Model and Fuzzy Controller Design Approaches for Stability of Modern Robot Manipulators
Round 1
Reviewer 1 Report
The article is devoted to solving the problems of controlling manipulators for robots.
The presence of two photographs - outdated and modern samples of manipulators - demonstrates only the fact that the authors are able to download photos from the sites of other organizations and used the site for this at the link [33]. It is far from certain that the authors of the article really have these manipulators and have studied them, otherwise it would be more informative to provide their own photographs when performing some measurements or other types of work with these manipulators.
The statement that the center of mass must necessarily remain within the base of the manipulator does not seem to be justified, since the manipulator must be rigidly attached to the base, so the purpose of controlling this device is, apparently, to perform operations on the part. If the base is heavy and stable enough, then the location of the center of mass of the manipulator does not matter, it is quite possible to assume that it is outside the own base of such a manipulator. The unit will not topple over if it is attached to the floor or to an additional solid base with a large footprint.
Thus, the very formulation of the problem is not clear to readers.
It is not clear to the reader why two manipulators are chosen as an example, and not one. In this case, some kind of mapping between their properties is expected. What then is the purpose of comparison? If one manipulator is more modern, then it is obvious that the outdated model does not need to be investigated, because it is outdated, therefore, obviously worse.
Meanwhile, lines 107 - 108 say: "As a case study, we chose the most recent ABB model, CRB 15000 from Walton Company Limited Bangladesh and a contemporary ABB version model shown in Figure 1", however, in the caption to this figure otherwise stated: “Figure 1. Captured image of old model of ABB Manipulator from WALTON Company Ltd. Bangladesh (right) and Modern Model of ABB Manipulator [33]”. The caption under the figure contradicts the comment in the text - is the old or the latest model used?
If the authors were engaged in the study of serial manipulators, then such manipulators are supplied together with control devices. Why then is independent research required to write some other control algorithms? If the authors found that the software and hardware supplied with the manipulators to control them did not work effectively enough, then this problem should have been described in the introduction to the article, and not instead give an overview of other people's articles in this area in general, and it was not necessary to explain the completely obvious truth with reference to literary sources, since readers already understand that the manipulator has joints, and that there are motors in the joints, and so on, so the text in lines 61-75 is completely redundant.
Lines 110–117 convince readers that, apparently, the authors of the article did not have these manipulators in front of them as physical objects of study (for their modification, for example), but simply used information about them from the site at the link [33]. That is, the authors do not have an object of study, they only investigated their idea of ​​this object on the basis of a technical description. Could such an article be of practical value? There is reason to believe that the results that the authors claim in the article are only their declaration, wish, and are not supported by anything.
It is very strange that the article gives illustrations of two different manipulators, and Table 1 gives specific information about a particular manipulator, apparently the one shown in Figure 1 on the right. Therefore, the left side of Figure 1 has nothing to do with the article at all. It is not customary to give two photographs in one figure without marking them, for example, with the letters “a” and “b”, if two illustrations were given, it was necessary to give these subparagraphs under the figure, and in the figure caption or in the text to clarify which of illustrations of which species it belongs to. This is an elementary culture of writing articles, but in general, the whole figure 1 is redundant, it was enough to give a link to the original source.
Table 2 claims that it is possible to give a single formula for calculating the stiffness and deflection of all arms and, apparently, the play of all nodes. This is impossible in this example, and the presented numerical values, which are given with the highest accuracy, obviously do not correspond to anything specific in practice. Indeed, if, for example, the manipulator is fully extended, then the moment that acts on the first node will not coincide at all with the moment for the case when the manipulator is grouped into a compact structure. It is impossible to predict and calculate the deflection for all cases, all the more so with such accuracy as indicated in Table 2, where values are given for nine significant figures! After all, this on a shoulder 1 meter long should have provided an error at the level of 1 nanometer!
The table gives the values of quantities, such as m, k, I, fc, which are not disclosed, not explained. And it cannot be that for each joint these are the same parameters, they are different every time. It seems that the authors themselves do not understand the meaning of these parameters and how to use them to determine some specific numerical values of the calculated values of the manipulator parameters.
Table 3 is surprising. Three different servo parameters are taken from three different bibliographic sources. Are we talking about the same servomotor here? Why are the three parameters taken from different sources?
Table 4 also raises doubts about the competence of the authors. For example, in the first line, the winding resistance is calculated as voltage divided by current. This is at best the active component of the resistance of the winding, but there is still a reactive component, if no torque is applied to the shaft, then the current will not be the same as if an external torque is applied to the shaft, with the same servomotor supply voltage. In addition, a servo drive is called not just a drive, but a complex system that has a drive, a rotation angle sensor and feedback that compensates for all external and internal factors. If the servo works perfectly, then its model is given by the developer, in which case the voltage applied to it or the applied current uniquely determines the angle of rotation or rotation speed.
Either the authors create a system with servos, and then their operation requires models of drives as such, but not models of servos, or the authors use ready-made servos, and then no mathematical models are needed at all.
Table 5 also raises a lot of questions. If the individual joints are numbered from nearest to the base to nearest to the end, then it is natural to expect that the joint with a lower number has more inertia and less acceleration, as well as more torque, more power. As you move away from the base, the inertia should fall, the possible speed and acceleration should increase. Table 5 shows no such pattern. At the very least, it should explain what is presented in this table, and for what reason such parameters are given.
Apparently, the authors consider the mathematical model to be the main achievement. The formulas in section 3 are given very sloppily. Instead of a sum with an ellipsis, the sum sign should have been used, which is customary in mathematics, indicating the limits of the indices over which the summation is carried out. Font sizes in formulas vary, as do the ratio of height to width of letters and numbers. This gives the impression of slovenliness. In line 188, italics were not used, which should have been done for the unity of notation in the formulas. The font in lines 223, 228 - 231 and beyond is unreasonably large.
It is not clear what "0 .... 00 ..... 01 ........ 00" means - how many numbers are in the line, what is "00" - are these two different zeros, or one value? How many numbers are there where the ellipsis is used?
In line 222, the well-known equation is written in such a way that it is difficult to recognize. Between the letters denoting matrices, either no signs should be written at all, or a multiplication sign can be written, for example, in the form of a dot located at half the height of the characters, but not at the base of the characters, because such a dot means exactly the punctuation mark “dot” or decimal sign, but not the multiplication symbol.
The ratio in line 271 is not clear, there is an “infinity” symbol, what exactly it means in this case is not clear.
In relation (15), at the beginning of the second, third and fourth lines, an incomprehensible combination of the equals symbol and a closed bracket is used three times: =)
Such a combination does not make any sense in mathematical relationships.
Perhaps the authors used a smiley?
Such a casual design of the article does not allow it to be taken seriously.
The results are not clear, as well as how they are obtained, and how they can be used.
It is recommended to reject the article.
Author Response
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Reviewer 2 Report
The paper deals with the analysis of the parameters of ABB industrial robots and the solution of their stability using Lagrangian mechanics and knowledge base rules in a fuzzy approach.
However, in the paper, the authors declare as a contribution also procedures that are common, e.g.:
p. 2, l. 90: "This focus on stability represents a novel concept within the field."
In fact, stability is a minimal requirement; others are precision and quality of control.
p. 11, l. 330-332: “A set of rules has been established to determine the status of stability within a fuzzy system, employing the Mamdani algorithm”.
Mamdani's algorithm is the simplest in fuzzy control, the question is why the authors did not use the more sophisticated Takagi-Sugeno algorithm.
There are a number of inaccuracies in the text:
p. 8, l. 224, 225: "U, C and D 224 are the matrix coefficient" - in fact in the state space description U represents the vector of input signals.
The triangle symbol for the derivative in formulas (6), (7), (8) is unusual.
The label of Table 2 is missing on page 4.
Some symbols from Table 2 are not explained.
The label for Figure 1 is on another page than the figure itself; floating objects should be used in the text to avoid such tearing.
Typos
p. 1, l. 37: "that exhibit s nonlinearity" - : "that exhibits nonlinearity
p. 4, l. 145: "Table 2.Table 2." - duplication
Typography:
The size of the mathematical symbols in the free text on pages 3, 4 and following greatly exceeds the size of the letters of the text. The rules for typesetting mathematical symbols in equations are not always respected. The text would benefit from the use of a LaTeX template.
Author Response
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Reviewer 3 Report
The paper is interesting and well structured. The topic is relevant and usable. I have few comments:
1. Why authors used for fuzzy variable Stability triangular values - trapezoidal or quadratic will be much better?
2. The overall architecture of fuzzy expert system is quite simple - what is the main advantage of this system?
3. I recommend to add other details about experimental verification of expert system.
Author Response
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Reviewer 4 Report
- The work on stability-based fuzzy controller design is interesting. However, it is limited to simulation environment. Authors are invited to add experimental results. - It is mentioned in the start of Abstract "In previous studies, stability has been evaluated based on a small number of manipulator parameters; as a result, little is known about stability.". This is not completely true since stability has been extensively studied in context to robotic manipulators. - It is claimed that "A novel mathematical approach to stability is developed". Please explicitly mention the novelty of the proposed modeling approach. - The title is too generic. I suggest adding the type of the controller designed in the title to give more specific information. - Abstract could mention the DOF of the arm you are considering in the study. - It seems that you are considering rigid-link manipulators. If this is the case, then the following statement is not relevant to the present research: "The flexibility of a robot is depending upon the flexibility of its joints, which in turn is influenced by the flexibility of its links [16]." - Also, [6], being the reference on a flexible robot is to be replaced with a reference to non-linear control of rigid link manipulators e.g. 'Fault-tolerant scheme for robotic manipulator - Nonlinear robust back-stepping control with friction compensation' - Some of the literature review needs to be updated. e.g. given the focus on stability using a fuzzy controller, 10.1109/LRA.2023.3286176 (2023) and 'Robust fuzzy sliding mode controller for a skid-steered vehicle subjected to friction variations' (2021) are relevant. - With reference to Table 1, please include a (labelled) kinematic representation diagram showing various links, joints and frames. - How has the novel formula given on Line 270 been validated? - How the authors compare their stability analysis with standard stability theorems (like e.g. Lyapunov)? - There are many typos and linguistic issues. SOME of them are mentioned below: -"exhibit s" - "are presented in Table 2.Table 2." - In Table 3, unit of voltage is missing - In Table 4, unit of Resistance is missing - Make the nomenclature consistent: L1 or L1(with 1 as subscript)? - In Table 5, units of acceleration and Moment of Inertia are missing. Same comment for Table 6. - Make sure that all symbols and nomenclature are defined before or immediately after their first usage. - Units for quantities plotted on x,y,z axes in Graphs are missing. - and so on...Moderate English language editing required.
Author Response
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Round 2
Reviewer 1 Report
The paper is OK
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Reviewer 2 Report
The paper deals with the analysis of the parameters of ABB industrial robots and the solution of their stability using Lagrangian mechanics and knowledge base rules in a fuzzy approach.
In my first review, I had several comments, e.g., on the questionable contribution of the paper, the choice of the fuzzy control algorithm, and the typography and format of the paper. The formulations have been corrected, the contribution has been more clearly justified, and the format of the text is now suitable. A number of additions have resulted from other reviewers' comments.
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Reviewer 3 Report
Thank you for comments and reply for all my comments, the paper can be accepted.
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Reviewer 4 Report
The revised paper has been significantly improved and may be considered for publication.
Moderate editing of English language required
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