Applications of Single and
Multiple UAV for Patrol and
Target Search.
Pinsky Simyon.
Supervisor: Dr. Mark Moulin
Summary of the Presentation.
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Definition of UAV Patrol and Search (P&S)
Problem.
Simplification and Explicit Definition of UAV
Patrol and Search (P&S) Problem.
Dijkstra Shortest Path Algorithm and its
application for P&S problem.
Single UAV P&S : Simulation Results.
Multi UAV P&S : Simulation Results.
Conclusions.
Background.
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Today, UAV’s are mainly human operated.
Area research task of today - Autonomous UAV.
Area research task of tomorrow - Autonomous Team of UAVs.
Applications: Search, Patrol, Mapping, Photographing etc.
Common Problem of all the applications under autonomous
mode - Optimal Path Planning under constrains:
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terrain topography
hazards
fuel ,changing weather, mission updates, cooperative task etc.
Theoretical Solution Methods.
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P&S automation problem is extremely complex.
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Numerous approaches to the problem definition and solution has
been investigated in resent years.
We have examined the applicability of 3 methods:
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Swarms Methodology : each individual UAV has little intelligence which
contributes to the group intelligence. It is interesting to investigate the
behavior of the group varying the intelligence of the individual UAV. The
main problem is a lack of mathematical approach.
Q-learning – Very Large State Space.
Dijkstra shortest path- is the applied method in this project.
Simplification of the original problem and its
explicit definition.
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Simplified Problem: A Patrol & target search under terrain constrains
The Map is discrete, and includes regions containing
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Hazards.
Preferred destinations.
The target.
Solution:
Find the Optimum Path between
the bases.
Applicability of the solution:
Patrol can be performed by single or multiple UAV.
Nowadays performed by human operators on the US and Mexico
Border by Hermes.
Discrete Model of Terrain.
G(N,A)- finite nonempty
set of N nodes and
collection A of arcs.
(n1 , n2 ,..., nl ) - sequence
of nodes.
(n1 , n2 ), (n2 , n3 ),..., (nl 1 , nl ) - each pair
is an arc of G.
w(ni , n j )  dist (ni , n j ) -the weight of the arc
represents the distance between the
two nodes.
On the plotted map one can see:
Home Bases, Hazards,
Preferential Areas and a
Target.
Optimization Problem formulation.
Given two nodes S and T (which represent the two bases) in a graph G=(N,A) , we
need to find the path P such that it minimizes the sum of the weights associated
with the edges constituting the path.
Let , P  (n1 , n 2 ,...n k ) where S  n1 and T  nk ni  N and ni 1   (ni )
( ni 1   (ni )
denotes the neighboring nodes of ni )
Hence we need to find:
k 1
min  w(n , n
P
i 0
i
i 1
)
When w(ni , ni 1 ) is the weight between the two nodes.
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Available Algorithms: Dijkstra, Floyd's(O(v^3)), Bellman-Ford(negative),…
Dijkstra Shortest Path Algorithm.
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Solves the single-source shortest-paths problem on a weighted, directed
graph G = (N, A) for the case in which all arcs weights are nonnegative.
Maintains a set S of vertices whose final shortest-path weights from the
source s have already been determined.
Repeatedly selects the vertex with the minimum shortest-path estimate,
adds n to S, and relaxes all edges leaving n.
DIJKSTRA(G, w, s)
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INITIALIZE-SINGLE-SOURCE(G, s)
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S← 
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Q ← V[G]
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while Q ≠ 
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do n ← EXTRACT-MIN(Q)
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S ← S + {n}
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for each arc a Adj[n]
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do RELAX(n, v, w)
Application to the UAV case.
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The field is being represented
as an Adjacency Matrix.
For a grid of the dimensions
NN  N 2 nodes, create a
matrix of the dimensions
N 2 N 2  N 4 where matrix value
in the row i and column j is:
  unconnectedNodes

dist (n , n )  connectedNodes 
i
j
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mij  

M

dist
(
n
,
n
)

hazardArea
i
j
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m  dist (ni , n j )  preferedArea 
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
Application to the UAV case.
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For iteration number k
update the map :
mij [k ]    mij [k  1]
while:   1
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And update the visited preferred
areas.
The running time for n nodes
and m=8n edges in current
configuration is
O(n(n+8))=O(n^2).(n=resX*resY)
Simulation Results - The width of the path.
1000
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100
100
0
0
200
400
600
Path Width=1
800
1000
0
0
200
400
600
Path Width=2
The width of the path is a factor of an efficiency of the patrol.
The wider path has smaller probability to be a ’useless’ sortie.
800
1000
Simulation Results-The size of the preferred area.
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100
0
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Radius = 2
800
1000
0
0
200
400
600
800
Radius = 4
• The vertices leading toward the preferred area has relatively law weight.
• The radius around this area reflects the relative priority of this area.
• The bigger radius causes higher priority of the region which defines how fast the UAV will
choose to visit this area.
1000
Simulation Results - The target location relative to the
shortest path.
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“Shortest Path” definition: the
shortest route connecting the
initial and the final points
(bases) on a map with no
hazards and no preferred
areas.
Intuition: if the distance of the
target from the shortest path is
bigger, it is harder to find it more sorties are needed.
Results of two simulations for
two different distances are
presented.
Simulation Results - The target location relative to the
shortest path.
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Two results are not sufficient
for final conclusions.
Two different aspects are
found to be interesting for
dipper investigation:
1. The correlation between the
distance of the target from
the ‘main’ (shortest) route,
and the number of sorties
needed to reveal the target.
2. The connection between the
different Hazards densities,
and the average number of
sorties needed for detection.
Simulation Results - The target location relative to the
shortest path.
Number of Sorties via Target Distance from center-10 Hazards
14
real Values
3rd Degree polinom
12
Number of Sorties
10
8
6
4
2
0
0
100
200
300
400
Distance from the shortest route
500
600
• The graph presents the number of sorties needed to reveal the target via the distance of the
target from the “shortest path”. (for fixed hazards density-10 hazards)
• The more distant the target is located, the higher the number of the sorties which are
needed for detection.
Simulation Results - The target location relative to the
shortest path.
Number of Sorties via Target Distance from center
12
10 Hazards
20 Hazards
30 Hazards
40 Hazards
50 Hazards
60 Hazards
Number of Sorties
10
8
6
4
2
0
0
100
200
300
Distance[]
400
500
600
• The graph presents the number of needed sorties via distance from the “shortest path” for
different hazard density levels:10-60Haz/Field.
• The same behavior takes place for the fields with different hazard density.
Simulation Results - The target location relative to the
shortest path.
Average Number of Sorties via Increasing Hazard Number
40Haz  40%FieldArea
3.2
real Values
3rd Degree polynom
3
Average Number of Sorties
2.8
2.6
2.4
2.2
2
1.8
1.6
10
15
20
25
30
35
40
Number of Hazards
45
50
55
60
• The graph presents the average number of sorties via increasing Hazard Density.
• An increase of the density yields an easier reveal of the target, until the optimum is reached.
• After the optimum point, the task is becoming harder. Why?
• An increase of low density means searching in fewer regions.
• An increase of high density means searching inside a labyrinth.
Application for Multi UAV search.
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Simulation scenario :
Number of UAVs=2
4 bases
50 hazards
18 Preferred Areas
1 Target
The UAV Group is provided an
updated map of hazards and
preferred areas.
Each UAV updates the map
according to its planned sortie.
Serial planning: each UAV plans
its route taking into account the
plans of other group members.
Animation-Multi UAV search.
Legend :
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Blue Six Pointed StarsBases 1-4.
Yellow Dots-Preferred
areas.
Red Dot-The Target.
Red Trace-UAV1.
Blue Trace-UAV2.
The Hazards
represent the terrain.
Result: The patrol area
is being divided
between two UAVs into
the inner and the outer
parts.
Conclusions:
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We have examined Several methods for solving the
Patrol & Search problem.
We have found Dijkstra algorithm to be the most promising one.
For each application the right parameters have to be found and
tuned.
For the simulated conditions:
 The path width = 2 nodes.
 The preferred area radius = 2 nodes.
 40% Hazards density has been found to be the optimum.
The project results show the practical applicability of the “shortest
path” problem solved using the Dijkstra algorithm for:
 Sorties planning for multiple/single UAV.
 Search/Patrol performed by multiple/single UAV.
Thanks…
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To Dr. Mark Moulin for the guidance.
To the rest of you for your attention.