Design and Analysis of a Robust UAV Flight Guidance and Control System Based on a Modified Nonlinear Dynamic Inversion

Round 1

Reviewer 1 Report

The paper is generally good (contributing and well written).

I left with very fiew comments on the paper.

 

The steps presented on Pages 4 and 5 should not be called algorithms, otherwise the questions on complexity, correctness would arise. It would be better if the steps are expressed as a series of numbered equations which have to be referred accordingly. The problem on Line 141 is not clearly defined. It would be better to express it as a standard optimisation problem. Line 199: 50 [Hz] --->  50 Hz. please correct.

 

 

 

Author Response

We greatly appreciate the valuable comments. In the revised manuscript, we have changed the word algorithm to be Pseudo Code as it represent the sequence of generating the desired guidance command based on carrot chasing or Pure Pursuit and LOS Guidance law.

The problem of line 141, we are sorry for some confusion in explaining our problem statement. We have added a minimization cost function to clarify the missing objectives.

In the revised manuscript we have corrected the frequency unit to be Hz which is highlighted with red font color in line 199.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper was redone adequately to my comments. The videos helped a lot to understand some aspects of the paper, I recommend to attach them to the paper web page, if it will be approved for publishing. Some images are still little messy (e.g. second picture on the Fig.7), however, other new images are adequate and explanatory. The Fig.2 is messy too, because it has different font sizes and the letters are rotated.

 

Author Response

Thanks for your comment. You are right, we have polished all figures again in the revised manuscript and the revised manuscript revised figures have red font color caption (Figure 2&7).

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The paper describes two alternative methods for following a path and two alternative methods for controlling the aircraft. The two parts seems to have nothing in common.

The description of each part is hard to follow – partially due to language problems,
e.g. second sentence in section 4 (line 215?): “However, considering the current control surface deflection in computing the new deflection has been decreased the dependency of the flight control on the inaccurate model” - “… new deflection has been decreased...”??

Line 227: “Due to the robustness of the modified NDI flight controller than NDI, it is” ??
Line 377/378 is bad too.

The calculations in section 2 are in a different style compared to section 3 and 4, but there is one thing in common: figures do not follow the text.

In figure 2: Theta is the angle to the next waypoint, but in the text – I think – is the same as Theta_d. Further Psi_d in line 166 (bank angle calculation) is not the same as Psi_d in figure 2.

In figure 3: the three inputs are Theta_c, Beta_c, Phi_c but in the text the same values seems to be called Alpha_c, Beta_c, Phi_c. The two constants K1 and K2 in the figure may be omega in the text. Omega is often used for frequency and this makes the paper unnecessary hard to read.

Beta is used in section 2.1 and 3 with different meaning.

I miss a figure with the the notation of the axis and rotations for the UAV, i.e. p=roll, q=pitch and r=yaw, x=forward, y=left … or?.

I fail to understand the significance of the simplifications in the modified NDI, and why this should be better.

Figure 6 and 7 has descriptions on the axis e.g. “Pitch angle Theta” - this is nice.

The figures (6 and 7) are assumed to show a simulation with an sequence of pitch steps. The roll angle and roll rate do not match for the unmodified NDI, why is the pulse at 8 seconds positive and the one at 2 seconds negative, when the derivative is the same. Further the pulses are less than 10e-17 degrees, and thus totally insignificant.

In line 274 signale c_l, c_m, c_n are introduced as moment coefficients, but with no reference to equations or reference in figure 3. In Figure 10, what is the difference in “accurate” and “perturbed”, i.e. where in the control loop?

In figure 12, 14 and 16, what is the significance of “Desired NDI Attitude Rate”, and how is it calculated or where in the control loop?

Figure 17 and 18 should show superiority of the PLOS method – wind or not, but there seems to be minor differences only. Furthermore, it seems like the figures 17 and 18 are swapped, as figure 17 seems to be affected by wind. There is a difference, but this is not visible in the figures.

The speed and height response is minor and only interesting if there had been a difference in control law.

The cross track error in figure 21 is missing units on the Y axis.

Figure 22: What is the units on the x-axis? (and on the Y-axis).

Reviewer 2 Report

Authors presented а research focused on the design of a robust nonlinear flight control system for a small fixed-wing UAV against uncertainties and external disturbances. They presented a detailed analysis of two autonomous path-following guidance algorithms which was performed with NDI and modified NDI flight control systems using a small UAV model.  The simulation results demonstrate the effectiveness and accuracy of the proposed algorithms. 

Authors made a strong reasearch which is valuable in UAV control area. Although the simulation results are great it is interesting to see the vbaluation of the propsed algorithms in real life.

Work may be accepted in present form.

Reviewer 3 Report

The paper proposes the control of a small fixed-wing UAV for flight control and guidance for following of straight line paths. The inner loops, rates

and wind attitude, are controlled using a standard NDI approach and by a so-called "modified NDI". The guidance is by 2 standard approaches. The study

is supported by extensive simulation results.

The paper is rather shoddily written. Although the English is good, but there are limitations in the presentation which do not engender much confidence 

in the work.

Detailed comments:

- First sentence in Introduction - in Europe this statement is not true. The biggest application is photography and video. It may be true for 

fixed-wing applications. Anyway, it needs a citation to a credible source. However the statement is not really relevant and could be deleted.

- page 1 line 27 - replace "windy" by "gusty". Windy could refer to constant winds as well as gusts. Also I am not sure how the external disturbance 

can be controlled at all, let alone "completely".

- page 1 line 29 - "ride the path" does not have a clear meaning, use "follow the path"

- page 2 line 32 - the meaning of "practically nominated" is not clear

- page 2 line 46 - ref [13] is for rotary wing - it has no relevance to fixed wing because the constraints for fixed wing and rotary wing path 

following are very different and require very different techniques

- page 2 lines 63-71 - there are no citations to justify the statements in this paragraph

- page 3 line 95 - it is not clear what is meant by a "sharp" maneuver.

- page 3 line 99 - these are not "methodologies", but are really the "contributions"

- page 4 line 139 - there are just 2 waypoints shown, usually this is a subset of the set of waypoints. replace "a set" by "two"

- page 4 lines 150-167 - these are steps that must be "tracked"? this is a strange term. The steps are not really steps of anything. It is not an 

algorithm either. It is not clear why the guidance law has been defined in this way.

- page 4 line 152 - why is the i+1 waypoint not "initialized"?

- page 4 line 154&156 - the atan2 operation is incorrectly used here. It should be atan2(x,y) not atan2(x/y)

- page 4 line 159 - surely the Wp_{i+1} waypoint has a position (x_{i+1}, y_{i+1})

- page 4 line 164 - what is the purpose of distance S?

- page 4 line 166 - V_a is not defined. Is it the airspeed? perhaps the groundspeed?

- Section 2.2 - what is delta? Is it constant or time varying? how is it chosen?

- page 5 - the sentence "The main task ... as shown in Figure 2." makes little sense. Surely the point here is that there is a confict in the requirements for reduing the cross-track error to zero and in requiring a zero heading angle error.

Both are required for good path following, so both errors should be fed back in the guidance law.

- page 5 line 171 - it is not clear what is meant by "calculated gradually"

..... and so on

Some general comments

- the figures are poor; very untidy with a mixture of fonts, font sizes and notations that differ from the text and arbitrary colors

- there is conflicting notation, for example theta and beta

- the "modified NDI" appears to be just a linearized NDI (if that makes any sense)?

- the NDI is based on reference [20], but NDI is a well-established method. Some additional references to original or definitive sources should be included.

- the references are poorly presented, incomplete and inconsistent

- the presentation of the equations, with the equation numbers in the text amd appearing just prior to the equation, is vry odd.

 

Reviewer 4 Report

The article has serious flaws:

- The sentence "Simulation results showed that the modified NDI flight control system is robust against wind disturbances and model mismatch." was not proved in the article.

- the chapter 2.2 (Carrot Chasing Guidance Algorithm) has errors or mistakes. E.g.

the term vector Wi is described as position only, without its magnitude and direction (at least mentioned)

if p is current position, then the coordinates should be marked x_p,y_p, h_p

The R_u on the figure 2 describes the distance between last and current position, but the equation on the row 158 (bullet 6) describe different value

Chapter 3.3 - there is stated Figure 25, which is not present in the article. Probably typing error (should be equation 25?)

equation 26 - what is D?

equation 28 - what is H.O.T?

In the article, there is no clear evidence about the effectivity of proposed method:

- Fig.7 and following figures - The modified NDI curve is missing or not (badly) visible.

- The testing environment is described weakly (hard to replicate the experiments).

- According to figures 8 to 16 is eminent, that UAV reactions (to wind disturbance) in the slide-slip, roll or pitch angles are almost zero for modified NDI. It means that according to described wind gusts of 10m/s speed, the roll, pitch and slide-slip angles are stable all the time, which is from my point of expertise physically impossible. Need a proof video.

- in the row 360 authors stated that the PLOS proves to be more practical than carrot chasing - this is not eminent from the charts at all. Also figure 17 & 18 o not show any differences between methods. I very doubt that according to Figure 21 the means (described on the figure 22) would be such different.

- so the statement (row 376-378) "The simulation results confirmed that PLOS path following algorithm accurately follows the path than carrot chasing" was not proved (or I did not found the proof).

In such form, I cannot recommend the paper to be published.

Reviewer 5 Report

Minor errors:

- The abstract needs to be improved by elaborating on the importance/relevance of the underlying problem.

- Make the citation style consistent. For instance Line 43, authors and numbers are used and this is not the case for many other lines such as Line 39.

-Paragraphh starting from Line 100: reference to the parameter is not clear. clarify on the way the order is respective.

- The minimization objective is not very clear. The objective function and constraints needs to be clear.

- The steps presented from Line 152 and from Line 173 hide information on the structure of the final formula of the guidance law. The implementation of such steps is  much more costly (complexity-wise) than working with the final formula.