Probabilistic Planning for Maritime Search and Rescue
Lu
´
ıs Marques
1
, Jose Javier Escribano Macias
1
, Panagiotis Angeloudis
1∗
1
Imperial College London
∗
p.angeloudis@imperial.ac.uk
Abstract— Maritime accidents cause thousands of disappear-
ances every year, with migrant crossings being particularly dan-
gerous and under-reported. Current coastal and NGO search
and rescue services are unable to provide a timely response,
so new technologies such as autonomous UAVs are needed. We
present a thorough formalization of the maritime search and
rescue problem considering its time-critical and probabilistic
nature. Further, we introduce a method for determining the
optimal search altitude for any aerial thermal-based detection
system, so as to maximize overall mission success.
I. INTRODUCTION
Drowning is the 3rd leading cause of death worldwide
according to a 2021 WHO report [1]. Migrant crossings of
the Mediterranean Sea lead to massive loss of life with over
26,832 disappearances registered since 2014 [2]. The real
number of casualties is however much higher, as unnoticed
accidents cannot be reported.
The current search and rescue (SAR) resources of southern
European countries are understandably strained and unable
to cover such an extensive area in a timely manner. Coast-
guard boats are slower than desired, and helicopters require
expensive maintenance and expert operation, while only
being capable of rescuing a limited number of people. Thus
unmanned aerial vehicles (UAVs) are being increasingly
considered to provide timely first-aid to people at sea [3].
Besides being a cheaper solution than conventional search
and rescue units (SRUs), autonomous UAVs are not subject
to fatigue and prevent placing SAR operators in danger.
UAVs can achieve a lower time-to-target (TTT) than other
SRUs due to their shorter setup time and higher cruise
speeds. This is crucial for maritime SAR (MSAR) where
drowning can be fatal within minutes, and hypothermia can
lead to loss of life in as fast as 30 min [4].
While autonomous UAVs can provide first aid directly,
our ongoing work focuses on the application of autonomous
UAVs to augment our coverage of Mediterranean Sea cross-
ings (with conventional SRUs or other specialized UAVs pro-
viding aid). Improving the coverage along common migrant
flow paths would provide us with more accurate and up-to-
date accident data, allowing for a better allocation of rescue
resources. Most importantly, it would decrease the response
time of SRUs and allow us to locate accidents at deep sea
that would previously be invisible.
The contributions of this work are as follows: (a) formal-
ization of the MSAR task as a constrained optimization prob-
lem, considering its time-critical and probabilistic nature; (b)
development of a method for determining the optimal search
altitude for any aerial thermal-based detection system.
II. METHODOLOGY
A. Problem Definition
In this Sub-Section, we formalize the overall MSAR task
as an optimization problem, allowing us to compare and
design search paths for the SRUs. Take N to denote the
total number of people to be rescued in a given MSAR
scenario. If an accident is observed, an estimate of N along
with an approximate accident location is available. Ongoing
work leverages the definition below, and methods from Sub-
Section B, to improve the coverage of migrant paths using
multiple autonomous UAVs.
A random variable N
saved
(t) ≤ N is defined to represent
the number of people saved up to a given instant t. Due
to the probabilistic nature of MSAR operations, N
saved
(t)
depends on multiple factors such as the: 1) initial distribution
of people along the search area; 2) weather conditions; 3)
physical condition of the migrants; 4) quality of information
provided to the SRUs; 5) initial distance between SRUs
and the accident (determines cruise duration); 6) probability
of detecting a target in water. The search has duration
∆t
search
= t
f
−t
0
, where t
f
is the earliest of either complete
fuel depletion of the allocated SRUs or safe recovery of all
the targets. Let us consider the single-agent case where only
one SRU is deployed. The vehicle workspace W = R
3
and
the obstacle region O(t) ⊂ W follow their conventional
definitions. Note that O is a function of time as obstacles
need not be stationary. A candidate search trajectory is
denoted by σ ∈ Σ, where Σ corresponds to the set of all
possible trajectories.
Thus, we can encode the MSAR task in the following
constrained optimization problem with objective function J:
min
σ∈Σ
J(σ) =
1
N
Z
t
f
t
0
(N −E[N
saved
(t)]) dt (1)
s.t. σ(t) ∈ W
free
= W \ O, ∀t ∈ [t
0
, t
f
] (2)
F (q, ˙q, t) = 0, ∀t ∈ [t
0
, t
f
] (3)
Z
t
f
t
0
P (t) dt ≤ E
total
(4)
Constraint (2) indicates that trajectories should only tra-
verse the free space. Constraint (3) enforces the non-
holonomic constraints of boat, helicopter or UAV motion,
with q representing the vehicle’s configuration. For example,
when approximating the dynamics of a fixed-wing UAV
via the unicycle model, q = [x, y, ψ] and (3) becomes
˙q−[u cos ψ, u sin ψ, ω]
T
= 0, where u is the forward velocity
and ω the yaw rate. Constraint (4), where P represents power
arXiv:2306.03871v1 [eess.SY] 6 Jun 2023
