Adaptive Neural-Network-Based Nonsingular Fast Terminal Sliding Mode Control for a Quadrotor with Dynamic Uncertainty
Round 1
Reviewer 1 Report
This paper proposes an interesting method to address the trajectory tracking control problem of a quadrotor in the presence of model uncertainties and external disturbances. The authors base their claims on theoretical analysis supported by experimental results.
The presentation starts well but loses quality after the third paragraph of the introduction, which affects the quality of the work considerably. This must be improved.
The authors should also check the references and fix related issues in the text. An example is the case of explanations concerning Equation (3), where the reader is pointed to refence [5] for explanations regarding Matrix R_t and R_r. That paper (reference [5]) does not provide details regarding those matrices, but rather point towards other references. The authors should fix this and verify other references in the text for correctness.
The presentation in section 2 and 3 should be revised and improved for language and style.
Author Response
Response to the Reviewer 1 Comments
Dear Reviewer
Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions in the re-submitted files.
Point 1: The presentation starts well but loses quality after the third paragraph of the introduction, which affects the quality of the work considerably. This must be improved.
Response 1: Thank you very much for your suggestion on the introduction. I have rewritten some sentences in the Line 66-96 to improve the logicality and systematization of the introduction. Then, I have corrected some grammar mistakes to make the introduction more fluently expressed. In addition, I have replaced some references to promote the association of the references with this manuscript.
Point 2: The authors should also check the references and fix related issues in the text. An example is the case of explanations concerning Equation (3), where the reader is pointed to refence [5] for explanations regarding Matrix R_t and R_r. That paper (reference [5]) does not provide details regarding those matrices, but rather point towards other references. The authors should fix this and verify other references in the text for correctness.
Response 2: Thank you very much for pointing out the problem of the references. I have replaced the reference [24] in the Line 145 by reference [4], where the specific expression of Matrix R_t and R_r can be provided. Then, I have checked all the references of this this manuscript and fixed the unsuitable ones to promote the quality of this manuscript. In addition, I have corrected the order of the references. For example, the reference [26] in the Line 175 has been replaced by reference [25].
Point 3: The presentation in section 2 and 3 should be revised and improved for language and style.
Response 3: Thank you very much for the suggestion for the language and style of section 2 and 3. I have fixed some grammatical errors and modified some words to make the manuscript more coherent and intelligible. For example, we have replaced “the vector’s maximum element” by “the maximum element of a vector” in the Line 137 page 3, and the sentence in the Line 145 page 4 is replaced by “that describes the position and attitude of the quadrotor”.
All the responses to the reviewer’s comments are given in the manuscript in a red color.
I hope that the revised manuscript is accepted for publication in drones.
Looking to hearing from you soon.
With kindest regards,
Yours Sincerely
Shurui Huang
Author Response File: 
Author Response.docx
Reviewer 2 Report
The paper is well writen and objectives clear.
Comments :
1) please correct all your bad references to equations, no numbers appears
2) equation 4, write (4) and not (4
3) in equation 6, double dot is difficult to see on \eta in \delta J*ddot(\eta), maybe a bad position of braces
4) page 5, ligne 154 : "angle" and not "angel"
5) Euler angles are not the best framework to describe the behavior of the kinematic of the rotation. This gives non linear and dicontinuous equations. Please, try to take a look to some works based on rotation matrix or quaternions. The model is simplier and standard SMCs give good results.
6) It could be interesting to discuss the nomber of iterations of the algorithm 1 to know if it is acceptable in real time (in simulation, time is not an issue)
Author Response
Response to the Reviewer 2 Comments
Dear Reviewer
Thanks very much for taking your time to review this manuscript. I really appreciate all your comments and suggestions! Please find my itemized responses in below and my revisions in the re-submitted files.
Point 1: please correct all your bad references to equations, no numbers appears.
Response 1: Thank you very much for your suggestion on the bad reference. I have checked all the references and corrected the wrong ones. In addition, the order of the references is corrected. For example, the Ref. [24] in Line 145 page 4 has been placed by Ref. [4], and the Ref. [25,26] in Line 175 page 5 has been placed by Ref. [25], and the Ref. [27] in Line 217 page 7 has been placed by Ref. [26].
Point 2: equation 4, write (4) and not (4.
Response 2: Thank you very much for pointing out the equation number. I have corrected the wrong equation number.
Point 3: in equation 6, double dot is difficult to see on \eta in \delta J*ddot(\eta), maybe a bad position of braces.
Response 3: Thank you very much for your suggestion on the forms of the equation 6. I have modified the style and size of Eq. (4) in page 5, line 154 to make it clearer.
Point 4: page 5, ligne 154 : "angle" and not "angel".
Response 4: Thank you very much for your suggestion on the words spelling. I have checked all the words spelling of this manuscript and fixed the wrong ones. For example, “sate” in page 5, line 172 has been replaced by “state”, and “angel” in page 5, line 175 has been replaced by “angle”.
Point 5: Euler angles are not the best framework to describe the behavior of the kinematic of the rotation. This gives non linear and dicontinuous equations. Please, try to take a look to some works based on rotation matrix or quaternions. The model is simplier and standard SMCs give good results.
Response 5: Thank you very much for pointing out this interesting question. Indeed, Euler angles may cause the singularity and discontinuous problem. And, I have looked into some references to study this method to describe the behavior of the quadrotor kinematic of the rotation. Therefore, I will use quaternions to model the quadrotor in my future work.
Point 6: It could be interesting to discuss the number of iterations of the algorithm 1 to know if it is acceptable in real time (in simulation, time is not an issue)
Response 6: Thank you very much for pointing out this constructive question. In fact, the algorithm 1 uses four order Runge Kutta method to construct the simulation, where the number of iterations are set as 0.005s. And it can used in the real-time simulation.
All the responses to the reviewer’s comments are given in the manuscript in a red color.
I hope that the revised manuscript is accepted for publication in drones.
Looking to hearing from you soon.
With kindest regards,
Yours Sincerely
Shurui Huang
Author Response File: Author Response.docx
