Modeling and Analysis in Trajectory Tracking Control for Wheeled Mobile Robots with Wheel Skidding and Slipping: Disturbance Rejection Perspective

Round 1

Reviewer 1 Report

General comments

This paper presents a control scheme that considers not only the dynamics of a Differential Drive Wheeled Mobile Robot (DDWMR) but also takes into account the dynamic effects of skidding and slipping. Such an approach uses the disturbance rejection perspective for solving the trajectory tracking task.

Comments and suggestions for Authors

1.- The paper should comprise the following structure proposed by MDPI: Introduction, Materials and Methods, Results, Conclusions, Funding Information, Author Contributions, Conflict of Interest.

2.- The abstract should not be ambiguous; that is, using words like “etc.” with the aim of avoiding enlarge the paragraph could be interpreted in two fashions: (1) the authors do not know what else could be solved with their own proposal or (2) the authors think they proposal can solve many things. Please, be concise.

3a.- The topic of this paper is clearly of scientific soundness. However, the literature review related to the specific problem of considering skidding and slipping is not deep at all; on the one hand, the References included are minimum (from reference [15] to reference [24]) and just one of those dates from the 2018. Thus, the paper is not well supported and the innovation can’t be observed clearly.

3b.- Nowadays the literature regarding DDWMRs has increased exponentially. Most of the control strategies proposed by the robotics, automatic control, and mechatronics communities considers only the mathematical models of the mechanical structure and, in some cases, the actuators ones. However, new papers also have included the dynamics of the power stage. Thus, it would be convenient that such papers be revised by the authors; since also a convenient classification of mathematical models were included in those works. Hence, it is advisable to check the following papers:  

[a] “A novel dynamic three-level tracking controller for mobile robots considering actuators and power stage subsystems: Experimental assessment”, Sensors, vol. 20, no. 17, September 2020.

[b] “Robust switched tracking control for wheeled mobile robots considering the actuators and drivers”, Sensors, vol. 18, no. 12, December 2018.

4.- How can you guarantee that “Assumption 1” will be fulfilled? Such an assumption seems to be unreal, since perturbations are not known a priori; thus, it is somewhat complicated to guarantee that \psi_v, \psi_omega, and u are going to be small regarding the reference velocity. In addition, how do you establish the positive constants \delta_1, \delta_2 and \delta_3?

5.- Related to “Assumption 2”. How can you guarantee the existence of positive constants \alpha and \beta? Because those constants are limiting the value of D and \dot{D}.

6.- The control gains defined at the bottom of page 8 specifies that the elements of the diagonal matrix \Lambda are equal to 1 and also k_1=k_2=1. The question is, how did you find those values? Because gains equal to numeric value 1 are useless in control schemes, since they are not modifying the dynamic behavior of the closed-loop system. Please clarify.

7.- The simulation results use the parameters specified in Table 1. However, authors never mention why they use such parameters. Are those the same of the experimental prototype?

8.- Based on the title of this piece of research, the reviewer did not see anything related to some kind of robustness tests when parametric variations appear, neither simulation ones none experimental ones. In this direction, since the proposed control is robust, it would be important if such robustness tests were included.

9.- Authors claim that experimental tests were included. However, no kind of specifications were added related to the testbed, neither the prototype none the sensing/acquisition/processing signals.

10.- What kind of perturbations can be considered over the system? Is there some “special” perturbations to be considered in this kind of systems? If so, it would be nice if authors include some kind of table where the potential perturbations were specified.

11.- More experiments need to be added, since authors claim that the proposed approach is robust enough to achieve disturbance attenuation and, consequently, to solve the tracking problem. Thus, some comparison should be done regarding the published literature.

12.- English must be verified.

13.- The proposed paper could be published in Actuators Journal after major changes be executed. It is important to highlight that, nowadays, Actuators Journal is in a growing up process; thus, the quality of the published works must be superior.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper provides a method to track a reference trajectory for a mobile robot in the presence of skidding and slipping.

There are several issues with the paper. The novelty is unclear. There seem to be errors in the equations of motion and/or they are not correctly written, the conventional method against which the results are compared is not explained, the results do not really make a case that the approach works in simulation and hardware.

Title: Avoid acronyms in the title. (e.g., WMR)

What is the difference between skidding and slipping? Please describe in the introduction. Also, does one need different control techniques to deal with both? It might be best to organize the literature review around that. Which methods work for skidding, which for slipping, and which for both. 

What is the novelty of the work? 

Eqn 1. Isn't "A" a suitable jacobian. Please elaborate on the form and how it is obtained. 
There is ambiguity in the kinematic relation A(q) J(q) (see below). 

Eqn 2. Please elaborate the -d phidot term in the first equation. 

J(q) is the jacobian of what point? 

I don't understand how A(q) qdot = A(q) J(q)? qdot is not equal to J(q). 

Please elaborate on how P(q) is obtained. 

What is NDO. Please define acronyms before using them. What is Z here? 

What is NDOISMC (Figure 2)?

Figure 2 block diagram needs to be explained. Only few of the blocks are explained in the writeup. Also, please reference this figure in the writeup. 

Figure 3, 4 are color coded. Can't read when printed in Black and White.

Figure 5. What is human-computer interaction block? 

What is ISMC? It needs to be explained with details in the writeup as one is comparing the two methods. How is it different from the proposed approach.

In the simulations, reference tracking with skidding and with slipping needs to be demonstrated separately. 

In the experimental results, it is really hard to see how the proposed approach is better than the conventional approach. 

Can we see a video of the experiment and/or the simulation?

A discussion section detailing how this research compares with the broader field is needed. What are the limitations of the approach?

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The paper goal is the modeling and analysis in trajectory tracking control of a wheeled mobile robot in case of skidding and slipping conditions. The paper has a good structure and has an appropriate presentation. However to increase the readability of the paper the following points are suggested for improvement:

• The state-of-the-art part of the paper enumerates topics and works found in literature, without too much elaborated comments or remarks from authors perspective;
• skidding and slipping conditions are common in aeronautics, so introduction the concept for ground vehicles can be considered;
• Lines 51-52: In "The trajectory tracking results in [23,24] were not as desirable as expected" expressing if possible in a quantifiable way would give a more precise clue about the performance of the mentioned solution;
• Labeling the axes from Figure 1 can be considered;
• In Property 1 and after it, terms with (straight) hat are no defined;
• In Eq. 5, in the explanation following Eq. 6, line 103 comma is used as separator between the vectors elements;
• Next line after line 105, acronym is better to be placed after the term that define (see NDO);
• Before Eq. 20, ISMC term not defined;
• Idem. for NDOISMC (first occurrence in caption if Fig. 2);
• In Section  5 tool(s) involved in performing the simulation can be mentioned.
• In Fig 4a one would have to guess where reference trajectory is located;
• In Fig 5 "human-machine interface" would not be more appropriate?
• In Fig 6 in case of R485, to what type of bus authors referred? Also a legend for some not so popular term can be considered (eg. for SLAM);
• When dealing with robust control approach its performances is also evaluated through appropriate robustness indices. In this case mainly only the error is considered.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

General comments

The authors have revised this manuscript carefully according to my comments and an effort was done in this new version.

Comments and suggestions for Authors

1.- It is advisable that authors do not name the sections as: “2. Methods of system modeling”, “3. Methods of tracking problem for nonholonomic WMR”, etc. The purpose of the first comment was not to decompose in such a way the subsection “Methods”. Instead, the authors should declare only one section named “2. Methods” and as subsections “2.1. System Modeling”, “2.3. Tracking Problem…”, etc. Please verify this, since the MDPI rules are very clear.

2.- Although the authors make another revision of literature, the References remains out of date. Thus, as this reviewer stated on the first review, the paper is not well supported and the innovation can’t be observed. On the other hand, the reviewer is not asking you to increase the references section, but to review appropriately the state of the art on the topic and maybe replace some references outdated.

3.- Based on the authors’ answer related to the control gains associated with the diagonal matrix \Lambda and gains k_1 and k_2. Authors did not answer appropriately the comment; thus, the question remains. Please give a deeper explanation, because you are not describing the meaning of having gains that are not modifying the closed-loop dynamics. In this sense, the control purpose is lost.

4.- The proposed paper could be published in Actuators Journal after the authors update the sections names and the References. Also, a clear answer related to gains is necessary.

Author Response

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Author Response File: Author Response.pdf