# Correction: Jurj et al. Towards Safe and Sustainable Autonomous Vehicles Using Environmentally-Friendly Criticality Metrics. Sustainability 2022, 14, 6988

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- The old “Abstract” section mentions terms such as well-definedness and the intendedness of the metrics, which can be understood by the reader as if some of the metrics of Westhofen et al. [2] analyzed by us in the manuscript are not well-defined and do not work as intended. This is not what we mean. What we mean is if these metrics can be used as rewards in Artificial Intelligence (AI) for training Reinforcement Learning (RL) agents. Furthermore, in the abstract section, it is mentioned that we discuss the possibility of applying these metrics in RL training and propose a way to apply some of the metrics in a simple car-following scenario. This can be understood as if we already applied some of the metrics to the training process of the RL in this simple car-following scenario, which we did not. However, in the updated version of the manuscript, all the above-mentioned aspects are solved by us, and there is no more room for confusion or possible misunderstandings.

_{2}emissions of traditional vehicles as well as measuring the motor power used by electric vehicles. Third, we discuss the usefulness of using criticality metrics for Artificial Intelligence (AI) training. Finally, we apply a selected number of criticality metrics as RL reward component in a simple simulated car-following scenario. More exactly, we applied them together in an RL task, with the objective of learning a policy for following a lead vehicle that suddenly stops at two different opportunities. As demonstrated by our experimental results, this work serves as an example for the research community of applying metrics both as reward components in RL and as measures of the safety and environmental impact of AVs.

- 2.
- The old “Introduction” section only shortly mentions the existent criticality metrics found in the literature and does not clearly explain to the reader how such criticality metrics can be used for AI training. However, in the updated version of the manuscript, all the above-mentioned aspects are solved by us, and there is no more room for confusion or possible misunderstandings.

_{2}footprint explicitly into account. Furthermore, due to recent emergent paradigms, such as Green AI [13], which encourage researchers to move towards more sustainable methods that are environmentally friendly and inclusive, we also propose several environmentally friendly metrics that are used to create an environmentally friendly criticality metric, which is suitable for evaluating a critical scenario not only regarding safety but also regarding the environmental impact in a car-following scenario.

- 3.
- The old “Related Work” section mentions that the use of criticality metrics is not restricted to the evaluation of traffic scenarios but can be extended to the training of autonomous driving agents by integrating suitable metrics into the reward function. However, the reader can misunderstand this and think that such an application has not been proposed already and that we are the first ones who do it. We solved this problem in the updated version of the manuscript by stating and citing that such an application has already been proposed and we analyze in more depth the general requirements of such metrics for the use case of RL.

_{2}emission estimation. The power consumption of electric vehicles was also measured by [22–24].

- 4.
- The old “Mathematical Analysis of Criticality Metrics” section presents definitions of the criticality metrics that can make the reader think it is our own definition of the metrics because it is not clearly mentioned and cited by us which parts of the definition is from the original paper source and which is from the Westhofen et al. paper. Furthermore, as mentioned earlier regarding the “Abstract” section, the terms well-definedness, intendedness, and optimality do not clearly portray the scope and purpose of our paper. In the new version of the manuscript, we solve all the mentioned aspects and clearly marked the sources, verbatim quotations, and necessary adaptations.While Westhofen et al. put a lot of emphasis on an abstract, unifying presentation of the metrics, in our old paper, the necessary concretization for the case of a car-following scenario read, in parts, as unjustified criticism of Westhofen et al. We have removed this erroneous impression in the new version.

- (1)
- Replacing the title on page 3:

- (2)
- Replacing the paragraph spanning pages 3, 4, and 5:

_{i}, that measures the progress of actor i from an arbitrary reference point relative to a given route. All actor positions refer to the same reference point, so, for every two actors, i and j, it can be effectively decided whether actor i is in front of actor j (p

_{i}> p

_{j}), the other way around (p

_{i}< p

_{j}), or whether both actors are in the same position (p

_{i}= p

_{j}), which usually indicates the presence of a collision. Only in a few cases do we consider the position of the actor i as a vector quantity, p

_{i}, in the two-dimensional plane.

_{i}(t)), velocity (v

_{i}(t)) and acceleration (a

_{i}(t)), specific to actor i, are functions over time. The current time of a scene is denoted by t

_{0}, and if we refer to a state variable at time t

_{0}, we often omit the time parameter; i.e., we briefly write p

_{i}instead of p

_{i}(t

_{0}).

_{i}(t) is applied to future time points, then it is mandatory to specify a DMM for an in-situ computation. Typical DMMs arise from the assumption of constant velocity (p

_{i}(t

_{0}+ t) = p

_{i}+ v

_{i}t) or constant acceleration (${p}_{i}({t}_{0}+t)={p}_{i}+{v}_{i}t+\frac{1}{2}{a}_{i}{t}^{2}$).

- (3)
- Replacing the paragraph on page 5:

_{1}evidently should not pass with high speed.

**Crit. Metric 1**(Encroachment Time (ET), verbatim quote of [7]; see also [8,36])

_{1}takes to encroach a designated conflict area CA, i.e.,

**Applicability as a Reward Component in RL**

_{exit}and t

_{entry}exist, are uniquely determined, and methods to evaluate t

_{exit}and t

_{entry}are provided. According to [8], there is no prediction model for ET, and, hence, cannot be used for an in-situ assignment.

- (4)
- Replacing the paragraph on pages 5 and 6:

_{1}until A

_{1}exits the conflict area.

**Crit. Metric 2**(Post-Encroachment Time (PET); verbatim quote of [7] with agents’ identifiers swapped; see also [8,36])

_{2}passes CA before A

_{1}, the formula is

**Applicability as a Reward Component in RL**

_{exit}and t

_{entry}exist, are uniquely determined, and methods to evaluate t

_{exit}and t

_{entry}are provided. According to [8] there is no prediction model for PET, and, hence, it cannot be used for an in-situ assignment.

- (5)
- Replacing the paragraph on page 6:

**Crit. Metric 3**(Predictive Encroachment Time (PrET); see also [6–8])

**Applicability as a Reward Component in RL**

- (6)
- Replacing the paragraph on page 6:

**Crit. Metric 4**(Time Headway (THW), verbatim quote of [7] with the alignment of variable names; see also [8,37])

_{1}reaches the position of a lead vehicle A

_{2}, i.e.,

**Applicability as a Reward Component in RL**

- (7)
- Replacing the paragraph on pages 6 and 7:

**Crit. Metric 5**(Time to Collision (TTC), verbatim quote of [7] with formula adjustment to a car-following scenario and alignment of variable names; see also [8,38])

_{1}and A

_{2}collide …, or infinity if the predicted trajectories do not intersect …. It is defined by

**Applicability as a Reward Component in RL**

- (8)
- Replacing the paragraph on page 7:

**Crit. Metric 6**(Time Exposed TTC (TET), verbatim quote of [7] with the alignment of variable names; see also [8,39,40])

**1**denotes the indicator function.

**Applicability as a Reward Component in RL**

- (9)
- Replacing the paragraph on pages 7 and 8:

**Crit. Metric 7**(Time Integrated TTC (TIT), verbatim quote of [7] with alignment of variable names; see also [8])

**Applicability as a Reward Component in RL**

- (10)
- Adding one new paragraph on page 8 explaining the Time to Arrival of Second Actor (T2) metric and how it can be used for RL.
- (11)
- Replacing the paragraph on pages 8 and 9:

**Crit. Metric 9**(Potential Time to Collision (PTTC) [7]; see also [8,41])

_{1}and constant deceleration of A

_{2}in a car following scenario, where A

_{1}is following A

_{2}.” The PTTC is defined as follows:

_{0}= p

_{2}− p

_{1}, v

_{0}= v

_{2}− v

_{1}, and d

_{2}is the deceleration of A

_{2}.

**Notes**

_{1}, and the leading vehicle, A

_{2}, describes a downward opening parabola: $s({t}_{0}+t)={s}_{0}+{v}_{0}t-{\textstyle \frac{1}{2}}{d}_{2}{t}^{2}$. In a car-following scenario the distance is clearly greater or equal to zero at time t

_{0}. This guarantees the existence of a collision point where the distance is zero. Moreover, as we are interested in a collision at a time greater or equal to t

_{0}, the PTTC is given as the greater of the two roots. With d

_{2}> 0, we, therefore, obtain the Formula (9).

**Applicability as a Reward Component in RL**

- (12)
- Adding a new figure (Figure 1) on page 9:

- (13)
- Replacing the paragraph on page 9:

**Crit. Metric 10**(Worst Time to Collision (WTTC); verbatim quote of [7] with formula adjustment to a car-following scenario and alignment of variable names; see also [8])

_{1}(t

_{0}) resp. Tr

_{2}(t) denotes the set of all possible trajectories available to actor A

_{1}resp. A

_{2}at time t

_{0}….

**Applicability as a Reward Component in RL**

_{1}(t) is to be learned; therefore, one would have to consider only different traces for A

_{2}. The issues that TTC implies remain valid. In the already suggested challenging situations, one could think of training with respect to WTTC as some kind of robust RL training method, where several adversarial actions of A

_{2}are taken into account instead of restricting training to one (realized) maneuver of A

_{2}.

- (14)
- Replacing the paragraph on page 9:

**Crit. Metric 11**(Time to Maneuver (TTM) [7]; see also [8,42])

_{1}leads to collision avoidance or −∞ if a collision cannot be avoided.” The following definition of TTM is also from [7] and has been adapted to a car-following scenario:

_{1},m(t

_{0}+ t, t

_{0}+ s) denotes the predicted position of A

_{1}at time t

_{0}+ t if A

_{1}started performing the maneuver m at time t

_{0}+ s.

**Applicability as a Reward Component in RL**

- (15)
- Replacing the paragraph on page 10:

**Crit. Metric 12**(Time to React (TTR), verbatim quote of [7], with the alignment of variable names; see also [8,42])

**Applicability as a Reward Component in RL**

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- Replacing the paragraph on page 10:

**Crit. Metric 13**(Time to Zebra (TTZ), verbatim quote of [7] with formula adjustment to a car-following scenario and alignment of variable names; see also [8,43])

_{1}reaches a zebra crossing CA, hence

**Applicability as a Reward Component in RL**

- (17)
- Replacing the paragraph on page 10:

**Crit. Metric 14**(Time to Closest Encounter (TTCE) [7]; see also [8,44])

**Applicability as a Reward Component in RL**

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**Crit. Metric 15**(Headway (HW); verbatim quote of [7] with the alignment of variable names; see also [8,37])

**Applicability as a Reward Component in RL**

_{1}for velocities measured in m/s. Note that a velocity-dependent penalty term in the form (1.8v

_{1}− HW) is equivalent to the term v

_{1}(1.8 − THW) using the THW metric with constant velocity assumption for actor A

_{1}.

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- Replacing the paragraph on page 11:

**Crit. Metric 16**(Accepted Gap Size (AGS), verbatim quote of [7] with the alignment of variable names; see also [8])

_{1}at time t, the AGS … is the spatial distance that is predicted for A

_{1}to act, i.e.,

_{1}, t

_{0}, s) predicts […] whether A

_{1}decides to act given the gap size s.

**Applicability as a Reward Component in RL**

- (20)
- Replacing the paragraph on page 11:

**Crit. Metric 17**(Distance to Closest Encounter (DCE) [7]; see also [8,44])

**Applicability as a Reward Component in RL**

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**Crit. Metric 18**(Proportion of Stopping Distance (PSD), verbatim quote of [7] with formula adjustment to a car-following scenario and alignment of variable names; see also [8,36])

_{1,max}is the maximal deceleration available for actor A

_{1}.

**Applicability as a Reward Component in RL**

- (22)
- Replacing the paragraph on page 12:

**Crit. Metric 20**(Conflict Severity (CS) [7]; see also [8,32,46])

_{1}and A

_{2}. As an estimate for t

_{evasive}, Laureshyn et al. [32] proposed using the T2 indicator, i.e., t

_{evasive}= T2(A

_{1}, A

_{2}, t

_{0}).

**Applicability as a Reward Component in RL**

- (23)
- Replacing the paragraph on page 12:

**Crit. Metric 19**(Delta-v (∆v) [7,32]; see also [8,45])

_{1}and A

_{2}.

**Applicability as a Reward Component in RL**

- (24)
- Replacing the paragraph on page 13:

_{1}following another actor A

_{2}, the DST metric intends … required acceleration is always comfortable for the person in the vehicle.

**Crit. Metric 21**(Deceleration to Safety Time (DST), verbatim quote of [7] with formula adjustment to a car-following scenario and alignment of variable names; see also [8,47–49])

_{1}in order to maintain a safety time of t

_{s}≥ 0 s under the assumption of constant velocity v

_{2}of actor A

_{2}… The corresponding formula can be written as

_{0}= p

_{2}− p

_{1}.

**Applicability as a Reward Component in RL**

_{1}> v

_{2}and v

_{2}t

_{s}< s

_{0}, as under these conditions the formula provides correct values for the required deceleration in order to maintain a safety time. Large positive values should be avoided; positive values close to zero indicate that the Safety Time Distance has almost been reached.

_{s}= 0, this is possible, as shown in the following section on a

_{long,req}.

- (25)
- Adding one new paragraph on pages 13 and 15 about the DST metric and the limitations of its use for RL.
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- (27)
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_{long,req}) For two actors A

_{1}, A

_{2}at time t, a

_{long,req}is supposed to measure … Similarly, as for DST, this required acceleration should be comfortable.

**Crit. Metric 22**(Required Longitudinal Acceleration (a

_{long,req}) [7]; see also [8])

_{long,req}measures the maximum longitudinal backward acceleration required … by actor A

_{1}to avoid a collision [with A

_{2}] in the future.” We propose using the following modification of the definition in [7], where we assume that the maximal backward acceleration is constant over time.

**Applicability as a Reward Component in RL**

_{long,req}is an interesting metric that indicates the magnitude of deceleration required so that the following vehicle does not rear-end.

_{long,req}metric does not take into account any safety time, so in relation to the DST this means t

_{s}= 0. The DST with t

_{s}= 0 is then a variant of the metric (with swapped sign) for the case where the leading car drives with constant speed. Because t

_{s}= 0, cases (b) and (d) discussed for the DST do not apply.

_{long,req}metric thanks to its abstract definition: in this particular case, the following vehicle may still accelerate (at least for a short moment), and the inequality ${p}_{2}+{v}_{2}t\ge {p}_{1}+{v}_{1}t+{\textstyle \frac{1}{2}}{a}_{1}{t}^{2}$ has a positive solution a

_{1}> 0. However, since only non-positive values for a

_{1}are considered, the metric would return the value zero. Hence, we propose using the following definition for a

_{long,req}under a constant speed assumption for the leading vehicle:

_{0}= p

_{2}− p

_{1}.

_{long,req}can be used as a reward term that penalizes large negative values, especially values that indicate a required deceleration that is larger than the maximal possible deceleration of the agent. For a version of this metric that takes the maximal deceleration into account, see the BTN.

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_{lat,req}) The metric is intended to provide the minimal absolute lateral acceleration in either direction that is required … Similarly, as for DST, this required acceleration should be comfortable

**Crit. Metric 23**(Required Lateral Acceleration (a

_{lat,req}), see [7] and [8,37])

_{lat,req}[metric] is defined as the minimal absolute lateral acceleration in either direction that is required for a steering maneuver to evade collision.” Under the assumption of a constant acceleration model, the required lateral acceleration can be computed as follows [37]:

_{y}

_{,i}and v

_{y}

_{,i}denote the lateral components of the position and velocity vectors, respectively, of actor A

_{i}, and s

_{y}is the minimal lateral distance of the actors that is required to evade the collision. It can be calculated from the respective widths w

_{1}and w

_{2}of actors A

_{1}and A

_{2}as ${s}_{y}=\frac{{w}_{1}+{w}_{2}}{2}$.

**Applicability as a Reward Component in RL**

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- Replacing the paragraph on page 16:

**Crit. Metric 24**(Required Acceleration (areq) [7]; see also [8,37])

_{req}is in general an aggregate of the a

_{long,req}and a

_{lat,req}. We follow [7] and adopt the proposed definition of the metric “by taking the norm of the required acceleration of both directions”, verbatim with alignment of variable names as

**Applicability as a Reward Component in RL**

_{lat,req}is also included in this metric, criticality-reducing parallel movements to the vehicle in front cannot be excluded here without further countermeasures.

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- Replacing the paragraph on pages 16 and 17:

**Crit. Metric 25**(Lateral Jerk (LatJ); Longitudinal Jerk (LongJ) [7]; see also [8])

_{1,long}(t) or j

_{1,lat}(t), the longitudinal or lateral jerks of actor 1 at time t, and are taken verbatim from [7] with the alignment of variable names:

**Applicability as a Reward Component in RL**

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**Crit. Metric 26**(Accident Metric (AM), verbatim quote of [7]; see also [8])

**Applicability as a Reward Component in RL**

- (32)
- Adding one new paragraph on page 17 regarding the Collision Indicator (CollI) metric and its use for RL.
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_{1}, the BTN metric is defined as … so BTN has to be always smaller than 1.

**Crit. Metric 28**(Brake Threat Number (BTN); verbatim quote of [7] with the alignment of variable names; see also [8])

**Applicability as a Reward Component in RL**

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**Crit. Metric 29**(Steer Threat Number (STN); verbatim quote of [7] with the alignment of variable names; see also [8,37])

_{1}in that direction:

**Applicability as a Reward Component in RL**

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**Crit. Metric 30**(Conflict Index (CI); verbatim quote of [7]; see also [8,50])

_{e}is the predicted absolute change in kinetic energy acting on the vehicle’s body before and after the predicted collision.

**Applicability as a Reward Component in RL**

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**Crit. Metric 31**(Crash Potential Index (CPI), verbatim quote of [7] with the alignment of variable names; see also [8,51])

**Applicability as a Reward Component in RL**

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**Crit. Metric 32**(Aggregated Crash Index (ACI) [7]; see also [8,52])

_{j}in a tree where the parent nodes represent the corresponding conditions. Given a probabilistic causal model, let P(L

_{j}, t

_{0}) be the probability to reach L

_{j}, starting from the state in t

_{0}and let C

_{Lj}be the indicator, whether L

_{j}includes a collision (C

_{Lj}= 1) or not (C

_{Lj}= 0), so that the collision risk at S at t

_{0}is CR

_{Lj}(S, t

_{0}) = P(L

_{j}, t

_{0}) · C

_{Lj}.

**Applicability as a Reward Component in RL**

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**Crit. Metric 33**(Pedestrian Risk Index (PRI); verbatim quote of [7] with the alignment of variable names; see also [8])

**Applicability as a Reward Component in RL**

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**Crit. Metric 34**(Responsibility Sensitive Safety Dangerous Situation (RSS-DS); verbatim quote of [7]; see also [8,53]):

**Applicability as a Reward Component in RL**

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**Crit. Metric 35**(Space Occupancy Index (SOI) [7]; see also [8,54])

_{s}, t

_{e}]. The SOI is defined as

**Applicability as a Reward Component in RL**

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**Crit. Metric 36**(Trajectory Criticality Index (TCI); verbatim quote of [7] with the alignment of variable names; see also [8,55])

**Applicability as a Reward Component in RL**

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**Crit. Metric 37**(Collision Probability via Monte Carlo (P-MC); see also [7,8,56])

**Applicability as a Reward Component in RL**

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**Crit. Metric 38**(Collision Probability via Scoring Multiple Hypotheses (P-SMH) [7]; see also [8,57])

**Applicability as a Reward Component in RL**

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**Crit. Metric 39**(Collision Probability via Stochastic Reachable Sets (P-SRS) [7]; see also [8,58])

^{h}(t

_{k}) denote the probability vector of the states reached in time step t

_{k}for input partition h. These probability vectors are updated by a Markov chain model. The goal is to approximate the probability of a crash.

**Applicability as a Reward Component in RL**

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- Adding new paragraphs on pages 22 and 23 regarding the Lane Potential, Road Potential, Car Potential, and Velocity Potential, as well as their use for RL.
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**Crit. Metric 44**(Safety Potential (SP) [7]; see also [8,59])

**Applicability as a Reward Component in RL**

- (47)
- Adding new paragraphs on page 24 regarding the Off-Road Loss and Yaw Loss and their use for RL.
- 5.
- The old “Proposed Green-Based Criticality Metrics” chapter presents metrics that can give the reader the impression that they can be used on their own as reward components when training RL agents. However, this is not the case, and, therefore, in the new version of the manuscript, we present new, environmentally friendly metrics and explain their applicability as a reward component in RL.

- (1)
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- (2)
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_{2}emissions, in this section, we both collect corresponding metrics from the literature and propose an environmentally friendly criticality metric that combines not only the environmental impact but also the safety in a car-following scenario.

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_{2}Emissions Per KM According to the European Environment Agency [34], the average CO

_{2}emissions per km of a diesel-powered car … where d is the distance travelled by the vehicle in the drive in kilometers.

**Crit. Metric 47**(Dynamic-based Car CO

_{2}Emissions (DCCO2E))

_{2}emitted by the car on a given drive.

**Applicability as a Reward Component in RL**

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_{2}Emissions Saved (GECO2ES) The GECO2ES metric measures how much CO

_{2}is saved in an electric vehicle … where d is the distance travelled by the vehicle in the drive in kilometers.

**Crit. Metric 48**(Dynamic-based CO

_{2}Emissions Weighted Vehicle Performance (DCO2-EWVP))

_{2}emissions of the vehicle. We define it as follows:

**Applicability as a Reward Component in RL**

_{2}emissions are produced on average by different types of vehicles (powered by diesel, petrol, electricity from the grid, or by green energy) in the scenario.

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_{2}Emissions Weighted Safety Distance (CO2EWSD) With the previous metrics defined in this chapter, we now create a novel green-based criticality … is the ratio of time spent driving at a safe distance of the total time.

**Crit. Metric 49**(Electric vehicle’s power consumption (EVP))

_{2}emissions of petrol and diesel cars cannot be applied to electric vehicles, however, they also use power and are, therefore, not emission-free. As the amount of petrol or diesel can be expressed in terms of energy, it would be desirable to also compute the amount of energy used for electric vehicles. We use the approach of [22] here in order to compute the necessary motor power of an electric vehicle, being aware that there are very similar approaches in other works such as [24] or [23].

**Applicability as a Reward Component in RL**

- 6.
- The old “Usage of Criticality Metrics for AI Training” section presents a noncomplete theoretical discussion about the usefulness of the metrics for AI training. However, in the new version of the manuscript, we extended the discussion and provide the reader with a better understanding of the metrics and better explain how some metrics can be more interesting than others when selecting them for AI training.

- 7.
- The old “Application of the Metrics” chapter presents only a way to apply the metrics in a simple scenario, which, despite proving that certain metrics can be used for evaluating a critical situation in a scenario, are not actually applied as reward components in AI training. This is another major minus in the old version of the paper because it proves to the reader that the existing work lacks in quality and is incomplete without this aspect being covered. In the new version of the manuscript, we much better explained the scope and purpose of our experiments and described the entire scenario and the considered metrics used as reward components in RL training by also presenting the mathematical equations regarding the reward functions. We also compared all the trained metrics in order to provide the reader with a better understanding of which agent performed better by which metric. On top of that, we also evaluated how many CO
_{2}emissions were produced by different types of vehicles on the trained metrics.

- (1)
- Replacing the title on page 28:

- (2)
- Adding new paragraphs on pages 28–39 describing the implementation of the metrics as a reward function in RL as well as describing the simulation setup and the training results, followed by a comparison of the trained metrics results and an evaluation regarding their environmental impact, also including all relevant figures and tables.
- 8.
- The old “Conclusions and Future Work” section mentions that the paper investigates if the existent criticality metrics are well defined and work as intended. This can be misunderstood by the reader, as mentioned earlier, as meaning that some of the metrics of Westhofen et al. are not well defined or do not work as intended. In the new version of the manuscript, we clearly stated the scope and intention of the performed metrics analysis as being their applicability as a reward component in RL, as well as that the metrics were applied in AI training, providing the reader with valuable information regarding the reward choice.

_{2}emissions of traditional vehicles and a metric to measure the motor power used by electric vehicles, with the goal being the facilitation of their selection by future researchers who want to evaluate both the safety and environmental impact of AVs. Regarding the application of the metrics, we applied some of the metrics in a simple car-following scenario and showed in a simulation that our proposed environmentally friendly criticality metric, called DCO2EWVP, can be successfully used to evaluate AVs from the performance and environmental points of view. We also showed that AVs powered by diesel emitted the most carbon emissions (447 g of CO

_{2}), followed closely by petrol-powered AVs (379 g of CO

_{2}). Similar results are found using the EVP metric, and we find a correlation between the DCCO2E metric and the EVP metric. Considering that in our evaluation regarding the training of criticality metrics as reward components in RL, all models were trained for the same amount of training iterations, the fact that these results were so different, shows the importance of the reward choice. In conclusion, our work encourages future researchers and the industry to develop more actively sustainable methods and metrics that can be used to power AVs and evaluate them regarding both safety and environmental impact. Regarding the limitations of this work, we are aware that safety and sustainability are just two facets of autonomous driving and that their acceptance also depends on other aspects such as performance-to-price value, travel time, or symbolic value, as seen in the work presented in [61]. As this work considers the training of an autonomous agent where safety, sustainability, and travel time can be optimized, the price or social values cannot be affected by AI training itself, therefore, this work is restricted to the former aspects. In future work, we plan to make use of these criticality metrics when training an AI in selected real use cases such as an overtaking scenario.

- 9.
- The old “Abbreviations” section gives the reader the impression that we entirely used our own abbreviations, which is not correct. In the new version of the manuscript, we clearly mention the original source of the abbreviations and extended them by including Collision Indicator, Time to Arrival of Second Actor, Lane Potential, Road Potential, Car Potential, Velocity Potential, Off-Road Loss, Yaw Loss, Dynamic-Based Car CO
_{2}Emissions, Dynamic-Based CO_{2}Emissions, Weighted Vehicle Performance, and Electric Vehicle’s Power Consumption. - 10.
- The old “Nomenclature” section did not separate the symbols between Scenario/Scene and actor-specific symbols or short and general notations. In the new version of the manuscript, this problem is solved, thus providing the reader with a better understanding of the symbols presented in the manuscript. We also added scenario/scene and actor-specific symbols as well as short notations and general notations.
- 11.
- Other questions

## References

- Jurj, S.L.; Werner, T.; Grundt, D.; Hagemann, W.; Möhlmann, E. Towards safe and sustainable autonomous vehicles using environmentally-friendly criticality metrics. Sustainability
**2022**, 14, 6988. [Google Scholar] [CrossRef] - Westhofen, L.; Neurohr, C.; Koopmann, T.; Butz, M.; Schütt, B.; Utesch, F.; Kramer, B.; Gutenkunst, C.; Böde, E. Criticality metrics for automated driving: A review and suitability analysis of the state of the art. Arch. Comput. Methods Eng.
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**Figure 2.**Behavior of DST in cases (

**a**–

**d**). (

**a**) ${A}_{1}$ approaches ${A}_{2}$ with a high relative velocity. The safety time distance has not yet been established. The computed DST is positive and ${t}_{d}$ is a future time point.; (

**b**) ${A}_{1}$ approaches ${A}_{2}$ with a high relative velocity. The safety time distance has already been undershot. The computed DST is negative and ${t}_{d}$ is a past time point; (

**c**) ${A}_{1}$ drives slower then ${A}_{2}$. The safety time distance has not yet been established. The computed DST is positive and ${t}_{d}$ is a past time point; (

**d**) ${A}_{1}$ drives slower then ${A}_{2}$. The safety time distance has already been undershot. The computed DST is negative and ${t}_{d}$ is a future time point.

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## Share and Cite

**MDPI and ACS Style**

Jurj, S.L.; Werner, T.; Grundt, D.; Hagemann, W.; Möhlmann, E.
Correction: Jurj et al. Towards Safe and Sustainable Autonomous Vehicles Using Environmentally-Friendly Criticality Metrics. *Sustainability* 2022, *14*, 6988. *Sustainability* **2023**, *15*, 7791.
https://doi.org/10.3390/su15107791

**AMA Style**

Jurj SL, Werner T, Grundt D, Hagemann W, Möhlmann E.
Correction: Jurj et al. Towards Safe and Sustainable Autonomous Vehicles Using Environmentally-Friendly Criticality Metrics. *Sustainability* 2022, *14*, 6988. *Sustainability*. 2023; 15(10):7791.
https://doi.org/10.3390/su15107791

**Chicago/Turabian Style**

Jurj, Sorin Liviu, Tino Werner, Dominik Grundt, Willem Hagemann, and Eike Möhlmann.
2023. "Correction: Jurj et al. Towards Safe and Sustainable Autonomous Vehicles Using Environmentally-Friendly Criticality Metrics. *Sustainability* 2022, *14*, 6988" *Sustainability* 15, no. 10: 7791.
https://doi.org/10.3390/su15107791