Multi-Risk Assessment and Management in the Presence of Personal
Light Electric Vehicles
Emmanuel Alao
1 a
, Lounis Adouane
1 b
and Philippe Martinet
2 c
1
Universit
´
e de Technologie de Compi
`
egne (UTC), CNRS, Heudiasyc, Compi
`
egne, France
2
Centre Inria d’Universit
´
e C
ˆ
ote d’Azur, (INRIA), ACENTAURI, Sophia Antipolis, France
Keywords:
Autonomous Vehicles, Autonomous Driving, Predictive Navigation, Risk Assessment and Risk Management,
PLEVs, Multi-Modal Prediction, Multi-Risk.
Abstract:
This paper presents an approach to autonomous vehicle navigation in urban environments with dynamic and
multi-modal agents like Personal Light Electric Vehicles (PLEVs). The traditional Predictive Inter-Distance
Profile (PIDP) risk assessment metric (Bellingard et al., 2023) is extended to handle multiple multi-modal
motions using a fusion of PIDPs (F-PIDP). This approach accounts for the uncertainties in the various tra-
jectories that PLEVs can follow on the road. A priority-based strategy is then developed to select the most
dangerous agent. Then F-PIDP and Model Predictive Control (MPC) algorithm is employed for risk man-
agement, ensuring safe and reliable navigation. The efficiency of the proposed method is validated through
several simulations.
1 INTRODUCTION
As Autonomous Vehicles (AV) become more inte-
grated in real-world environments, there navigation
among humans becomes increasingly critical. While
research has focused on navigation among pedestri-
ans, less attention has been given to Personal Light
Electric Vehicles (PLEVs) such as electric bikes and
scooters. AVs usually predict the motion of surround-
ing traffic agents to plan a safe trajectory. Most trajec-
tory prediction algorithms predict a single most prob-
able trajectory (Luo et al., 2018), (Lee et al., 2017).
However, as opposed to walking pedestrians, PLEVs
can exhibit varying speed profiles ranging from low
to high speeds as much as five times that of pedestri-
ans. This results in multiple possible predictions of
the motion of the PLEV. Many multi-modal predic-
tion algorithms have been developed in the literature
to predict multiple future trajectories for such agents.
For example, in (Jo et al., 2016) and (Lefkopoulos
et al., 2020) a tracking algorithm that combines mul-
tiple models was proposed to predict the possible mo-
tions of traffic agents.
Once the future trajectories of the traffic agents
a
https://orcid.org/0000-0002-8790-3338
b
https://orcid.org/0000-0002-5686-5279
c
https://orcid.org/0000-0001-5827-0431
or PLEVs are predicted, the AV needs to compute a
safe trajectory towards its desired destination. Model
Predictive Control (MPC) (Yu et al., 2021), (Saljanin
et al., 2022) has emerged as a powerful and robust
tool for controlling and optimizing the motion of AVs.
Unlike traditional control algorithms, MPC uses the
dynamic model of the system to predict future states
and optimize the control actions of the system over
specific time horizons. It can also handle various con-
straints, such as speed limits, and safety margins, en-
suring feasible and safe control actions. Nevertheless,
the presence of multiple trajectories for a single agent
makes the computation of risk-free trajectories more
challenging for autonomous driving systems.
This paper proposes to perform risk assessment
using a fusion of PIDPs (F-PIDP) (Alao et al., 2024)
to reduce the PIDPs to a single prediction. Multi-risk
management is then performed using a priority-based
target selection and F-PIDP+MPC method. Unlike
the conservative MPC method that considers all the
trajectories, the F-PIDP+MPC uses the F-PIDP as a
safety reference.
Contributions. This work presents a method to per-
form risk assessment and management in the presence
of multi-modal agents. We extend the approach pro-
posed in (Alao et al., 2024) to handle multiple PLEVs.
The method used in (Alao et al., 2024) handles un-
Alao, E., Adouane, L. and Martinet, P.
Multi-Risk Assessment and Management in the Presence of Personal Light Electric Vehicles.
DOI: 10.5220/0013059500003822
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics (ICINCO 2024) - Volume 1, pages 137-145
ISBN: 978-989-758-717-7; ISSN: 2184-2809
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
137

certainties in the possible trajectories that a single
agent can take. On the other hand, we describe in
this study a priority-based collision avoidance method
that also supports multiple agents. Additionally, an
approach based on MPC was compared with the pro-
posed method.
The structure of this paper is laid out as follows:
Section 2 presents the related works. Section 3 in-
troduces the preliminaries on PIDP, MPC, and mo-
tion prediction of traffic agents. Section 4 presents
the proposed F-PIDP for multi-risk assessment of the
future motion of multiple PLEVs. Section 5 then de-
scribes the proposed risk management strategy using
F-PIDP+MPC and a priority-based collision avoid-
ance strategy. Section 6 presents the results of various
evaluations of the proposed method. Finally, Section
7 summarizes the paper’s primary contributions and
offers some prospects.
2 RELATED WORKS
Most criticality metrics for assessing and managing
risk in traffic environments check for situations when
or where safety is violated. For instance, the Time
to Collision (TTC) (Westhofen et al., 2023) and Time
to React (TTR) (Hillenbrand et al., 2006) risk met-
rics respectively check for the time when a collision
occurs and the remaining time when the driver can
perform a maneuver to avoid a collision. The Predic-
tive Inter-Distance Profile (PIDP) (Bellingard et al.,
2023) (Iberraken et al., 2018) (cf. Section 3.3), and
the fusion of PIDPs (Alao et al., 2024) as the name
implies computes the inter-distances between two or
more agents and has been found to possess many fea-
tures that can be harnessed to assess the risk of multi-
ple agents. The main advantage of such methods lies
in their low computational complexity, though they
fail in dealing with situations with various uncertain-
ties in the maneuvers of the agents.
Probability-based risk assessment and manage-
ment methods have been developed to address these
problems by modeling the uncertainty of the motion
as a probability distribution. Therefore, probabilis-
tic frameworks such as the Hidden Markov Model
(HMM) (Laugier et al., 2011) and Dynamic Bayesian
Network (DBN) (Li et al., 2019) & (Iberraken and
Adouane, 2022) have been proposed to perform risk-
aware navigation in the presence of uncertainties.
Optimization methods have also been extended to
compute safe control actions for autonomous vehi-
cles while respecting constraints related to the vehi-
cle and the traffic environment. Among them, the
Model Predictive Control (MPC) (Kim and Kumar,
2014) method is a prominent solution in this domain,
known for its capacity to predict future states and
make real-time adjustments. MPC has been applied to
solve problems in many fields of engineering as high-
lighted in (Mayne, 2014). Its performance is undeni-
able in autonomous driving systems due to constraints
on vehicle actuators and physical limits that are not
explicitly considered in several other methods, such
as the PID controller and sliding mode controllers (Vu
et al., 2021). In general, it is possible to perform both
risk assessment and management using MPC, where
risk assessment is formulated as collision constraints
and risk management becomes the optimal control
problem for the MPC algorithm to solve, as done
in (Philippe et al., 2018) (Fiasch
´
e et al., 2023) (Nan
et al., 2021) (Miao and Han, 2023). Nonetheless, con-
sidering collision risk is not sufficient for safe naviga-
tion since there exist multiple uncertainties in the traf-
fic environment, such as the prediction uncertainties
in the multiple maneuvers that PLEVs can perform in
urban areas (Rudenko et al., 2020).
Learning-based methods have also been leveraged
to compute safe trajectories for autonomous systems.
For example, using Neural networks (Li et al., 2018)
and (Kuderer et al., 2015) were able to learn from real
driving scenarios. The authors in (Cimurs et al., 2021)
presented a Deep Reinforcement Learning (DRL)
based decision-making framework for automated ex-
ploration. In general, Learning-based methods can
handle uncertainties implicitly, however, they require
a large amount of data to generalize to multiple sce-
narios.
3 PRELIMINARIES
3.1 AV Motion Model
The motion of the ego-vehicle is considered a nonlin-
ear motion model of the form:
x
AV
t+1
= f (x
AV
t
,u
AV
t
) (1)
where at time step t, the state of the ego-vehicle
is x
AV
t
∈ R
n
x
, u
AV
t
∈ R
n
u
denotes the control inputs,
and the function f : R
n
x
× R
n
u
−→ R
n
x
, is the ve-
hicle dynamic model. The control inputs to the AV,
u
AV
t
= [v,δ] are the velocity v and steering angle δ of
the AV with control limits u
min
≤ u
AV
≤ u
max
.
3.2 PLEVs Motion Model
Surrounding agents including PLEVs, are considered
to be dynamic obstacles. Using suitable multi-modal
motion prediction algorithms as in (Jo et al., 2016),
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138

the possible future trajectories of the agents (cf. Fig-
ure 1) can be expressed as a linearized dynamic mo-
tion
x
PV
j,t+1
= Ax
PV
j,t
+ Bu
PV
j,t
(2)
where x
PV
t
=

x
PV
t
,y
PV
t
,θ
PV
t

T
are the longitudinal po-
sition, lateral position and orientation of the PLEV.
The control action of the PLEV split into forward and
angular velocity is denoted u
PV
t
= [v
PV
t
,w
PV
t
] based
on the unicycle motion model. The variable j ∈
{1,2,·· · , N
tra j
} denotes a specific trajectory out of
the multi-modal trajectories of the agent. Each tra-
jectory is assumed to have a probability Pr( j). A and
B are linearized state and control matrices.
Figure 1: Urban traffic scenario with AV (in red) and mul-
tiple PLEVs (in purple): with multiple possible trajectories.
3.3 Predictive Inter-Distance Profile
(PIDP)
The Predictive Inter-Distance Profile (PIDP) is a met-
ric for assessing the risk of collision in traffic scenar-
ios. It evaluates the potential for accidents by mea-
suring the distance between the traffic agents, such as
an autonomous vehicle and another road user, over a
specified time horizon. Unlike other risk assessment
methods, PIDP does not rely on the geometric shapes
of the future trajectories of road users, making it ver-
satile for various traffic situations. PIDP functions
as a dual measure of risk, encompassing both spatial
and temporal scales. As a spatial risk measure, PIDP
shows the separation distance between traffic partici-
pants which is crucial for understanding the proxim-
ity of vehicles, pedestrians, or other road users. For
example, when calculating the Euclidean distance be-
tween trajectories, PIDP considers the safety distance
as a threshold. Let the radii of two interacting agents
be R and r respectively, then the safety distance is de-
fined as:
d
sa f e
= R + r + d
margin
(3)
where d
margin
is a safety margin which can be static or
dynamic. If the minimum PIDP value (minPIDP(t) ≤
R + r) falls below this threshold, it indicates a poten-
tial collision in the future (cf. Figure 2).
As a temporal risk measure, PIDP considers how
long it will take for the entities to reach a critical dis-
tance where a collision might occur. That is, PIDP
provides insights into the urgency of potential colli-
sion scenarios. The time when safety is not respected
(t
SNR
) is the point when the safety distance is first vi-
olated, which can give an idea of the criticality of the
situation (cf. Figure 2).
By combining spatial and time scales, PIDP de-
livers a comprehensive risk assessment that takes into
account the urgency and physical proximity of poten-
tial collisions. While effective, PIDP assumes a uni-
modal motion prediction for each traffic participant,
which is not sufficient for safe navigation in the pres-
ence of multi-modal agents like PLEVs. To address
this problem, this paper proposes the Fusion of PIDPs
(F-PIDP) to account for multi-modal motion.
Figure 2: Predictive Inter-distance Profile (PIDP): showing
the time when safety is not respected t
SNR
and the minimum
PIDP.
3.4 Model Predictive Control (MPC)
Model Predictive Control (MPC) is an optimization-
based control method. It computes the system’s fu-
ture behavior over a finite prediction horizon and opti-
mizes control inputs to minimize a cost function while
satisfying desired constraints. The optimization prob-
lem is to minimize the objective function:
min
U
N−1
∑
t=0

||∆x
AV
t
||
2
Q
+ ||u
AV
t
||
2
R

+ ||∆x
AV
N
||
2
S
(4)
such that:
x
AV
t+1
= f (x
AV
t
,u
AV
t
), t ∈ N
N
(5)
x
PV
t+1
= f (x
PV
t
,u
PV
t
), t ∈ N
N
(6)
u
AV
t
∈ U
t
, t ∈ N
N
, (7)
x
PV
p, j,t
∈ Ξ
sa f e
, p ∈ N
N
p
× j ∈ N
N
tra j
×t ∈ N
N
(8)
Multi-Risk Assessment and Management in the Presence of Personal Light Electric Vehicles
139

where the control input to the AV is U =
(u
0
,. .. ,u
N−1
)
T
and ||x||
2
M
= x
T
Mx. The cost to reach
the reference state ∆x
AV
t
= x
AV
t
− x
AV
t,re f
, with weight-
ing matrices Q,S ∈ R
3×3
and R ∈ R
2×2
, the prediction
model of the AV is f (x
AV
t
,u
AV
t
). The constraints on
the inputs and collision-safe states are U
t
and Ξ
sa f e
,
respectively. Observe that the size of the state col-
lision avoidance constraint is a product of the num-
ber of agents N
p
, the number of predicted trajectories
N
tra j
, and the size of the prediction steps N. This ex-
ponential increase in the constraint results in a con-
servative behavior, where the algorithm often fails to
find a safe solution to the optimization problem.
4 MULTI-RISK ASSESSMENT
USING FUSION OF PIDPs
(F-PIDP)
The traditional PIDP method for risk assessment can
not handle multi-modal motion prediction directly.
This is because predicting multiple trajectories for a
single agent makes it difficult to decide which of the
PIDPs to consider for collision avoidance (cf. Fig-
ure 1 & 3). A trivial solution may be to avoid all the
trajectories, but this usually leads to conservative be-
haviors, where the AV slow down to a stop or perform
unsafe maneuvers to avoid the agent. Therefore, we
propose to perform a fusion of PIDPs (F-PIDPs) as
presented in (Alao et al., 2024). F-PIDP takes ad-
vantage of the information on the likelihood of each
trajectory to combine the PIDPs from multiple predic-
tions. The following subsections highlight the meth-
ods to compute the F-PIDP.
4.1 Multi-Modal PIDP
For each of the possible trajectories that the PLEV can
execute j ∈ P , we evaluate the inter-distance between
the predicted motion of the AV and the PLEV, such
that
PIDP
j
(t) = {d
j
(t)| j ∈ P , 0 ≤ t ≤ t
horizon
} (9)
d
j
(t) =
q
(x
AV
(t) − x
j
(t)) + (y
AV
(t) − y
j
(t))
(10)
where the predictive inter-distance between the AV
and the j
th
trajectory of the PLEV is denoted PIDP
j
.
The variables (x
AV
,y
AV
) represent the position coor-
dinates of the AV while (x
j
,y
j
) represent the position
coordinates of the j
th
trajectory of a PLEV at time
step t. t
horizon
is the specified time horizon of the pre-
diction.
4.2 Extraction and Fusion of PIDP
Features
From each of the PIDPs evaluated above we require
certain features to perform the fusion of the PIDPs:
(1) the start point of the trajectory PIDP(t
0
), (2) the
minimum point of the PIDP(t
min
), (3) and the end-
point of the trajectory PIDP(t
horizon
).
Next, a weighted fusion of all the extracted fea-
tures of the PIDP is calculated to obtain only three
features that represent the information from all the
trajectories. The fusion of the features is obtained by
computing the probabilistic center of mass (pCOM)
of all the PIDPs. The definition of the pCOM for each
of the feature points is given by (11)
pCOM(t) =
N
tra j
∑
j=1
Pr( j) × PIDP
j
(t) (11)
where Pr( j) is the probability of maneuver j,
PIDP
j
(t) represents the PIDP at any of the feature
points t ∈ {t
0
,t
min
,t
horizon
} and N
tra j
∈ N is the num-
ber of trajectories being considered. The pCOM gives
a weighted average of the feature points based on the
likelihood of the PLEV trajectory. Therefore, the re-
sulting parameters for the F-PIDP are:
• F PIDP(t
0
) := pCOM(t
0
) fusion of the
start points PIDP
j
(t
0
), the
value is same for all trajec-
tories of a PLEV
• F PIDP(t
min
) := pCOM(t
min
) fusion of
all the minimum points
PIDP
j
(t
min
) of the possible
trajectories
• F PIDP(t
horizon
) := pCOM(t
end
) fusion
of all the end points
PIDP
j
(t
horizon
)
4.3 Fusion of PIDP (F-PIDP) Curve
The aim of the fusion of PIDPs is to have a sin-
gle PIDP curve that represents all the predicted inter-
distance based on their likelihood. Assuming the mo-
tion of the AV follow a smooth trajectory, the PIDP
can be approximated by a quadratic polynomial curve
derived from the Euclidean distance of the agents.
Hence, the F-PIDP is modeled as a single curve that
fuses the features extracted from all the PIDPs of a
particular PLEV.
The features from the previous section are em-
ployed to compute the variables of a quadratic curve
that passes through the points. From the equation of a
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140

quadratic curve



F PIDP(t
0
)
.
.
.
F PIDP(t
horizon
)



=



1 t
0
t
2
0
.
.
.
.
.
.
.
.
.
1 t
horizon
t
2
horizon



·


q
0
q
1
q
2


(12)
where the variables [q
0
,q
1
,q
2
] characterize the F-
PIDP curve and are found by evaluating the matrix
(or pseudo) inverse at t ∈ [t
0
,t
min
,t
horizon
] in order to
solve the linear equation (12). The result is a singular
F-PIDP curve that integrates the information from all
PIDPs, as demonstrated in Figure 3.
Figure 3: Fusion of PIDPs (F-PIDP) of an AV and multiple
PLEVs with three (3) possible multi-modal trajectories.
4.4 F-PIDP Setpoint Determined by the
Safety Distance
The Risk management algorithm requires the defini-
tion of an appropriate F-PIDP and a coherent setpoint
to guarantee safety. However, one or more PIDPs may
be below the safety distance and potentially in the col-
lision zone (cf. Figures 2 and 3). This is usually prop-
agated to the F-PIDP curve, depending on the likeli-
hood of such PIDP. Therefore, a setpoint interpolation
step is implemented, ensuring that the fused PIDP is
always above the future safety distance. This is an
interpolation step that translates the minimum of the
F-PIDP curve to be above the established d
sa f e
(Iber-
raken and Adouane, 2022).
F
PIDP(t
min
) ≜ max{F PIDP(t
min
),d
sa f e
} (13)
d
sa f e
≜ R + r + v × ET TC(1sec) (14)
The safety distance, denoted as d
sa f e
, is determined
based on the AV’s current linear velocity v and an
extended time to collision (ET TC) (Iberraken et al.,
2018) of 1 second.
The new curve termed as F-PIDP setpoint (cf. Fig-
ure 3) is then sent to the risk management algorithm
to serve as a reference point (cf. Section 5). This step
is therefore crucial for the proactive and preventive
reduction of any risk of collision.
5 F-PIDP + MPC FOR MULTI
RISK MANAGEMENT WITH
SAFETY GUARANTEE
We prioritize safety in the proposed approach through
the addition of various constraints to the optimization
problem. The constraints depend on the dimensions
of the vehicles, the road, and the limits on the control
inputs of the AV.
5.1 Road Boundary Constraint
The position of the AV is expected to stay within the
lane of the road, such that the following constraint is
satisfied,
y
lane
min
≤ y
AV
t
≤ y
lane
max
(15)
this ensures that the lateral position of the AV denoted
y
AV
t
at each time step t, is bounded by y
lane
min
and y
lane
max
based on the width of the road and the vehicle.
5.2 Control Input Constraint
The motion of the AV is also constrained by the physi-
cal limit on the velocity and acceleration of the wheels
of the vehicle. These limits also have a direct influ-
ence on the comfort of the passengers. They are for-
mulated as
u
AV
min
≤ u
AV
t
≤ u
AV
max
(16)
where the vector u
AV
min
and u
AV
max
are respectively the
bounds on the minimum and maximum values of the
control inputs.
5.3 Priority-Based Collision Avoidance
Strategy
Using MPC to compute the trajectory of multiple
agents like PLEVs in urban roads is too conservative
because of the narrow constraint of the road bound-
ary as shown in the simulation Section 6. Therefore,
a priority-based strategy is proposed to select a tar-
get agent to avoid, instead of trying to avoid collision
with all the agents and their possible trajectories.
• Step 1: Compute the F-PIDP of all the agents,
Multi-Risk Assessment and Management in the Presence of Personal Light Electric Vehicles
141

• Step 2: Find P
dmin
: the PLEV with the minimum
inter-distance to the AV, and P
tSNR
: the PLEV
with the minimum t
SNR
,
• Step 3: If P
dmin
< d
sa f e
max
, that is, no collision
predicted, then set the priority target PLEV P
T
,
to avoid collision with P
dmin
, else set the priority
target PLEV P
T
as P
tSNR
. P
T
is considered to be
the most dangerous agent.
• Step 4: Compute collision free trajectory between
target PLEV and AV using F-PIDP+MPC, goto to
Step 1.
Algorithm 1 summarizes the steps above.
while Goal not reached do
Data: x
AV
[t,···,N]
, x
PV
[t,···,N]
Compute F-PIDP of all the PLEVs;
Compute P
dmin
: the PLEV with the
minimum inter-distance to the AV;
Compute P
tSNR
: the PLEV with the
minimum t
SNR
;
if P
dmin
< d
sa f e
max
then
P
T
:= P
dmin
;
else
P
T
:= P
tSNR
;
end
U
AV
:= F-PIDP+MPC(P
T
);
end
Algorithm 1: Priority-based Target Selection Algorithm us-
ing F-PIDP.
5.4 F-PIDP+MPC Formulation
Considering the vehicle constraints, road constraints,
and the priority-based target, the F-PIDP+MPC algo-
rithm becomes:
min
U
w
0
· F
1
+ (1 − w
0
) · F
2
(17)
such that:
x
AV
t+1
= f (x
AV
t
,u
AV
t
), t ∈ N
N
(18)
x
PT
t+1
= f (x
PT
t
,u
PT
t
), t ∈ N
N
(19)
u
AV
t
∈ U
t
, t ∈ N
N
, (20)
x
P
T
t
∈ Ξ
P
T
sa f e
, t ∈ N
N
(21)
where F
1
denotes the MPC objective costs defined
in Section 3.4, augmented by the inter-distance cost
function F
2
≜ ||F PIDP −d
j
(t)||
2
. The inter-distance
function d
j
(t) is given in (9) and w
0
is a weight that
compensates for the influence of the F-PIDP on the
motion of the AV. The safety constraint Ξ
P
T
sa f e
, con-
siders only the state x
P
T
t
of the target PLEV P
T
. All
other parameters are defined in Section 3.4. This ap-
proach is less conservative since in (21), the size of
the state collision avoidance constraint is simply the
size of the prediction horizon N as compared to (8)
using only MPC.
6 SIMULATION RESULTS
The proposed risk assessment and management
method, F-PIDP+MPC, has been tested in MATLAB.
The simulation environment consists of an AV and
multiple PLEVs moving in a dual-lane traffic environ-
ment. We consider a challenging scenario (cf. Fig-
ure 4) with an AV (in red), a PLEV 1 (in yellow)
with multi-modal predictions trying to overtake an-
other PLEV 2 (in blue) with multi-modal predictions.
For clarity, it is assumed that at each time step the
PLEVs have three (3) possible trajectories they can
follow: Left Turn (in Red), Forward (in Green), Right
Turn (in blue) (cf. Figure 4).
(cf. Video link https://youtu.be/oH6yPuocRJk)
Therefore, two types of challenges arise: (1) the
uncertainty on the true trajectory the agents are exe-
cuting, and (2) the possibility of the PLEV changing
its behavior (speed). The parameters of the agents are
given in table 1, note that the speed of PLEV 1 can
change from the initial 2 m/s to about 10 m/s. The
agents are assumed to be enclosed by circles to sim-
plify and reduce the computational complexity. How-
ever, a less conservative approach using multiple cir-
cumcircles may be employed as in (Bellingard et al.,
2023).
PLEV 1 accelerate its speed in the simulation
setup after about 1 second. Five speed levels are con-
sidered v ∈ {2, 4,6, 8,10}m/s. The first speed level
assumes that PLEV 1 maintains its initial speed of 2
m/s throughout the motion, while other speed levels
indicate a sudden acceleration. The simulation time is
set to run for 7.5 s, where at each time step, ∆t = 0.05
the prediction horizon t
horizon
= ∆t × N = 2s.
6.1 Result Using MPC
First, we analyse the results of the simulation using
MPC. The results for the first two speed levels of 2
m/s and 4 m/s show that the MPC can handle small
changes in the speed of the agents without violating
the collision constraints (cf. Figure 4). The PIDP
is above d
sa f e
which implies safe navigation over the
prediction horizon. This can be observed in the inter-
distance plot between the AV and the two PLEVs at
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Table 1: Agents Parameters and initial states.
AV Parameters Value Unit
radius 2 m
initial position [0, -6] m
initial velocity [8, 0] m/s
u
AV
max
[8, 35] [m/s,
◦
]
u
AV
min
[0, -35] [m/s,
◦
]
PLEV 1 Parameters Value Unit
radius 0.5 m
initial position [10, -9] m
initial velocity [2, 0] m/s
v
max
10 m/s
PLEV 2 Parameters Value Unit
radius 0.5 m
initial position [16, -6] m
initial velocity [2, 0] m/s
v
max
2 m/s
time t ≤ 1s (cf. Figure 6 (a) & (c)).
However, MPC is very conservative because it
slows down to almost a stop due to the possibility
of collision with PLEV 2. This is because the PIDP
of a possible Left turn trajectory (cf. Figure 6 (d),
in red) by PLEV 2 may lead to a collision. There-
fore, the MPC algorithm tries to minimize the risk by
maintaining some distance behind PLEV 2, instead
of overtaking it. This is why even at the end of the
simulation t = 7.5, the AV is far from the reference
position of X
re f
= [−2, 60]m (cf. Figure 4 (b)).
Furthermore, at high speeds of 6 m/s and above,
the MPC algorithm could not find a solution that sat-
isfies all the safety constraints. Most especially, as
seen in (cf. Figure 5), the AV violates the road bound-
ary constraint to avoid collision with the other agents
after the sudden acceleration of the PLEV.
6.2 Result Using Priority-Based
F-PIDP+MPC
The proposed method using F-PIDP+MPC performs
better than MPC for all speed changes considered.
Here, the weight w
0
= 0.2 in (17) penalises the de-
viations from the F-PIDP setpoints, whereas setting
w
0
= 1.0 using the previous MPC method ignores the
setpoints. By employing the F-PIDP as a risk measure
and focusing on the target PLEV deemed the most
dangerous, the AV can find a less conservative trajec-
tory that satisfies the safety constraints. For instance,
at t = 1s, the priority target P
T
is PLEV 1 (cf. Fig-
ure 7 (a)). After the fusion of the PIDPs, the F-PIDP
setpoint suggests that the AV should create more dis-
Figure 4: A scenario using MPC showing an AV (in red)
and multi-modal PLEVs (1 in Yellow & 2 in Blue): (a) At t
= 1 s, the actual speed of both PLEVs is 2 m/s (b) At t = 7.5
s, AV overtakes PLEV 1 but stays beside PLEV 2 to avoid
a possible collision with a possible Left turn trajectory of
PLEV 2.
Figure 5: At t = 3 s, MPC violates the boundary constraint
due to the sudden change in speed of PLEV 2.
tance between itself and PLEV 1 to avoid possible
collision (cf. Figure 8 (a)). And since the focus is
only on the priority target, PLEV 1, the proposed so-
lution from the F-PIDP+MPC algorithm is to safely
overtake PLEV 1. Then at t = 5s, PLEV 2 became
the priority target that the AV overtook after PLEV 1
(cf. Figure 7 (b)).
This priority-based behavior enables the AV to
quickly leave the dangerous region instead of consid-
ering all the multi-modal agents simultaneously lead-
ing to conservative behaviors. Hence, the AV can
cover more distance in less time as compared to the
MPC method that remains beside PLEV 2, after 7.5 s
(cf. Figure 7 (b)). Overall, the PIDPs of all the agents
during the simulation are always above the safety dis-
tance using the proposed method (cf. Figure 8). This
approach applies to both PLEVs and other road vehi-
cles.
Multi-Risk Assessment and Management in the Presence of Personal Light Electric Vehicles
143

Figure 6: Inter-Distance plot between the AV and the
PLEVs using MPC: (a) & (c) At t = 1 s, all PIDPs (red,
blue, green) of PLEV 1 & 2 are above safety distance d
sa f e
,
(b) & (d) At t = 7.5 s, the PIDPs of PLEV 1 are above d
sa f e
while a PIDP of PLEV 2 may lead to collision.
Figure 7: A scenario using the proposed method: (a) At t
= 1 s, AV overtakes the priority target PLEV 1 (in red) (b)
then at t = 5 s, AV overtakes the new priority target PLEV 2
(in red).
7 CONCLUSION
We propose in this paper a method for risk assessment
and management for autonomous navigation among
Personal Light Electric Vehicles (PLEVs). The pro-
posed method hinges on modeling the behavior of
PLEVs as multi-modal predictions. Then the Pre-
dictive Inter-Distance Profiles (PIDPs) of the PLEVs’
predictions are fused using a Fusion of PIDPs (F-
PIDP). This method reduces the complexity of the
problem from multiple predictions to a single F-PIDP
for each agent. A priority-based strategy is developed
to choose a target agent considered to be the most dan-
Figure 8: Inter-Distance plot between the AV and the
PLEVs using proposed method: (a) At t = 1 s, F-PIDP
suggest creating more distance between AV and PLEV 1
(b),(c), & (d) All PIDPs are above d
sa f e
.
gerous. Safe control actions are then computed using
F-PIDP+MPC.
Results from various simulations obtained from
varying the behavior of the agents show that the pro-
posed method is efficient for risk assessment and
management. A comparison with the traditional MPC
method shows that the proposed method is less con-
servative. Future works will focus on considering dis-
turbances in the predicted states of the agents and to
further optimizing the method for real-time experi-
mentation.
ACKNOWLEDGEMENTS
This research is part of the ANNAPOLIS project
(https://project.inria.fr/annapolis/), funded by the
French National Research Agency (ANR-21-CE22-
0014).
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