Cooperative Target Tracking using a Fleet of UA Vs [619790]

Cooperative Target Tracking using a Fleet of UA Vs
with Collision and Obstacle Avoidance
Lili Ma
Deptartment of Computer Engineering Technology
New York City College of Technology
New York, USA
[anonimizat]
Abstract —In this paper, our earlier results on cooperative
target tracking using a fleet of unmanned aerial vehicles (UA Vs)
is enhanced with both collision and obstacle avoidance capability.
The existing control input that has two decoupled control efforts
with one handling the tracking and the other dedicated for
formation is now further augmented with a repulsion term that
resolves collision with other team members and obstacles nearby.
Assuming that each UA V takes the same and constant velocity.
This newly-added control component adjusts the UA V’s heading
angle to the opposite direction in relation to the UA V’s closet
neighbors and obstacles where collision may occur. This repulsion
term can also be expressed as a function of relative bearing angles
alone, making it possible to be estimated/measured by onboard
vision sensors in the presence of communication loss. Regarding
communication topologies, an all-to-all communication, a ring
topology, and a cyclic pursuit topology are studied. The effec-
tiveness of the proposed collision/obstacle avoidance scheme is
demonstrated by numerical simulation examples.
Index Terms —Cooperative target tracking, balanced circular
formation, cyclic pursuit, collision avoidance, obstacle avoidance,
potential field
I. I NTRODUCTION
Coordinated control and formation control have become an
active and hot research area for many years. In addition to the
studies of fundamental formation schemes such as collective
motion [1], [2], cyclic pursuit [3]–[6], and circular motion [7]–
[9], research efforts have also been devoted to applying these
research findings in suitable applications. One application of
these coordinated control schemes is cooperative target track-
ing. Recently, cooperative control for tracking and enclosing
of moving target(s) have drawn researchers’ attention. Many
results have been published on coordinating a group of robots
to track static or moving targets [10]–[15]. It is believed that
sending multiple coordinated robots with less complex sensors
can lead to a better target tracking than sending one with a
sensor that costs twice as much. Moreover, the probability of
mission success increases as the loss of a single robot in a
flock of vehicles is less severe than the loss of the only robot
sent on the mission.
Along this line, our past research proposed an inverse-
kinematics based guidance law that regulates the 2D horizontal
range between a single UA V and a ground target moving
with unknown velocity [16]. This controller was used in [17]
to command a fleet of UA Vs to track the moving target. A
formation scheme was in-cooperated that spreads all UA Vsevenly on a circle, resulting in cooperative target tracking in
balanced circular formation. We also investigated more flexible
formation patterns in [18] by modifying the controller to be
able to regulate the relative 2D range to a pre-specified time-
varying range reference. In this paper, we aim at further en-
hancement of the multi-UA V system by adding the capability
of avoiding both inter-vehicle collision and obstacle collision.
Collision may occur between either agents or external
obstacles. Clearly, a collision algorithm is important to guar-
antee safety. Tremendous results have been reported on colli-
sion avoidance [19]–[23] and/or obstacle avoidance [24]–[28],
among which the potential field method [29]–[35] remains as
a popular method since it is easy to implement and does not
require intensive real-time computation. A comparative study
of collision avoidance techniques is given in [36].
For our multi-UA V system, each UA V is assumed to take
the same constant velocity. Control of the UA Vs are via their
yaw rates. The collision/obstacle avoidance scheme proposed
in this paper belongs to the category of the potential field
method. To avoid collisions, a repulsion term is added into
the control input of each UA V . This newly-added avoidance
control component adjusts the UA V’s heading angle to the
opposite direction in relation to the UA V’s closet neighbors
and obstacles where collision may occur. The proposed avoid-
ance control law has another advantage of being able to
be expressed as a function of relative bearing angles alone,
making it possible to be estimated/measured by onboard vision
sensors in the presence of communication loss.
Regarding the communication topology, three communica-
tion topologies are considered, including an all-to-all com-
munication, a ring topology, and a cyclic pursuit topology.
Thorough simulation results are presented confirming the
effectiveness of the proposed collision avoidance method
under these three communication topologies, for target that
moves with both constant and time-varying velocities, and for
obstacles that are in the way of the planned trajectories.
The paper is organized as follows. Section II describes the
problem formulation and our existing results on cooperative
target tracking of a moving ground vehicle using a fleet of
UA Vs. Main results for collision avoidance are presented in
Sec. III, where a repulsion term, which is dedicated for colli-
sion avoidance, is added into the control input. The collision
avoidance scheme can be further applied to the scenario ofCONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 22nd International Conference on System
Theory, Control and Computing. Received May 31, 2018.

xyz
{}Ibp
tpgVr
{B}
tVrcI
CpRp=uavVrρ
h{C} γ(a)3D Demonstration

xNorth
Down z
UA V
Target λ ψ η
tψgVpλ
gλ
tVy (b)2D Demonstration
Fig. 1. Relative kinematics of UA V-target motion.
obstacle avoidance, by treating the detected obstacles in the
same manner as treating other UA Vs. Simulation results are
provided in Sec. V. Section VI concludes the paper.
II. P ROBLEM FORMULATION AND OUREARLIER RESULTS
Consider a group of nUA Vs (agents) moving at the same
speed. Each UA V is capable of sensing or receiving infor-
mation from its neighbors. The neighborhood set of agents
i, denoted byNi, is the set of UA Vs whose information can
be obtained by the agent ivia sensing and/or communication.
The size of the neighborhood depends on the characteristics
of the sensors and/or the communication network. We are
interested in coordinating a multi-UA V system to track a
moving ground vehicle where all UA Vs should keep a balanced
circular formation at any time instant and the formation radius
should follow a time-varying prescribed reference.
Refer to Fig. 1. Let pi(t)be the position of the target w.r.t.
theithUA V in the inertial frame; i(t)be the UA V’s heading;
i(t)be the line-of-sight angle; i(t)be the horizontal range
between the UA V and the target; Vg(t)be the projection of the
UA V’s velocity onto the horizontal plane; Vt(t)and t(t)be
the amplitude and orientation of the target’s velocity !(t) =
[!1(t);!2(t)]>;i(t)be the angle between the UA V’s velocity
vector and the vector perpendicular to the line-of-sight; and
_ i(t)be the UA V’s yaw rate, which is the control input to be
designed.
The kinematic equations for the ithUA V tracking a ground
target is given below [16]–[18]:
8
>>>>><
>>>>>:_i(t) =Vg(t) sini(t) +Vt(t) sin[ t(t)( i(t)i(t))]
=1i(!i(t)) sin (i(t) +2i(!i(t)));
_i(t) =Vg(t) cosi(t)Vt(t) cos[ t(t)( i(t)i(t))]
i(t)
+_ i(t);
(1)
where
1i(!(t)) = sign(si(t))q
2
si(t) +2
ci(t);
2i(!(t)) = tan1ci(t)
si(t)
;(2)and
si(t) =Vg(t) +Vt(t) cos( t(t) i(t));
ci(t) =Vt(t) sin( t(t) i(t));
Vt(t) =q
!2
1(t) +!2
2(t);
t(t) = tan1!1(t)
!2(t)
:(3)
Assuming that the linear velocity Vg(t)of all UA Vs is the
same and constant. Control of the UA Vs is via their yaw rates
_ i(t).
Our earlier results on cooperative target tracking coordi-
nated a multi-UA V system so that all the nUA Vs track the
target with a prescribed time-varing range distance d(t)in a
balanced circular formation. This is achieved by designing a
control input that is the combination of two control efforts :
_ i(t) =ui(t) =uit(t) +uic(t); (4)
where:
1) The first control component uit(t), referred to as track-
ing control law , regulates the 2D horizontal range be-
tween each UA V and the moving target to a specified
time-varying range d(t)[18]. This tracking control law
was given in (8) in [18] and is not repeated here. This
tracking control law brings the UA V to orbit above the
moving target, thus achieving tracking.
2) The second control effort uic(t), referred to as co-
ordination control law , spreads all UA Vs evenly on
a circle at any time instance. The relative separation
angles between each two adjacent UA Vs are controlled
to approach360(n1)
nfor all agents, thus achieving
balanced circular formation.
The coordination control laws uic(t)for the three consid-
ered communication topologies are summarized below:
1) Under all-to-all communication [17], [28]:
uic(t) =nX
j=1
j6=icosij(t); > 0: (5)
2) Under ring topology [17], [28]:
uic(t) =[cosi(i+1)(t)+cosi(i1)(t)];> 0:(6)
3) Under cyclic pursuit strategy [17]:
uic(t) =h
cosi(i+1)(t)cos
ni
; > 0:(7)
In (5), (6), and (7), the quantity ij(t)fori;j= 1;2;:::;n
denotes the relative bearing angle between agents iandj
as measured in the local coordinate frame of agent i. More
specifically, ij(t)denotes the angle from the velocity vector
of agentito the vector pointing from the position of agent i
to the position of agent j. Notice that these three coordination
control laws can be expressed as functions of just one quantity,
the relative bearing angle. This has the advantage of possibly
using each UA V’s onboard vision sensors to estimate/measure
ij(t)during communication loss to still maintain formation.
Please refer to [17] for more details and descriptions.CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 22nd International Conference on System
Theory, Control and Computing. Received May 31, 2018.

0 2 04 06 08 0 1 0 0
x (m)-20-100102030405060 y (m)
12
3
4(a) 2D Trajectory
0123456789 1 0
time t (sec)46810121416 Minimum distance among all agents (b) Min Distance
-10 -5 0 5 10 15 20 25
x(m)-15-10-505101520 y(m) (c)n= 4
Fig. 2. Illustration of occurrence of inter-vehicle collision.
III. I NTER -VEHICLE COLLISION AVOIDANCE
Our earlier results on cooperative target tracking have not
considered the problem of inter-vehicle collision. Fig. 2 shows
a simulation example illustrating the possibility of having
inter-vehicle collision. For simplicity, the target is assumed
to move with an unknown but constant velocity. That is, the
target moves along a straight line as shown in Fig. 2 (a).
By checking the minimal distance between any two UA Vs,
it is clear that collision may occur at the earlier stage when
trying to acquire formation, see Fig. 2 (b). Fig. 2 (c) shows
the circumstances when the minimal distance drops below a
threshold, for example 5(m). The distances between the two
agents that are too close to each other are highlighted in bold.
In this simulation, the following parameters are used: Vg= 40 ,
d= 11 (m), andn= 4.
Among the methods that tackle collision avoidance, a com-
mon way is the potential field method. To avoid collision,
the force of potential field should repel the agents once they
become too close to each other. The potential field should also
be strong enough to defend any force that push the agent to a
collision [19]–[23].
Letd0denote the minimal distance allowed between two
UA Vs before collision may occur; ridenote the position of
agenti;rijdenote the vector pointing from the position of
agentito the position of agent j, i.e.,rij=rjri;dij=jrijj
be the distance between the pair of agents iandj, andqij
be the unit-length bearing vector between agents iandj, i.e.,
qij=rij=jrijj. We start by considering a simple potential
function:
fij=d0
jrijj: (8)
This potential function has the following properties:
fijis a differentiable, non-negative function of the dis-
tancedij=jrijjbetween agents iandj.
fij!1 asdij!0.
fijis a symmetric function of the distance dijbetween
agentsiandj.
fijprovides a repulsive force when the pair of agents i
andjget too close to each other.
The total potential of agent ifor collision avoidance is given
by:
fi=X
j2N(ri)fij(jrijj); (9)whereN(ri)denotes the set of neighbors of agent iwith
relative distances less than the minimal allowed value, i.e.,
N(ri) =fjrirjj<d0g (10)
forj= 1;2;:::;n andi6=j. The gradient of fijcan be
computed as:
rrij(fij) =rij
jrijjd0
jrijj2=d0
d2
ijrij
jrijj=d0
d2
ijqij:(11)
As done in (4), the tasks of tracking and formation are
achieved by adding two decoupled terms in the control law. In
a similar manner, the problem of collision avoidance can be
resolved by adding another term that avoids collision. Let i
denote the angle of the agent i’s velocity vector with respect
to the positive x-axis, i.e.,i==2 i. Since the repulsive
force needs to be perpendicular to agent i’s velocity vector
vi= [cosi;sini]>and be along v?
i, the collision avoidance
control component, denoted by uia(t), must have the following
form:
uia(t) =Kr<v?
i;rri(fi)>; K r>0; (12)
where
rri(fi) =r rij(fi) =X
j2N(ri)rrij(fij)
=X
j2N(ri)d0
d2
ijqij:(13)
Plugging (13) into (12) yields:
uia(t) =Kr<v?
i;X
j2N(ri)d0
d2
ijqij>
=KrX
j2N(ri)<v?
i;d0
dijqij>:(14)
Notice that the inner product of two vectors is independent
from the coordinate system where they are expressed. Consid-
ering the body-fixed frame of the agent i, we have:
vi=1
0
;v?
i=0
1
;qij=cosij
sinij
: (15)
Equation (14) can be further written as:
uia(t) =KrX
j2N(ri)0
1
;d0
dijcosij
sinij
=KrX
j2N(ri)d0
dijsinij:(16)
The idea behind the repulsion term in (16) is that the agent
itries to balance its heading angle with its closest neighbors
N(ri). This results in an adjustment of agent i’s heading to
the opposite direction in relation to N(ri).
Having designed the collision avoidance control law (16),
the overall control input to each agent now has three control
components . That is:
ui(t) =uit(t) +uic(t) +uia(t); (17)CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 22nd International Conference on System
Theory, Control and Computing. Received May 31, 2018.

whereuit(t)was given in (8) in [18], uic(t)is reviewed in
Sec. II for the three considered communication topologies as
given in (5), (6), and (7), respectively, and uia(t)is provided
in (16) above. By applying this control input (17), cooperative
target tracking using the multi-UA V system will be improved
with the capability of inter-vehicle collision avoidance.
For clarity, we would like to clarify the difference between
N(ri)andNi.Ni, typically called the neighborhood set
of agenti, is the set of agents whose information can be
obtained by the agent ivia communication according to
the communication topology. For example, in the all-to-all
communication,Niincludes all the rest of agents; in a ring
topology,Niincludes two agents i1(modulen); and in
cyclic pursuit,Nionly includes the “next” agent i+1(module
n). Different from Nithat depends on the communication
topology,N(ri)denotes the set of all agents that are too
close to agent i, based on the relative distance in between.
The underlying assumption is that each agent is able to either
acquire (via information exchange through the communication
network) or obtain (via onboard sensing and measurement) this
relative distance.
IV. O BSTACLE AVOIDANCE
In addition to the inter-vehicle collision that may occur
during formation/coordination of a multi-agent system, another
main issue that arises is that all agents need to carry out the
required task in the presence of obstacles. The problem of
obstacle avoidance has been widely studied in the literature,
leading to typical solutions including via local optimiza-
tion [24], via behavioural approach [25], via first splitting
and then regrouping [26], by path re-planning [27], and by
potential field functions [29]–[35]. A comparative study of
collision avoidance techniques is given in [36].
The method described in Sec. III can be readily extended
to avoid obstacles as well. The idea is to expand the neigh-
borhood of agent ifor collision avoidance to further include
obstacles that fall within, i.e., lying within a circle with radius
d0centered at the agent i. With an abuse of the notation,
we still useN(ri)to denote the neighborhood of agent ifor
avoiding not only the rest of the agents but also those obstacles
that are detected nearby. Let nodenote the number of obstacles
that are observed by the agent i.N(ri), now updated for
both inter-vehicle avoidance and obstacle avoidance, takes the
following form:
N(ri) =fjrirjj<d0orjriokj<d0g (18)
forj= 1;2;:::;n; j6=iandk= 1;2;:::;n o. In (18),
okdenotes the position of the kthobstacle. As a result, the
avoidance law in (16) should now be understood as having
already incorporated the detected obstacles. In other words,
ijcould also denote the relative bearing angle between agent
iand obstacle j.
V. S IMULATION RESULTS
Matlab simulations are presented in this section for n= 4
agents. Four examples are given to demonstrate the effective-
ness of the proposed collision/obstacle avoidance scheme:Example 1 (Fig. 3) focuses on showing the effectiveness
of the proposed inter-vehicle collision avoidance method
under the three mentioned communication topologies,
i.e., all-to-all, ring, and cyclic pursuit. For simplicity, the
ground target is assumed to undergo a constant velocity
such that it travels along a straight line. The trajectories
of all participating agents, along with the trajectory of the
target, are plotted in the first column of Fig. 3. At the end
of the simulation, a circle centered at the target with the
pre-specified range dis plotted. Velocity vectors of all
four UA Vs are indicated by arrows. It can be seen that the
velocity vectors of all agents are tangential to this circle.
All agents spread evenly around the circle, highlighting
the achievement of cooperative target tracking in balanced
circular formation.
Having evaluated the cooperative target tracking in bal-
anced circular formation, we now examine the minimal
distances among all agents, shown in the second column
of Fig. 3. In this example, the allowed minimal distance
is selected to be d0= 8 (m). It can be seen that once
formation is achieved, the relative distances approach
approximately 15:5(m), which is greater than d0(m).
Thus, collision unlikely occurs upon successful forma-
tion. However, collision may occur during the earlier
stage when trying to achieve formation. With the help
of the proposed collision avoidance control law (16),
generally speaking, the minimal distances among all
agents are controlled to be greater than d0, under all the
studied communication topologies.
Example 2 (Fig. 4): The second example concentrates
on the performance of the collision avoidance control
law (16) for different values of d0, e.g., when d0= 6
(m),d0= 7 (m), andd0= 8 (m) respectively. For an
illustration purpose, only results under the ring topology
are presented. Similar results under the other two commu-
nication topologies are obtained but are not provided here.
From Fig. 4, it can be seen that the minimal distances
among all agents are controlled to be greater than (or
around, or at least not significantly smaller than) the
specified/allowed d0values.
Example 3 (Fig. 5): Both examples 1 and 2 assume that
the target moves with constant velocity. In this example,
the target undergoes a time-varying velocity. Results
under the cyclic pursuit strategy are presented. It can
be observed that successful cooperative target tracking
is achieved with balanced circular formation and inter-
vehicle collision avoidance.
Example 4 (Fig. 6): The three examples presented above
focus on showing the effectiveness of the proposed
avoidance method resolving inter-vehicle collision. This
example extends the methodology to avoiding obstacles
as well, assuming that the agents are able to detect the
positions of the obstacles using their onboard sensors. In
this example, three static obstacles exist fairly close to the
trajectories of the UA Vs. For easy implementation, the
allowed minimal distance between the agents and eachCONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 22nd International Conference on System
Theory, Control and Computing. Received May 31, 2018.

-10 0 10 20 30 40 50 60 70 80
x (m)-20-1001020304050 y (m)
12
3
4(a) All-to-All: Trajectories
0 1 2 3 4 5 6 7 8
time t (sec)78910111213141516 Minimum distance among all agents (b) All-to-All: Min Dist
-10 0 10 20 30 40 50 60 70 80
x (m)-20-1001020304050 y (m)
12
3
4
(c) Ring: Trajectories
0 1 2 3 4 5 6 7 8
time t (sec)78910111213141516 Minimum distance among all agents (d) Ring: Min Dist
-10 0 10 20 30 40 50 60 70 80
x (m)-20-1001020304050 y (m)
12
3
4
(e) Cyclic: Trajectories
0 1 2 3 4 5 6 7 8
time t (sec)78910111213141516 Minimum distance among all agents (f) Cyclic: Min Dist
Fig. 3. Cooperative target tracking with inter-vehicle collision avoidance
under three communication topologies ( Example 1 ).
0 1 2 3 4 5 6 7 8
time t (sec)46810121416 Minimum distance among all agents
(a) Ring: d0= 6 (m)
0 1 2 3 4 5 6 7 8
time t (sec)678910111213141516 Minimum distance among all agents (b) Ring: d0= 7 (m)
0 1 2 3 4 5 6 7 8
time t (sec)78910111213141516 Minimum distance among all agents (c) Ring: d0= 8 (m)
Fig. 4. Inter-vehicle collision avoidance with different specified/allowed
minimal distance under ring topology ( Example 2 ).
-40 -20 0 20 40 60
x (m)-20-1001020304050607080 y (m)
12
3
4
(a) Cyclic: Trajectories
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
time t (sec)56789101112131415 Minimum distance among all agents (b) Cyclic: Min Dist
Fig. 5. Cooperative target tracking for unknonwn time-varying target velocity
with inter-vehicle collision avoidance under cyclic pursuit ( Example 3 ).
0 20 40 60 80 100 120
x (m)-20-1001020304050607080 y (m)
12
3
4(a) Obstacle Free: Trajectories
0 2 4 6 8 10 12 14
time t (sec)46810121416 Minimum distance among all agents and obstacles (b) Obstacle Free: Min Dist
-20 0 20 40 60 80 100 120 140
x (m)-20020406080 y (m)
12
3
4
(c) With Obstacles: Trajectories
0 2 4 6 8 10 12 14
time t (sec)4681012141618 Minimum distance among all agents and obstacles (d) With Obstacles: Min Dist
Fig. 6. Cooperative target tracking with both inter-vehicle collision avoidance
and obstacle avoidance under all-to-all communication ( Example 4 ).
obstacle is also d0. The simulation is performed under
the all-to-all communication.
Both the obstacle-free scenario and the scenario with ob-
stacles are presented for comparison. Generally speaking,
all agents fulfill the tasks of cooperatively tracking the
ground target in balanced circular formation with both
inter-vehicle avoidance and obstacle avoidance.
Careful examination of Fig.6 (c) shows that the agents
behave differently depending on how close the obstacles
are to their trajectories. They may either steer away from
the obstacles or go around them. Fig. 6 (d) shows the
minimal distances among all agents and obstacles. The
portions where the minimal distance drops close to d0=
6(m) are due to either collision avoidance or obstacle
avoidance. The three zig-zag areas where the minimal
distance deviates from 15:5(m) are results of agents’
response/reaction to the three obstacles that are in the
way.
VI. C ONCLUSIONS AND FUTURE INVESTIGATIONS
This paper extends our earlier results on cooperative track-
ing of a ground moving target using a fleet of UA Vs in
balanced circular formation with enhanced collision-avoidance
and obstacle-avoidance capabilities. The methodology for
avoiding both inter-vehicle collision and obstacle collision is
the same, both via a newly-added repulsion term based on
potential field method. This repulsion term adjusts the heading
angle of each agent to the opposite direction in relation to its
collision neighbors including both other agents and obstacles.
The proposed avoidance control law has an advantage of
being expressed in terms of only one quantity, the relative
bearing angle. This could potential make onboard sensing,
measurement, and estimation easier for detection of both otherCONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 22nd International Conference on System
Theory, Control and Computing. Received May 31, 2018.

agents and the obstacles. Thorough simulation results are pre-
sented confirming the effectiveness of the proposed collision
avoidance approach under different communication topologies,
for target that moves with both constant and time-varying
velocities, and for obstacles that are in the way of the planned
trajectories of all agents. Under all circumstances, the minimal
distances among all agents and obstacles are maintained to be
greater than the allowed values fairly well. Future research will
investigate the application of the proposed avoidance scheme
to more challanging scenarios such as clustered obstacles
and/or slowly-moving/fast-moving obstacles.
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Preprint submitted to 22nd International Conference on System
Theory, Control and Computing. Received May 31, 2018.