Formation Control of Mobile Robots Based on Pin Control of Complex Networks

Round 1

Reviewer 1 Report

Dear authors,

in my opinion the paper is well written, the problem is formulated in a correct way and enough references have been included.

But I would like to include some comments:

- It is not clear what are the contributions of this work, it looks more like an engineering job than a scientific paper.

- In this work, the "pinning control technique" has been applied without any justification. Why could these methodologies have better results than others?.

- This solution has been checked in differential drive robots. In my opinon, it is an aproximation very simple when we are thinking about complex networks.

- The authors should be include in this work , what happen o what they think that will happen when other kind of robots (e.g. quadotors, UAVs, AUVs, etc.) are included in this system.

Best regards.

Author Response

Formation control of mobile robots based on pin control of complex networks

Manuscript ID: machines-1932279

Authors: Jorge D. Rios, Daniel Ríos-Rivera, Jesus Hernandez-Barragan, Marco Antonio Pérez-Cisneros, and Alma Y. Alanis *

Answer to reviewers

First, we would like to express our sincere gratitude to the Associate Editor and the Reviewers. The paper has been carefully revised and corrected according to their valuable comments. Mayor changes in the manuscript have been highlight in yellow, and a point-to-point answer to each of the reviewers’ comments is presented in this document. 

Answer to Reviewer 1

We like to thank Reviewer 1 for his/her valuable comments. We present a point-to-point answer to the comments where the reviewer’s comment is written in bold format.

 

Reviewer 1

English language and style are fine/minor spell check required

Authors revised the document and minor changes were made in the document to fix grammar issues.

Does the introduction provide sufficient background and include all relevant references?

Must be improved

Some lines were added to the introduction section, to answer specific comments of the reviewers, no new citations were added.

Are all the cited references relevant to the research?

            Can be improved

Some lines were added to the introduction section, to answer specific comments of the reviewers, no new citations were added.

Is the research design appropriate?

            Must be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added.

Are the methods adequately described?

            Must be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added.

Are the results clearly presented?

            Must be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added.

Are the conclusions supported by the results?

            Must be improved

In the new version of the document, the conclusions were improved and better supported by improving the results section and the addition of section 5 Results Discussion

Dear authors,

In my opinion the paper is well written, the problem is formulated in a correct way and enough references have been included.

But I would like to include some comments:

- It is not clear what are the contributions of this work, it looks more like an engineering job than a scientific paper.

To highlight the contribution of the paper, in the new version of the document, we added the following text to the Introduction section beginning at line 59.

The results of these previous works motivate the idea of pinning control for the formation of mobile robots. In this way, it is only necessary to design the position control for just one of the node robots of the network, meaning that only one knows the final position. This is an advantage when adding more nodes or the position control strategy is thought to be changed in the future.

It is important to remark that the selected node is known as the pinned node; this is the reason of why is called pin control. It has a similar function as a leader in a leader-follower approach. However, it is not a leader; it may receive information from other nodes in the network; in the leader-follower approach, the leader does not receive information from other nodes.

Also, we would like to highlight the following text beginning at line 68.

The proposed formation control based on pin control of complex networks has the following characteristics: the formation is achieved through synchronizing the designed complex network, where a node is selected as the pinned control node, and the formation is achieved on a set point which is only known by a selected robot as a pinned node, and just a number of the remaining robots are connected to it. Collison avoidance is assured against other robots and objects, not only between robots; a mounted LiDAR (Light Detection and Ranging) sensor obtains the distances between a robot and any object. Simulation and experimental test results are included in this work using a different number of robots per test. Tests end at the desired position at the desired formation. In contrast to previous works that use the robot’s known position to avoid a collision, this work uses the mounted LiDAR on the selected equipment Turtlebot3® robots.

Moreover, we added Section 5 beginning in line 296, where results are discussed to highlight their advantages, this section also introduces comparison results against two published schemes.

5. Results Discussion

We also would like to highlight the following text added in section 5, this text begins in line 311.

Another important point to discuss is that all nodes in the proposed work are differential-drive robots. However, using complex networks, it would be possible to combine different kinds of robots, including, for example, unmanned aerial vehicles and omnidirectional robots. Let us consider the works [10,11] where non-identical chaotic nodes are used in the same complex network. Judging by their results, we could expect similar results for the proposed control scheme using different robotic platforms. However, the relevant variables to each of the different robots must be first defined.

- In this work, the "pinning control technique" has been applied without any justification. Why could these methodologies have better results than others?

We would like to highlight the following lines in the Introduction Section begin at line 59

The results of these previous works motivate the idea of pinning control for the formation of mobile robots. In this way, it is only necessary to design the position control for just one of the node robots of the network, meaning that only one knows the final position. This is an advantage when adding more nodes or the position control strategy is thought to be changed in the future.

It is important to remark that the selected node is known as the pinned node; this is the reason of why is called pin control. It has a similar function as a leader in a leader-follower approach. However, it is not a leader; it may receive information from other nodes in the network; in the leader-follower approach, the leader does not receive information from other nodes.

We also would like to highlight the following text added in section 5, this text begins in line 311.

Another important point to discuss is that all nodes in the proposed work are differential-drive robots. However, using complex networks, it would be possible to combine different kinds of robots, including, for example, unmanned aerial vehicles and omnidirectional robots. Let us consider the works [10,11] where non-identical chaotic nodes are used in the same complex network. Judging by their results, we could expect similar results for the proposed control scheme using different robotic platforms. However, the relevant variables to each of the different robots must be first defined.

- This solution has been checked in differential drive robots. In my opinion, it is an approximation very simple when we are thinking about complex networks.

We would like to highlight the following text added in section 5, this text begins in line 311.

Another important point to discuss is that all nodes in the proposed work are differential-drive robots. However, using complex networks, it would be possible to combine different kinds of robots, including, for example, unmanned aerial vehicles and omnidirectional robots. Let us consider the works [10,11] where non-identical chaotic nodes are used in the same complex network. Judging by their results, we could expect similar results for the proposed control scheme using different robotic platforms. However, the relevant variables to each of the different robots must be first defined.

Also, the following lines at the conclusion section, this text begins in line 381.

Also, as mentioned in section 5, combining different kinds of robots would be possible based on previous works of complex networks where non-identical chaotic nodes were used in the same complex network. Some extra work would be necessary, and this idea is left as future work.

And, from the conclusion section, this text begins in line 392.

Besides using different robots in the complex network, more future work can be proposed, trajectory tracking in formation and dynamic topology of the form complex networks.

- The authors should be included in this work, what happen o what they think that will happen when other kind of robots (e.g. quadrotors, UAVs, AUVs, etc.) are included in this system.

We would like to highlight the following text added in section 5, this text begins in line 311.

Another important point to discuss is that all nodes in the proposed work are differential-drive robots. However, using complex networks, it would be possible to combine different kinds of robots, including, for example, unmanned aerial vehicles and omnidirectional robots. Let us consider the works [10,11] where non-identical chaotic nodes are used in the same complex network. Judging by their results, we could expect similar results for the proposed control scheme using different robotic platforms. However, the relevant variables to each of the different robots must be first defined.

Also, the following lines at the conclusion section, this text begins in line 381.

Also, as mentioned in section 5, combining different kinds of robots would be possible based on previous works of complex networks where non-identical chaotic nodes were used in the same complex network. Some extra work would be necessary, and this idea is left as future work.

And, from the conclusion section, this text begins in line 392.

Besides using different robots in the complex network, more future work can be proposed, trajectory tracking in formation and dynamic topology of the form complex networks.

 

Best regards.

Thank you very much for your comments, the authors of this work wish you a great day.

 

Reviewer 2 Report

This paper presents control of different groups of robots to achieve a desired formation based on pinning control of complex networks and coordinate translation. The validity of the proposed method is verified through simulations and experiments. This study is interesting and important to mobile robots, but some aspects in this paper should be reconsidered and revised as follows.

 

1. The novelty of this paper should be refined to highlight its improvement and differences compared with the existing study on the formation control.

2. Fig10 and Fig16 show the simulation and test data results of 4-robot trajectory follower respectively. The results of simulation and test are obviously different. How to explain this phenomenon.

3. The proposed control method is verified by simulation and experiment. How to measure the trajectory of mobile robot in simulation and experiment? Does the robot have relevant sensors to obtain the trajectory data of the robot in time during the experiment? What is the measurement accuracy?

 

4. The figures should be revised to be more clear, such as Fig.15, it is not clear.

 

5. The Formation control in this paper should be compared with the existing method to show its advantages.

Author Response

Formation control of mobile robots based on pin control of complex networks

Manuscript ID: machines-1932279

Authors: Jorge D. Rios, Daniel Ríos-Rivera, Jesus Hernandez-Barragan, Marco Antonio Pérez-Cisneros, and Alma Y. Alanis *

Answer to reviewers

First, we would like to express our sincere gratitude to the Associate Editor and the Reviewers. The paper has been carefully revised and corrected according to their valuable comments. Mayor changes in the manuscript have been highlight in yellow, and a point-to-point answer to each of the reviewers’ comments is presented in this document. 

Answer to Reviewer 2

We like to thank Reviewer 2 for his/her valuable comments. We present a point-to-point answer to the comments where the reviewer’s comment is written in bold format.

 Reviewer 2

English language and style are fine/minor spell check required

Authors revised the document and minor changes were made in the document to fix grammar issues.

Does the introduction provide sufficient background and include all relevant references?

           Yes

Some lines were added to the introduction section, to answer specific comments of the reviewers, no new citations were added.

Are all the cited references relevant to the research?

            Can be improved

Some lines were added to the introduction section, to answer specific comments of the reviewers, no new citations were added.

Is the research design appropriate?

            Must be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added.

Are the methods adequately described?

            Must be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added

Are the results clearly presented?

Can be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added.

Are the conclusions supported by the results?

           Must be improved

The presentation of the experiment implementation and the results is improved in the new version of the document. Moreover, Section 5 discussing the results and presenting comparison against other works was added.

This paper presents control of different groups of robots to achieve a desired formation based on pinning control of complex networks and coordinate translation. The validity of the proposed method is verified through simulations and experiments. This study is interesting and important to mobile robots, but some aspects in this paper should be reconsidered and revised as follows.

1. The novelty of this paper should be refined to highlight its improvement and differences compared with the existing study on the formation control.

In the new version of the document, we added a Section 5 Results Discussion, where the obtained results of both simulation and real implementation are discussed, moreover this section includes comparison against two related published methodologies.

From this section we would like to highlight the following text beginning in line 343.

It is important to note that in favor of the scheme of work [21], a final formation and position where collisions would not be a problem was previously selected for this test. However, for most final formations and positions, it would be a task impossible to achieve by the scheme of [22]. The lack of collision avoidance in a real scenario is not something to be left unattended. Moreover, in work [22], every robot has a reference controller, which would get more challenging to design if a different, more complex controller is to be implemented in a future application, as it would be necessary to implement one for every robot.

And the following texts which begins in line 367.

Both schemes reach the goal; however, there is an oscillation when robots get near to achieving formation in the scheme of [17]. Collision avoidance in [17] is done following a particular counterclockwise turning movement. In contrast, the proposal presented in this paper follows a more natural path search in every direction as the LiDAR senses all of the surrounding environment, which makes it more practical for real applications. Figure 25 shows the trajectories where the oscillation at the end can also be observed. It can also be seen that our proposal is a bit faster judging by the number of iterations, even if we were to finish the test where oscillations begin.

2. Fig10 and Fig16 show the simulation and test data results of 4-robot trajectory follower respectively. The results of simulation and test are obviously different. How to explain this phenomenon.

In the new version of the document, we added Section 5 “Result Discussion” from where we would like to highlight the following text beginning at line 276.

There are visible differences between the performance of simulation tests under the Gazebo environment and experimental tests with the actual hardware. Many motives explain these differences. Let us begin by discussing the Gazebo platform, a robot simulator environment used in industry and academia. Gazebo computes the robot's physical and sensory responses in a scenario similar to a real-world one. Even if Gazebo does not consider some real-world factors, it gives results that give us a general idea of the performance of the robots and the algorithms in a real-world application.

Then, the main difference between our simulation and real-world test results. Gazebo simulations were performed locally; all the ROS packages never left localhost. In the experimental test case, the package passes through a local network via Wi-Fi communications involving loss of packages and delays affecting the performance. Moreover, the scenario where the robots moved is not a perfect flat surface as in the simulation; it has irregularities. Furthermore, the simulation does not consider robot wear conditions and non-model dynamics.

Another important point to discuss is that all nodes in the proposed work are differential-drive robots. However, using complex networks, it would be possible to combine different kinds of robots, including, for example, unmanned aerial vehicles and omnidirectional robots. Let us consider the works [10,11] where non-identical chaotic nodes are used in the same complex network. Judging by their results, we could expect similar results for the proposed control scheme using different robotic platforms. However, the relevant variables to each of the different robots must be first defined.

3. The proposed control method is verified by simulation and experiment. How to measure the trajectory of mobile robot in simulation and experiment? Does the robot have relevant sensors to obtain the trajectory data of the robot in time during the experiment? What is the measurement accuracy? 

In the new version of the document, we added in Section 4.1 “Experiment Description” the following lines beginning at line 158.

Among the hardware elements of a Turtlebot3® Waffle Pi robot, it has a Raspberry Pi 3, actuators XL430-W20, LiDAR sensor 360 laser Distance Sensor LDS-01, IMU with gyroscope 3 axis, and accelerometer 3 axis. The robot pose is calculated by the robot giving an odometry ROS message with its position and orientation. It is important to note that the accuracy of this measurement varies in function of the terrain conditions and wear of the robot equipment.

4. The figures should be revised to be more clear, such as Fig.15, it is not clear.

In the new version of the document, in section 4.2 we change the figures to a vectorized format to have a better quality, moreover, at line 264 we added the following text to explain the referred figure.

Figures 9, 12 and 15 show the control signals  and  of each of the nodes; these figures can be compared against Figures 8, 11 and 14, respectively. Figures 8, 11 and 14 show the nodes changing their position through time (iterations). In Figures 9, 12 and 15, the saturation of signals is noticeable, resulting of a saturation imposed by us to protect the equipment; however, even with this saturation, the proposed approach achieved the desired reference point and formation.

5. The Formation control in this paper should be compared with the existing method to show its advantages.

In the new version of the document, we added a Section 5 Results Discussion, where the obtained results of both simulation and real implementation are discussed, moreover this section includes comparison against two related published methodologies.

From this section we would like to highlight the following text beginning at line 343.

It is important to note that in favor of the scheme of work [21], a final formation and position where collisions would not be a problem was previously selected for this test. However, for most final formations and positions, it would be a task impossible to achieve by the scheme of [22]. The lack of collision avoidance in a real scenario is not something to be left unattended. Moreover, in work [22], every robot has a reference controller, which would get more challenging to design if a different, more complex controller is to be implemented in a future application, as it would be necessary to implement one for every robot.

And the following text beginning at line 366,

Both schemes reach the goal; however, there is an oscillation when robots get near to achieving formation in the scheme of [17]. Collision avoidance in [17] is done following a particular counterclockwise turning movement. In contrast, the proposal presented in this paper follows a more natural path search in every direction as the LiDAR senses all of the surrounding environment, which makes it more practical for real applications. Figure 25 shows the trajectories where the oscillation at the end can also be observed. It can also be seen that our proposal is a bit faster judging by the number of iterations, even if we were to finish the test where oscillations begin.

 

Thank you very much for your comments, the authors of this work wish you a great day.

 

 

Round 2

Reviewer 1 Report

Dear Authors,

in my opinion, the quality of the paper has been significantly improved.

Best regards

Reviewer 2 Report

This paper presents control of different groups of robots to achieve a desired formation based on pinning control of complex networks and coordinate translation. The validity of the proposed method is verified through simulations and experiments. This study is interesting and important to mobile robots. In this version, the authors have already replied all the questions I proposed before. I will clarify the comments as well as giving new comments.

 

The references can be expanded, the authors might cite the references below:

[1] Title: Accurate and robust body position trajectory tracking of six-legged walking robots with nonsingular terminal sliding mode control method.

[2] Title: Nonsingular fast terminal sliding mode posture control for six-legged walking robots with redundant actuation.

[3] Title: Reinforcement learning control for the swimming motions of a beaver-like, single-legged robot based on biological inspiration.

After the above revisions, the paper can be considered for publication.