applied
sciences
Article
Cooperative Multi-UAV Collision Avoidance
Based on Distributed Dynamic Optimization and
Causal Analysis
Mingrui Lao 1,2 and Jun Tang 1,3, *
1
2
3
*
Science and Technology on Information Systems Engineering Laboratory,
National University of Defense Technology, Changsha 410073, China; [email protected]
The School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Department of Telecommunication and System Engineering, Universitat Autònoma de Barcelona,
Sabadell 08201, Spain
Correspondence: [email protected]; Tel.: +34-688-113-447
Academic Editor: Josep M. Guerrero
Received: 1 December 2016; Accepted: 12 January 2017; Published: 17 January 2017
Abstract: A critical requirement for unmanned aerial vehicles (UAV) is the collision avoidance (CA)
capability to meet safety and flexibility issues in an environment of increasing air traffic densities.
This paper proposes two efficient algorithms: conflict detection (CD) algorithm and conflict resolution
(CR) algorithm. These two algorithms are the key components of the cooperative multi-UAV CA
system. The CD sub-module analyzes the spatial-temporal information of four dimensional (4D)
trajectory to detect potential collisions. The CR sub-module calculates the minimum deviation of
the planned trajectory by an objective function integrated with track adjustment, distance, and time
costs, taking into account the vehicle performance, state and separation constraints. Additionally,
we extend the CR sub-module with causal analysis to generate all possible solution states in order
to select the optimal strategy for a multi-threat scenario, considering the potential interactions
among neighboring UAVs with a global scope of a cluster. Quantitative simulation experiments are
conducted to validate the feasibility and scalability of the proposed CA system, as well as to test its
efficiency with variable parameters.
Keywords: collision avoidance; UAV; 4D trajectory; distributed dynamic optimization; casual analysis
1. Introduction
Recently, the unmanned aerial vehicle (UAV) has received a wide range of urban, civilian
and warfare applications [1]. It offers several extraordinary features, especially the acceptance of
long-endurance and high-risk missions that could not be reasonably performed by manned aircraft.
For any assignment, a common problem is that the UAVs may encounter each other. Consequently,
an effective collision avoidance (CA) system is a prerequisite for free flight.
There are several existing widely used or adequately evaluated CA systems for conventional
aviation, and these can be applied on UAVs, such as the efficient Medium Term CA approach based
on four-dimensional (4D) trajectories (trajectories defined in the three spatial dimensions together
with a time-stamp) to resolve conflicts in a terminal maneuvering area (TMA) [2], the Traffic Alert
and Collision Avoidance System (TCAS) equipped to issue advisories on how to maneuver vertically
to prevent collisions [3], and the Airborne Separation Assurance System (ASAS) that enables the
flight crew to maintain separation of an aircraft from one or more other aircraft and provides flight
information concerning the surrounding traffic [4]. There are also several auxiliary systems that could
provide the aircraft (or UAVs) with precise information about the state of the nearby traffic, such as the
Automatic Dependent Surveillance Broadcast (ADS-B) system [5–7].
Appl. Sci. 2017, 7, 83; doi:10.3390/app7010083
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Appl. Sci. 2017, 7, 83
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In addition, an extensive and meticulous survey of various methodologies ranging from abstract
concepts to prototype systems for avoiding collisions between UAVs has been summarized in [4].
Typical techniques applied to escort UAV safety include the Monte Carlo approach [8], geometric
optimization model [9], symbiotic simulation [10], probabilistic approach [11], consensus [12],
evolutionary algorithm [13,14], Kalman filter [15], Markov decision process [16], Dubins curve based
algorithm [17], Predictive Control [18], reachable sets based methods [19], and so on. Each method
has its own advantages and characteristics, and no matter which is employed, it aims to guarantee
minimum separation between UAVs. However, some of the studies only focus on the two-UAV
scenarios (not multiple vehicles). Furthermore, most of these methodologies could not support
exploring the emergent dynamics between the generated trajectories and the surrounding traffic.
Thus, there is a need to check the detailed states of the CA process with a global view to achieve the
optimal strategy, while it is essential to understand the cause–effect relationship of each CA action
and how the effects of a maneuver impact on the neighboring aircraft. Note that tight couplings
between aircraft trajectories in dense scenarios (i.e., flocks applications) can deal with the propagation
of non-controllable upstream and downstream maneuvers between trajectories.
The overextended UAV usage of flock applications would lead to a higher number of threats,
which could raise the risk of potential collisions. For simplicity, the CA problem is currently being
discussed on UAVs (without pilot intervention) that are flying in a segregated airspace. In this paper,
it is assumed that a group of cooperative UAVs, which are stabilized by the autopilot, are flying
to their own destination and having to avoid collisions with other UAVs in an efficient real-time
communication. Each vehicle is equipped with a trajectory control unit which relies on the CA
algorithm that is used as a predictive control considering real-time data-link communication with
surrounding traffic. In this research, we propose two efficient algorithms: conflict detection (CD) and
conflict resolution (CR), which, as two sub-modules, constitute a novel CA system for multi-UAV.
The main contributions of this paper are as follows:
•
•
•
This paper presents an innovative strategy, distributed dynamic optimization approach
(DDOA), to provide alternative trajectories for each UAV, by adding some essential constraints
(i.e., performance, cost and distance) to make the problem treatable while the feasible trajectory
generation for multi-UAV is a non-deterministic polynomial (NP) problem.
The novel causal analysis is developed to choose a preferred resolution trajectory, performing an
analysis of scenario state space in order to explore the dynamic evolution and then determine all
reachable states. By decomposing the complex scenario into several common clusters, the solution
space is greatly reduced.
Quantitative measurement experiments are carried out to validate the feasibility and scalability of
the CA system for the free flight of multi-UAV. In addition, the average computation time does
not grow exponentially as the airspace density increases.
To prevent mid-air collisions between UAVs, the proposed CA system has been developed to
serve as the last-resort safety net, which is an on-board CDR system providing resolution advisories.
This paper is organized as follows: Section 2 illustrates the CA system functional architecture; Section 3
presents the core algorithm of the CD and CR sub-modules; Section 4 achieves the simulation results
using the proposed system; finally, conclusions and future work are summarized in Section 5.
2. The Proposed CA System Architecture
The CA system should be supported by vigorous algorithms to increase the airspace capacity.
Figure 1 illustrates the detailed fundamental processes of the complete CA system, in which the
input is the 4D (three dimensions (3D) position + time) trajectory information belonging to each
UAV; a high speed processor equipped with CD algorithm deals with the trajectories and obtains
relevant information to predict whether a collision is going to occur in the future. If a potential
collision is detected, DDOA computes the feasible solutions and causal analysis selects the optimal
95
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Appl. Sci. 2017, 7, 83
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Appl. 2016, 6,xFOR PEER
3 of 14
one.
The control
command is sent to the involved UAVs to resolve current threats and the states
Appl. 2016,
3 of 14
one.
The 6,xFOR
controlPEER
command is sent to the involved UAVs to resolve current threats and the states
improve online.
improve online.
one. The control command is sent to the involved UAVs to resolve current threats and the states
improve online.
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113
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114
115
Figure 1.
Functionalarchitecture
architecture of
of the
the novel
novel collision
collision avoidance
avoidance (CA)
(CA) system.
system.
1.Functional
Figure
1.FunctionalCA
architecture
of the novel
collision
avoidance (CA) system.
The
system consists
consists
of two
two
components:
The core
core of
of the
the operational
operational CA
system
of
components:
• The CD module that analyzes the flight information depending on 4D trajectory has two
The core of the operational CA system consists of two components:
The CD
module
that analyzes
the flight representation
information depending
4Dinforming
trajectory the
has CR
twomodule.
different
•
different
roles:
generating
the intuitionistic
of threatson
and
• The CD module that analyzes the flight information depending on 4D trajectory has two
roles:The
generating
the intuitionistic
representation
threats
and informing
CRstages:
module.
•
CR module
integrates CD
and resolvesofthe
detected
conflicts inthe
two
DDOA
different roles: generating the intuitionistic representation of threats and informing the CR module.
aims
to avoid
collisions
by generating
alternative
trajectories
each UAV
with
a local
optimization
•
The
CR module
integrates
CD and
resolves the
detectedfor
conflicts
in two
stages:
DDOA
aims to
• The CR module integrates CD and resolves the detected conflicts in two stages: DDOA
scope;
causal
analysis
focuses on
exploring
the emergent
the alternative
avoid
collisions
by generating
alternative
trajectories
for eachdynamics
UAV with abetween
local optimization
scope;
aims to avoid collisions by generating alternative trajectories for each UAV with a local optimization
trajectories
generated
by
DDOA
and
the
rest
involved
trajectories.
Based
on
the
detected
threats,
the
causal analysis focuses on exploring the emergent dynamics between the alternative trajectories
scope; causal analysis focuses on exploring the emergent dynamics between the alternative
CR should
be informed
with
thethe
geographical
coordinates
where
theon
collision
would threats,
occur, the
generated
by DDOA
and
rest involved
trajectories.
Based
the detected
thetime
CR
trajectories generated by DDOA and the rest involved trajectories. Based on the detected threats, the
whenshould
the collision
wouldwith
occur,
the involved
UAVs. Though
CRcollision
is a combinatorial
problem
in
be informed
theand
geographical
coordinates
where the
would occur,
the time
CR should be informed with the geographical coordinates where the collision would occur, the time
exponential
growth
with
the
increasing
number
of
UAVs,
in
our
research
several
strategies
such
as
when the collision would occur, and the involved UAVs. Though CR is a combinatorial problem in
when the collision would occur, and the involved UAVs. Though CR is a combinatorial problem in
setting
constraints
are needed
narrow the
solution
spaceinprogressively
to get the
final optimal
exponential
growth
with thetoincreasing
number
of UAVs,
our research several
strategies
such as
exponential growth with the increasing number of UAVs, in our research several strategies such as
solution.
Figure
2 conceptually
The DDOA
several
setting
constraints
are neededillustrates
to narrowthe
thesolution
solution procedure.
space progressively
to getgenerates
the final optimal
setting constraints are needed to narrow the solution space progressively to get the final optimal
locally-optimal
CA trajectories
considering
different
constraints,
e.g., the
two
UAVsgenerates
should meet
the
solution. Figure
2 conceptually
illustrates
the solution
procedure.
The
DDOA
several
solution. Figure 2 conceptually illustrates the solution procedure. The DDOA generates several
performance
requirements,
satisfy considering
the state equation,
keep a e.g.,
safe the
distance,
etc. should
This causal
locally-optimal
CA trajectories
differentand
constraints,
two UAVs
meet
locally-optimal CA trajectories considering different constraints, e.g., the two UAVs should meet the
analysis
allows takingrequirements,
into consideration
possible
solutions
that
ensure
the completeness
of
the performance
satisfy all
thethe
state
equation,
and keep
a safe
distance,
etc. This causal
performance requirements, satisfy the state equation, and keep a safe distance, etc. This causal
the solution
theninto
reduces
the spaceallonce
again based
on some
constraints
(e.g.,
analysisspace,
allowsand
taking
consideration
the possible
solutions
that specific
ensure the
completeness
analysis allows taking into consideration all the possible solutions that ensure the completeness of
the least
cost).
of the
solution space, and then reduces the space once again based on some specific constraints
the solution space, and then reduces the space once again based on some specific constraints (e.g.,
(e.g., the least cost).
the least cost).
Causal analysis
with constraints
Causal analysis
with constraints
Causal
analysis
Optimal
Solution
Optimal
Solution
DDOA
Causal
analysis
with
constraints
DDOA
with DDOA
constraints
DDOA
116
117
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Figure 2.Step‐by‐step optimal process.
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123
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125
Figure
2.
Step-by-step
optimal
Figure
2.Step‐by‐step
optimal
process.
The hardware architecture of
the novel
CA system
consists
of the following major components:
CA processor—performs airspace surveillance, intruder tracking, own UAV state tracking, conflict
The hardware
hardware architecture
architecture of
of the
the novel CA
CA system
system consists
consists of
of the
the following
following major
major components:
components:
The
detection
and conflict resolution,
and novel
it uses discrete
status inputs
of involved UAVs
to control the
CA processor—performs
processor—performs airspace
airspace surveillance,
surveillance, intruder
tracking,
own UAV
state tracking,
tracking, conflict
conflict
CA
intruder
tracking,
logic parameters that determine
the protection
volume
around own
ownUAV
UAV;state
State transmitter—is
detection
and
conflict
resolution,
and
it
uses
discrete
status
inputs
of
involved
UAVs
to
control
the
detection
and conflict
resolution,
and it usesbetween
discrete UAVs
status inputs
involved UAVs
to control the CA
CA
used
to provide
air-to-air
data exchange
so thatofcoordinated,
complementary
CA
logic
parameters
that
determine
the
protection
volume
around
own
UAV;
State
transmitter—is
logic parameters
determine
protection
volume
around own UAV;
State transmitter—is
to
trajectories
can bethat
issued
when the
required;
Control
unit—guarantees
the multiple
cooperativeused
UAVs
used
to
provide
air-to-air
data
exchange
between
UAVs
so
that
coordinated,
complementary
CA
provide air-to-air
data exchange
between UAVs
so that
following
the generated
optimal trajectory
to resolve
thecoordinated,
conflicts. complementary CA trajectories
trajectories can be issued when required; Control unit—guarantees the multiple cooperative UAVs
following
the generated
optimal trajectory to resolve the conflicts.
3.
Core Algorithm
Analysis
125
3. Core Algorithm Analysis
Appl. Sci. 2017, 7, 83
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can be issued when required; Control unit—guarantees the multiple cooperative UAVs following the
generated optimal trajectory to resolve the conflicts.
3. Core Algorithm Analysis
3.1. Representation of 4D Trajectory and Conflict Detection
The continuous trajectory of UAV can be modeled as a sequence of discrete points (waypoints)
expediently for computer processes. There is a direction between every two adjacent waypoints
due to the velocity vector. The position of 3D and corresponding time—called spatial-temporal
information—makes up the 4D trajectory of each UAV. For U AVi (i = 1, 2, ..., n), its dynamic
characteristics can be described in a Cartesian coordinate system [20]. The region formed by x
and y axes indicates the horizontal plane, and z stands for the altitude.


xti


pit =  yit , vit =
zit
dϕit
dt
= ωti ,

dpit
dt
 

vix,t
vit cos ϕit cos θti

 

=  viy,t  =  vit cos ϕit sin θti 
vit sin ϕit
viz,t
0 < θti < 2π,
− π2 ≤ ϕit ≤
(1)
π
2
The formula defines pit and vit , respectively, as the position and velocity of UAVi in 3D; let θti
represent the course angle, the orientation of velocity vector vit in the x-y plane (measured from the x
axis in counter-clockwise direction); let ϕit delegate the pitch angle, the orientation of velocity vector
vit in the vertical plane (measured from the horizontal plane up as positive and down as negative);
and ωti is the angular velocity.
Considered simply, each UAV is supposed to keep its own velocity vi , i ∈ {1, 2, · · · , n} during
regular flight. In the detection sub-module, the UAV that detects the conflict will read out the sensed
data from sensor unit and check whether any intruder enters its safety zone. At each moment t,
the relative distance between UAVi and nearby UAVj in the airspace can be simply calculated as:
r
ij
Rt
=
j 2
j 2
j 2
( xti − xt ) + (yit − yt ) + (zit − zt )
(2)
In this research, the conflict detection logic can be defined as follows: if the current relative
ij
distance of the two UAVs is smaller than the Rcf ( Rt < Rc f ), and they have a trend to be closer,
ij
i.e., when the value of Rt that is the relative distance between UAVi and nearby UAVj is getting
smaller, the resolution maneuver fires regardless of whether the coming closest point of approach
(CPA) [21] is in collision volume Rcl or not. Despite the fact that this way certainly may touch off
several unnecessary resolution maneuvers, the collision risk is highly reduced since the situation in
whichthe intruder suddenly changes its direction near the CPA is prevented.
ij
j
Let pt = pit − pt be the distance vector in 3D space between UAVi and nearby UAVj at time t;
ij
j
let vt = vit − vt be the relative velocity (closing speed) between the UAVs at time t. Distinctly, when
ij
ij
the two UAVs are getting closer to each other (i.e., pt · vt > 0), a conflict is detected and it has to be
ij
ij
resolved immediately; when the two UAVs are getting further apart (i.e., pt · vt < 0), there is no risk
to deteriorate into a collision at all.
3.2. Conflict Resolution Algorithm
This section focuses on the CR algorithm consisting of two subsections: DDOA and causal analysis.
Different alternative trajectories for each involved UAV are generated by DDOA in a collision, and the
globally optimal one is selected by causal analysis considering the follow-up effects.
Appl. Sci. 2017, 7, 83
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3.2.1. Distributed Dynamic Optimization Approach
The UAVi trajectory is discrete and the sampling interval is ∆t. Therefore, in the m-th moment,
the related position and pitch angle of UAVi are xi (m), yi (m), zi (m), ϕi (m), m ∈ N. The discrete
kinematic model of UAVi is:

 

x i ( m + 1)
xi (m) + vi cos( ϕi (m)) cos θi · ∆t
 y (m + 1)   y (m) + v cos( ϕ (m)) sin θ · ∆t 

 i
  i
i
i
i
(3)

=

 z i ( m + 1)  

zi (m) + vi (sin ϕi (m)) · ∆t
ϕ i ( m + 1)
ϕi (m) + ωti · ∆t
In order to generate an amending trajectory for CA, it is better if each UAV could adjust its track
as few times as possible, execute the trajectory as shorter as possible and reach the target point as soon
as possible. Therefore, at time m, the objective function Oi (m) of UAVi comprises three aspects above:
Oi (m) = w1 Ci (m) + w2 Di (m) + w3 Ti (m)
(4)
In this formula, w1 , w2 , w3 are the corresponding weight coefficients of the three indexes Ci (m),
Di (m), Ti (m). Their values reflect different application contexts, e.g., w3 > w1 indicates that the
controllers prefer shorter time to achieve the destination even if the fuel cost is higher. Before the
computation, normalization processing is needed. The three indexes can be calculated using the
following formulas.
(
| ϕi (m) − ϕi (m − 1)| i f m ≥ 1
Ci (m) =
(5)
0 if m = 0
where Ci (m) expresses the track adjustment cost of UAVi, which is defined as the change value of
pitch angle.
h
i
2
2
2 1/2
Di (m) = k pi (m) − pid k2 = ( xi (m) − xid ) + (yi (m) − yid ) + (zi (m) − zid )
(6)
T
where Di (m) indicates the distance from current location to its destination pid = ( xid , yid , zid ) .
Ti (m) = m · ∆t + Di (m)/vi
(7)
where Ti (m) represents the total flight time of UAVi.
Assume that there are N intervals from time m to the destination, thus the position and
corresponding pitch angle sequences of UAVi in [m, m + N − 1] are respectively:
∆
Pi = [ pi (m), pi (m + 1), · · · , pi (m + r ), · · · , pi (m + N − 1)] T
∆
Ψi = [ ϕi (m), ϕi (m + 1), · · · , ϕi (m + r ), · · · , ϕi (m + N − 1)] T
∀r ∈ [0, N − 1]
(8)
The objective function for progressive optimization is:
N −1
minOi (m + r ) = min(
∑
(w1 Di (m + r ) + w2 Ti (m + r ) + w3 Ci (m + r )))
(9)
r =0
Note that it should meet the following constraints in the optimization process:
"
q( ϕi (m + r )) =
1
−1
#
"
Ci (m + r ) −
B
−A
#
"
=
1
−1
#
"
( ϕi (m + r ) − ϕi (m + r − 1)) −
B
−A
#
≤0
(10)
Appl. 2016, 6, 83
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 xi (m  r )  [ xi (m  r  1)  vi cos(i (m  r  1)) cos i  t ]
6 of 14
 y (m  r )  [ y (m  r  1)  v cos( (m  r  1))sin   t ]
i
i
i
i
i
0
ei ( pi (m  r ))  
(11)
 zi (m  r )  [ zi (m  r  1)  vi (sin i (m  r  1))  t ] 




xi (m + r ) − [ xi (m + r − 1(m
)+
 rv)i cos
i ((mϕi (rm) + r − 1)) cos θi · ∆t] 
i
 y (m +r ) − [y (m + r −
1
)
+
v
cos
( ϕi (m + r − 1)) sin θi · ∆t] 
 i
i
i
(11)
ei ( pi (m + r )) = 
=0

di ( piz(im
(m +
)−
[zi (rm))+rd−
1) + vi (sin
+
r−
r ),r p
r ) ϕi (pmj (m
r ) 1))·0∆t]
(12)
j (m 
0  pi (m
2
ϕi ( m + r ) − ϕi ( m + r )
In the above formulas, q(i (m  r ))  0 explains that the value change of UAVi pitch angle
di ( pi (m + r ), p j (m + r )) = d0 − k pi (m + r ) − p j (m + r )k2 ≤ 0
(12)
should be in the variation range of (A,B); ei ( pi (m  r ))  0 shows that the
calculation of UAVi
In the above formulas, q( ϕi (m + r )) ≤ 0 explains that the value change of UAVi pitch angle
position and pitch angle at time
m + r is based on the corresponding information at m + r − 1;
should be in the variation range of (A,B); ei ( pi (m + r )) = 0 shows that the calculation of UAVi
di ( pi (m  r ), p j (m  r ))  0 illustrates that the distance between UAVi and UAVj must not be shorter
position
and pitch angle at time m + r is based on the corresponding information at m + r − 1;
the
minimum
d0.
dthan
(
p
(
m
+
r ), p j (m +safe
r )) distance
≤ 0 illustrates
that the distance between UAVi and UAVj must not be shorter
i i
Integrating
the
objective
function
with constraints, the next waypoint ( pi (m  1), i (m  1)) can
than the minimum safe distance d0 .
be calculated
based
the current
statewith
the optimization
( pi (constraints,
m), i (m)) . Repeating
Integrating
the on
objective
function
the next waypoint
( pi (m +procedure,
1), ϕi (m + the
1))
can
be
calculated
based
on
the
current
state
(
p
(
m
)
,
ϕ
(
m
))
.
Repeating
the
optimization
procedure,
complete amending trajectory made up of a series
of discrete
waypoints is generated.
i
i
the complete
trajectory
made up of
a series
of discrete
waypoints
is generated.
Besides, amending
the algorithm
for generating
CA
waypoints
is robust
enough
to resolve successive
Besides,
the algorithm
for generating
waypoints
is robust
enough in
to resolve
threats.
threats.
For example,
if UAV1
encountersCA
UAV2
and UAV3
seperately
a short successive
interval, the
two
For
example,
if
UAV1
encounters
UAV2
and
UAV3
seperately
in
a
short
interval,
the
two
threats
threats could be resolved via a compositive CA trajectory withonly a distance constraint between
could
resolved
via a compositive
CA trajectory
withonly a distance
constraintminimum
between UAV1
and
UAV1 be
and
UAV3 added
to the optimization
calculation.This
section calculates
deviation
UAV3
to the
optimization
section
calculates
minimum
deviation of
the planned
of the added
planned
trajectory
by an calculation.This
objective function
integrated
with
track adjustment,
distance,
and
trajectory
by
an
objective
function
integrated
with
track
adjustment,
distance,
and
time
costs,
taking
time costs, taking into account the vehicle performance, state and separation constraints.
into account the vehicle performance, state and separation constraints.
3.2.2. Causal Analysis
3.2.2. Causal Analysis
The size (computational complexity) of the conflict resolution problem is typically very large,
The
size (computational
complexity)
of the
resolution
problem
is typically
large,
which
represents
a real challenge
to deal with
theconflict
exponential
growth
of the state
space invery
a realistic
which
represents
a
real
challenge
to
deal
with
the
exponential
growth
of
the
state
space
in
a
realistic
environment containing dozens of UAVs. A highly efficient technique to reduce the problem size is
environment
containing
dozens
A highly
efficient
to reduce the
problem
sizeon
is
clustering [22].
The scenario
can of
beUAVs.
decomposed
into
severaltechnique
sets of independent
clusters
based
clustering
[22]. between
The scenario
can trajectories
be decomposed
into several
setsThe
of independent
clusters
based on
the interaction
planned
for a period
of time.
partition principle
is mainly
in
the
interaction
between
planned
trajectories
for
a
period
of
time.
The
partition
principle
is
mainly
in
view of the distances between the neighboring UAVs. These independent clusters can be processed
view
of theto
distances
between
the neighboring
UAVs. 3These
clusters can be processed in
in parallel
significantly
improve
efficiency. Figure
is theindependent
concept illustration.
parallel to significantly improve efficiency. Figure 3 is the concept illustration.
Appl. Sci. 2017, 7, 83
U
UA
V3
Tr 3
Cluster B
UA T
V1 r2
Tr 1
Tr1
1
r 11
1T
UAV
Tr1
UAV1
Cluster A
Tr11
Tr1
UAV2
V2
A
T r2
Cluster C
Solution for original situation
Without clusters
Solution for
cluster B
UAV2
Tr2
Solution for
cluster C
Tr21
UAV3
Tr3
Tr31
Solution for
cluster A
Figure 3. Concept illustration of clustering.
Figure 3. Concept illustration of clustering.
The
is decomposed
into several
clustersclusters
with treatable
sizes withsizes
few trajectories.
The original
originalproblem
problem
is decomposed
into several
with treatable
with few
Thus,
the
overall
solution
is
a
combination
of
conflict-free
solutions
obtained
by
a
causal
trajectories. Thus, the overall solution is a combination of conflict-free solutions obtained by analysis
a causal
for
thesefor
regional
clusters.clusters.
The core
idea
ofidea
the of
causal
analysis
is to explore
the state
space
of the
analysis
these regional
The
core
the causal
analysis
is to explore
the state
space
of
CA
scenario
to
achieve
the
optimal
resolution.
It
utilizes
the
alternative
trajectories
and
relevant
cost
the CA scenario to achieve the optimal resolution. It utilizes the alternative trajectories and relevant
cost generated by the DDOA, which includes the track adjustment, distance, and time costs.
Appl. Sci. 2017, 7, 83
Appl. 2016, 6, 83
Appl. 2016, 6, 83
7 of 14
7 of 14
7 of 14
generated
DDOA,
which includes
the track
adjustment,
and
time costs.amendment
Therefore,
Therefore, by
forthe
n UAVs
involved
in the same
scenario,
the total distance,
cost of the
trajectories
Therefore, for n UAVs involved in the same scenario, the total cost of the trajectories amendment
for
n
UAVs
involved
in
the
same
scenario,
the
total
cost
of
the
trajectories
amendment
can
be
defined
as:
can be defined as:
can be defined as:
n Nn−N1 1
n N 1
Cost
 
C(im
(m rr)) +
D
mm+r )r) T
m  r)
CostCost
=∑
CC
Di i(((m
+ii ((T
i (m+
∑
 
 r)  D
 r)  T
mi (mr )+ r )
i
i 1 r  0 i
(13)
(13)
(13)
i =1 ir=
1 0r  0
The process state could be described by a specific four-tuple:
The process state could be described by a specific four-tuple:
four-tuple:


•

•

•


•
conflict , cost ,(active UAV ),(resolution trajectories)
(14)
, cost(,(active
active U
UAV
))}
conflict
(14)
f lict, cost,
AV),(
), (resolution
resolution trajectories
trajectories
(14)
{con
An instance state a = {2,1,(1,2,3),(11,111,31,32)} is used to explain the tuple.
An instance state a = {2,1,(1,2,3),(11,111,31,32)} is used to explain the tuple.
An instance state a = {2,1,(1,2,3),(11,111,31,32)} is used to explain the tuple.
Conflict: indicates the threat that will be resolved (conflict 2 is active in state a).
Conflict: indicates the threat that will be resolved (conflict 2 is active in state a).
Conflict:
indicates
threat
that willfor
bethe
resolved
(conflict
2 is active
in state a).
Accumulated
cost:the
Cost
summation
respective
resolution
trajectories
(cost = 1 in state a).
Accumulated cost: Cost summation for the respective resolution trajectories (cost = 1 in state a).
Accumulated
Cost summation
for the
respective
(cost =among
1 in state
a).
Active UAVs:cost:
is a processed
tuple and
represents
allresolution
the UAVstrajectories
in this scenario,
them
Active UAVs: is a processed tuple and represents all the UAVs in this scenario, among them
the
active
one
would
be
underlined
(UAV1
and
UAV3
are
active
to
have
conflict
2
in
state
a).
Active UAVs: is a processed tuple and represents all the UAVs in this scenario, among them the
the active one would be underlined (UAV1 and UAV3 are active to have conflict 2 in state a).
Activeone
resolution
toand
store
solution
trajectories
and the2 active
active
would betrajectories:
underlined used
(UAV1
UAV3
are active
to have conflict
in stateresolution
a).
Active resolution trajectories: used to store solution trajectories and the active resolution
trajectories
are
represented
with
underlines
to
resolve
the
active
collision
(111,
31
or
32 can be
Active resolution
trajectories:
to store
solutionthe
trajectories
and the
active
trajectories
are represented
withused
underlines
to resolve
active collision
(111,
31 orresolution
32 can be
used to resolve
conflict 2 in state
a). Here
the number
is composed
with
the aircraft
trajectories
are represented
underlines
to resolve
the active
(111,
31 or
can be
used
to resolve
conflict 2 with
in state
a). Here
the number
is collision
composed
with
the32aircraft
identification
i and
amending
strategy
descend/climb
(1/2).
used
to
resolve
conflict
2
in
state
a).
Here
the
number
is
composed
with
the
aircraft
identification
identification i and amending strategy descend/climb (1/2).
iThe
andcausal
amending
strategycan
descend/climb
(1/2).
exploration
be summarized
with the following steps in Figure 4:
The causal exploration can be summarized with the following steps in Figure 4:
The causal exploration can be summarized with the following steps in Figure 4:
yes
yes
DDOA
Generate
Active DDOA Generate
solution
Active
conflict
solution
trajectory
conflict
trajectory
Produce
Produce
Process
Process
state
state
Create a
Create a
branch
branch
Update
Update
cost
and
cost
and
active
active
conflict
conflict
Active
Active
conflict
conflict
no
no
Select
Select
optimal
optimal
solution
solution
Figure 4. Causal exploration flow chart.
Figure 4. Causal
Causal exploration flow chart.
As an explanatory case, Figure 5 illustrates the whole feasible solutions of a case scenario, and
As
an explanatory
case,
5 illustrates
thethe
whole
feasible
solutions
of a of
case
scenario,
and
As
explanatory
case,Figure
Figure
illustrates
whole
feasible
solutions
a case
Figure 6an
shows
its reachability
tree. 5Using
the causal
exploration
algorithm,
there
are scenario,
six final
Figure
6
shows
its
reachability
tree.
Using
the
causal
exploration
algorithm,
there
are
six
final
and
Figure
6 shows
reachability
tree.Evidently,
Using thestate
causal
algorithm,
there
final
process
states
as theits
feasible
solutions.
d isexploration
preferred to
be utilized
thanare
thesixothers
process
states
as
the
feasible
solutions.
Evidently,
state
d
is
preferred
to
be
utilized
than
the
others
process
states
as the feasible
due to the
minimum
cost. solutions. Evidently, state d is preferred to be utilized than the others due
due
tominimum
the minimum
to the
cost.cost.
Tr2
Tr2
1
C=
=1
Tr11 C
Tr11
Tr2
Tr2
Tr3
Tr3
Tr2
Tr2
Tr1
Tr1
(a)
(a)
(f) Total Cost=1.5
(f) Total Cost=1.5
Tr31
C=
1
Tr31
C=
1
(g)
(g)
(c)
(c)
Tr3
Tr3
Total Cost=1.5
Total Cost=1.5
Tr2
Tr2
1
C=
=1
Tr11 C
Tr11
Tr1
Tr1
C=
1
C=
1(d)
C=1C.5=1.5
Tr1
Tr1
Tr3
Tr3
Tr3
Tr3
Tr11
Tr21
Tr21
Tr22
Tr22
Tr2
Tr2
1
C=
=1
Tr11 C
(b)
(b)
Tr3
Tr3
.5 .5
=1 1
C C=
Tr12
Tr12
Tr2
Tr2
1.5
C= .5
1
Tr111C=
Tr111
Tr3
Tr3
(d)
Total Cost=1
Total Cost=1
(e) Total Cost=1.5
(e) Total Cost=1.5
Figure 5. The feasible solutions.
Figure 5. The feasible solutions.
Total Cost=2
Total Cost=2
Tr32
Tr32
C=1.5
C=1.5
(h) Total Cost=2.5
(h) Total Cost=2.5
Appl. Sci. 2017, 7, 83
Appl. 2016, 6, 83
8 of 14
8 of 14
(a)
{1,0,(1,2,3),(11,12,21,22)}
(b)
(c)
{2,1,(1,2,3),(11,111,31,32)} {0,1.5,(1,2,3),12}
(d)
{0,1,(1,2,3),21}
(e)
{0,1.5,(1,2,3),22}
(f)
(g)
(h)
{0,1.5,(1,2,3),111}{0,2,(1,2,3),(11,31)}{0,2.5,(1,2,3),(11,32)}
Figure
Figure 6.
6. The CA reachability
reachability tree.
tree.
4. Simulation and Results
4.
this section,
section, we
we carry
carry out
out simulation
simulation experiments to evaluate the efficacy of
of the
the proposed
proposed
In this
the CA
CA system.
system. The computational results represent collision-free maneuvers
maneuvers for
for
algorithms for the
multiple UAVs
UAVsthat
thatare
aremodeled
modeledwith
withdetailed
detaileddynamics.
dynamics.
multiple
4.1.
4.1. A Case Scenario
To
our
simulation
experiments
areare
performed
on
Toverify
verifythe
thefeasibility
feasibilityofofthe
theproposed
proposedalgorithms,
algorithms,
our
simulation
experiments
performed
aonmanually
generated
scenario
of five
(with (with
the corresponding
trajectories
Tr1, Tr2,Tr1,
Tr3,Tr2,
Tr4 and
a manually
generated
scenario
ofUAVs
five UAVs
the corresponding
trajectories
Tr3,
Tr5),
illustrated
in Figurein
7. Figure
This scenario
the following
characteristics:
Tr4 and
Tr5), illustrated
7. This includes
scenario includes
the following
characteristics:
(1) It
fairly complex
complex scenario
scenario with
with multiple
multiple UAVs.
UAVs. Indeed,
three trajectories,
trajectories,
(1)
It is
is aa fairly
Indeed, among
among the
the first
first three
Tr1
imposes
sequent
threats
to
both
Tr2
and
Tr3;
moreover,
an
encounter
emerges
between
Tr4
Tr1 imposes sequent threats to both Tr2 and Tr3; moreover, an encounter emerges between Tr4
and
Tr5,
which
further
increases
the
complexity
of
the
scenario.
and Tr5, which further increases the complexity of the scenario.
(2)
It
domino
effect)
between
neighboring
threats.
For
(2) It involves
involves the
theinterrelationship
interrelationship(also
(alsocalled
called
domino
effect)
between
neighboring
threats.
instance,
a
new
secondary
threat
between
UAV3
and
UAV5
may
emerge
in
the
process
of
For instance, a new secondary threat between UAV3 and UAV5 may emerge in the process
resolving
their
respective
previous
threat.
of resolving their respective previous threat.
(3)
It
resolvessuccessive
successivethreats
threats
a compositive
CA trajectory,
i.e.,is UAV1
is todetected
to
(3) It resolves
via via
a compositive
CA trajectory,
i.e., UAV1
detected
encounter
encounter
UAV2
and
UAV3
separately
in
a
short
continuous
time
period
and
the
two
UAV2 and UAV3 separately in a short continuous time period and the two successive conflicts
successive
conflictsoverall
can berather
considered
overall
rather than one by one.
can be considered
than one
by one.
Appl. 2016,
6, 83above
In the
9 of 14
scenario, each UAV is assumed to be heading towards its own target position
along the straight line. Simulations start with the initial information about the position and velocity
of the UAVs in a scenario. For the local area, the UAV states have been treated as broadcast
information with efficient real-time communication. The assumptions and the parameter setup
values are given in Table 1. The proposed algorithms are coded in C++ and the simulation is
performed on an EliteBook laptop with a processor Intel i5 of 2.6 GHz and 4 GB of RAM.
Table 1.The assumptions of parameters and unmanned aerial vehicle (UAV) properties
Rcf
(km)
1.2
Rcl
(m)
100
Velocity
(m/s)
30
Δt
(s)
1
A
(rad)
−1.047
B
(rad)
1.047
w1  w2  w3
Figure
Five-UAV
scenario with
the generated
generated optimal
optimal resolution.
resolution.
Figure 7.
7. the
Five-UAV
the
In this causal analysis,
cost ofscenario
variouswith
feasible
CA trajectories
assists
the decision making of
solution selection. After executing the proposed CA system, the optimal strategy, that Tr1
The entirety of the reachable states of this multi‐UAV scenario are displayed in Figure 8. From
synthetically
amends
upward
UAV5
climbs, to
is implemented.
In the above
scenario,
eachand
UAV
is assumed
be heading towards its own target position along
the proposed multi‐threat resolution point of view, solo UAV1 climbs (Tr11) or UAV2 descends
the straight line. Simulations start with the initial information about the position and velocity of the
(Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with
UAVs in a scenario. For the local area, the UAV states have been treated as broadcast information
Tr3 if trajectory Tr11 is applied (see state b). Then UAV1 could climb again and a composite CA
with efficient real-time communication. The assumptions and the parameter setup values are given in
trajectory (Tr111) is generated (see state d). Meanwhile, UAV3 could descend (Tr31) to resolve the
new encounter (see state e). For resolving the threat between UAV4 and UAV5, UAV4 amends
downward (Tr41) or UAV5 turns upward (Tr51). In state d, there would be no domino effect
between the neighboring UAVs (see state h and state i), while a new threat would appear between
the descending UAV3 and climbing UAV5 (see state k) and have to be resolved through the
Appl. Sci.
2016,
6, 837, 83
Appl.
2017,
9 of 14
Table 1. The proposed algorithms are coded in C++ and the simulation is performed on an EliteBook
laptop with a processor Intel i5 of 2.6 GHz and 4 GB of RAM.
Table 1. The assumptions of parameters and unmanned aerial vehicle (UAV) properties.
Rcf
(km)
Rcl
(m)
1.2
100
Velocity
(m/s)
∆t
(s)
30
1
w1 = w2 = w3
A
(rad)
B
(rad)
−1.047
1.047
In this causal analysis, the cost of various feasible CA trajectories assists the decision making of
Figure
7. Five-UAV
scenario with
generated
optimal strategy,
resolution.that Tr1 synthetically
solution selection. After
executing
the proposed
CAthe
system,
the optimal
amends upward and UAV5 climbs, is implemented.
The entirety of the reachable states of this multi‐UAV scenario are displayed in Figure 8. From
The entirety of the reachable states of this multi-UAV scenario are displayed in Figure 8.
the proposed multi‐threat resolution point of view, solo UAV1 climbs (Tr11) or UAV2 descends
From the proposed multi-threat resolution point of view, solo UAV1 climbs (Tr11) or UAV2 descends
(Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with
(Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with Tr3
Tr3 if trajectory Tr11 is applied (see state b). Then UAV1 could climb again and a composite CA
if trajectory Tr11 is applied (see state b). Then UAV1 could climb again and a composite CA trajectory
trajectory (Tr111) is generated (see state d). Meanwhile, UAV3 could descend (Tr31) to resolve the
(Tr111) is generated (see state d). Meanwhile, UAV3 could descend (Tr31) to resolve the new encounter
new encounter (see state e). For resolving the threat between UAV4 and UAV5, UAV4 amends
(see state e). For resolving the threat between UAV4 and UAV5, UAV4 amends downward (Tr41) or
downward (Tr41) or UAV5 turns upward (Tr51). In state d, there would be no domino effect
UAV5 turns upward (Tr51). In state d, there would be no domino effect between the neighboring
between the neighboring UAVs (see state h and state i), while a new threat would appear between
UAVs (see state h and state i), while a new threat would appear between the descending UAV3 and
the descending UAV3 and climbing UAV5 (see state k) and have to be resolved through the
climbing UAV5 (see state k) and have to be resolved through the following heading change (see state p
following heading change (see state p and state q).
and state q).
Figure 8. The reachability tree of this multi-UAV
multi-UAV scenario.
scenario.
On the
the other
other branch,
branch, the
the first
first threat
threat is
is resolved
resolved by
by the
the amendment
amendment of
(see state
state c),
c), and
and two
two
On
of Tr2
Tr2 (see
options
are
considered
to
solve
the
encounter
between
UAV1
and
UAV3
(see
state
f
and
state
g).
In
options are considered to solve the encounter between UAV1 and UAV3 (see state f and state g). In state
state
the collision
between
and UAV5
be avoided
directly
without
domino
effect
(seel
f,
the f,
collision
between
UAV4UAV4
and UAV5
could could
be avoided
directly
without
domino
effect (see
state
state
l
and
state
m).
However
in
state
g,
a
new
threat
(see
state
n)
would
appear
between
the
and state m). However in state g, a new threat (see state n) would appear between the descending
descending
UAV3 and
climbing
UAV5be
and
it could
resolved
by one of
the involved
UAV3
and climbing
UAV5
and it could
resolved
bybe
one
of the involved
trajectories
(see trajectories
state r and
(see
state
r
and
state
s).
state s).
Since the
the cost
costcriterion
criterionisistaken
taken
into
consideration
in the
decision-making
process,
is clear
Since
into
consideration
in the
decision-making
process,
it is it
clear
that
that
state
i
(UAV1
climbs
twice
for
the
sequent
threats
with
UAV2
and
UAV3,
and
UAV5
amends
state i (UAV1 climbs twice for the sequent threats with UAV2 and UAV3, and UAV5 amends upward
upward
to avoid
thewith
collision
with
UAV4)
is the
bestfeasible
one ofscenarios.
the feasible
amended
to
avoid the
collision
UAV4)
is the
best one
of the
Thescenarios.
amendedThe
trajectories
of
trajectories
of
UAV1
and
UAV5are
represented
in
Figure
7.
UAV1 and UAV5are represented in Figure 7.
Table 2. UAV1 and UAV5 modified trajectories.
Time
ID
Appl. Sci. 2017, 7, 83
Amended Trajectory
X (m) Y (m) Z (m)
Time
ID
Amended Trajectory
X (m) Y (m) Z (m)
10 of 14
17:17:48 UAV 1 370.43 510.68 669.57
UAV 1 593.19 733.44 721.53
17:18:10
17:17:50 UAV 1 387.85 528.10 686.68
UAV 5 628.79 779.87 572.48
Table
2 summarizes406.44
the amended
of UAV1 and UAV5
(for the sake of simplicity,
17:17:52
564.10 waypoints
701.14
UAV 1
UAV 1 614.07 754.32 716.18
17:18:12
the data are recorded every two seconds). UAV1 starts
to change its headings at 17:17:48 and returns
17:17:54 UAV 1 425.92 566.17 713.00
UAV 5 614.12 754.47 578.76
to the original trajectories at 17:18:18, while UAV5 starts at 17:18:04 and ends at 17:18:24.
17:17:56 UAV 1 446.44 586.69 720.60
UAV 1 633.94 774.19 705.67
17:18:14
17:17:58 UAV 1 467.54
UAV 5 599.14 728.52 580.34
Table597.79
2. UAV1 723.66
and UAV5 modified trajectories.
17:18:00 UAV 1
17:18:02ID UAV 1
Time
488.67 628.92 721.03
Amended
Trajectory
509.24
649.50
713.75
X (m)
UAV 1 529.85
17:17:48
U AV1
370.43
17:18:04
668.57
UAV 5387.85
17:17:50
U AV1
550.95
17:17:52
U AV1UAV 1 406.44
17:18:06
17:17:54
U AV1
425.92
UAV 5 656.73
Y (m)
Z (m)
17:18:16
Time
UAV 1
UAV
ID5
651.64 791.89 689.14
584.16Amended
702.58 Trajectory
578.76
X (m)
Y (m)
Z (m)
670.10
510.68
848.77
528.10
720.90
669.57
532.96
686.68
17:18:18
691.20
564.10
566.17
828.26
723.99
701.14
713.00
551.38
17:18:20
17:18:12
17:18:22
UAV 1 667.72 807.97 669.57
U AV1
593.19
733.44
721.53
UAV
5 569.50
U AV5
628.79 677.18
779.87572.48572.48
UAV
5 555.03
U AV1
614.07 652.12
754.32564.58716.18
U
AV5
614.12
754.47
541.56
628.78
551.38578.76
UAV 5
17:17:56
U AV1UAV 1 446.44
572.14 586.69
712.39
17:18:08
17:17:58
U AV1
467.54
597.79
643.26 804.93
720.60
725.25
723.66
564.58
17:18:24
U AV1
633.94 608.28
774.19532.96705.67
UAV
5 529.72
UAV 5
17:18:10
17:18:14
U AV5
599.14
728.52
17:18:00
U AV1
488.67
628.92
721.03
U AV1
651.64
791.89
17:18:16
17:18:02
U
AV1
509.24
649.50
713.75
U
AV5
584.16
702.58
Figure 9 depicts the relative distance of each pair of UAVs that are involved in a
AV1 figure,
529.85
U AV1 region
667.72of each
807.97
threat.
FromUthis
we can670.10
see that 720.90
the minimum
separation
UAV
17:18:04
17:18:18
U AV5
848.77 effect
532.96
U AV5
569.50
677.18
intruded upon,
thanks 668.57
to the favorable
attained by the CA
algorithm.
580.34
689.14
578.76
detected
is669.57
never
572.48
U AV1
550.95
691.20
723.99 of 17:18:20
AV5 that
555.03
652.12
564.58
Figure 10
illustrates
the pitch
angle profiles
UAV1 andUUAV5
amending
their headings
U
AV5
656.73
828.26
551.38
17:18:22
U
AV5
541.56
628.78
for the avoidance of corresponding threats in this scenario. At 17:17:48, UAV1 follows the 551.38
control
U
AV1
572.14
712.39
725.25
17:18:24
U
AV5
529.72
608.28
532.96
input
that changes its pitch angle from 0 to 0.71 and climbs subsequently. At 17:17:58, UAV1 and
17:18:08
AV5 and 643.26
804.93
564.58
UAV2 reach UCPA
UAV1 begins
to return
to its original path. However, UAV1 climbs again at
17:18:02 because of the encounter with UAV3. At 17:18:18, UAV1 recoveries its course when both the
Figure
9 depicts
the relative
distance
of each
pair
of UAVs that
are involved
a detected
threat.
involved
threats
are resolved.
And
meanwhile,
the
neighboring
collision
betweeninUAV4
and UAV5
is
From
avoided
this figure,
via thewe
upward
can seeamendment
that the minimum
of UAV5.
separation
Using this
region
CA of
advisory,
each UAV
there
is never
is no intruded
domino effect
upon,
between
sub-scenarios.
thanks tothe
thetwo
favorable
effect attained by the CA algorithm.
17:18:06
Figure
Figure 9.
9. Relative
Relative distance.
distance.
Figure 10 illustrates the pitch angle profiles of UAV1 and UAV5 that amending their headings for
the avoidance of corresponding threats in this scenario. At 17:17:48, UAV1 follows the control input
that changes its pitch angle from 0 to 0.71 and climbs subsequently. At 17:17:58, UAV1 and UAV2
reach CPA and UAV1 begins to return to its original path. However, UAV1 climbs again at 17:18:02
because of the encounter with UAV3. At 17:18:18, UAV1 recoveries its course when both the involved
threats are resolved. And meanwhile, the neighboring collision between UAV4 and UAV5 is avoided
via the upward amendment of UAV5. Using this CA advisory, there is no domino effect between the
two sub-scenarios.
Appl. Sci. 2017, 7, 83
Appl. 2016, 6, 83
11 of 14
11 of 14
Figure
Figure10.
10.Pitch
Pitchangle
angleprofile
profileof
ofboth
bothUAVs.
UAVs.
4.2. Further Investigation
4.2. Further Investigation
In
this section, we conduct additional experiments to test the scalability of the proposed
In this section, we conduct additional experiments to test the scalability of the proposed algorithms.
algorithms. In [23], scalability is defined as the ability of an algorithm, system, or model to deal
In [23], scalability is defined as the ability of an algorithm, system, or model to deal with increasing
with increasing numbers of missions at a reasonable cost, or its ability to be effectively enlarged to
numbers of missions at a reasonable cost, or its ability to be effectively enlarged to commensurate
commensurate that growth.
that growth.
In practical applications, we may encounter different settings of UAVs, which depend on
In practical applications, we may encounter different settings of UAVs, which depend on different
different values of densities, variable Rcf and sense range. For instance, with the increase of
values of densities, variable Rcf and sense range. For instance, with the increase of applications such
applications such as surveillance in which various UAVs owning different capabilities and
as surveillance in which various UAVs owning different capabilities and properties would cooperate
properties would cooperate and compete for a certain target, it is expected that the airspace traffic
and compete for a certain target, it is expected that the airspace traffic density will grow considerably
density will grow considerably in certain reduced areas during short time periods. Since the CA
in certain reduced areas during short time periods. Since the CA system is applied independently to
system is applied independently to each cluster, the increasing UAV number in the whole airspace
each cluster, the increasing UAV number in the whole airspace may improve the encounter possibility,
may improve the encounter possibility, thereby raising the number of clusters, rather than the
thereby raising the number of clusters, rather than the number of UAVs involved in a specific cluster.
number of UAVs involved in a specific cluster.
To validate the scalability, we use the computation time as a parameter to record the performance
To validate the scalability, we use the computation time as a parameter to record the
of the proposed CA system in handling different-density scenarios. Based on the simulation results in
performance of the proposed CA system in handling different-density scenarios. Based on the
Table 3, the average computation time (over 100 runs of random flight tests) for low density (20 UAVs),
simulation results in Table 3, the average computation time (over 100 runs of random flight tests)
medium density (60 UAVs), and high density (100 UAVs) traffic do not grow exponentially as the
for low density (20 UAVs), medium density (60 UAVs), and high density (100 UAVs) traffic do not
airspace density increases, attributing the high scalability to the independent clusters, which can be
grow exponentially as the airspace density increases, attributing the high scalability to the
frequently processed.
independent clusters, which can be frequently processed.
Table 3. Time taken in different densities.
Table 3.Time taken in different densities
UAVNumber
Number
UAV
2020
6060
100
100
Computation
Time
(s) (s)
Computation
Time
0.92
0.92
5.28
5.28
17.62
17.62
In addition,
addition, several
with
varying
values
of tuning
parameters
Rcf and
In
severalextensive
extensivesimulations
simulations
with
varying
values
of tuning
parameters
Rcfsense
and
range range
(SR) are
constructed
to observe
the performance
in terms of
The CA maneuvers
sense
(SR)
are constructed
to observe
the performance
in efficiency.
terms of efficiency.
The CA
should be optimal
UAVs
at can
theirarrive
respective
destination
minimum possible
time.
maneuvers
should so
be that
optimal
socan
thatarrive
UAVs
at their
respectiveindestination
in minimum
e
e
Define ti time.
as theDefine
expectant
flight
(not toflight
maketime
any deviation
of the
planned
trajectory)
tri as
possible
the time
expectant
(not to make
any
deviation
of the and
planned
ti as
the realistic flight time (fully follow the CA maneuvers) of U AVi (i = 1, 2, .., n), and the efficiency is
trajectory) and tir as the realistic flight time (fully follow the CA maneuvers) of UAVi(i  1, 2,.., n) ,
given as [24]:
and the efficiency is given as [24]:
1 n te
E f f iciency = ∑ e ri
(15)
1n in=1ti ti
Efficiency   r
(15)
n i 1 ti
Figure 11 depicts the simulation results of efficiency with variable parameters. We could
conclude the following:
Appl. Sci. 2017, 7, 83
12 of 14
Figure 11 depicts the simulation results of efficiency with variable parameters. We could conclude
the following:
Appl.
83
• 2016,
The6,efficiency
of 14
is decreasing as the Rcf value increases, because extensive conflict volume12leads
to more threats that would be detected by the CD algorithm, thus more waypoints have to be
• The efficiency is decreasing as the Rcf value increases, because extensive conflict volume
amended to avoid potential collisions resulting in the higher realistic flight time.
leads to more threats that would be detected by the CD algorithm, thus more waypoints have to be
•
Compared to SR = 9 km, the efficiency is lower when SR is equal to three kilometers with the
amended to avoid potential collisions resulting in the higher realistic flight time.
same Rcf , because the restricting sensor range may ignore the neighboring threats that could
• Compared
to SR = 9 km, the efficiency is lower when SR is equal to three kilometers with
be synthetically resolved, and lately detect the intruder UAV, causing the number of amended
the same Rcf, because the restricting sensor range may ignore the neighboring threats that could be
waypoints to be higher.
synthetically resolved, and lately detect the intruder UAV, causing the number of amended
•
With the same parameters of Rcf and sense range, high efficiency is obtained if the complete CR
waypoints to be higher.
algorithm including the causal analysis is utilized rather than only the DDOA. With the positive
• With the same parameters of Rcf and sense range, high efficiency is obtained if the
impact of causal analysis, the average increment of efficiency is respectively 2.83% and 3.47%
complete CR algorithm including the causal analysis is utilized rather than only the DDOA. With
for SR = 9 km and SR = 3 km. Consequently, the causal analysis is effective for the selection of
the positive impact of causal analysis, the average increment of efficiency is respectively 2.83% and 3.47%
optimal resolution trajectory.
for SR = 9 km and SR = 3 km. Consequently, the causal analysis is effective for the selection of
optimal resolution trajectory.
Figure
Figure11.
11.Variation
Variationof
ofefficiency
efficiency with
with RRcfcfand
andsense
senserange
rangefor
forthe
thetraffic
trafficdensity
densityof
of20
20UAVs.
UAVs.
5.
5.Conclusions
Conclusions
This
twotwo
efficient
algorithms:
CD algorithm
and CR
algorithm,
which
This paper
paperhas
haspresented
presented
efficient
algorithms:
CD algorithm
and
CR algorithm,
constitute
a
novel
CA
system
for
multiple
cooperative
UAVs
aiming
to
detect
and
resolve
threats
by
which constitute a novel CA system for multiple cooperative UAVs aiming to detect and resolve
generating
an optimalan
trajectory
an overall
minimum
cost in 3Dcost
airspace.
The CD module
threats by generating
optimal with
trajectory
with an
overall minimum
in 3D airspace.
The CD
analyzes
the
spatial-temporal
information
composing
a
set
of
discrete
4D
trajectories
generate the
module analyzes the spatial-temporal information composing a set of discrete 4Dtotrajectories
to
intuitionistic
representation
of
detected
conflicts.
The
CR
algorithm
integrates
with
the
CD
portion
generate the intuitionistic representation of detected conflicts. The CR algorithm integrates with the
and
solves the
through
causal
The DDOA
provides
new
CD portion
and detected
solves thethreats
detected
threatsDDOA
throughand
DDOA
andanalysis.
causal analysis.
The DDOA
provides
feasible
alternative
trajectories
for
each
UAV
involved
in
an
encounter
with
a
local
optimization
new feasible alternative trajectories for each UAV involved in an encounter with a local optimization
scope,
scope, and
and itit generates
generates alternative
alternative avoiding
avoiding trajectories
trajectories by
by an
an objective
objective function
function (integrating
(integrating track
track
adjustment,
cost,
distance,
and
time)
in
consideration
of
several
constraints
(i.e.,
performance,
adjustment, cost, distance, and time) in consideration of several constraints (i.e., performance,state,
state,
and
distance).
The
causal
analysis
explores
the
emergent
dynamics
between
the
alternative
and distance). The causal analysis explores the emergent dynamics between the alternative trajectories
trajectories
generated
by DDOA
and the surrounding
It hasadvantages
numerous advantages
such the
as
generated by
DDOA and
the surrounding
traffic. It hastraffic.
numerous
such as splitting
splitting
the
scenario
to
separate
clusters,
reducing
the
size
of
solution
space,
and
exploring
the
scenario to separate clusters, reducing the size of solution space, and exploring the global optimal
global
optimal
Based on the
quantitative
simulation
results,
proposed
CA validated
system has
solution.
Basedsolution.
on the quantitative
simulation
results,
the proposed
CAthe
system
has been
to
been
validated
to
be
feasible
and
effective
in
resolving
conflicts
for
multiple
UAVs
and
high
be feasible and effective in resolving conflicts for multiple UAVs and has high scalability forhas
different
scalability
for different
trafficdecreases
densities;asthe
decreases
as the
value of
volume
traffic densities;
the efficiency
theefficiency
value of conflict
volume
increases,
andconflict
increases
as the
increases,
and
increases
as
the
sense
range
increases;
the
causal
analysis
is
effective
for
the
selection
sense range increases; the causal analysis is effective for the selection of an optimal resolution trajectory.
of an optimal resolution trajectory.
Future research will be dedicated to: (1) using a heuristic-based algorithm to improve our
proposed approach, which could tackle the collision avoidance problem of more UAVs in
high-density scenarios, while it also may require more computation time; (2) making a
comprehensive review of the existing best performing methods that consider UAV factors and
Appl. Sci. 2017, 7, 83
13 of 14
Future research will be dedicated to: (1) using a heuristic-based algorithm to improve our
proposed approach, which could tackle the collision avoidance problem of more UAVs in high-density
scenarios, while it also may require more computation time; (2) making a comprehensive review of
the existing best performing methods that consider UAV factors and integrating them to our system
in order to improve its performance; (3) considering several disturbances (e.g., wind) to improve the
current system logic in order to hold the complex field situations; (4) integrating UAVs into(manned)
general aviation to operate in a non-segregated airspace.
Acknowledgments: The author(s) disclosed receipt of the following financial support for the research, authorship,
and/or publication of this article: This work was supported by the National Natural Science Foundation of
China (71601181), the Military Scientific Research Project (162017160500A21XXX), and the State Key Laboratory of
Management and Control for Complex Systems-Open Project (20160109).
Author Contributions: Mingrui Lao and Jun Tang designed the distributed dynamic optimization approach
and causal analysis, conducted the simulations of the core algorithms and co-wrote the initial manuscript.
Besides, Jun Tang helped improve the system design and put forward several construction suggestions. The final
manuscript was read and approved by all authors.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:
3D
4D
ADS-B
ASAS
CA
CD
CPA
CR
DDOA
NP
TCAS
TMA
UAV
Three dimensional
Four dimensional
Automatic Dependent Surveillance Broadcast
Airborne Separation Assurance System
Collision avoidance
Conflict detection
Closet point of approach
Conflict resolution
Distributed dynamic optimization approach
Non-deterministic polynomial
Traffic Alert and Collision Avoidance System
Terminal Maneuvering Area
Unmanned aerial vehicle
References
1.
2.
3.
4.
5.
6.
7.
Borra-Serrano, I.; Peña, J.M.; Torres-Sánchez, J.; Mesas-Carrascosa, F.J.; López-Granados, F. Spatial Quality
Evaluation of Resampled Unmanned Aerial Vehicle-Imagery for Weed Mapping. Sensors 2015, 15,
19688–19708. [CrossRef] [PubMed]
Ruiz, S.; Piera, M.A.; Del Pozo, I. A medium term conflict detection and resolution system for terminal
maneuvering area based on spatial data structures and 4D trajectories. Transp. Res. C Emerg. Technol. 2013,
26, 396–417. [CrossRef]
Netjasov, F.; Vidosavljevic, A.; Tosic, V.; Everdij, M.H.; Blom, H.A. Development, validation and application
of stochastically and dynamically coloured Petri net model of ACAS operations for safety assessment
purposes. Transp. Res. C Emerg. Technol. 2013, 33, 167–195. [CrossRef]
Brooker, P. Airborne Separation Assurance Systems: Towards a work programme to prove safety. Saf. Sci.
2004, 42, 723–754. [CrossRef]
Lai, C.P.; Ren, Y.J.; Lin, C. ADS-B based collision avoidance radar for unmanned aerial vehicles.
In Proceedings of the IEEE MTT-S International Microwave Symposium Digest, Boston, MA, USA,
7–9 June 2009; pp. 85–88.
Lin, Y.; Saripalli, S. Sense and avoid for Unmanned Aerial Vehicles using ADS-B. In Proceedings of the 2015
IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26–30 May 2015;
pp. 6402–6407.
BaraldiSesso, D.; Vismari, L.F.; Camargo, J.B. An approach to assess the safety of ADS-B based unmanned
aerial systems. In Proceedings of the 2014 International Conference on Unmanned Aircraft Systems (ICUAS),
Orlando, FL, USA, 27–30 May 2014; pp. 669–676.
Appl. Sci. 2017, 7, 83
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
14 of 14
Wolf, T.B.; Kochenderfer, M.J. Aircraft collision avoidance using Monte Carlo real-time belief space search.
J. Intell. Rob. Syst. 2011, 64, 277–298. [CrossRef]
Tang, J.; Fan, L.; Lao, S. Collision Avoidance for Multi-UAV Based on Geometric Optimization Model in 3D
Airspace. Arabian J. Sci. Eng. 2014, 39, 8409–8416. [CrossRef]
Holt, J.; Biaz, S.; Yilmaz, L.; Aji, C.A. A symbiotic simulation architecture for evaluating UAVs collision
avoidance techniques. J. Simul. 2014, 8, 64–75. [CrossRef]
Prandini, M.; Hu, J.; Lygeros, J.; Sastry, S. A Probabilistic Approach to Aircraft Conflict Detection. IEEE Trans.
Intell. Transp. Syst. 2000, 1, 99–220. [CrossRef]
Manathara, J.G.; Ghose, D. Rendezvous of multiple UAVs with collision avoidance using consensus.
J. Aerosp. Eng. 2011, 25, 480–489. [CrossRef]
Mujumdar, A.; Padhi, R. Reactive Collision Avoidance of Using Nonlinear Geometric and Differential
Geometric Guidance. J. Guid. Control Dyn. 2011, 34, 303–311. [CrossRef]
Nikolos, I.K.; Valavanis, K.P.; Tsourveloudis, N.C.; Kostaras, A.N. Evolutionary algorithm based
offline/online path planner for UAV navigation. IEEE Trans. Syst. Man Cybern. B 2003, 33, 898–912.
[CrossRef] [PubMed]
Luo, C.; McClean, S.I.; Parr, G.; Teacy, L.; De Nardi, R. UAV position estimation and collision avoidance
using the extended Kalman filter. IEEE Trans. Veh. Technol. 2013, 62, 2749–2762. [CrossRef]
Ragi, S.; Chong, E.K. UAV path planning in a dynamic environment via partially observable markov decision
process. IEEE Trans. Aerosp. Electron. Syst. 2013, 49, 2397–2412. [CrossRef]
Lin, Y.; Saripalli, S. Path planning using 3D Dubins Curve for Unmanned Aerial Vehicles. In Proceedings
of the 2014 International Conference on Unmanned Aircraft Systems (ICUAS), Orlando, FL, USA,
27–30 May 2014; pp. 296–304.
Shim, D.H.; Sastry, S. An Evasive Maneuvering Algorithm for UAVs in See-and-Avoid Situations.
In Proceedings of the 2007 American Control Conference, New York, NY, USA, 11–13 July 2007;
pp. 3886–3891.
Lin, Y.; Saripalli, S. Collision avoidance for UAVs using reachable sets. In Proceedings of the 2015
International Conference on Unmanned Aircraft Systems (ICUAS), Denver, CO, USA, 9–12 June 2015;
pp. 226–235.
Netjasov, F.; Vidosavljevic, A.; Tosic, V.; Everdij, M.H.C.; Blom, H.A.P. Stochastically and dynamically
coloured Petri net model of ACAS operations. In Proceedings of the 4th International Conference on
Research in Air Transportation (ICRAT), Budapest, Hungary, 1–4 June 2010; pp. 449–456.
Kochenderfer, M.J.; Holland, J.E.; Chryssanthacopoulos, J.P. Next-generation airborne collision avoidance
system. Lincoln Lab. J. 2012, 19, 17–33.
Ruiz, S.; Piera, M.A.; Nosedal, J.; Ranieri, A. Strategic de-confliction in the presence of a large number of 4D
trajectories using a causal modeling approach. Transp. Res. C Emerg. Technol. 2014, 39, 129–147. [CrossRef]
Ross, A.M.; Rhodes, D.H.; Hastings, D.E. Defining changeability: Reconciling flexibility, adaptability,
scalability, modifiability, and robustness for maintaining system lifecycle value. J. Syst. Eng. 2008, 11,
246–262. [CrossRef]
George, J.; Ghose, D. A reactive inverse PN algorithm for collision avoidance among multiple unmanned
aerial vehicles. In Proceedings of the 2009 American Control Conference, St. Louis, MO, USA,
10–12 June 2009; pp. 3890–3895.
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