex. This scenario shows the avoidance of the obstacles and also the limit of our algorithm. Secondly, we modify figures 17 and 18. The optimal path is drawn thicker to see it more clearly. Finally, we added a third figure to see the altitude of the aircraft and to show the avoidance of the obstacles.

There is much effort devoted to describe well known solutions (in the state of the art sections, the anexes, ...), and not so much to your actual innovations. You should more clearly state what is yours and what is others. For instance, discussion on RRT vs RRT* is misleading, as it is not yours, and comparisons between approaches in the literature are not so relevant. What is important is that you clearly show with results the improvements over other solutions. Again, including all Dubins curves descriptions, which are not yours, is misleading. Please focus on your contribution.

We have significantly reduced some parts of the state of the art. The sections on Dubins curves and RRT have been greatly reduced. We say that the previous works focused on the impact of the failure.  Our goal is to have a very efficient algorithm. This topic is less studied in the literature.

There is little effort devoted to compare it with other solutions, as I previously discussed.

In the results part, we added a comparison with a very efficient emergency trajectory generation algorithm. "Ligny et al. present in their paper different computational performance tests on similar scenarios. Their algorithm generates a trajectory very quickly (about 1s). However, their trajectories are not 100% flyable. Moreover, the algorithm is constrained to a fixed descent plane, which prevents U-turns. This can be problematic if the landing site is behind the aircraft. The proposed method is certainly slower but  it computes a trajectory whatever the position of the landing site and takes into account aeronautical constraints."

Finally, please provide the times in milliseconds without rounding. This is again very misleading.

We have modified the computation times

 

Round 3

Reviewer 2 Report

Dear authors, 

The paper is much better now, much more focused in your actual contribution, and you addressed all my main concerns.

For me it is ready for publication as it is.