Nonlinear UGV Identification Methods via the Gaussian Process Regression Model for Control System Design

Round 1

Reviewer 1 Report

In this paper, two kinds of black box models are identified aimed to estimate the output of a ground robotic system. One model is based on Gaussian Process Regression (GPR) and the other is based on Wavelet-based Nonlinear Autoregressive Exogenous (WANARX) modeling. Both modeling strategies are applied to experimentally identify the dynamic behavior of an AeroSpace AuTonomous Robot.

 

The paper is clear and well-written. This reviewer suggests pointing out not only the application but the theoretical novelty of the paper, as well as, making available to the general public the data for training and validation, as it is common in most of the mdpi journals. Data curation is also a procedure that should be included and discussed.

Author Response

Dear reviewer,

we thank you for the review and for the insightful comments. The theoretical background is presented in:
"Juš Kocijan, Agathe Girard, Blaž Banko & Roderick Murray-Smith (2005) Dynamic systems identification with Gaussian processes, Mathematical and Computer Modelling of Dynamical Systems, 11:4, 411-424, DOI: 10.1080/13873950500068567 ",
which is included in the references.
Also, we added a paragraph about data curation (paragraph 2.3), as you kindly suggested.

Reviewer 2 Report

In this paper a Gaussian Process (GP) Regression is proposed as nonlinear modeling technique for System Identification. GP framework is introduced and a practical implementation is reported to demonstrate the validity of the method alongside a classic NARX.

1.     The manuscript is interesting and well written. The novel contributions of the study need to be further highlighted. For instance, please explain your novelty in context of the following recent relevant article.

Chang, A. H., Hubicki, C. M., Aguilar, J. J., Goldman, D. I., Ames, A. D., & Vela, P. A. (2020). Learning terrain dynamics: A gaussian process modeling and optimal control adaptation framework applied to robotic jumping. IEEE Transactions on Control Systems Technology, 29(4), 1581-1596.

2.     The latest trends in NARX systems identification are not discussed. For instance, fractional calculus based adaptive algorithms and evolutionary/swarm optimization techniques. On order to give a complete and current state of the art about NARX system identification, please provide a detailed literature review of NARX identification. In this regard, you may see the profiles of Prof. Zeshan Aslam Khan and Prof. Ammara Mehmood.

3.     What is FIT in Eq. (19)? What extra information one can get from (19) when comparing with (18)?

4.     Please rewrite the conclusions to summarize the main findings of the study.

5.     Check the whole manuscript for typos or grammatical errors.

Author Response

Dear reviewer,

thank you for the review and for the insightful comments.

1. Chang et al. provide a GP model that describes an unknown external force to improve the performance of a 1D jumping robot. The disturbance-free dynamical model of the robot is found using first principle modeling, since it is a simple 1D dynamical system. The GP is employed to model the behavior of the external force given the position of the foot and the rod, modeling the major external disturbance whose influence is taken into account in the dynamical model. Instead, our paper uses a system identification nonlinear model (NARX) to describe both dynamics and, implicitly, disturbances of a ground robot, resulting in a black-box, data-driven approach, in which we don't specify any a priori knowledge about the robot dynamics. Our approach should be used if, for some reason, the dynamics and disturbances of the robot are difficult to be modeled by physical equations. This is a different scenario with respect to Chang et al., in which the dynamical model is easily derived.
2. We added in the introduction a discussion about latest trends in NARX system identification as you kindly suggested.
3. The FIT is 1 - NRMSE (Normalized Root Mean Square). It is a measure of how much better the model is in reproducing the observed data relative to the mean of the data. We added the definition in section 3.3.

We also re-wrote some parts of both conclusion and introduction as to further highlight the contribution

Reviewer 3 Report

The paper proposes identification methods for a ground robotic system. Overall, the paper is well written. I have two comments as follows.

1) Please give a proof of closed-loop stability in control.

2) Some control methods did not use any identification procedures, e.g., Robust adaptive dynamic programming based online tracking control algorithm for real wheeled mobile robot with omni-directional vision system. Transactions of the Institute of Measurement and Control. 2017;39(6):832-847. doi:10.1177/0142331215620267, Luy NT, Thanh NT, Tri HM. Reinforcement learning-based intelligent tracking control for wheeled mobile robot. Transactions of the Institute of Measurement and Control. 2014;36(7):868-877. doi:10.1177/0142331213509828. Why do the authors employ the identification in control design. Please compare and analyze with the existing ones.

Author Response

Dear reviewer,

thank you for the review and for the insightful comments.
In our paper, we discussed the design and validation of a nonlinear ARX model using a Gaussian Process as nonlinear function to model the dynamics of our ground robot. This model shows good performance and exhibits some advantages over "classical" methods. Furthermore, we briefly discussed how identified models can be controlled by several controller structures, without providing a detailed study and implementation of this aspect. For this reason, no proof of closed-loop stability and tracking problems are analyzed, since a control system is not included in the paper. We are considering methods based on GP for the identification of the model, which will be used in future for a definition of a model-based control system.

Reviewer 4 Report

please see the attachment.

Comments for author File: Comments.pdf

Author Response

Dear reviewer,

thank you for the detailed review and for all the insightful comments.

1. GP-NARX is discussed in section 2 for what concerns the GP theoretical background, and in section 3.1, which has been revised.
2. We provided a more complete explanation of the system identification process in section 3.
3. We modified both introduction and conclusion to better highlight the paper contribution.
4. and 6. We added a discussion relative to Figure 7. The GP-NARX provides better performance with respect to WANARX as detailed in Table 3.
5. We added section 2.3 (Data Curation) in which we provide some methods used in literature to tackle the GP high computational cost.

Lastly, we corrected the statement regarding the hyperparameters, which are found directly by the toolboxes we used in Matlab, as specified in the manuscript in section 4.2 and 4.3.

 

Reviewer 5 Report

Trombetta et al. validated the Gaussian Process Regression model with clear illustration, comparison with NARX model and the experimental data using a ground robot. The reviewer has one question: The authors mentioned the high training time of the GP model. Is there any potential approach to address this issue?

Author Response

Dear reviewer,

thank you for the review and for the insightful comments.
As for you question, we added paragraph 2.3 (Data curation) in which we discuss the computational cost and how to address this major drawback of the GP.

Round 2

Reviewer 4 Report

I think this article can be accepted after some minor modifications. For example, "is N" in equation (21) should be changed to "N is".