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Cooperative Driving of Connected Autonomous Vehicles Using Responsibility-Sensitive Safety (RSS) Rules

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Connected Autonomous Vehicles (CAVs) are expected to enable reliable and efficient transportation systems. Most cooperative driving approaches for CAVs and motion planning algorithms for multi-agent systems are not completely safe because they implicitly assume that all vehicles/agents will execute the expected plan with a small error. This assumption, however, is hard to keep since CAVs may have to slow down (e.g. to yield to a jaywalker) or are forced to stop (e.g. break down), sometimes even without a notice. Responsibility-Sensitive Safety (RSS) defines a set of safety rules for each driving scenario to ensure that a vehicle will not cause an accident irrespective of other vehicles' behavior. However, RSS rules fall short to cover many scenarios such as merges, intersections , and unstructured roads. In addition, deadlock situations can happen that are not considered by the RSS. In this paper, we propose a generic version of RSS rules for CAVs that can be applied to any driving scenario. We integrate the proposed RSS rules with the CAV's motion planning algorithm to enable cooperative driving of CAVs. Our approach can also detect and resolve deadlocks in a decentralized manner. We have conducted experiments to verify that a CAV does not cause an accident no matter when other CAVs slow down or stop. We also showcase our deadlock detection and resolution mechanism. Finally, we compare the average velocity and fuel consumption of vehicles when they drive autonomously but not connected with the case that they are connected.
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Cooperative Driving of Connected Autonomous Vehicles Using
Responsibility-Sensitive Safety (RSS) Rules
Mohammad Khayatian1, Mohammadreza Mehrabian1, Harshith Allamsetti2, Kai Wei3, Po Yu3,
Chung-Wei Lin3, Aviral Shrivastava1
1Arizona State University, 2Western Digital, 3National Taiwan University
ABSTRACT
Connected Autonomous Vehicles (CAVs) are expected to enable reli-
able and ecient transportation systems. Most cooperative driving
approaches for CAVs and motion planning algorithms for multi-
agent systems are not completely safe because they implicitly as-
sume that all vehicles/agents will execute the expected plan with
a small error. This assumption, however, is hard to keep since
CAVs may have to slow down (e.g. to yield to a jaywalker) or are
forced to stop (e.g. break down), sometimes even without a notice.
Responsibility-Sensitive Safety (RSS) denes a set of safety rules
for each driving scenario to ensure that a vehicle will not cause
an accident irrespective of other vehicles’ behavior. However, RSS
rules fall short to cover many scenarios such as merges, intersec-
tions, and unstructured roads. In addition, deadlock situations can
happen that are not considered by the RSS. In this paper, we pro-
pose a generic version of RSS rules for CAVs that can be applied to
any driving scenario. We integrate the proposed RSS rules with the
CAV’s motion planning algorithm to enable cooperative driving
of CAVs. Our approach can also detect and resolve deadlocks in a
decentralized manner. We have conducted experiments to verify
that a CAV does not cause an accident no matter when other CAVs
slow down or stop. We also showcase our deadlock detection and
resolution mechanism. Finally, we compare the average velocity
and fuel consumption of vehicles when they drive autonomously
but not connected with the case that they are connected.
KEYWORDS
Connected Autonomous Vehicles, City-Wide Trac Management,
Intelligent Transportation Systems
1 INTRODUCTION
Autonomous Vehicles (AVs) have the potential to make transporta-
tion safer by reducing the number of accidents that are caused due
to human error. When AVs become connected (which are referred
to as Connected Autonomous Vehicles (CAVs)), they can further
improve road safety by sharing their information with each other
such as position, velocity, future plans, etc. In addition, CAVs are
projected to improve fuel consumption, travel time, and passenger
comfort through cooperative driving.
Achieving cooperative behaviors among robots is typically stud-
ied under multi-agent motion planning in the robotics domain [
1
,
2
].
Existing techniques can be categorized into two groups: i) cen-
tralized [
3
] and ii) decentralized (distributed) [
4
]. In centralized
approaches, it is assumed that a central planner exists that has
access to all information and computes the trajectory for robots
e.g. path-velocity decomposition technique, while in decentralized
approaches, each robot is assumed to have incomplete informa-
tion and autonomously determines a plan while avoiding static
and moving obstacles as well as other robots. Although centralized
approaches can nd the optimal solution, they are computationally
demanding and less tolerant of uncertainty. On the same lines, in
the Intelligent Transportation System (ITS) domain, centralized and
decentralized techniques [
5
] are proposed where CAVs share their
information with each other (through V2V) or the infrastructure
(through V2I) to perform trac management at intersections [
6
9
],
merges [10–12].
In general, existing motion planning algorithms and trac man-
agement techniques consider a safety buer around each vehicle to
cover for uncertainties in the localization and trajectory tracking,
and then a reference trajectory is determined. A trajectory is con-
sidered to be safe if the safety buer of the vehicle does not overlap
with obstacles or other vehicles’ safety buer at any point in time.
While reasonable, this denition may not provide absolute safety
because it implicitly assumes that all vehicles will follow the plan
(with small errors that are within the safety buer). However, any
disruption in the plan can cause an accident. For example, consider
a scenario when two vehicles are driving on a street, one behind
the other. If the front vehicle suddenly stops for any unplanned
reason (e.g. yielding to a jaywalker), then the rear vehicle may hit
the front car. In common driving parlance – the rear vehicle should
not tail-gate the front vehicle.
Responsibility-Sensitive Safety (RSS) approach [
13
] from Mobil-
eye+Intel addresses the safety issue from the legal/blame perspec-
tive and allows vehicles that have the right-of-the-way according
to the rules of the road to change their plans. RSS proposes a set
of safety rules such that if a vehicle abides by these rules, then it
cannot be blamed for an accident. In the scenario that is mentioned
above, RSS rules are used to determine the minimum distance at
which the rear vehicle should follow the front one so that it will be
able to stop without causing an accident even in the worst-case sce-
nario. RSS uses a lane-based coordinate system to dene lateral and
longitudinal distances between vehicles depending on the driving
scenario. For example, there is a longitudinal rule for the scenario
when two vehicles are one in front of the other, and there is a lateral
rule for the scenario in which two vehicles are driving in parallel to
each other. The longitudinal direction is toward the center-line of
the lane and the lateral direction is perpendicular to the center-line
of the lane. The main shortcoming of RSS is that it is scenario-based
and not all scenarios are covered because longitudinal and lateral
distances cannot be computed for merges, intersections, and un-
structured roads where lane markings are not provided. The rst
contribution of this paper is to provide a trajectory-based deni-
tion for RSS rules, that works in all situations, including merges,
intersections, and unstructured roads.
When CAVs interact with each other in dierent scenarios, they
may face a deadlock situation where CAVs yield to each other for an
indenite time. Researchers have proposed methods to detect and
resolve deadlocks at intersections [
8
,
14
,
15
] and roundabouts [
16
].
In existing approaches, the intersection/roundabout area is divided
into a grid of zones, and vehicles that intend to occupy the same
zone are said to have a conict. Then, the dependencies between
CAVs (who should enter a conict zone rst and who enters second)
are represented with a directed graph, and deadlocks are resolved
by removing cycles in the graph. One of the limitations of existing
approaches is that they use xed zones to detect conicts between
vehicles and the size of each zone aects the eciency and compu-
tational complexity of the conict detection algorithm since using
coarse grids makes the schedule pessimistic and using ne grids in-
creases the number of checks. Furthermore, in existing approaches,
the dependency graph is computed individually by each CAV, which
is extremely inecient because the same computing is done redun-
dantly and the overhead grows as the number of vehicles increases.
As the second contribution of this paper, we propose an ecient
and decentralized approach to detect and resolve deadlock where
each CAV determines only its own conicts.
In this paper, we present a cooperative driving and deadlock
resolution approach for CAVs. Instead of a lane-based coordinate
system, we use future trajectories of CAVs to represent their con-
icts, which can be applied to any road geometries and situations.
Inspired by the RSS legal/blame perspective, we develop a new set
of safety rules for CAVs to guarantee that no accidents happen if
CAVs abide by proposed RSS rules. We also provide an ecient
and decentralized deadlock detection and resolution algorithm for
CAVs. The integration of the proposed RSS safety rules and dead-
lock resolution algorithms with motion planning is also provided.
Results from conducting experiments on our realistic simulator
–that considers vehicle dynamics and network delay– demonstrate
that all CAVs remain safe even if one or more CAVs slow down or
stop at any point in time. We evaluate the eciency of our approach
by comparing the average travel time of CAVs with a case that ve-
hicles are autonomous but not connected. Finally, we showcase our
deadlock resolution mechanism for an intersection scenario.
In section 2, we study related works and point out their limita-
tion, and in section 3, we present a new version of RSS rules. Our
proposed cooperative driving approach is presented in section 4.
Section 5 shows the experimental results and nally in section 6,
we conclude with suggestions for future works.
2 RELATED WORK
In the ITS domain, many researchers have proposed methods to
cooperatively manage CAVs at intersections [
5
9
,
17
20
], round-
abouts [
21
], ramp-merging [
10
12
], performing cooperative lane
changing [
22
,
23
], forming platooning in highways [
24
,
25
]. Such
approaches can only be applied to a specic scenario and do not
scale. There have been a number of cooperative approaches that
are not scenario-based. In the method proposed by During et al.
[
26
,
27
], the ego CAV rst determines a set of possible maneuvers
that can resolve the conict and then, select the one that has the
lowest cost. The cost is determined based on energy consumption,
time of maneuver, and driving comfort. In another work, Chen et
al. [
28
] proposed a cooperative driving algorithm where the driv-
ing information of neighboring CAVs is obtained and the desired
velocity is predicted using a Recursive Neural Network (RNN). A
motion planner is developed using the predicted velocity using a
fuzzy path-following controller. These approaches, however, do
not consider cases where a CAV is unable to perform the desired
maneuver/follow the assigned trajectory.
In the robotics domain, many researchers have focused on multi-
agent motion planning algorithms problem [
1
,
2
]. In general, co-
operative motion planning algorithms can be categorized as dis-
tributed [
4
] and centralized [
3
]. In distributed approaches, each
agent computes a path such that it avoids obstacles and other agents
while in centralized approaches, a central planner (could be on each
agent) computes the plan for all agents by exploring the whole
design space. In general, distributed approaches are more popular
as they require less computation and more resilient to changes in
the plan or uncertainty. Existing motion planning algorithms for
multi-agent systems and trac management approaches for CAVs
provide safety proofs based on the assumption that all agents stick
to their plan or error is small. In the real world, CAVs may have
to slow down and stop due to unforeseen reasons e.g. a CAV may
break down. As a result, existing techniques are not absolutely safe
for CAVs.
In 2017, researchers from Mobileye proposed a set of rules called
RSS [
13
], which determines the minimum distance that an AV must
maintain from other vehicles in order to remain safe and not being
blamed for an accident. RSS rules consider the worst-case scenario
for other vehicles and the ego vehicle (during the response time)
to provide safety guarantees. RSS rules have been used to develop
a monitoring system [
29
] and are implemented in the Apollo [
30
]
open-source software.
The main issue with RSS is that it uses a lane-based coordinate
system and safety rules are dened based on longitudinal (towards
the lane) and lateral (perpendicular to the lane) distances, which
cannot be applied to all driving scenarios such as intersections,
merges or unstructured road where no road markings are present.
In addition, RSS rules do not consider the interaction among other
CAVs and therefore, cannot detect cases where a deadlock happens.
Researchers have proposed algorithms to detect and resolve
deadlocks at intersections [
8
,
14
], roundabouts [
16
] and network of
intersections[
15
]. In such approaches, a set of pre-dened zones is
used to represent the occupancy of CAVs. Next, a wait-for graph
is created to represent dependency between vehicles for entering
conict zones, and deadlocks are identied by detecting cycles in
the graph. However, using xed conict zones to detect a conict
and perform deadlock resolution is either inecient (for coarse
zones) or compute-intensive (for ne zones). Furthermore, existing
approaches do not consider vehicle dynamics when resolving a
deadlock and assume that a deadlock is resolved in one-shot. While
in reality, it takes some time for CAVs to slow down/speed up and
resolve a deadlock.
Next, we will present our approach that is developed by modify-
ing RSS rules to support all driving scenarios and represent conict
in a more ecient way. We also present a realistic deadlock de-
tection algorithm where each CAV computes its own dependency
graph and by sharing it with other CAVs, they can detect deadlocks.
2
3 GENERIC FORMULATION OF RSS RULES
In this section, we introduce a trajectory-based formulation for RSS
rules. The advantage of this approach is that the rules are generic
and can be applied to all cases, including unstructured roads.
Given the future paths of CAVs are known, each CAV can deter-
mine the set of conict zone
C
. A conict zone,
CiC
is dened
as a convex contour that includes a subset of two CAVs’ future path
(
FP
) where the distance between the future paths is less than a
threshold,
dth
. Since two CAVs may have more than one conict,
only consecutive edges that have a distance of less than
dth
are
considered to be a part of the same conict zone. The midpoints
of the edges are used to calculate the distance between two edges
from two future paths. To specify the boundaries of a conict zone,
midpoints of rst and last edges are used.
Based on the road geometry and rules of the road, every pair of
CAVs can determine who has the advantage to enter the conict
zone rst and who has the disadvantage. For simplicity, we assume
the CAV with the earlier arrival time has the advantage. Without
loss of generality, we assume that one of the CAVs has the advantage
and the other one has disadvantage. We represent the distance of
the CAV with the advantage from the beginning of the conict
zone and from the end of the conict zone with
dA
be дi n
and
dA
end
,
respectively. Similarly, we represent the distance of the CAV with
disadvantage from the beginning of the conict zone with
dD
be дi n
.
Figures 1, 2, and 3 show dierent scenario where the
dA
be дi n
,
dA
end
and
dD
be дi n
are shown. We assume that Equation1 represents the
dynamics of each CAV. We assume the following vehicle dynamics
for the CAV.
Ûx=vcos(ϕ)
Ûy=vsin(ϕ)
Û
ϕ=v
Ltan(ψ)
Ûv=a
(1)
where
x
and
y
represents the position of the ego CAV in Carte-
sian coordinates,
ϕ
is the CAV’s heading angle from the x-axis,
v
and
a
are linear velocity and acceleration of the CAV respec-
tively,
L
is CAV’s wheelbase distance and
ψ
is steering angle of
front wheels with respect to the heading of the CAV. In order to
make the model more realistic, we consider an upper bound and a
lower bound on the acceleration rate and steering angle of a CAV
as:
a∈ [amin ,am ax ]
and
ψ∈ [ψmin,ψmax ]
where
amax
and
ami n
are the maximum acceleration and deceleration rates and
ψmax
and
ψmi n
are the maximum and minimum steering angles of the
vehicle.
For simplicity, the trajectory of each CAV is projected onto its
path and represented with the double-integrator model. As a result,
the stop distance of the CAV with advantage is calculated as:
dA
st op =
v2
A
2|abr a ke |(2)
We assume that each CAV broadcast its information every
T
mil-
liseconds and the worst-case end-to-end delay (
ρ
) is 2
T
. Taking into
account the delay, the worst-case stop distance of the CAV with
disadvantage is calculated as:
dD
st op =vDρ+1
2aACC ρ2+(vD+aACC ρ)2
|2abr ak e |(3)
The rst two terms (
vDρ
and
1
2aACC ρ2
) indicate that the CAV with
disadvantage may be accelerating in the worst-case scenario while
waiting for broadcast information from the CAV with advantage. If
the distance of the CAV with advantage form the end of the con-
ict zone is greater or equal to the stop distance of the CAV with
advantage (
dA
end dA
st op
), there is a possibility that it may slow
down and stop inside the conict zone and block the CAV with
the disadvantage. Otherwise, there is no conict. Accordingly, we
dene the modied RSS rule as:
Definition 1.
General RSS Rule:
Given the entering order of
CAVs to a conict zone is known, the minimum safe distance to main-
tain from the conict zone (
dD
SA F E
) for the CAV with disadvantage
is:
dD
SA F E =(dD
st op dA
sc e nar i o +V LA+V LD
2if dA
end >dA
st op
0otherwise
(4)
where
dA
sc e nar i o
is the scenario-dependent distance that the CAV
with advantage travels inside the conict zone, and
V LA
and
V LD
are the vehicle length for the vehicle with advantage and disadvan-
tage, respectively. Since the distance values are calculated based on
the center of CAVs, the term
V LA+V LD
2
is added. In addition, the
following rule should be satised:
dD
SA F E >vDρ+1
2aACC ρ2(5)
To make sure the travelled distance during the response time of the
CAV with disadvantage is not greater than the safe distance.
Lemma 3.1. If the CAV with disadvantage always maintains a
distance of at least
dD
SA F E
from its conict zone, it will not hit the
CAV with advantage even if it changes its plan and decelerates at any
point in time.
Proof. If the distance of the CAV with the advantage from the
end of the conict zone is smaller than its stop distance,
dA
end <
dA
st op
, it will stop outside of the conict zone even if it decelerates
at a rate of smaller than or equal to abr ak e .
If the distance of the CAV with the advantage from the end of
the conict zone is greater than its stop distance,
dA
end >dA
st op
, it
may stop inside the conict zone if it decelerates. In this case, the
CAV with disadvantage will be notied after
ρ
milliseconds in the
worst-case scenario. If the CAV with disadvantage accelerates at a
rate of smaller than or equal to
aACC
during this time interval (
ρ
)
and then decelerates at a rate of
abr a ke
, its stop distance will be
equal to
dD
st op
(Eq. (3)) and it will not enter the conict zone and no
accident will happen. For scenarios where the scenario-dependent
distance is not zero,
dA
sc e nar i o >
0(same lane and merge), the paths
of the CAVs overlap and if the CAV with advantage decelerates, it
will allow the CAV with disadvantage to travel through the conict
3
zone by
dA
sc e nar i o
and still be safe. As a result, the required safe
distance is dD
st op dA
sc e nar i o .
Next, we study a few case studies and show how the safe RSS
distance is calculated for each scenario.
3.1 Same Lane
Let us consider a scenario where two CAVs are driving in the same
lane as depicted in Figure 1. The front CAV has the advantage since


Rear Front

 
Conflict Zone
Figure 1: An example of a same lane scenario with two CAVs.
The front CAV has the advantage and its distance from the
conict zone is zero. The conict zone is highlighted in or-
ange.
its arrival time at the conict zone is smaller than the rear CAV.
Since the paths of the front CAV overlaps with the path of rear
CAV,
dA
sc e nar i o =dA
st op
, which means the front CAV travels
dA
st op
meters inside the conict zone before a complete stop and the rear
CAV has
dA
st op
meters more to stop. According to Equation (4), the
required safe distance for the rear CAV (
dD
SA F E
) to maintain from
the conict zone/front CAV is:
dD
SA F E =dD
st op dA
st op +V LD+V L A
2
dD
st op and dA
st op are calculated according to Equation2 and 3.
3.2 Intersection
Now, let us consider a scenario where two CAVs approach an inter-
section and their future path crosses inside the intersection area as
it is depicted in Figure 2. We assume the arrival time of the green



Advantage
Disadvantage
Conflict
zone
Figure 2: A scenario with two CAVs approaching an inter-
section and their future path intersect. It is safe to enter the
conict zone after the other CAV leaves conict zone.
CAV to be earlier than the blue CAV and therefore, it has the ad-
vantage. If the green CAV stops anywhere inside the conict zone,
it’s not safe for the blue CAV to enter the conict zone. Therefore,
the scenario-dependent distance is zero,
dA
sc e nar i o =
0. As a result,
we have:
dD
SA F E =(dD
st op +V LA+V LD
2if dA
end dA
st op
0otherwise
If the distance of the green CAV from the end of the conict zone
is smaller than its stop distance, even in the worst-case (if it decel-
erates at the maximum rate), it will stop outside the conict zone
and does not cause a conict for the blue CAV. In this case, there
will be no conicts and dD
SA F E =0.
3.3 Merge
Next, we consider a merge scenario where two CAVs merge into
the same lane as it is shown in Figure 3. Without loss of generality,


Advantage
Conflict
Zone


Figure 3: A scenario where two CAVs are expected to be
merged into the same lane. The CAV with earlier arrival
time has the advantage.
we assume one of the CAVs (green one) has the advantage and
the other CAV has disadvantage respectively. In this scenario, the
scenario-dependent distance is
dA
sc e nar i o =min(
0
,dA
st op dA
me r дe)
,
where
dA
me r дe
is the distance of the CAV with advantage from the
merging point, which is indicated in Figure 3. As a result, the blue
CAV must maintain a minimum distance of
dD
SA F E =dD
st op min(0,dA
st op dA
me r дe)+V LD+V L A
2
from the conict zone. Note that once the blue CAV reaches the
merge point, the
dA
sc e nar i o
is changed. The lateral case in the origi-
nal RSS rules (two CAVs driving on adjacent lanes) can be modeled
like a merging case. If any of the CAVs attempts to merge into the
other CAV’s lane, it is only allowed if the created conict zone is
far enough from the other CAV i.e. at least dmax .
4 PROPOSED COOPERATIVE DRIVING
APPROACH
In this section, we rst present the algorithm that runs on each
CAV assuming no deadlock situation happens. In the next section,
we explain the deadlock resolution algorithm.
4
4.1 Main Algorithm
Given the initial position and nal destination of a CAV are known,
the motionPlanner uses the world’s map to determine the shortest
route (
R
) that connects CAV’s current position to the destination.
We assume that at least one feasible path exists that connects CAV’s
current location to its destination. The map,
M(N,E)
, is a directed
graph where
N
is the set of nodes or waypoints and
E
is the set of
edges or connections between waypoints. Each edge of the map
graph has a weight,
w
, which indicates the maximum velocity for
that segment of the road. In our algorithm, we assume that the ego
CAV’s computation time and communication time are bounded by
T.
In a periodic manner, each CAV broadcasts its ID, position, ve-
locity, timestamp, and its future path (
FP
), which is an array of
x-y coordinates. We assume that all CAVs synchronize their clock
using GPS so that timestamps are captured with clocks that have
almost the same notion of time. When the CAV receives the in-
formation of other CAVs, it checks if their paths intersect or the
distance between their paths is less than a threshold. If so, the
CAV computes a set of conict zones (
C
). For each conict zone,
the CAV determines which vehicle has the advantage to enter the
conict zone rst based on who is expected to reach the conicting
zone rst. To detect possible deadlocks, the CAV computes a graph
called Partial Dependency Graph (PDG), which represents the de-
pendency among other CAVs and itself (who should yield to who
over a conict zone). Next, the CAV broadcasts the computed PDG,
and after receiving other CAVs PDG, it constructs the Complete
Dependency Graph (CDG) to detect and resolve possible deadlocks.
Finally, if the CAV has disadvantage over a conict zone, it com-
putes a safe velocity so that it always maintains a safe distance from
that conict zone. Based on the determined velocity, the weight
of some of the edges are updated to reect the presence of other
CAVs and to make sure a safe distance is always maintained from
the conict zone. Then, the motion planner runs the shortest path
algorithm again to check if a shorter path exists that does not cause
a new conict. Finally, the motion controller uses a subset of future
waypoints and velocities of corresponding edges to determine the
desired velocity and control inputs (steering angle and acceleration)
for the CAV. Alg. 1 shows the pseudo-code of our algorithm that
is executed on each CAV. To have a better understanding of our
algorithm, we have depicted dierent components of our approach
and their relationship in Figure 4. Next, we will focus on explaining
the functionality of each component of the algorithm.
4.2 Future Path Computation
Each CAV broadcasts its ID, position (
x,y
), velocity (
v
), and the cor-
responding timestamp (
ts
) as well as its future path (
(x1,y1), ..., (xn,yn)
).
Assuming the CAV’s motion controller is tuned to have a short set-
tling time, the CAV will track its path with a negligible error. As a
result, we represent the future position of the CAV with a subset of
its expected route (
R
). Given
RM(N,E)
is the route of the CAV,
the future path of the CAV,
FP R
is calculated as follows which
consists from npoints:
Algorithm 1: CAVs algorithm
while has not reached the destination do
FP = compute_future_path();
CAV_info = [x, y, v, ts, FP, ID];
broadcast(CAV_info);
others_info = receive_other_CAVs_info();
for each member of other_CAVs_info do
[C, PDG] = nd_conict_zones(CAV_info,
others_info);
end
broadcast(PDG);
others_PDG = receive_other_PDGs();
CDG = construct_CDG(PDG, other_PDGs);
C = deadlock_resolution(C, CDG);
if ego CAV has disadvantage over a conict zone then
[FP, velocity] = motion_planner(C, Map);
end
motionController(FP, Velocity);
end
Map
Graph
Other CAVs'
Future
Trajectories
Motion
Planner
(4.4)
CDG
Construction
(5)
Deadlock
Detection &
Resolution
(5)
Conflict Zone
Detection
(4.3)
Future Path
Computation
(4.2)
Map V2V Module
Other CAVs’
PDGs
PDG
CAV's Future Path
Updated Set
of Conflict
Zones (C)
CDG
Waypoints and Velocities
Set of
Conflict
Zones (C)
Motion
Controller
(4.5)
(( ))
Throttle, Brake,
and Steering
Vehicle State
Figure 4: Overview of our approach. Details of each compo-
nent –except V2X module and map– are explained later.
FP =((xi,yi) ∈ Ri=n
Õ
i=2q(xixi1)2+(yiyi1)2<dmax )
(6)
where dmax is the xed length of the future path calculated as:
dmax =vm ax (ρ+tb)(7)
ρ
represents the worst-case end-to-end delay from one CAV captur-
ing its information and broadcasting it, to another CAV’s actuation
based on the received information (see Figure 5) and
tb
is the worst-
case brake time which can be calculated as
tb=vma x
|abr a k e |
. Figure 5
shows the execution prole of our algorithm on two CAVs (
i
and
j
). Let us assume that CAVs
i
and
j
have a conict and CAV
i
(top)
has the advantage. If CAV
i
slows down due to any reason right
5
after sensing and broadcasting its info, the CAV
j
will not be noti-
ed until receiving the next broadcast. As a result, the worst-case
end-to-end delay (
ρ
) is bounded by 2
T
as depicted in Figure 5. By
𝑇 𝑇 𝑇
𝐶𝐴𝑉
𝑖
𝐶𝐴𝑉
𝑗
Sensing Actuation
worst-case end-to-end delay
info
PDG
info
PDG
info
PDG
Figure 5: CAVs perform computation and communication in
a synchronized manner. The worst-case sensing to actuation
delay corresponds to the case that CAVibreaks down right
after sensing.
computing the
dmax
based on the worst-case info sharing delay
and worst-case braking time, we ensure that for the rst time that
two CAVs detect that they have a conict, the CAV with the disad-
vantage have enough distance to safely stop without entering the
conict zone, even in the worst-case scenario.
4.3 Conict Zone Detection
Despite existing approaches that use xed conict zones, we use
CAV’s expected trajectory to detect a conict zone. As mentioned
before, CAVs’ future paths (
FP
) are used to represents their expected
future position. First, CAVs computes the distance between the
mid point of edges on their path. All contiguous edges that have
a distance less than
dth
are considered to be a part of the same
conict zone. Two CAVs may have multiple conicts on their path
as depicted in Fig. 6. Each conict zone
Ci
is a data structure that
Figure 6: An example of two CAVs with arbitrary paths and
two conict zones. The conict zone includes parts of the
CAV path (waypoints) where the distance between paths of
CAVs is less than a threshold.
includes waypoints that are inside the conict zones, distance of
CAVs from the the beginning and end of the conict zone, their
expected arrival time at the conict zone (Equation 8) and the ID
of the CAV that has the advantage. We compute the arrival time
assuming the CAV drives at a constant velocity.
TOAi=
di
be дi n
vi
(8)
where
di
be дi n
is the distance of the CAV
i
from the conict zone
and
vi
is the velocity of the CAV
i
. Since the algorithm is executed
periodically (every
T
ms), the value of
TOAi
is updated as the
velocity of the CAV changes. If a CAV is stopped inside a conict
zone, its arrival time is set to zero. By default, the CAV with the
earliest arrival time will have the advantage unless it is changed to
resolve a deadlock (explained in the next section) or the other CAV
has a priority (e.g. opposite direction). If two CAVs have the same
arrival time, the CAV with the lower ID will have the advantage to
break the tie. In addition, if the dierence between the arrival times
of two CAVs is within the accuracy of the clock synchronization (
±
10 nanoseconds for GPS), they use CAVs ID to determine who has
the advantage.
4.4 Motion Planner
If a CAV has disadvantage over a conict zone, it rst checks if
an alternative path exists such that it avoids all the conicts. If
such a path exists, the CAV selects that path and if not, the CAV
calculates a safe velocity (
vSA F E
) to be maintained so that the CAV
is always safe. The safe velocity,
vSA F E
, is determined based on
the minimum safe distance that the ego CAV must maintain from
the conict zone given that other CAV –which has the advantage–
may slow down at any point in time and stop inside the conict
zone.
Maximum Safe Velocity:
For each segment of the road that
has a distance of
dC
from the conict zone, the maximum safe
velocity is computed using Equation 9.
vSA F E =−(2ρaACC +2|ab r ak e |) +
2(9)
where
=
4
(a2
br a ke +
2
aACC ρab r ak e aACC ρ2abr a ke
2
dC|abr a ke |
.
Equation 9 is determined by solving Equation 3 for
vD
when the
distance from the conict zone is
dC
.
dC
can be calculated using
Equation 12. Equation (9) ensures that the CAV with disadvantage
has always a minimum distance of dD
SA F E from the conict zone.
Once the safe velocity is determined for each conict zone (
Ci
),
the motion planner updates weights of the map
M(N,E)
, to account
for the presence of other CAVs and generates safe velocities for
the motion controller. To account for the presence of other CAVs,
the motion planner determines,
U
the set of all edges (
ei
) that are
connected to waypoints that are on the future path of other CAVs
U={eiE|eiconnected (F P )} (10)
where
connect ed (F P )
is the set of all edges that are connected to
waypoints in the set
FP
. To account for the safe RSS distance, the
motion planner determines
UD
, the set of all edges that are con-
nected to the waypoints that are on the future path of the CAV with
disadvantage (
FPD
) and are either a member of the conict zone
set (C) or within the safe distance (dD
SA F E ) of the conict zone.
UD={eiE|eiconnected (F P C
D)} (11)
where
connect ed (F P C
D)
is the set of all edges that are connected to
waypoints in the set
FPC
D
. Figure 7 shows a merge scenario and
CAV’s future paths. Weights of all edges connected to nodes that
are on the path of the CAV with advantage (depicted in green) and
all edges that are on the path of the ego CAV and are either within
the safe distance of or inside the conict zone are updated. The set
UD
and
U
are highlighted on the path of CAVs. The subset of future
6
Advantage
Updated
Weights
𝑑𝑆𝐴𝐹𝐸
𝐷
Conflict
Zone
𝑈𝐷
𝑈
Figure 7: Weights of the edges on the path of the other CAV
and edges on path of the ego CAV are updated to account for
the presence of other CAVs as well as the conict zone and
the required safe distance.
point, FPC
D, is determined as:
FPC
D={niN|niFPDand niC or niwit hin(Cj)}
wit hin(Cj)
is the set of all waypoints that where their distance from
the conict zone
j
is less than
dSA F E
. To calculate the distance
between two waypoints, we use the following equation:
distance =
N
Õ
i=2q(xixi1)2+(yiyi1)2(12)
where
N
is the number of waypoints including the rst and last way-
points. Finally, weights of each edge in set
U
and
UD
are updated
based on their distance from the conict zone using Equation 9:
wi=l
vi
SA F E
(13)
where
i
refers to each segment of the road,
l
is the length of the
corresponding edge and
vi
SA F E
is the safe velocity calculated for
each segment of the road (edge). Since the weight of an edge may
be updated multiple times –as it may be involved in more than
one conict–, the maximum weight is considered (the slowest safe
velocity) for an edge. If the safe velocity (
vSA F E
is equal to zero,
instead of innity, the weight is set to be a large constant number.
After updating the weights, the motion planner uses the Dijk-
stra algorithm to nd the shortest path to the destination. The
summation of weights (
Íwi
) from the source to the destination
corresponds to the travel duration.
4.5 Motion Controller
The motion controller uses the future waypoints and safe velocities
to calculate the reference heading angle
θr ef
and the safe velocity
vr ef
for the CAV. For the desired heading angle (
θr ef
), the motion
controller selects a look-ahead point similar to the pure pursuit
algorithm [
31
] and calculates the bearing angle from its current
location (x,y) to the look-ahead point:
θr ef =atan2(xxl,yyl)(14)
where
xl
and
yl
correspond to the x-y coordinate of the look-
ahead point. We assume that each vehicle has an initial desired
velocity of
v0
and never drives faster than that. The motion con-
troller uses the weight of the next edge to determine the reference
velocity (
vr ef =di
wi
). If the calculated velocity is greater than CAV’s
initial desired velocity (
v0
), it sets the reference velocity to be
v0
.
If the reference velocity is close to zero, (
v<ϵ
), it is set to zero.
Once the reference heading and velocity are calculated, they are
passed to two Proportional Integral Derivative (PID) controllers to
calculate the steering angle and acceleration for the vehicle:
(ψ=kPeθ+kIeθ+kDÛeθ
a=k
Pev+k
Iev+k
DÛev
(15)
where
kP,kI,kD
and
k
P,k
I,k
D
are constant (controller gains) that
are tuned to achieve a fast response while the overshoot is small
(short settling time),
eθ=θrθ
and
ev=vSA F E v
, and
Ûev
and
Ûeθare the derivative of evand eθ, respectively.
5 DEADLOCK DETECTION AND
RESOLUTION
In order to detect and resolve deadlocks, all CAVs create a directed
graph called the dependency graph. Nodes of the dependency graph
are vehicle IDs and edges indicate that if a CAV is yielding to
another CAV over a conict zone. There will be a directed edge
from node
Vi
to node
Vj
if CAV
Vi
is yielding to the CAV
Vj
over a
conict zone. Since a CAV determines only the conicts between
itself and other CAVs –and not the conicts between other CAVs,
the constructed dependency graph is not complete. We refer to the
dependency graph of each CAV as the “partial dependency graph”
or PDG. To compute the complete graph, each CAV broadcasts its
PDG to inform other CAVs about its conict zones with other CAVs
and to receive other CAVs’ PDG. From the received PDGs of other
CAVs and the PDG of the ego CAV, the complete dependency graph
(CDG) is constructed. To build the CDG, the PDG is incrementally
updated by adding nodes and edges for each received PDG. Finally,
all edges between two nodes are merged into one. Figure 8 shows a
scenario with 5 CAVs that have determined their PDG and the nal
consensual CDG.
(1)
(2)
(3)
(4)
(5)
𝑉
1
𝑉
2
𝑉
1
𝑉
2
𝑉
3
𝑉
4𝑉
5
𝑉
5
𝑉
2𝑉
4
𝑉
2
𝑉
3
𝑉
4
𝑉
4
𝑉
5𝑉
3
𝑉
2
𝑉
1
𝑉
2
𝑉
3
𝑉
4𝑉
5
Reconstructed CCG
Figure 8: Each CAV determines and broadcasts its PDG. After
receiving other CAVs’ PDG, CAVs construct the CDG and can
resolve deadlocks.
After constructing the CDG, each CAV checks if the CDG has
a cycle. We use the Depth-First Search (DFS) algorithm to detect
cycles. If a deadlock is detected, each CAV calculates a score for
each CAV that is involved in the cycle based on its average time of
7
Figure 9: A snapshot of a map retrieved from the OpenStreetMap (left), its corresponding directed graph in MATLAB (middle)
and a scenario with randomly spawned vehicles on the map (Right).
arrival at corresponding conict zones. If a CAV has
m
conicts, its
score is calculated as:
S=Ím
i=1TOAi
m
where
TOAi
is the time of arrival of the CAV at its
i
th conict zone.
We select the CAV with the least average time of arrival to have
the advantage over all of its conict zones because on average, it
can reach its conict zone earlier than others. We refer to this CAV
as the leader. Once the leader is determined, the direction of all
incoming edges to the leader’s node is reversed. If two CAVs have
the same score, the CAV with the lower ID number will be selected
as the leader. Since there can be more than one cycle in a graph,
this process is repeated until all cycles are removed.
Lemma 5.1. If the CDG has no cycles, then there is no deadlock
involving the ego CAV.
Proof.
Once the CDG is modied to be acyclic, there is no path
(set of sequential edges) starting at node
Veдo
that eventually loops
back to node
Veдo
again, which means the ego CAV never yields to
other CAVs that are yielding to the ego CAV and therefore, there is
no deadlock involving the ego CAV.
It takes some time to resolve a deadlock due to the vehicle’s
dynamic –CAVs cannot change their velocity and expected arrival
time instantly. As a result, CAVs may face the same deadline again
when they compute the CDG after
T
. It can be shown that the
result of deadlock resolution will be the same (the same CAV will
be selected as the leader) until the deadlock is resolved. Since the
leader has the least average time of arrival in the rst iteration, it
does not yield to any other CAV while other CAVs involved in the
deadlock slow down to yield to at least one CAV. Therefore, the
average time of arrival of the leader will be less than other CAVs in
the second iteration and so on.
6 EXPERIMENTAL RESULT
We evaluated our algorithm on a simulator that is developed in
Matlab. We created a tool in Python to automatically extract a
desired map from the OpenStreetMap
1
(OSM format) and then
1https://www.openstreetmap.org/
generate the world map graph for it. Once the map is generated, a
driving scenario is created where initial position and velocity and
the destination of CAVs are randomly selected. We used dierential
equations represented in (1) to model vehicle’s dynamics. The size
of each vehicle is 5x2 m, the lane width is 5 m and the distance
between waypoints of the map is 0.5 m. Gains of the controller for
both heading and velocity control are
KP=
5and
KD=
0
.
1. Other
parameters of the vehicle are listed in Table 1. CAVs communication
vmi n vmax ami n ama x ψmi n ψma x Tρ
0m
s23m
s8m
s25m
s2π
3rad π
3rad 0.1s0.2s
Table 1: Parameters of the CAVs for simulation.
delay is modeled by queuing the broadcast packets. In Figure 9, a
randomly generated map from openStreetMap, its corresponding
map graph and a random scenario with 20 CAVs are depicted.
6.1 Safety Evaluation
To demonstrate the safety of the proposed algorithm, we created a
merge and an intersection scenario where two CAVs have a conict
on their future path as it is depicted in Figure 10.
Figure 10: An Intersection and a merge scenario are created.
The CAV with advantage suddenly decelerates and stops.
To verify that CAVs are always safe, we force the CAV with
the advantage to suddenly decelerate at dierent times. We show
8
that no accident will happen regardless of the deceleration time
and CAVs maintain a minimum safe distance of 5 meters. Using
brute-force testing, the deceleration time of the CAV with the ad-
vantage varies in a 30-second interval with a 0.1 s increment that
includes critical times that stops inside the conict zone. Figure 11
and 12 show the distance between CAVs for the intersection and
merge scenarios, respectively. In the intersection scenario, the CAV
Figure 11: Brute-force evaluation of an intersection scenario.
CAVs distance is always greater than a threshold regardless
of the deceleration time of the CAV with the advantage –if it
stops before entering the conict zone (dark green), inside
the conict zone (yellow), or after the conict zone (blue).
with the advantage may stop before, inside, or after the conict
zone where distances between CAVs are depicted in dark green,
yellow, and blue colors, respectively. For cases that the CAV with
advantage stops before or after the conict zone, the CAV with
disadvantage continues while in cases that the CAV with advantage
stops inside the conict zone, the CAV with advantage slows down
and stops (depicted in yellow). In the merge scenario, the conict
Figure 12: Merge scenario - CAVs distance remains greater
than a threshold for all cases where the CAV with advantage
stops before entering the merge (Yellow) or after the merge
(dark green).
zone moves with the CAV with the advantage after it reaches the
merging point. As a result, the CAV with the advantage either stops
before the conict zone or inside it. For cases that the CAV with
the advantage stops before the merging point, the CAV with the
advantage continues and enters the merge (depicted in dark green)
and for the rest of the cases, the CAV with the disadvantage slows
down and stops (depicted in yellow).
6.2 Deadlock Resolution Demonstration
To evaluate our deadlock detection and resolution approach, we
created a deadlock situation at the intersection (Figure 13). The
right part of Figure 13 shows the CCG for the scenario. We xed the
3
4
1
2
1
4
2
3
Z1
Z2 Z3
Z4
Figure 13: A deadlock scenario where 4 CAVs approach the
intersection with same velocity (left) and the corresponding
CDG (right).
paths of CAVs to make a left turn at the intersection while having
the same distance from the intersection and the same velocity. We
simulated CAVs’ behavior with and with our deadlock detection.
Figure 14 shows the velocities of CAVs for both cases. For the case
that no deadlock resolution is done, CAVs slow down to yield to
other CAVs and eventually stop and will wait forever. For the case
with deadlock resolution, CAVs slow down at rst but speed up
when their conict zone is cleared. We can observe that after 7s,
0123456789
Time (s)
0
2
4
6
8
10
12
Velocity (m/s)
CAV1
CAV2
CAV3
CAV4
Figure 14: Velocity proles of CAVs with and without dead-
lock resolution for the scenario in Figure 13
all CAVs reach their desired velocity (10m/s) while in no deadlock
detection case, their velocity converges to zero.
6.3 Eciency Evaluation
To evaluate the eciency of our approach, we compared the perfor-
mance of our approach with the case that vehicles are autonomous
but not connected. For the non-connected case, the intersections
are managed by stop signs and all other conicts among CAVs are
handled by the AV’s perception system e.g. adaptive cruise control
9
(ACC) system. We extracted a map from the OpenStreetMap (Fig-
ure 9) and simulated three scenarios, i) light trac with 5 vehicles,
ii) moderate trac with 10 vehicles, and iii) heavy trac with 20
vehicles being present at the same time. When a vehicle exits the
map boundary, a new vehicle is spawned. We measured the average
velocities of CAVs and reported them in Table 2. We also computed
the fuel consumption of CAVs using the following model [
32
] and
reported them in Table 2:
f=(0if PT>0
fi
3600 +β1PT+β2aPIotherwise (16)
where
PT=min(Pmax ,PC+PI)
is the total tractive power (kW),
PC=b1v+b2v3
is the cruise component of total power (kW),
PI=mav
1000
is the inertia component of the total power (kW),
fi=
888
.
8
mL/h
is the instantaneous fuel consumption rate (mL/s),
Pmax
is the maximum engine power (kW),
m
is the vehicle mass,
a
and
v
are the instantaneous acceleration and velocity,
b1
is rolling resis-
tant factor (kN), and
b2
is the aerodynamic drag factor (kN/(m/s)
2
),
β1
and
β2
are the eciency factors for non-accelerating and accel-
erating cases.
Light
Trac
Moderate
Trac
Heavy
Trac
AVs
CAVs
AVs
CAVs
AVs
CAVs
Average Velocity
(m/s)
10.51 11.55 10.91 11.83 11.21 11.96
Average Fuel Con-
sumption (mL/s)
1.271 0.495 1.089 0.479 1.017 0.485
Table 2: Comparing the average velocity and fuel consump-
tion of vehicles when they navigate autonomously (non-
connected) and cooperatively (connected).
With the help of shared information, CAVs not only drive at
higher velocities, they drive smoother than non-connected case
because they slow down and stop less frequently and therefore,
their fuel consumption is less than the connected case.
7 CONCLUSION AND FUTURE WORKS
In this paper, a new denition is introduced for the RSS rules that
can be applied to any scenario, and CAVs’ safety is ensured by
considering the worst-case scenario. Next, we presented a coopera-
tive driving algorithm for CAVs based on proposed RSS rules. Our
algorithm can also detect and resolve deadlocks in a distributed
manner. The correctness of our approach is veried by conducting
experiments using our simulator. Future works include taking into
account various fault models (e.g. the network delay is larger than
T
or a CAV is unable to communicate, a CAV is being compromised
and lies about its position and/or its future trajectory, etc.) with the
help of infrastructure (e.g. installed cameras).
8 ACKNOWLEDGEMENT
This work was partially supported by funding from NIST Award
70NANB19H144, and by National Science Foundation grants CNS
1525855 and CPS 1645578.
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... Transportation systems all around the world experience different traffic problems, such as increased traffic flow, poor safety, and road accidents. According to the 2019 Urban Mobility report [1], traffic congestion resulted in Americans traveling an extra 8.8 billion h, consuming an extra 3.3 billion gallons of fuel leading to an estimated cost of $166 billion. To cope up with issues, the general idea is to build additional highways, which is impractical now, as most cosmopolitan cities are running out of land. ...
... Prominent work has been done on developing the solution approaches for various single test scenarios (i.e., platooning, intersection crossing, lane change and merge) of collaborative driving guiding vehicles on how to behave cooperatively in the given situations. The limitation of these solution approaches is that they work well for the scenarios for which they are developed, thus providing no general suggestions in other scenarios [1,88]. For example, an algorithm developed for cooperative lane change directs the vehicles on how to change the lane cooperatively, but, at the same time, the algorithm provides no recommendations when the vehicles cross the intersection. ...
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Thesis
Intersections are at the core of urban congestion. For more than a decade, new approaches based on autonomous and connected driving have been proposed. They aim to improve the performance of traffic control at intersections, by harnessing connectivity and driving automation (longitudinal control). These approaches have in common the fact that vehicles can negotiate together their right of way to use the conflicting space. However, they are different in terms of the way they share the space and optimization techniques. The challenge is to define the sequence of access of vehicles to the common space (which one goes first, which is the second, and so on) and the speed profile of vehicles to avoid, if possible, unnecessary stops. The literature shows that it is difficult to optimally solve both problems simultaneously in a dynamic context under strong real-time constraints.To solve the problem with respect to reality, the thesis explores the negotiation protocol as well as the policy that meets the safety requirements and respects the hard real-time constraints of the system. From the safety standpoint, vehicles access conflicting spaces by forming virtual platoons. In this way, they can maintain a sufficient safety gap to be ready to react safely in the case of danger. Regarding the real-time constraints, a rule-based system was chosen to form the sequences. In order to improve the performance of the intersection, two properties were exploited. The rules allow vehicles that follow each other (property 1) or those that can pass in parallel (property 2) to form groups. The group crosses the intersection together. A distributed right-of-way negotiation algorithm is proposed and compared to other policies of the literature. The simulation shows a significant gain in terms of intersection capacity.To further improve the performance of the proposed cooperative traffic control at intersections, the thesis focused on the longitudinal control issue. It defines an optimal output state achievable, using optimal control theory. Control based on quadratic programming shows the interest of the approach on an elementary intersection. On the one hand, the optimal output state minimizes the headway times between two conflicting vehicles. This improves the throughput of the intersection. On the other hand, it allows the modification of the sequences during the longitudinal control to improve the sequence dynamically according to the new incoming vehicles. The new approach was extended to a complex intersection. Several optimal output state-based sequence formation policies were simulated. The simulation shows that the policy based on distributed particle swarm optimization significantly improves the performance of the intersection in terms of capacity and speed. Distributed particle swarm optimization allows the formed group of platoons to be adapted to the dynamic traffic demand patterns.
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