Mathematical Considerations for Unmanned Aerial Vehicle Navigation in the Magnetic Field of Two Parallel Transmission Lines

Round 1

Reviewer 1 Report

The paper, after minor revision according to the attached report, can be published. Best regards. 

Comments for author File: Comments.pdf

Author Response

Thank you. We wish to express our gratitude to you for the detailed review of our paper and for the valuable comments and remarks.

With the exception of comment 3, we have taken over all of the comments and incorporated them into the publication. All changes we made in the text are highlighted in red. These are

comment 1: pg. 1 line 1, title changed according to your suggestion

comment 2: pg. 1 lines 3 and 4, sentence removed

comment 4: pg. 4 line 6, equations are now double numbered

comment 5: pg. 9 formula (25), starting from formula (22) on page 8 several changes are made in the text as well as in the equations providing more details and hints for better understanding of the proof. The changes are highlighted in red on pages 8 and 9.

 

Response concerning comment 3: Multipath and fading effects have been very well researched and are generally known, for example, in cellular communications. Therefore we think that it is not necessary to provide additional literature information at this point. In addition, these effects do not play a role in the approach presented, since in the case of the transmission line system it is a quasi-stationary field problem, where these effects cannot occur.

Reviewer 2 Report

Very interesting research, great work. Some of my comments:

1. The roll axis oscillation, is it because the mag interference causing the attitude estimation error, or positioning error.
2. If it's position error, they can be tuned out on the flight control.
3. If it's attitude estimation error, should mag info not be considered to calculate attitude. 
4. Does the simulation specify where on earth the testing is? How important is this compared to the transmission line interference?
5. Is inertial data used to help with heading estimation?

Author Response

Thank you. We are glad that we properly addressed all the comments and grateful for having improved the quality of our paper based on your comments.

We checked your answers carefully and provide the following answers:

1. in order to be able to calculate the UAV position, the attitude must first be calculated. Since this is calculated independently and only from the measured values of the magnetometers, the magnetic interference directly causes an error in the calculation of the flight attitude. Thus you are right and in the case of too large magnetic interference as for example in the case of indoor applications where only low currents in the cables are used, it is good to have another technical possibility to calculate the attitude. However, close to the transmission lines there is in general a very good signal-to-noise ratio so the attitude errors become small as can be seen from the simulation results.

 

2. see 1

3. see 1

 

4. No, the testing place is not specified. The publication looks at medium-voltage networks that have a similar signal-to-noise ratio, regardless of where they are on earth. In addition, it is the electric drives of the UAV that make up most of the magnetic noise.

 

5. No. If the UAV starts close enough to the transmission lines (lets say 2 meters) in an area of sufficient high signal-to-noise ratio, theoretically the UAV can navigate directly using only the magnetic info.

Reviewer 3 Report

The paper entitled “Mathematical considerations for UAV navigation in the magnetic field of two parallel transmission lines” studies the navigation of unmanned aerial vehicles (UAV) moving in the magnetic field of two parallel transmission lines.

 

Overall, this work studies an interesting topic. My main concern is about the applicability of the proposed method, specifically since the respected authors considered the UAV as a point mass and it is not clear to me how the respected authors consider the complex nonlinear dynamics of the UAV in their proposed method?

 

Technical aspect:

 

• There are many articles addressing the navigation and control of the UAVs considering their complex nonlinear dynamics. I would suggest that the respected authors carefully review the following articles (and the references therein) and to offer a more thorough justification. In other words, how the respected authors consider the complex nonlinear dynamics of the UAV in their proposed method?

 

• Valavanis, K.P. and Vachtsevanos, G.J. eds., 2015. Handbook of unmanned aerial vehicles (pp. 2993-3009). Dordrecht, The Netherlands:: Springer.

 

• Nascimento, T.P. and Saska, M., 2019. Position and attitude control of multi-rotor aerial vehicles: A survey. Annual Reviews in Control.

 

• Michailidis, M. G., Rutherford, M. J., & Valavanis, K. P. (2020). A survey of controller designs for new generation UAVs: The challenge of uncertain aerodynamic parameters. International Journal of Control, Automation and Systems, 18(4), 801-816.

 

• Carrillo, L.R.G. and Vamvoudakis, K.G., 2019. Deep-Learning Tracking for Autonomous Flying Systems Under Adversarial Inputs. IEEE Transactions on Aerospace and Electronic Systems.

 

• Rezaee, H., & Abdollahi, F. (2012, July). Adaptive artificial potential field approach for obstacle avoidance of unmanned aircrafts. In 2012 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) (pp. 1-6). IEEE.

 

• Jafari, M., Xu, H. and Garcia Carrillo, L.R., 2019. A neurobiologically-inspired intelligent trajectory tracking control for unmanned aircraft systems with uncertain system dynamics and disturbance. Transactions of the Institute of Measurement and Control, 41(2), pp.417-432.

 

• Yasin, J. N., Mohamed, S. A., Haghbayan, M. H., Heikkonen, J., Tenhunen, H., & Plosila, J. (2020). Unmanned aerial vehicles (uavs): Collision avoidance systems and approaches. IEEE Access, 8, 105139-105155.

 

• Jafari, M. and Xu, H., 2018. Intelligent control for unmanned aerial systems with system uncertainties and disturbances using artificial neural network. Drones, 2(3), p.30.

 

• Singh, J., Dhuheir, M., Refaey, A., Erbad, A., Mohamed, A., & Guizani, M. Navigation and Obstacle Avoidance System in Unknown Environment. In 2020 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE) (pp. 1-4). IEEE.

 

• Madani, T. and Benallegue, A., 2006, October. Backstepping control for a quadrotor helicopter. In 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 3255-3260). IEEE.

 

• Shao, X., Liu, J., Cao, H., Shen, C. and Wang, H., 2018. Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer. International Journal of Robust and Nonlinear Control, 28(7), pp.2700-2719.

 

• Wang, N., Su, S.F., Han, M. and Chen, W.H., 2018. Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49(7), pp.1322-1337.

 

• Liu, H., Zhao, W., Hong, S., Lewis, F.L. and Yu, Y., 2019. Robust backstepping-based trajectory tracking control for quadrotors with time delays. IET Control Theory & Applications, 13(12), pp.1945-1954.

 

Presentation aspect:

 

• The paper needs improvement in presentation. Linguistics and readability of the paper need to be improved, and the authors should restructure the paper in order to have a smooth transition among the sections.

Author Response

Thank you. We wish to express our gratitude to you for the detailed
review of our paper.

 

This work does not deal with the nonlinear dynamics of a UAV. The aim is rather to show how the position and orientation of a UAV relative to the transmission lines can be analytically determined from the magnetic field measurements captured with several magnetometers. In general, it does not matter whether it is a UAV or another object. For example, if you were to look at a robotic arm on a high crane that has completely different dynamics, the equations derived in this work would be exactly the same. The dynamics of a UAV therefore have no influence on the presented results.

 

Concerning the linguistics: Before submitting the paper, we checked the entire text again with the InstaText application.