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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Energy-Efficient Routing in UAVs Supported Perimeter Security Networks</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alexander K. Alexandrov</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Anastass N. Madzharov</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute of Robotics, Bulgarian Academy of Sciences</institution>
          ,
          <addr-line>Acad. G. Bonchev str., 1113 Sofia</addr-line>
          ,
          <country country="BG">Bulgaria</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>UAV-assisted ground and underwater perimeter security sensor networks represent a sophisticated integration of aerial, ground, and underwater technologies for surveillance and security purposes. This system combines Unmanned Aerial Vehicles (UAVs) with underwater sensors to monitor and protect strategic areas like harbors, ofshore installations, and coastal facilities. Unmanned Aerial Vehicles (UAVs) have become pivotal in modern surveillance and security operations. Their versatility, mobility, and technological adaptability make them ideal for perimeter security systems. This study examines the integration of group of UAVs into perimeter security, evaluating their efectiveness, operational frameworks, technological advancements, and potential future developments. We analyze and implement a PSO (Particle Swarm Optimization) algorithm, related to group of UAVs trajectory optimization, review case studies, and identify key considerations for efective development.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;UAV</kwd>
        <kwd>PSO</kwd>
        <kwd>sensor network</kwd>
        <kwd>perimeter security</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>sensors is analyzed, processed, and fused to form a
comprehensive operational picture. Control center assesses
UAV-assisted underwater perimeter security sensor net- potential threats based on the gathered information and
works represent a cutting-edge blend of aerial and mar- coordinates appropriate responses.
itime technologies, designed to enhance the security of One of the challenges in the UAVs assisted underwater
critical aquatic areas. This integration of Unmanned perimeter security sensor networks is the energy
manAerial Vehicles (UAVs) and underwater sensors provides agement. Both the UAVs and underwater sensors must
a robust solution for monitoring and safeguarding sen- eficiently manage their power to ensure prolonged
opersitive zones like naval bases, coastal areas, ports, and ational capabilities. The present study focuses on energy
ofshore installations. management, especially in energy-eficient and reliable</p>
      <p>The key components in the UAV-assisted underwater routing of groups of UAVs. The UAVs energy-eficient
perimeter security sensor networks are the sensors, UAVs, routing is a multifaceted challenge that involves
optimizand the control center. ing the flight paths and operational strategies of UAVs.</p>
      <p>Underwater sensors typically include acoustic sensors The objective is to maintain vigilant monitoring and
(such as sonars), geophones, hydrophones for detecting rapid response capabilities while minimizing energy
consound under water, and magnetic anomaly detectors for sumption, which is critical for the longevity and
efecidentifying metallic objects. These sensors continuously tiveness of the UAVs in defense operations. The aim is
scan underwater environments to detect and track po- to create routes and operational patterns that minimize
tential threats, like submarines, divers, or unmanned energy usage while ensuring comprehensive security
underwater vehicles (UUVs). coverage.</p>
      <p>UAVs provide real-time aerial surveillance, signifi- Altitude and speed optimization in UAV-supported
uncantly extending the range of observation beyond the derwater perimeter security sensor networks is a critical
immediate perimeter. They act as a vital link between the aspect of ensuring energy-eficient routing and efective
underwater sensors and the control center, especially im- operation. The right balance of altitude and speed
diportant in deep-water areas where direct communication rectly impacts the UAVs’ energy consumption, coverage
is dificult. area, sensor efectiveness, and response times.</p>
      <p>Control center provides data processing and decision
making. Here the data from both UAVs and underwater</p>
      <sec id="sec-1-1">
        <title>1.1. Altitude optimization</title>
        <sec id="sec-1-1-1">
          <title>Higher altitudes can ofer less air resistance, but the ben</title>
          <p>efit must be balanced against increased energy
requirements for climbing and maintaining altitude. Higher
altitudes may increase the coverage area but could
reconditions. For example, flying above or below certain
weather layers (like fog or clouds) can be crucial.</p>
          <p>
            The optimized altitude can ensure communication
with both the underwater sensor network and the control
station [
            <xref ref-type="bibr" rid="ref1">1</xref>
            ].
1.2. Speed optimization
intrusions. The system is integrated with
existing security infrastructure, providing a bird’s-eye
view when a ground sensor is triggered.
• General Atomics Predator B - used for
national border surveillance, can be used in
conjunction with ground sensor arrays for detecting
and tracking movements and is equipped with
high-resolution cameras and advanced signal
intelligence equipment that can integrate with
sensor network data.
          </p>
        </sec>
        <sec id="sec-1-1-2">
          <title>Generally, faster speeds increase energy consumption.</title>
          <p>The optimization algorithm should identify the most
energy-eficient cruising speed for each UAV model.</p>
          <p>Faster speeds allow for quicker coverage of an area but All the mentioned UAVs have a custom design
navigamight reduce the efectiveness of sensors due to motion tion systems with included energy-eficient software
algoblur or reduced processing time. rithms for routing and altitude/speed optimization, using</p>
          <p>
            Speed must be optimized to balance routine surveil- various algorithms such as RL (Reinforcement
Learnlance with the need for rapid response in case of detected ing, Dynamic Programming, Dijkstra, GA (Genetic
algothreats [
            <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
            ]. Tailwind can be exploited to reduce energy rithms) in diferent combinations.
consumption, whereas flying into headwinds will require
more energy, afecting optimal speed decisions.
          </p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>3. Proposed solution</title>
    </sec>
    <sec id="sec-3">
      <title>2. Related works</title>
      <p>There are some existing solutions related to the UAVs
assisted underwater perimeter security sensor networks
as:
• DJI Enterprise Drones - the solution is used for
inspection and surveillance of commercial and
military complexes. The drone is equipped with
thermal imaging sensors, high-resolution
cameras, and programmable flight paths and is
programmed for routine patrols or dispatched upon
alerts from ground and underwater sensors.
• AeroVironment Raven RQ-11B - the solution
is used for battlefield reconnaissance and
surveillance. The UAV is equipped with GA (Genetic
Algorithms), based trajectory optimization
system and interfaces with ground and underwater
control systems and sensor networks.
• Elbit Systems Skylark I-LEX – this is
electrically propelled UAV equipped with MPC (Model
Predictive Control) trajectory optimization
system, designed to collect data and interface with
ground and underwater sensors for a
comprehensive security net and is utilized by military and
homeland security for national borders and
sensitive areas.
• Anduril Industries’ Lattice – this is a complete
system that integrates drones, ground and
underwater sensors, and AI-powered analysis to detect,
classify, and respond to threats.
• Asylon DroneCore - automated drone
deployment system that works with perimeter sensors
to conduct autonomous patrols and respond to</p>
      <sec id="sec-3-1">
        <title>The current research is focused on the development and</title>
        <p>implementation of altitude (elevation) and speed
optimization algorithm in custom designed UAVs.</p>
        <p>
          The proposed algorithm is based on PSO (Particle
Swarm Optimization) [
          <xref ref-type="bibr" rid="ref4 ref5 ref6">4, 5, 6</xref>
          ]. This is a computational
method that optimizes a problem by iteratively trying
to improve a candidate solution with regard to a given
measure of quality.
        </p>
        <p>It solves a problem by having a population of
candidate solutions, here dubbed particles, and moving these
particles around in the search-space according to simple
mathematical formulae over the particle’s position and
velocity.</p>
        <p>Each particle’s movement is influenced by its local
best known position but is also guided toward the best
known positions in the search-space, which are updated
as better positions are found by other particles. When
applying PSO for altitude and speed optimization in UAVs
supporting underwater perimeter security sensor
networks, the goal is to determine the optimal flight paths,
altitudes, and speeds for the UAVs to maximize coverage,
eficiency, and responsiveness while minimizing energy
consumption.</p>
        <sec id="sec-3-1-1">
          <title>3.1. Challenges in the speed and elevation optimization</title>
          <p>
            The following challenges related to the speed/elevation
optimization problem were defined during the research:
• High Dimensionality: The speed/elevation
optimization problem can be high-dimensional,
especially when considering 3D space and time,
making it computationally intensive [
            <xref ref-type="bibr" rid="ref7">7</xref>
            ].
• Dynamic Constraints: UAVs must respond to dy- where  is the inertia weight, 1 and 2 are cognitive
namic changes in the environment, which
reand social coeficients, respectively,
1, 2 are random
quires the PSO to be adaptable and responsive
          </p>
          <p>numbers between 0 and 1.</p>
          <p>in real-time.
• Local Minima: The PSO algorithm may get</p>
          <p>
            Position update:
mplementing a Particle Swarm Optimization (PSO) al- tion. Update the global best   if any particle
trapped in local minima. This issue can be
mitigated by tuning the parameters (, 1, 2) or by
hybridizing PSO with other optimization
techniques.
• Safety and Collision Avoidance: Ensuring safety
is paramount. The algorithm must incorporate
collision avoidance with other UAVs, terrain, and
obstacles [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ].
          </p>
        </sec>
        <sec id="sec-3-1-2">
          <title>3.2. Implementation</title>
          <p>gorithm for altitude and speed optimization in
UAVsupported underwater perimeter security sensor
networks involves several mathematical concepts. Here’s
an mathematical overview of the proposed algorithm
algorithm and serve as a guide for actual programming.
Constraints
({max}, {min}).</p>
        </sec>
      </sec>
      <sec id="sec-3-2">
        <title>Include constraints like battery life (B), maximum and</title>
        <p>minimum altitude ({max}, {min}), and speed limits</p>
        <sec id="sec-3-2-1">
          <title>PSO Algorithm Structure</title>
          <p>resents a potential solution, with its position pi indicating
a particular set of altitudes and speeds for a UAV.</p>
        </sec>
      </sec>
      <sec id="sec-3-3">
        <title>Initialization: randomly initialize the position pi and ifned by the constraints.</title>
        <p>Velocity and Position Update Rules
Velocity update:
+1 = 
() + 11
︁(
, −</p>
        <p>())︁
velocity vi of each particle within the feasible space de- such as constriction factors or varying inertia weight,</p>
        <p>Remember that PSO is inherently iterative and works Related to the pseudocode above please note:
with a population of solutions, adjusting them over time Initialization: The initial positions and velocities are
based on a defined objective function. randomly assigned within the permissible ranges for
al</p>
        <p>The related PSO algorithm written in pseudocode is titude and speed. Each particle’s initial position is
conshown below: sidered its personal best (pbest).</p>
        <p>Updating Velocities and Positions: The velocities
PSO algorithm for UAVs elevation/speed are updated considering both the particle’s own best
pooptimization sition and the global best (gbest). The updated velocity
Inputs: influences the new position. It’s important to ensure that
- num_particles: Number of particles in the the updated positions are within the allowed ranges.</p>
        <p>swarm Evaluating and Updating Best Positions:
Af- max_iterations: Maximum number of ter updating positions, evaluate them using the
objeciterations tive_function. If a particle’s new position is better than
- objective_function: Function to optimize its pbest, update pbest. If it’s better than the current gbest,
(minimize or maximize) update gbest.
- A_max, A_min: Maximum and minimum Termination: The algorithm iterates through this
allowable altitudes process, gradually moving the swarm towards the best
- S_max, S_min: Maximum and minimum solution. The process repeats either until the maximum
allowable speeds number of iterations is reached or some other stopping
- omega: Inertia weight criterion (like a convergence threshold) is met.
- c1, c2: Cognitive and social coefficients Returning the Optimal Solution: Finally, the gbest
Initialize: after the last iteration is returned as the optimal set of
- Create num_particles particles with random altitude and speed parameters.</p>
        <p>positions and velocities Customization for the specific use-case : The
ob- for each particle i: jective function should be designed specifically for the
- position[i] = Random within UAV’s operational requirements, taking into account
fac[A_min, A_max] and [S_min, S_max] tors like energy consumption, area coverage, sensor
ef- velocity[i] = Random initial fectiveness, and other mission-specific metrics.
velocity Parameters such as , 1, and 2 may need tuning for
- pbest[i] = position[i] optimal performance in specific scenarios.
- gbest = position of the best particle based Additional constraints or enhancements can be
inteon objective_function grated into the algorithm based on specific requirements
Main Loop: and operational environments.
- for iter = 1 to max_iterations:
- for each particle i:
- Update velocity: 4. Key Takeaways
- r1, r2 = Random numbers
between 0 and 1 Enhanced Eficiency : The PSO algorithm efectively
- velocity[i] = omega * velocity[i] optimizes UAV flight parameters (altitude and speed),
+ c1 * r1 * (pbest[i] - position[i]) leading to improved energy eficiency. This results in
longer mission durations and reduced operational costs.</p>
        <p>Adaptive Flight Paths: The algorithm’s ability to
dynamically adapt flight paths in response to changing
environmental conditions and mission requirements is
a significant advantage, ensuring optimal coverage and
data collection.</p>
        <p>Collaborative Functionality: PSO inherently
supports multi-UAV coordination, allowing for efective</p>
        <p>- pbest[i] = position[i]
- If objective_function(position[i]) is
better than objective_function(gbest):</p>
        <p>- gbest = position[i]
- Return gbest as the optimal solution
End Algorithm</p>
        <p>Operational Flexibility: The algorithm’s flexibil- and maritime technologies, paving the way for enhanced
ity allows it to be tailored to various mission scenarios, security solutions in coastal and ofshore environments.
UAV types, and sensor network configurations, making In conclusion, PSO is a robust and versatile algorithm
it broadly applicable in underwater perimeter defense. widely used for solving complex optimization problems.
Its ongoing developments and applications across diverse
4.1. Challenges and Considerations ifelds highlight its relevance in the current technological
landscape.</p>
        <p>Complex Environmental Dynamics: The
underwater and aerial environments present unique challenges,
including variable weather conditions and underwater
currents, which can afect the algorithm’s performance.</p>
        <p>Communication Limitations: Ensuring reliable
communication between UAVs and underwater sensors
remains a challenge, impacting the coordination and
effectiveness of the network.</p>
        <p>Computational Demands: PSO, especially in
realtime applications, can be computationally intensive,
necessitating robust onboard processing capabilities.
Security and Robustness: The system must be secured against
potential cyber threats and robust enough to handle
operational uncertainties and potential system failures.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>5. Conclusion</title>
      <sec id="sec-4-1">
        <title>The implementation of a Particle Swarm Optimization</title>
        <p>(PSO) algorithm for altitude and speed optimization in
UAVs supporting underwater perimeter security sensor
networks is a sophisticated approach that leverages the
strengths of swarm intelligence for operational eficiency.
The conclusion drawn from this implementation can
highlight its significance, potential benefits, and areas
for future enhancement. Future steps:
• incorporating advanced variants of PSO or hybrid
algorithms could further optimize performance,
especially in highly dynamic or unpredictable
environments.
• leveraging AI for predictive analytics and
machine learning for continuous improvement of
lfight path algorithms based on historical data
can enhance operational eficiency.
• incorporating sustainable technologies, such as
solar-powered UAVs, can extend mission
durations and reduce environmental impact.</p>
        <p>
          The implementation of a PSO algorithm for
optimizing a group of UAVs’ altitude and speed in underwater
perimeter security sensor networks demonstrates
significant potential in improving maritime security
operations [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ]. While challenges remain, the continuous
advancements in technology and algorithmic strategies
hold promise for developing more sophisticated, eficient,
and robust defense networks in the future . This
approach exemplifies the innovative integration of aerial
aerial vehicle group, Frontiers of Information
Technology &amp; Electronic Engineering 21 (2020) 1671–
1694.
        </p>
      </sec>
    </sec>
  </body>
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