Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles

Round 1

Reviewer 1 Report

The presented work is very interesting and well written. It clearly describes a methodology for developing automated longitudinal control for battery electric vehicles based on nonlinear recursive B-spline approximation. I realise it is outside the scope of this paper as this paper presents the methodology but I would love to learn more about the implimentation/verification/validation of the proposed methodology. This is documented without much detail in the current work. Perhaps there is some other manuscript that can be referenced? 

The following is a list of minor questions/typos/advice I have to make the document even better. 

L86: "train of and by defining..." = "train and by defining..."

L105-108: the work does not take the power required by auxiliaries into account but in principle there is no reason why this could not be accounted for too right? Could it significantly alter the outcomes? and if so wouldn't that make it even more important for using the described method over other methods?

Figure 2: in the text it mentions that the Trajectory module has the "selected driving mode" as an input. is that part of "vehicle data"?. Also the text explains that ATFM and AEPM are calculated for "tracking the planned trajectory". do they not need some form of trajectory input? 

L150: it is explained that the models only consider braking via recuperation. so how is dealt with the situation that the hydraulic brakes are activated?

L219-220: what if there is no legal speed limit. for example on the German autobahn? how is dealt with such a case (certainly considering this work is being done in conjunction with a vehicle manufacturer known for its fast cars! 

L224-225: you mention "in test drives we adapted the characteristic curve to the vehicle characteristics". can you explain more how you did this? or give a reference to where more can be found on the method.

Page 9 first line: "Its value of is given by..." Do you mean "Its value is given by... "? 

L241: "This experimentally derived combination is used in the remainder of this work"  How did you find these? Maybe reference to other work? 

L257: "I denotes the I" ?? unclear what is meant. 

L296-297: for higher Rp-1... ...react more the road slope". Please explain a little bit more because my interpretation is the opposite - there is less reaction to road slope... 

L370: "...with fewer energy..." change fewer to smaller or less. 

L374-375. can you provide evidence that vlim,map,vdot was not exceeded?  

L381: "...achieves with the..." change to "... achieves the.." 

Author Response

Dear Reviewer,

We would like to thank you very much for taking the time for the review and your detailed comments and suggestions for further improvement of the manuscript. Please find our answers below. In the attachment ManuscriptWithHighLightedChanges we highlighted additional text green and reformulated paragraphs yellow. We hope that our adaptions meet your approval and look forward to your response.

The presented work is very interesting and well written. It clearly describes a methodology for developing automated longitudinal control for battery electric vehicles based on nonlinear recursive B-spline approximation. I realise it is outside the scope of this paper as this paper presents the methodology but I would love to learn more about the implimentation/verification/validation of the proposed methodology. This is documented without much detail in the current work. Perhaps there is some other manuscript that can be referenced? 

Assuming that with methodology you mean the algorithms RBA and NRBA, we added a sentence in the contributions section, in which we refer to the preceding publications that are the basis for the manuscript, in which we focus on an automotive application. In the additional sentence in L82-83 we state that investigations of theses algorithms as well as an implementations are provided in the previous publications.

The following is a list of minor questions/typos/advice I have to make the document even better. 

L86: "train of and by defining..." = "train and by defining..."

We corrected this error.

L105-108: the work does not take the power required by auxiliaries into account but in principle there is no reason why this could not be accounted for too right? Could it significantly alter the outcomes? and if so wouldn't that make it even more important for using the described method over other methods?

In principle, the power required by auxiliaries should be included. As stated in L126-128 and in the cited reference, they can contribute to the total energy consumption significantly. In the winter when the passenger cabin and HV battery needs to be heated, or during the summer, when the vehicle was parked in the sun and the air conditioning is needed, an investigation of the energy consumption for the following ride including the auxiliaries should come to very different results than under usual conditions. The reason why we decided to neglect auxiliaries, is the lack of data regarding the energy consumption of such components for certain environmental conditions.

There are also some auxiliaries that are only activated occasionally during a longer drive. An example is the air conditioning compressor, if there is only moderate demand for cooling. In these cases, a global optimization approach such as dynamic programming, to which knowledge about the whole route ahead is given, should be able to shift the activation times to some extent to situations with low total power requirements. For that reason I think that regarding the energy optimization potential such global methods, although they are much more computationally expensive, can be superior to local approaches such as the one we present.

Figure 2: in the text it mentions that the Trajectory module has the "selected driving mode" as an input. is that part of "vehicle data"?.

Thank you for that hint. We added in Fig. 2 the driving mode as an input because vehicle data mainly refers to sensor measurements.

Also the text explains that ATFM and AEPM are calculated for "tracking the planned trajectory". do they not need some form of trajectory input? 

Both ATFM and AEPM work independently of trajectories. They only return the required traction force and power, respectively, for a given combination of velocity and acceleration including the slope influence. These inputs are calculated while planning the trajectory at a certain point in time in case of AEPM and while evaluating the planned trajectory at a certain point in time in case of ATFM. We came to the conclusion that first two sentences in the subsections 3.3 and 3.4 were not precise enough and might confuse the reader, so we reworked them.

L150: it is explained that the models only consider braking via recuperation. so how is dealt with the situation that the hydraulic brakes are activated?

While hydraulic brakes are active, we do not update the models. The reason is that the force resulting from the hydraulic brake is not exactly known because the friction coefficient between brake disc and brake pad changes and therefore would need to be estimated as well. Therefore we only update models without presence of the additional uncertainty coming from the hydraulic brakes. We added a reference in section 3.2 (see L171-175) and the reason for not considering hydraulic brake force in the models.

L219-220: what if there is no legal speed limit. for example on the German autobahn? how is dealt with such a case (certainly considering this work is being done in conjunction with a vehicle manufacturer known for its fast cars! 

We added L245-247, in which we mention how we take into account the case that there is no legal speed limit. In this case, we set the upper limit to a value that varies with the selected driving mode.

L224-225: you mention "in test drives we adapted the characteristic curve to the vehicle characteristics". can you explain more how you did this? or give a reference to where more can be found on the method.

We added in section 3.6.1 an explanation of the characteristic curve in L251-254. The approach for adaption of the characteristic curve and other parameter is explained in section 4.2, which we significantly extended. The section describes not only the general approach but also which kind of road sections we used to adapt which parameters.

Page 9 first line: "Its value of is given by..." Do you mean "Its value is given by... "? 

That is right. We removed the redundant word.

L241: "This experimentally derived combination is used in the remainder of this work"  How did you find these? Maybe reference to other work? 

We moved the sentences that refer to the specific weighting combination to L289-290 and added a more detailed explanation of the origin of this weighting combination in L290-296. Thereby we also refer to previous publications.

L257: "I denotes the I" ?? unclear what is meant. 

Instead of the second I, the explanation of the parameter I should have been displayed. We corrected this and rearranged the following sentence, see L295-296.

L296-297: for higher Rp-1... ...react more the road slope". Please explain a little bit more because my interpretation is the opposite - there is less reaction to road slope... 

We added a more detailed explanation in L334-339.

L370: "...with fewer energy..." change fewer to smaller or less. 

We adopted your suggestion.

L374-375. can you provide evidence that vlim,map,vdot was not exceeded?  

As we solve an unconstrained trajectory optimization problem, it is not ensured for the general case that the trajectories stay below the upper speed limit but only avoided by the chosen parameterization. However, we added in L430-431 a reference to Fig. 5 in order to support our statement. In this figure we use the same temporal safety margin value to the upper speed limit and also penalize the power demand strongly.

L381: "...achieves with the..." change to "... achieves the.." 

We removed the redundant “the”.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper is well written and very interesting. Before the publication, some issues need to be addressed. 1) The novelty and contribution of this work could be further clarified. 2) The literature review could be further improved by adding some recent works,
for example: A review of motion planning techniques for automated vehicles;
driving-style-based co-design optimization of an automated electric vehicle: a cyber-physical system approach;
Control of connected and automated vehicles:State of the art and future challenges;
A Personalized Behavior Learning System for Human-Like Longitudinal Speed Control of Autonomous Vehicles.

Author Response

Dear Reviewer,

We would like to thank you very much for performing the review and for your suggestions for further improvement of the manuscript.

We found your suggested additional works very beneficial for the manuscript as they also include approaches, which had not been mentioned in the manuscript yet, e.g. learning-based methods. Therefore we added your suggested works to our literature review in L49-53 and L60-66.

Among your suggested references are also additional examples regarding battery electric vehicles which indicates that vehicle control systems for battery electric vehicles on their own are no novelty anymore. Keeping this and your suggestion for further clarification of the novelty and contribution in mind, we adapted sections 1.2 and 1.3. Thereby we tried to define the research gap more precisely and to state more clearly in which way and to which extent we think contribute to closing the identified gap.

In the attachment ManuscriptWithHighLightedChanges we highlighted additional text green and reformulated paragraphs yellow. We hope that our changes fulfill your expectations and look forward to your response.

Author Response File: Author Response.pdf