A Tube-Based Model Predictive Control for Path Tracking of Autonomous Articulated Vehicle

Round 1

Reviewer 1 Report

This paper presents the tube-based Model Predictive Control (MPC) for path and velocity tracking of an autonomous articulated vehicle. Simulation results show that the proposed algorithm achieves the smallest path-tracking error compared to the baseline algorithms and demonstrates robustness to several external disturbances. This topic is interesting and practical. Here are some questions/remarks to help improve the overall quality of this study.

1. For path tracking of autonomous articulated vehicles, the authors listed many publications, but what are their advantages and shortcomings? The literature review should point out the corresponding shortcomings to support the proposed method.

2. There are many methods proposed for path tracking control, but some representative literature is not introduced in the paper. Such as, Trajectory-Tracking Controller for Vehicles on Inclined Road Based on Udwadia-Kalaba Equation;

3.  The schematic diagram presented in Figure 1 is overly simplistic, making it difficult for readers to grasp the specific methodology and implementation logic proposed in this study.

4. How are the parameters Q and R adjusted for the MPC and Tube-based MPC controllers in the simulation tests? Furthermore, what measures have been taken to ensure that the controller parameters for MPC and Tube-based MPC are optimal? It is recommended that the authors provide relevant explanation to persuade readers in this regard.

5. Does the algorithm proposed in this paper impose an additional computational burden on the onboard controller?

6. The main differences or contributions between this paper and the following literature need to be explained in detail.

Jeong D, Choi S B. Tube-based Robust Model Predictive Control for Tracking Control of Autonomous Articulated Vehicles[J]. IEEE Transactions on Intelligent Vehicles, 2024, 9(1): 2184-2196.

7. In Figure 5 (k-l), both the front and rear body’s LTR from the Stanly algorithm exceed 1. Why doesn't the vehicle experience rollover and instead restore balance?

 Moderate editing of English language required

Author Response

Please check the attached file. Thank you for the comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presents a tube-based Model Predictive Control for path and velocity tracking of an autonomous articulated vehicle. A well-structured introduction and overall architecture is provided. The proposed algorithm is validated in simulation environment both noise-free and with noise injection to represent real-case scenarios.  Key performance indices are used to enrich path tracking performance evaluation giving a complete overview on results of the different algorithms.

Minor/typos

·       Line 88: “ symbol should be removed.

·       Line 357: “there is some set E that e remains inside for all time”, authors should make this sentence clearer.

·       Line 381: for ease of reading, label to figure “c” should be on the previous page.

·       Line 390: “DGPS” acronym is used but no explanation to what it stands for is given.

·       Line 694: “the proposed algorithm had the smallest maximum value for both lateral and heading errors” It is not true for heading errors based on table 3.

·       Line 714: “criteria” and “noise” are reported twice, it should substitute with “MPC” and “Proposed”

General considerations

·       4.2 section: Information about experimental results used to validate kinematic model should be provided (how they are acquired, on which vehicle), it could be better to distinguish this information from the “tube based mpc” paragraph.

·       5 section: The general workflow in “results” section should be revised, this section should include simulation environment referencing to already defined model for both plant and controller. In this case there is an introduction to a different plant model for simulation concerning a nonlinear dynamic bicycle model whose tire model is referred to as STI. Introducing a sub-section in previous chapters dedicated to employed plant models could be better, also explaining or referencing to this specific tire model.

Furthermore, the paragraph about “base algorithms” should not be included as a part of the results section. This section also introduces a model-free controller approach whose dissemination would be clearer if introduced in a dedicated “controller model section”.

·       5.3 section: Figure 6 (b)(c) it would be preferable to also have the noise-free signals reported in the same plot.

·       In abstract and conclusion (section 6) the author refers to “several external noises” but only one type of noise (gaussian white noise) is applied to every signal.

Minor/typos

·       Line 88: “ symbol should be removed.

·       Line 357: “there is some set E that e remains inside for all time”, authors should make this sentence clearer.

·       Line 381: for ease of reading, label to figure “c” should be on the previous page.

·       Line 390: “DGPS” acronym is used but no explanation to what it stands for is given.

·       Line 694: “the proposed algorithm had the smallest maximum value for both lateral and heading errors” It is not true for heading errors based on table 3.

·       Line 714: “criteria” and “noise” are reported twice, it should substitute with “MPC” and “Proposed”

Author Response

Please check the attached file. Thank you for the comments.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The revised version has reached the necessary quality level.