A Simplified Vehicle Dynamics Model for Motion Planner Designed by Nonlinear Model Predictive Control

Round 1

Reviewer 1 Report

The paper was written about finding a new vehicle dynamics model to be used for motion planning algorithm, aiming for low computation cost. There are some parts that are not so clear for me. The simplified model does not give any new findings about the vehicle dynamics model compared to the classical ones and clearly show why the computation time was reduced.

1. It is interesting to see the graph showing lateral and longitudinal acceleration in X-Y graph implying the range of equivalent tire force usage.
2. I could not see any results shown in the section 3 of the paper that SDM fit well with the real driving experiment data. Can the authors prove this point?
3. What is the function behind Figure 11. relationship between the curvature and the desired speed?
4. Can the authors show the driving course used in the motion planning part in Section 4?
5. In Figure 5, the graph of longitudinal force in con.1 does not clearly appear. Can the authors show it clearly?
6. In Figure 12 the range of desired velocity is only from 5m/s. It will be better if the model can handle the vehicle dynamics problem in extremely low speed region, useful for parking maneuver. How do the authors consider about this issue?  In addition , please indicate the units of each evaluation index in Fig.12.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, authors propose a simplified vehicle model for motion planner designed by nonlinear model predictive control. The manuscript subject falls into the journal topic and could be interesting for the automotive engineers. The manuscript is well documented and relatively well written.    

Reviewer’s concerns:

1. Lines 93-108. It is not clear what is really new in this paper.
2. Line 114. Terminology used is not consequent. For instance: line 114 – it refers to the normal driving conditions and in line 116 it is about of natural driving data collected. Both should be explained. Why the wet conditions are not included in? Because are not normal or natural?
3. Lines 159-160. Terminology is questionable: ‘According to the characteristics of the kinematic and single-track models [22],’ However, in ref. [22], Section II, there are: A. Kinematic bicycle model and B. Dynamic bicycle model. It is not so clear that the single-track model is identically with the dynamic model, and it needs a short explanation.
4. Authors refer to 4 models (see Fig. 9): KM, STM, CDM and SDM, but only two are described (CDM and SDM). Authors could give a brief description of the two models, kinematic and single-track, in an appendix to the manuscript, including the equations of motion in accordance with the notations used in this article for the reading comfort.
5. All models are the basic models’ ones: the bicycle model and the nonlinearities are only of geometric nature. More complex models are known from literature, including the models with two wheels per axle and the nonlinearity of the lateral force depending on the . Authors should address this matter.
6. 3. Model is not properly presented, and many notations are not explained: e1, e2 (are explained in the lines 280-281, too far from the model), alfaf, alfar, Fyf, Fyr and others. Other quantities should be represented in fig. 3: lf and lr. Further on, other quantities are not involved in the equations of motion: vf, vr, Fyf, Fyr e1, e2. It needs more detail to have a clear and comprehensive description of the model.
7. Table 1. it must be specified to which type of vehicle the parameter values correspond.
8. 10 should be carefully explained and the notations.
9. Table 2. Many symbols are not explained and do not appear in the mathematical model. For instance: N, T, Q, R.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thank you for answering the questions. 

Can the authors additionally explain the results shown in Figure 15  why the difference in vehicle trajectory Y occurs after X >=130m in the motion planning results?

The difference in steering angle and driving force can be observed. It is not clear about the reasons (in physical/vehicle dynamics manner) why such difference occur in the motion planning process.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript has been improved and can be published as is.

Round 3

Reviewer 1 Report

Thank you very much for your reply. I have confirmed the response.