Self-Adaptive Path Tracking Control for Mobile Robots under Slippage Conditions Based on an RBF Neural Network

Round 1

Reviewer 1 Report

The contribution deals with a self-adaptive path tracking control for mobile robots under slippage condition. The paper clearly explains the kinematic and dynamic model of the robots and the algorithm of the improved controller. The paper presents an extensive literature review with lots of methods with their strengths and weaknesses. It is also well structured.

Please find below some comments:

1. About the modelling of the wheeled mobile robot, why not using the multibody approach to take into account the holonomic constraint automatically and gather the inertia properties of each body individually: rotor inertia, wheel inertia, car body, etc...
2. For more realistic simulations, authors might want to include motor equations (including voltage computation and back eletromotive force) and gearbox inertia (+ reduction ratio).
3. Why the z direction (vertical) is not accounted in the model? It would be rather important to take into account the vertical stiffness of tyre penetrating into the ground (tyre model).
4. In the introduction, authors should also mention that predictive controllers have been used on wheeled mobile robot to decrease energy consumption and tracking error. Also, the following contribution presents a complete dynamic model of wheeled mobile robot:  H.N. Huynh, O. Verlinden, A.V. Wouwer, "Comparative application of model predictive control strategies to a wheeled mobile robot",
   Journal of Intelligent & Robotic Systems 87 (1), 81-95
5. What is alpha factor of momentum and how to determine it?
6. Where does equation 9 come from ? To my understanding, e_theta causes the error in position, why should authors sum both errors (lp * e_theta + ep) ?
7. What applications are targeted with this robot, and such speed (1 m/s)? Is the speed chosen to show slippage?
8. English should be reviewed. Find some corrections in the attached .pdf.

Author Response

Thanks for your comments concerning our manuscript algorithms-1267318 entitled “Self-Adaptive Path Tracking Control for Mobile Robots under Slippage Condition based on a RBF Neural Network”. Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and made the corresponding corrections, and please refer to the attachment for details.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors present the development of a complex controller involving an hybridization between neural networks and a traditional controller. The presentationo can be improved, but the theory behind it seems solid, although some aspects are obscure. The validation is via dynamics simulation. No experimental campaign is presented.

The paper has merit, but I'd like the authors to clarify some points. The following remarks have to be addressed before the paper can be considered, in my opinion.

- It is not clear to me if disturbances are added in the model to model real-world measuring accuracy and environmental factors (non-constant slip ratio, slippery surfaces, ground discontinuities etc.) I think the authors should clarify this point: how ideal is their implementation?

- How was the PID tuned? Please share details; the performance is highly influenced by the type of tuning.

- Fig 6 and 7; it seems that the robot undergoes a rapid change in direction at roughly X = 30 m and X = 160 m; why didn't you ease the robot in the sinusoidal path? In this case what I find important to see is precisely that moment. The authors shall present a zoomed version of the plots for either the initial point of the curve, to show the behavior of the system in that very sharp discontinuity. The sinusoidal curve is much less interesting, compared to this. Please replicate the a)b)c)d) structure of the figure, but for the discontinuity only; based on the timeline, I'd say between 25 and 40s. I'd like to state that, given the lack of physical implementation, this part is critical for the acceptance of the paper, so please have care of doing it transparently, clearly and accurately.

- Line 38: "A number of literatures", please correct, e.g. "A number of works in literature"; many such mistakes are present in the paper. I recommend a careful proofread.

- Regarding Fig. 1 and Section 2.1, the authors mention \phi_L and \phi_R, but the robot is 4-wheeled. Are the front wheels driven? Are they steered? Please address this.

- I'd rather not see the letter "i" used as anything else than the imaginary number, except in the case this is an established practice. I suggest the authors select another symbol.

- Eq. 15 and 16, please do without the \dot; the equations seem scalar and the \dot usually indicates the dot-product. If the intent was to indicate the simple product, the established syntax is to avoid the explicit symbol for the product operation.

- Line 211; never start a sentence with a symbol. Please correct, e.g. "The terms \Delta [...]".

- Fig. 5; why are the slip ratios of the left and right wheels different? Please discuss this in the text.

- Fig 6 and 7; please slim down the line widths in order to better show the plotlines, and fix colors. a) is fine in both figures, but the others would benefit from a replot. In b) c) and d) (both figures) use primary colors and avoid using dashed lines unless necessary (in c - there you could use blue and red plotlines).

The lack of physical implementation worries me, in general. This type of analysis usually breaks down in the experimental part because of the influence of exogenous factors (environment unpredictability, inaccuracy of characterization of parameters, discontinuities, etc.). For this reason, even though I acknowledge that they intend to do this in a future article, I'd like to strongly encourage the authors to implement at least a very simplified experimental campaign with a commercial robot. A non-optimal alternative would be to implement a dynamics simulation using commercial software (e.g. ADAMS).

Author Response

Thanks for your comments concerning our manuscript algorithms-1267318 entitled “Self-Adaptive Path Tracking Control for Mobile Robots under Slippage Condition based on a RBF Neural Network”. Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and made the corresponding corrections, and please refer to the attachment for details.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The reviewer thanks the authors for providing in depth corrections. The paper can be accepted in the present form.

Reviewer 2 Report

The authors addressed most of my concerns. The only open question remains whether or not a multibody dynamics simulator implementation or a physical implementation is required... I did suggest to include it, but I'll leave this to the authors to decide. The paper is acceptable.