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Abstract
Accurately predicting the future behavior of the surrounding traffic,
especially the velocity of the lead vehicle is important for optimizing
the energy consumption and improve the safety of Connected and
Automated Vehicles (CAVs). Several studies report methods to predict
short-to-mid-length lead vehicle velocity using stochastic models or
other data-driven techniques, which require availability of extensive
data and/or Vehicle-to-Vehicle (V2V) communication. In the absence
of connectivity, or in data-restricted cases, the prediction must rely
only on the measured position and relative velocity of the lead vehicle
at the current time. This paper proposes two velocity predictors to
predict short-to-mid-length lead vehicle velocity. The first predictor is
based on a Constant Acceleration (CA) with an augmented stop mode.
The second one is based on a modified Enhanced Driver Model (EDM-
LOS) with line-of-sight feature. Both predictors rely only on
information on the present values of lead vehicle position and velocity
to compute a future velocity estimate. An analysis is done to compare
the prediction accuracy of the proposed predictors with different
experimental driving data recorded using an OBD2 scanner plugged
into a passenger vehicle. Finally, the predicted lead vehicle velocity is
utilized to formulate time-gap constraints for the eco-driving optimal
control problem, solved via Model Predictive Control (MPC). The
energy savings of the considered velocity predictors are evaluated by
performing a large-scale simulation study. The proposed velocity
predictor provides closest energy savings to a wait-and-see solution for
a CAV in absence of V2V communication.
Introduction
Advancements in navigation systems and Vehicle-to-Everything
(V2X) communication have led to the access of a wealth of
information from the environment and infrastructure, such as traffic
density, location and velocity of surrounding vehicles, upcoming road
topology, grade, speed limits, etc. Connected and automated vehicles
(CAVs) can access such information to improve the safety and
comfort. In recent times, control strategies have been developed that
leverage the look-ahead information available to CAVs to save energy,
often referred to as eco-driving [1,2,3,4,5]. Despite the energy
efficiency improvements and other benefits demonstrated by these
technologies, uncertainties in the traffic environment can limit the
ability of eco-driving controllers to smoothen the velocity profile and
might eventually lead to decline in energy savings [6]. For real-time
implementation of eco-driving controllers with consistent energy
savings, it becomes necessary to include the dynamics of the traffic,
especially the estimated future lead vehicle velocity into the eco-
process. Fig. 1 describes an example of
an eco-driving controller that integrates the signal phase and timing
information from vehicle-to-infrastructure (V2I) communication and
lead vehicle velocity prediction from vehicle-to-vehicle (V2V)
communication into a short-term trajectory optimization framework.
Lead vehicle here refers to the immediately preceding vehicle to the
ego vehicle that can cause a potential rear-end collision. Predicting the
speed trajectory of a lead vehicle plays a vital role in improving the
safety and energy consumption of CAVs. In fact, inaccurate prediction
of the lead vehicle speed may lead to an overreaction of the ego CAV,
causing unwanted accelerations/decelerations and ultimately worse
energy consumption than a purely reactive control strategy [6,7].
Predicting
information on that vehicle and its surroundings, and the used
prediction method. A comprehensive overview of the existing
prediction methods can be found in [8]. The ego CAV can obtain
information on the lead vehicle and its surroundings using either
sensors and/or V2X communication, as shown in Fig. 1. The methods
found in the literature for predicting speed trajectories can be broadly
classified as data-driven or model-based.
Data-driven time-series prediction methods such as long-short-term
memory [1,12], or gated recurrent network [13], have been extensively
used to perform mid-long length speed predictions. However, these
methods require the availability of extensive training data and/or V2V
communication.
Model-based approaches include simple models such as constant
velocity and Constant Acceleration (CA). The constant velocity
predicts the lead vehicle to maintain the current speed over the future
prediction horizon while the CA assumes the future speed to
move with the same acceleration until it stops or exceeds a maximum
velocity. However, these models lack adaptability to variations in
driving styles and in certain cases are unrealistic. More sophisticated
microscopic car-following models such as the Intelligent Driver Model
[9], the Line-Of-Sight-based Enhanced Driver Model (EDM-LOS)
[10], or [11], which are in principle used to model driver
behavior, could also be used to predict the lead .
Such microscopic models include parameters for driving style
calibration, allowing to capture various driver behaviors. While model-
based methods loose accuracy over long term prediction, they perform
reasonably well in short term horizon, which is the main focus of this
paper.
This paper presents a comparison of two methods to predict the lead
vehicle velocity over a short-term horizon in the absence of
connectivity (V2V/V2X) or under data-restricted cases. In such
scenarios, the prediction must rely only on the measured position and
relative velocity of the lead vehicle at the current time. Two methods
are considered in this study, namely, a Constant Acceleration (CA)
model and a Line-of-Sight based Enhanced Driver Model (EDM-
LOS). The CA uses the current detected velocity and acceleration of
the lead vehicle to predict the future velocity for short instances of
time. However, when approaching a fixed obstacle such as a traffic
light or intersection, the CA model prediction may become inaccurate,
resulting in the inability to correctly stop the ego vehicle at the
intersection. The EDM-LOS model without the information about the
vehicle preceding the lead vehicle fails to predict braking events during
car-following.
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Figure 1. Hierarchical eco-driving control architecture leveraging V2X technology in presence of lead vehicle.
The contributions of this work are as follows. Two lead vehicle
velocity predictors are developed, namely Constant Acceleration-
Average Braking (CA-AB) and EDM-LOS based Predictor (EDM-
LOSP). The CA-AB is an improved model over CA in predicting
decelerations to a stop in the presence of an obstacle. The EDM-LOSP
is an improved model over EDM-LOS to identify and predict braking
events during car-following. The performance of the proposed
predictors is evaluated for energy efficiency and travel time in a
simulation-based environment using real-world driving profiles and
compared against CA as baseline and an ideal scenario with perfect
velocity prediction (wait-and-see) as benchmark.
The paper is organized with the following section describing the
vehicle model, formulation of the optimal control problem and the lead
vehicle constraint. The section after, describes the methods for
predicting the lead the following section
discusses the evaluation of the predictors in a simulation environment
along with its results. Concluding remarks are provided in the final
section.
Vehicle Model and Problem Formulation
This section describes the mild hybrid vehicle model considered in this
study and the eco-driving optimal control problem formulation.
Mild Hybrid Electric Vehicle Model
A forward-looking model of a P0 parallel mild-hybrid vehicle is
adopted in this work to predict the longitudinal dynamics and energy
consumption, as shown in Fig. 2 [14]. A Belted Starter Generator
(BSG) is connected to a 1.8 L turbocharged gasoline engine and a 48V
battery pack. The inputs to the model are obtained from a simplified
electronic control module (ECM) that contains a production level
torque split strategy and pedal position to desired
engine torque
and desired BSG torque
. The vehicle
simulator contains a low-frequency powertrain and longitudinal
vehicle dynamics model, as well as quasi-static models of engine (fuel
maps), BSG (torque limit and efficiency maps), torque converter and
transmission. Model validation was performed in a previous study [14]
on a chassis dynamometer over the FTP cycle. Despite few
mismatches in the state of charge, the error on the predicted fuel
consumption is less than 4%, which can be considered sufficiently
accurate for this work.
Figure 2. Qualitative schematics of a 48 V mild hybrid electric drivetrain.
Optimal Control Problem
The eco-driving control problem is formulated as a non-linear optimal
control problem in spatial domain, aimed at minimizing a trade-off
between fuel consumption and travel time over an itinerary of steps.
In this work, the state variables chosen are the vehicle velocity, battery
state of charge (SoC) and travel time: .
The engine torque and BSG torque are chosen as the control variables:
. Note that all predictions are denoted
using
and observed/measured signals are denoted using .
Consider a dynamic control problem discretized in the spatial domain
with the form:
(1)
where is the discrete position, and is a function that describes the
state dynamics and is derived in [13]. The admissible control maps at
position is denoted by , which satisfies the constraint
function , expressed as :
(2a)
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(2b)
(2c)
(2d)
(2e)
(2f)
(2g)
where refer to the minimum and maximum speed limit;
refer to the minimum and maximum SoC limits;
refer to the vehicle acceleration for comfort;
refer to the engine torque limits;
refer to the BSG torque
limits respectively. refers to the maximum travel time limit imposed
at the end of the route which can be estimated using the time taken to
complete the historical trips. To ensure charge-sustenance, .
The collection of admissible maps is referred as the policy of the
controller, denoted by . The controller minimizes a
cost functional over steps:
(3)
where is the per-stage cost, defined as the weighted
average of fuel consumption and travel time:
(4)
where is the trade-off, is the fuel flow rate, is the
normalizing factor, and
is the travel time per step. To account
for the variability in route conditions such as time-varying signal phase
and timing (SPaT) information, the eco-driving problem in Eq. (3) is
formulated for as a receding horizon optimal
control problem (RHOCP), minimizing the cost functional over a
reduced horizon steps () [14]:
(5)
where is the number of steps in the prediction horizon. In this work,
at a position , it is assumed that the lead vehicle acceleration is
predicted (as described in the following section) and can be used to
predict the lead vehicle velocity
and arrival time
for
, with a step size as:
(6a)
(6b)
It should be noted that the constraints (2a), (2b), (2e), (2f) and (2g)
remain the same in the RHOCP
. However, the constraint on the time is affected by imposing time-
gap constraint between the ego and lead vehicle as:
(7)
where represents the safety gap to the leader in time.
To include V2I information, additional constraints are imposed on the
time such that it lies in the feasible set of travel time for passing-at-
green at signalized intersection, [15].
The RHOCP (5) is solved using Approximate Dynamic Programming
(ADP), such that terminal cost of the RHOCP ( -term
optimization in Fig. 1) is approximated from the offline solution of a
full-route optimization -term optimization in Fig. 1)
under partial route information [14].
Predicting Lead Vehicle Velocity
The two models considered in this work to predict the lead vehicle
velocity within the RHOCP are the CA-AB and the EDM-LOSP.
These models are a result of significant improvements made to the CA
and EDM proposed in literature [2,3,10]. This section describes the CA
and EDM-LOS models, their drawbacks, and the improvements made
leading to the CA-AB and EDM-LOSP.
Constant Acceleration – Average Braking (CA-AB)
The CA model predicts the future velocity of the lead vehicle to have
a constant acceleration until it reaches the speed limit [17]:
(8)
where represents the acceleration of the lead vehicle at (also
current time). represents the predicted acceleration. The speed
limit of the route is given by However, when approaching an
obstacle such as a traffic light or a stop sign, the CA model is unable
to correctly predict where the lead vehicle will be stopping, resulting
in the lead vehicle stopping either before or after the traffic light.
To overcome this drawback, the current acceleration is here
replaced with an average braking acceleration. The average braking
acceleration is defined as:
(9)
where represents the position of the traffic light
represents the
position and represents the velocity of the lead vehicle at .
Note that this model formulation implies that the ego vehicle has
access to V2I information, namely road grade, speed limits and
location of stop signs and traffic signals within the prediction
horizon. Eq. (9) represents the minimum kinematic deceleration
required by the lead vehicle to come to a stop at the traffic light. The
modes of the CA-AB can be summarized as follows:
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(10)
where and stand for freeway driving and stop mode, respectively.
The stop mode is activated in the presence of either a stop-sign or a
traffic light with red signal phase within .
Enhanced-Driver-Model with Line-of-Sight based
Predictor (EDM-LOSP)
The existing EDM-LOS is a deterministic velocity predictor
representing various levels of driver aggressiveness [4]. The EDM-
LOS includes three distinct operating modes, namely, Car-Following
(CF), Freeway Driving (FD) and Stop Mode (S). The different
operating modes are represented by the following equations:
(11)
(12)
(13)
(14)
and
represents the lead vehicle velocity and position,
respectively. are the set of EDM-LOS calibration
parameters. represents the maximum acceleration and the exponent
, representing driver aggressiveness, controls how quickly the desired
speed is achieved. The freeway driving represents the transition to the
route speed limit in the absence of any vehicle preceding the lead
vehicle. The degree of aggressiveness is further characterized by a
calibration term , which determines the offset from the route speed
limit. As per this formulation, a relatively relaxed driver would drive
slightly below the speed limit. The term in the Stop mode represents
the comfortable deceleration. When approaching an obstacle, such as
a traffic light, the deceleration usually does not exceed and is
dynamically self-regulating towards a situation in which the kinematic
deceleration equals [3]. The driver aggressiveness on braking
distance is captured by , which is dependent on a calibration
term
The Line-Of-Sight (LOS) scheme in the EDM is used to
realistically model the drive response when approaching a traffic light.
The LOS is a distance parameter below which, in presence of a traffic
light, the driver can preview the signal phase of the upcoming traffic
light. The presence of a traffic light at sets the flag TL = 1, when
. The driver performs a stop maneuver
under two conditions, namely either if the previewed signal phase is
red (SP = 3) or, the signal phase is yellow (SP = 8) and the vehicle is
outside the critical braking zone The term
in
is
replaced by the position of the traffic light and set to zero.
Therefore, stop mode is activated when:
(15)
A detailed rule-based logic using LOS in the presence of a stop sign or
traffic light is described in [16]. Regarding the car-following mode,
and
represent the position and speed of the vehicle preceding
the lead vehicle. The absence of V2V communication makes this
information unavailable for the ego vehicle to predict the car-following
behavior, in particular deceleration events, of the lead vehicle. To
overcome this, a modification of the freeway driving and stop mode
equations is here developed (EDM-LOSP).
the FD mode uses only the current velocity, which is obtained by
setting
in Eq. (11). Given availability of the current
acceleration , it is possible to replace with:
(16)
with
, replacing with ensures that the first predicted
acceleration
. Ideally, this results into a perfect prediction for
the first step, as in the case of a constant acceleration assumption. In
addition, EDM-LOS is sensitive to the calibration parameters, in
particular and . When modelling driver behavior using EDM-LOS,
these parameters are either calibrated offline from recorded driving
data [17] or using online estimation techniques [18]. The sensitivity is
also minimized by making use of the available current acceleration .
The other parameters and remain calibratable, allowing one to
capture different driver aggressiveness. The FD mode is employed
when the current acceleration is non-negative. When is negative
and there is no traffic light within , the lead vehicle is assumed to
brake because of the vehicle in front of the lead vehicle. Since the car-
following mode in EDM-LOS cannot be employed, the stop mode is
modified to predict the braking behavior. The comfortable deceleration
is replaced by the current acceleration and
term in
is
replaced by assuming the lead vehicle is decelerating to a fixed
obstacle at a position given by
One can observe that doing the
above modifications to the stop mode results in converting to a
constant acceleration model, as shown in appendix A.1. Incorporating
the current acceleration of the lead vehicle, the equations of EDM-
LOSP is summarized as:
(17)
Comparison of Predictor Performance
To highlight and compare the performance of the proposed predictors,
a short driving profile was experimentally collected and used as
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reference for the lead vehicle velocity. The speed prediction
performance was quantified by computing the Root-Mean-Square-
Error (RMSE) between the actual speed and the predicted speed.
Prediction horizon lengths of 5, 10 and 15 seconds are evaluated for
each predictor. The results are summarized in Table 1, showing the
CA-AB and EDM-LOSP performing better over their counterparts.
Fig.3 provides a visual description of how each velocity predictor
performs (10 s prediction horizon) during a portion of the driving
profile. The difference between CA and CA-AB can be mostly
appreciated when the lead vehicle speed goes to zero in the presence
of red phase traffic light (e.g., around 80 s). The CA does not predict
the velocity to stop at the traffic light, as seen from the red lines close
to 80s, indeed, a longer prediction horizon causes the velocity to pass
the traffic light. The proposed CA-AB uses in the place of , hence
predicting the lead vehicle stop at the traffic light. Summarizing, the
advantages of using CA-AB over CA can be appreciated more in urban
routes, due to the high traffic light and stops density. The portions of
decreasing velocities of the lead vehicle, apart from the traffic light,
for instance at ~10s, 25s and 50s are due the presence of vehicles
preceding the lead vehicle. This behavior, given the availability of
information on the vehicle preceding the lead, is predicted using the
CF mode in EDM-LOS. However, without that information, this
predictor assumes the lead vehicle to always be in FD mode predicting
its velocity to reach a desired speed. The proposed EDM-LOSP
overcomes this by identifying ( and predicting decelerations
using the second mode abovementioned in Eq. (17).
Table 1. RMSE in m/s of the different speed predictors for 5s, 10s and 15s future
windows.
Prediction
Horizon, s
CA
CA-AB
EDM-LOS
EDM-LOSP
5
1.00
0.97
1.80
0.81
10
2.63
2.40
2.70
2.24
15
3.67
3.45
3.47
3.15
Figure 3. Speed predictions of the different for a 10 s prediciton window. In red, the velocities predicted at each timestep while in blue the actual lead vehicle speed.
Figure 4. Bar plots for fuel consumed in grams (on the left) and travel time in seconds (on the right) for the six different routes and the different lead vehicle velocity
predictors.
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Simulation and Results
This section provides an application of the aforementioned lead
vehicle velocity prediction methods. The performance of the proposed
predictors, CA-AB and EDM-LOSP, are evaluated for energy
efficiency and travel time using real-world driving profiles and
compared against CA as baseline and an ideal scenario with perfect
velocity prediction (wait-and-see) as benchmark. In general,
information on future lead vehicle velocity is of crucial importance for
the eco-driving optimal control problem, due to the knowledge needed
to obtain the globally optimal solution. Absence of such information
from V2V communication of any restriction of unavailability of data
imply the need for reliable and robust algorithms to predict the future
lead vehicle velocity trajectory. For conciseness, EDM-LOSP will be
referred to as EDM for the rest of this section including figures.
For this analysis, different driving scenarios and routes were
considered to demonstrate the utility of the speed predictors in the eco-
driving problem. Six different routes were selected and divided
between urban and mixed scenarios. The route data were obtained
using GPS information extracted from different vehicles driven along
the designated routes. It is worth mentioning that the location of traffic
lights was known, however the Signal Phasing and Timing (SPaT) was
not available, thus the need of defining a realistic SPaT by leveraging
the time spent at stops by the lead vehicle. Additional information on
the routes on traffic light density and average speed limits is provided
in Table 2. For the sake of completeness, the speed limits, lead vehicle
velocity and traffic light locations for the different routes are found in
the Appendix (see Fig. A1), as a function of distance travelled.
Table 2. Routes information for urban and mixed driving scenarios.
Route name
Traffic light density,
1/km
Average speed limits,
mph
Urban route 1
3.0
28
Urban route 2
1.2
40
Urban route 3
2.3
33
Mixed route 1
0.5
59
Mixed route 2
0.7
50
Mixed route 3
0.4
59
The results obtained using the rollout algorithm and the different speed
predictors are shown in Fig. 4, in terms of total fuel consumed and
travel time. As already mentioned, the optimization problem aims at
minimizing both terms with an equal trade-off given as a weight in the
cost function. It is worth noting that all the strategies implemented
result charge sustaining, i.e., the initial and final SOC are
approximately equal to 50%. The benchmark solution provided in
these results corresponds to a perfect knowledge of the lead vehicle
velocity in the prediction horizon (i.e., 200 m), and it is used to provide
a fair and exhaustive comparison with the velocity predictors. From
the bar plot in Fig. 4, it can be seen how the travel time remains
practically unchanged among the different speed predictors, whereas
the fuel consumed varies considerably. The highest differences are
found in urban routes, where EDM and CA-AB consume an average
of 3.9% and 7.9% more than the benchmark, respectively, while the
CA leads to a fuel consumption increment of approximately 12.4%. In
the mixed routes, no substantial changes are observed when applying
the different predictors, mainly stemming from the higher portion of
driving at constant speed where the different predictors act all
similarly. The reasons why the EDM and corresponding eco-driving
problem lead to an enhanced energy efficiency are worth analyzing in
terms of Root-Mean-Square (RMS) of the acceleration. The CA speed
predictor results in a higher RMS value for the acceleration in the
urban routes with an average of 0.52 m/s2, with respect to both CA-AB
and EDM eco-driving approaches (i.e., 0.51 m/s2 and 0.50 m/s2
respectively). The higher value for acceleration RMS can be associated
to higher fuel consumption, thus proving the differences just
mentioned. An example of how the eco-driving solution approaches
the traffic lights is shown in Fig. 5 and mostly visible in the zoomed
window that highlights two close traffic lights. It can be noticed how
the prediction of lead vehicle speed along with the signal phase
knowledge allows the ego vehicle to not stop at traffic lights when it is
feasible, thus avoiding inefficient deceleration to null speed and
subsequent acceleration. Analyzing further the zoomed window, it can
be seen that the benchmark solution starts decelerating long before the
first traffic light and accelerates only towards the end of the green
phase, just enough to avoid stopping. Further differences can be seen
also in the behavior of the CA eco-driving approach (in yellow in Fig.
5) that accelerates right after the lead vehicle leaves the traffic light
and then decelerates when the gap is low.
Figure 5. Traffic lights SPaT and trajectories of the lead vehicle and the
different eco-driving approach using the diverse velocity predictors.
For the sake of completeness, Fig. 6 illustrates the eco-driving
solutions with the different speed predictors implemented on Mixed
Route 2. In general, no visible differences are found among the
different predictors' solutions. However, all demonstrate smoother
velocities with respect to the lead vehicle avoiding unnecessary
slowdowns (see Fig. 6 around 840 m and 2815 m), thus improving
overall energy efficiency.
Figure 6. Velocity traces for the different speed predictors and eco-driving
problems in Mixed Route 2, as a function of distance.
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The reason why the travel time does not vary as noticeably as the fuel
consumption is attributable to the need of complying with traffic lights
phases and the impossibility of passing the lead vehicle. To confirm
this statement, two other rollout algorithms have been run with
different weights between fuel consumed and travel time (i.e.,
introduced in previous section). Even when orienting the cost function
to penalize more the travel time than the fuel consumption, no
substantial variations are found, as seen in Fig. 7 below concerning
simulations on Urban route 1. It is worth noting that the y-axis in Fig.
7 is magnified for the sake of clarity and that the differences between
the neutral cost function and the one mostly oriented towards travel
time (i.e., , respectively) are in the orders of seconds,
hence confirming that the constraints posed by the lead vehicle and the
traffic lights do not allow room for variation, as mentioned above.
Figure 7. Bar plots graph of the travel times obtained using different speed
predictors and different weights in the DP cost function in Urban Route 1.
Conclusions
The lead vehicle velocity prediction improves with the availability of
the V2V information about the vehicles preceding the lead vehicle.
However, in the absence of V2V communication or in data-restricted
environment, the prediction accuracy reduces. To mitigate this, two
predictors, namely CA-AB and EDM-LOSP, were developed to
predict lead vehicle velocity without the need of V2V communication.
First, a CA predictor was modified to incorporate an average
deceleration part while slowing down or stopping. Second, the EDM-
LOS was modified to incorporate current acceleration information in
capturing lead vehicle decelerations during car-following. A
comparative study was conducted to analyze the prediction accuracy
of the developed predictors over different prediction horizons. A time-
gap based constraint was designed leveraging the predicted lead
vehicle velocity over the prediction horizon. This information was then
integrated into a non-linear eco-driving optimal control problem.
Large scale simulations were performed over 6 real-world routes
representing urban and mixed driving scenarios to solve the eco-
driving problem as a MPC with the developed predictors. Results show
higher energy savings considering the EDM-LOSP for urban driving
with respect to the CA and CA-AB. This confirms the importance of
accurate predictions of preceding traffic to enhance energy efficiency,
especially in urban scenarios. Future work will include testing the eco-
driving controller embedding the information coming from the EDM-
LOSP using hardware-in-the-loop simulation.
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Conference, Pittsburgh,PA, 2020.
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17. Hegde, B., O'Keefe, M., Muldoon, S., Gonder, J., and Change
C. "Real-World Driving Features for Identifying Intelligent
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Contact Information
Vinith Kumar Lakshmanan, vinith-kumar.lakshmanan@ifp.fr
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Appendix
A.1: Proof of stop mode in EDM-LOSP is equivalent to CA
Following, a proof is given that the stop mode in EDM-LOSP is equivalent to a constant acceleration prediction. The proof is given for the predictor
equations in continuous time, but the same result holds for the discrete system.
Given the current instantaneous speed and acceleration , let be the lead vehicle position and speed, respectively, where:
(A1)
The stop mode in the EDM-LOSP is then given by:
(A2)
where is the distance of the lead vehicle from the next predicted stop.
Theorem 1:
If
, then
Proof:
The proof proceeds by showing that:
1. , is an equilibrium point for the acceleration.
2. By the definition of the equilibrium is attained at and
Let
, then:
(A3)
Hence entails that remains constant.
Now, from the definition of it follows
. By substitution in the expression for and recalling the initial condition on it can be
shown:
(A4)
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A.2: The urban and mixed routes with lead vehicle velocity and routes features
Figure A1. Speed limits, traffic lights locations and lead vehicle velocity profiles for the six different urban and mixed routes, as a function of the distance.
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Rebuttal
Reviewer #313607:
1. The authors should consider citing the recent work https://doi.org/10.4271/2022-01-0153
Thank you for the comment. The suggested citation is indeed a good reference. The authors added a citation in the first parag raph of the
introduction, including the technical paper as reference [5] (highlighted in red).
2. The dashed oval shape indicating the zoomed part of the figure seems misplaced in figure 5; the dashed grey line in figure 6 should be
included in the legend for easy readability of the associated plot.
Thank you for suggesting these improvements for the readability of the figures. The oval shape is correctly placed in figure 5, but the authors
modified the figure description in the text (highlighted in red) for a better understanding. The speed limits have been added to the legend of
figure 6.
3. Further, this reviewer provides one major criticism, which is that although the authors indicate issues with model-based prediction algorithms
in the second (or third) paragraph of the introductory section, based on the criticism of difficulties in the case of long time horizons, the paper
then proceeds to say in the next paragraph that the authors address short horizon case, which seems contradictory to the reader (although this
reviewer understands the core contributions of the manuscript). The authors are suggested to rewrite these parts of the introduction section
to avoid confusing the reader.
Authors have rephrased portion of the paragraphs in the introduction to remove the mentioned ambiguity (highlighted in red).
Reviewer #313619:
1.
Thank you for noticing it. We have defined the term in the paragraph above 6a (highlighted in red).
2.
The correction has been made (highlighted in red).
3. A kind suggestion is to stick with either the word forecasting or prediction. In the title and in the paper these words are interchangeably used.
Thank you for the suggestion. The authors have changed the term
(including the title). Only changes in the title and section headers have been highlighted in red.
