Decentralized Swarm Aggregation and Dispersion with Inter-Member Collision Avoidance for Non-holonomic Multi-Robot Systems

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Decentralized Swarm Aggregation and Dispersion with Inter-Member
Collision Avoidance for Non-holonomic Multi-Robot Systems
Dan M. Novischi1and Adina M. Florea1
Abstract— In this paper we present a formation control
approach for team of unicycle mobile robots that exhibits both
aggregation and dispersion behaviors. The approach is based on
a attractive/repulsive potential function that models the inter-
action between the robots using only local information, while
also accounting for the physical limitations of the actuators.
Throughout the paper we provide several simulation results and
further analyze the swarm cohesiveness which shows asymptotic
stability of the proposed controller.
I. INTRODUCTION
In the past two decades the field of multi-robot systems
has attracted the attention of many researchers from the
robotics community, e.g., see[1]–[5]. This attention has been
motivated by the potential applications that can be achieved
with a team of simple robots, including environmental ex-
ploration [6], search and rescue missions [7], surveillance
operations [8], convergence tasks [9] or agricultural foraging
[10]. Specifically, the field of swarm robotics focuses on
systems that comprise of a large number of units, in which
a collective behavior is expected to emerge from interaction
among the robots, e.g. aggregation, dispersion or flocking.
In this sense, several works can be found in the literature
that deal with these behaviors for both holonomic and non-
holonomic (e.g. unicycles) type robots [1], [2], [4], [5],
[11]–[14], where some also consider bounded control inputs
models. In [11] a robust control strategy based on artificial
potential functions and sliding mode control is developed.
The same type of potential functions is also used in [4]
as an application to the unicycle kinematic model, while a
staturated extension of the model under limitited vissibility
is presented in [5]. Similarly, a saturated control scheme for
time-varying uncycle robot formations is discussed in [14],
whereas limiting functions are used in [13]. A decentral-
ized aggregation strategy that maintains the conectivity of
underlying communication graph is presented in [2], whilst
a leader based approach that guarantees collision free motion
for a team of rovers is presented in [12]. For a more in-depth
overview of the swarm robotics field, the reader is refered
to [15] and [16].
In this paper we present a formation control approach
for a team of unicycle mobile robots that exhibits two
emergent behaviors via local interaction, namely aggregation
and dispersion. In particular, we explicitly consider the local
interaction in the presence of inherent actuator limitations
1Dan M. Novischi and Adina M. Florea are with Faculty of Automatic
Control and Computers, University of Politehnica of Bucharest, Splaiul
Independentei Nr. 313, Bucharest, Romania, 060042
dan marius.novischi@cs.pub.ro,
adina.florea@cs.pub.ro
(i.e. real robot motors can not generate arbitrary high ve-
locities), as well as account for inter-robot team member
collisions. The approach is founded on results originally
presented in [1] and the non-holonomic rendevous adaptation
discussed in [4]. In this respect, our original contributions
are: i) a symmetric potential force model that enables both
aggregation and dispersion behaviors at user specified clear-
ances, ii) a bounded discontinuous control strategy that takes
into account physical limitations of robot actuators, iii) the
design and integration of a collision avoidance rule with the
proposed strategy and lastly, iv) the design of a dispersion
activation rule which can be used to asynchronously trigger
this behavior.
Following this short introduction in Section II we provide
the the formal statement for our problem, while in Section III
we present the structure of the proposed aggregation control
approach. In Section IV we further extend this structure to
account for inter-robot collisions, whilst in Section V we
carryout the controller stability analysis. We deal with the
dispersion behavior in Section VI and highlight the benefits
of our approach in Section VII. Finally, in Section VIII we
conclude this paper.
II. PROB LEM STATE MENT
Consider a system of Nmobile non-holonomic robots
operating in the 2-dimensional plane (i.e in a workspace
W⊂R2). We represent the position of the i’th robot by
qi= [xiyi]Tand together the positions of all Nrobots form
the configuration space denoted by q= [q1, ... , qN]T. The
orientation of the robots is represented by θ= [θ1, ... , θN]T,
while the time evolving state of each robot is given by its
pose that is defined for the i’th robot as pi= [qiθi]T∈
R2×(−π,π]. Then the motion of the i’th robot is described
according to the uncycle kinematic model:
˙pi=

˙xi
˙yi
˙
θi
=

uicosθi
uisinθi
ωi
(1)
where uiand ωidenote the control inputs and represent
the translational and rotational robot velocities. The model
is subject to the non-holonomic constraint of pure rolling
defined as:
˙yicos(θi)−˙xisin(θi) = 0 (2)
which simply states the robot cannot move directly on its
normal axis, but instead it can travel either forward or
backward in a curved shaped motion. A graphical view of
this model is presented in Figure 1 where tiand nirepresent

the transnational and normal unit vectors attached to the
local robot reference frame [t,n]. In addition we assume
Fig. 1. Non-holonomic model for the i’th robot in the team.
that each of the Nthe robots in the team is equipped with
a local sensing or communication mechanisms (e.g. infra-
red sensors) such that it can sense the positions qjof its
direct line of sight neighbors at all times. That is, we assume
that the exchange of information between neighboring robots
can be described by a (strongly) connected graph which
remains connected throughout the evolution of the system.
Time varying network topologies are not considered in this
paper. Conversely, the communication graph Gconsists of a
finite set of elements V(G) = {vi|i=1,N}that represent
its vertices indexed by the team members and a finite
set edges E(G)⊂V×Vdescribing inter-robot information
exchanges. The existence of specific edges is encoded by the
graph adjacency matrix A(G)whose elements are defined
as:
ai j =1,E(vi,vj)∈E(G)
0,otherwise (3)
and leads us to model the local neighborhood set Niof the
i’th robot in relation to its jneighbors as:
Ni={vj∈V(G)\vi|ai j =1}(4)
Futhermore, acording to [1] the interaction dynamics of an
unconstrained system can be modeled for the generic i’th
robot as:
˙qi=∑
j∈Ni
g(qi−qj)(5)
with the interaction potential force function g(·)defined as:
g(y) = −y(ga(kyk)−gr(kyk)),y∈Rd(6)
where ga(·)and gr(·)are the magnitudes of attraction and
repulsion forces that act on the straight line connecting the
i’th robot with its j’th neighbor. The function must be odd,
i.e. g(y) = −g(−y), such that around a unique distance δthe
potential force draws or pulls apart the robots in question.
As stated in [1] this gives rise to the following (natural)
assumptions:
(A1)At the unique distance δwe have ga(δ) = gr(δ),
while ga(kyk)≥gr(kyk)for kyk≥δand ga(kyk)≤gr(kyk)
for kyk≤δ. Moreover, since the interaction is based on
the interplay between attractive/repulsive forces a second
assumption requires that:
(A2)For gaand grthere exists corresponding potentials
functions Ja:R+→R+and Jr:R+→R+such that
∇yJa(kyk) = yga(kyk)and ∇yJa(kyk) = ygr(kyk), where
yga(kyk)and ygr(kyk)are the actual potential forces.
In this context our objectives are as follows: i) design a for-
mation control law that enables aggregation at configurable
clearance distances while accounting for physical robot ac-
tuators limitations, ii) ensure that inter-member collisions
are avoided whilst maintaining the structure of the proposed
controller and iii) extend the controller such that the swarm
exhibits a smooth dispersion behavior that allows the user to
specify clearances similarly to aggregation.
III. BOU NDE D CONTROL INP UT AGG REG ATION
Consider a swarm composed out of Nnon-holonomic
mobile robots that exchange position information with their
adjacent neighbors as described in Section II. In order to
make the robots reach a common point given by the average
of their initial positions we base the control model for the
i’th robot on the rendvouz controller in [4] given as:
ui=−∑
j∈Ni
qT
di ti
=−∑
j∈Ni
[(xi−xj)cos(θi)+(yi−yj)sin(θi)]
ωi=−∑
j∈Ni
(θi−φi j)
=−∑
j∈Niθi−atan2yj−yi
xj−xi
(7)
where qdi = [xi−xjyi−yj]Trepresents a column vector of
the difference in positions between the i’th robot and its j’th
neighbor, while φij represents the relative angle between the
robots. This controller acts as to attract the robots such that
as they tend to rendezvous ui→0 and θi→0, where the
attractive potential is modeled as:
Ja(qdi) = 1
2kqdi k2
∇Ja(qdi) = qd i
(8)
which adheres to assumption A2.
Now let us denote the user defined clearance distance be-
tween robots with dc. In order for the team members to
aggregate around the clearance dcour proposal repulsive
force magnitude is modeled as:
gr(kqdi k) = σ(kqdik) = −2
1+e−(dc−kqdi k2)(9)
where σ(kqdi k)is a logistic like function that was scaled
and made symmetric with respect to the positive yaxis. Then
introducing in equation (6) the attractive and repulsive terms
in (8) and (9) yields the following potential force:
g(qdi ) = −qdi 1−2
1+e−(dc−kqdi k2)(10)
Note that for the above result it is trivial to check that
assumption A1 is satisfied. That is, at the unique distance
δ=√dcwe have: i) kqdik=√dc⇒qa(kqd ik) = qr(kqdik),
while ii) kqdi k≥√dc⇒qa(kqdi k)≥qr(kqdi k)and iii)
kqdi k≤√dc⇒qa(kqdi k)≤qr(kqdi k). Integrating this force

with the law in (7) results in the following form for our
symmetric repulsion aggregation proposal controller:
ui=−∑
j∈Ni
[qdi (1−σ(kqdi k))]Tti+ud
ωi=−∑
j∈Ni
[θi−(1−σ(kqdi k))φi j +σ(kqd ik)θd](11)
where udand θdspecifies the user desired swarm trajectory,
while 1 −σ(kqdi k)and σ(kqdik)are used in the second
equation in order to make the robots align as they reach the
configured aggregation clearance distance and then continue
in the desired direction. Note, that while the structure of
controller (11) is analogus to the one given in [4], the
generated force is fundamentally different since the repulsion
magnitude is a bounded symmetric function. In turn, this
results in a total potential force that has a symmetric response
around the desired aggregation distance dc, which also plays
a crucial role that enables the dispersion behavior presented
in Section VI. Moreover, since our goal is to account
for psychical limitation of the actuators we further model
controller (11) as follows:
ui=−kuVmax ∑
j∈Ni
sgn(qT
di ti) [(1−σ(kqdi k))] + ud
ωi=−∑
j∈Ni
[θi−(1−σ(kqdi k))φi j +σ(kqd ik)θd](12)
where kuis a tuning constant, Vmax a user defined speed limit
and sgn(x)is the sign function defined as:
sgn(x) = 


1,x>0
0,x=0
−1,x<0
(13)
As the reader may have noticed, the effect of applying
sgn(·)is two fold: i) coupled with the logistic like repulsion
magnitude produces a bounded response with regards to the
total force and secondly, ii) it allows the user to configure the
speed limit by tuning the kuVmax term. In Figure 2 we present
the result of running controller (12) for a team of 4 robots
with a clearance distance dc=1 m, a translational velocity
ud=0.05 m/s, θd=π/4 rad, ku=1, Vmax =0.02m/s and the
following initial conditions in standard units (i.e. meters and
radians): x= [−2,−2.5,1,2],y= [1.5,−3,−2.5,1]and
θ= [π/2,−π/3,π/4,π]. As can be distinguished form
this result, running controller (12) produces the following
sequence of events:
i) Starting in their initial positions the robots begin to
move in the direction of their local neighborhood.
ii) As the robots converge to the rendezvous point, they
aggregate at the desired clearance dcbetween members.
iii) After aggregating in a polygonal shaped formation they
align parallel to each other at the desired heading θd.
iv) Finally, the robots move ahead with heading θdand
velocity udwhile maintaining the formation at the
configured clearance distance dc.
IV. INT E R- MEM BER COLLISION AVOI DANC E
In previous section the aggregation controller (12)
achieved a bounded total force response. However, this also
Fig. 2. Top – Four robot aggregation and travel in formation (Grid – major:
1 m, minor 20 cm); Bottom – Root mean square error (ERMS) versus time.
implies that while converging to aggregate in formation
inter-robot collisions may occur between swarm members.
Nevertheless, as mentioned previously, the interplay between
attraction and repulsion for the potential force (10) is sym-
metric in respect to the clearance distance dc. That is, at equal
offsets around dcthe attractive and repulsive responses are
equal. Furthermore, consider the interaction between a single
pair of robots. Conceptually, if for one the robots we increase
the attraction such that its magnitude is twice as large, then
its corresponding repulsion cancels out. The converse is also
true due to the symmetry of the total potential force response.
Therefore, the idea is to temporary increase the magnitude
of repulsion in order to compensate the pool of attraction
generated by the local robot neighborhood in respect to the
neighbor(s) with which the collision may occur. We model
this by introducing a repulsion magnitude weight for the
potential force (10) as follows:
g(qdi ) = −qdi [1−σ(kqdi k)]
=−qdi 1−α2
1+e−(dc−kqdi k2)(14)
where the αrepresents the repulsion weight that is defined
based on a user configurable inter-robot safe distance dsand
the local neighborhood pool of attraction as:
α=kα|Ni|,
qi−qj
≤ds∧j∈Ni
1,otherwise (15)
where |Ni|represents the cardinality of set Niand kα≥1
an inter-member collision avoidance tuning factor. Using this

weight coupled with controller (12) generates an emergent
behavior where robots that are within collision distance
of each other (i.e. 
qi−qj
≤ds) increase their repulsion
magnitude in order to compensate the attractive force gen-
erated by all neighboring robots which are farther away, i.e.

qi−qj
>dc. Figure 3 shows an inter-member collision
example result while running the controller (12) where two
robots (i.e. orange and violet trace) were introduced in
addition to the ones used in the previous experiment. The
initial configuration for the previous robots is the same,
whereas the two additional robots initial states are as follows:
x= [2,1],y= [0.5,1]and θ= [π/3,−π/3]. The clearance
distance in this instance was set to dc=0.5 m, whilst other
parameters where left unchanged. Conversely, in Figure 4 we
present the result obtained by repeating the same experiment
while using the collision avoidance rule given in Equations
(14) and (15). For this case we used kα=1 and ds=0.2 m.
Fig. 3. Robot collision example: yellow robot collides with orange robot
(Grid – major: 1 m, minor 20 cm).
V. STABI LIT Y ANA LYSIS
Having introduced our proposal team formation controller
we proceed to analyze the system convergence to a steady
state. To this end, let us first consider the action of the
force generated by the attraction/repulsion potential on an
unconstrained swarm system with Ncopies of individuals
described by the following dynamics:
˙qi=−∑
j∈Ni
g(qdi ) = −∑
j∈Ni
qdi 1−2
1+ekqdi k2(16)
where the state of the system is q= [q1, .. . , qN]Twith
qi∈Rn,i=1,Nand let there be an invariant set of equilib-
rium points defined as: Ωe={q: ˙q=0}. In what follows we
use the same argument as in [1] to show that as t→∞the
state of the system q(t)→Ωe, i.e. the swarm reaches mutual
agreement on a constant configuration arrangement.
Proof: Let us consider the following (generalized)
Lyapunov function:
J(q) =
N
∑
i=1
∑
j∈Ni1
2kqdi k2+ln(1+e−kqdi k2)(17)
Fig. 4. Swarm behavior with inter-robot avoidance rule at two successive
instances (top-bottom) around the point of collision (Grid – major: 1 m,
minor 20 cm).
then its easy to see that with a shift of −ln(2)we have: i)
J(0) = 0, ii) J(q)>0,∀qdi 6=0 and iii) J(q)→∞as q→∞.
Taking the gradient of J(q)in respect to the an individual
member state qiyields the following:
∇qiJ(q) = ∇qi"∑
j∈Ni1
2kqdi k2+ln(1+e−kqdi k2)#
=∑
j∈Ni qdi −qdi
2e−kqdi k2
1+e−kqdi k2!
=∑
j∈Ni
qdi 1−2
1+ekqdi k2
(18)
which by the dynamics given in Equations (16) implies
∇qiJ(q) = −˙qi. Now, computing the time derivative of the
Lyapunov candidate function along the motion of the system
results in:
˙
J(q) = N
∑
i=1
[∇qiJ(q)]T˙qi]
=N
∑
i=1
[−˙qi]T˙qi
=−N
∑
i=1k˙qik2≤0,∀t≥0
(19)
which means that J(q)decreases unless ˙qi=0,∀i=1,N,
implying that the uncostrained system composed of the N

individuals will eventually reach a steady state. In particular,
using the LaSalle’s Invariance Principle as in [17] it follows
that as t→∞the state converges to the largest invariant
subset of the set defined as:
Ω={q:˙
J(q) = 0}={q: ˙q=0}=Ωe(20)
And since Ωeis composed out of equilibrium points we have
q(t)→Ωeas t→∞.
In light of the above result note that introducing a
clearance distance as in Equation (10) only serves to shift
the equilibrium to the desired offset. Moreover, the same
argument holds for Equation (14) where we introduced the
weight αto account for inter-member collisions. That is, α
acts as a temporary increase in the clearance distance such
that the correct interplay takes place between robots in close
proximity where kqdi k2≤ds. On the part of non-holonomic
constraints, the stability analysis is identical to [4] and hence
not repeated here. However, the discontinuous nature of the
proposed controller (12) requires further treatment. To this
end, notice that due sgn(qT
di ti)the one-sided Lyapunov
candidates have the same form as [4], only with signs of
the difference in position vector qdi interchanged:
V+=
N
∑
i=1
∑
j∈Ni
1
2[qdi ]T[qdi ](21)
for qi∈M+={qi,qj|(qT
di ti)>0}\{0}and
V−=
N
∑
i=1
∑
j∈Ni
1
2[−qdi ]T[−qdi ](22)
for qi∈M−={qi,qj|(qT
di ti)<0}\{0}. And since
{qi,qj|(qT
di ti) = 0}/∈M+,M−means that V+,V−are well
defined and in both instances equality is satisfied by qdi ≡0
for all θ. And due to the definition of φi j where atan2(0
0) = 0
we have θi≡0. Therefore, by LaSalle’s invariance priciple
we can still conclude asymptotic stability in both closures of
M\{qi,qj|(qT
di ti) = 0}and M+\{qi,qj|(qT
di ti) = 0}where
traversability is satisfied (c.f. Lemma 2.2 in [18]).
Q.E.D.
VI. NO N -HOLONOMIC SWARM DISPERSION
As discussed in Section III and Section IV our potential
force model integrates a bounded repulsion that is designed
such that its response is symmetric in respect to a con-
figurable clearance distance dc. This means that at equal
offsets around dcthe control input generated has the same
magnitude in both attraction and repulsion. Thus, our model
can be directly used to generate a dispersion behavior in
the same manner as its aggregation counter part (i.e. at
user defined clearances). However, there are several appli-
cations for which prior information about the environment
is unknown (e.g. exploration, search and rescue). In such
instances practical application of the proposed controller may
require an initial swarm aggregation to take place and then
disperse according to the user specification. To this end, let
us introduce the following measure of agreement:
λ=∑j∈Niσ(kqdi k)
|Ni|(23)
Note that λ→1 as kqdi k2→dc(i.e. the robots reach aggre-
gation). Based on this measure we define a new clearance
distance d0
cas a dispersion activation function of the allowed
deviation εfrom agreement:
d0
c=dλ,|λ−1| ≤ ε
dc,otherwise (24)
where dλis the dispersion clearance that can be changed
according to the user specification (e.g. modeled as a function
of the environment precepts). In Figure 5 we present the
usage of this rule with the controller (12), where we have
set dλ=2 m and ε=0.01. The controller parameters are:
dc=1 m, ud=0.05 m/s, θd=0 rad and kα=1, while the
initial robot configurations is: x= [−2,−1.5,−1,1],y=
[1.5,−2.5,−4.5,−1]and θ= [3π/4,−3π/4,−π/4,π/4].
Fig. 5. Top – Swarm behavior with dispersion clearance rule (Grid – major:
1 m, minor 20 cm). Bottom – Root mean square error versus time.
Note that using rule (24) produces a similar sequence of
events as in the case of pure aggregation. However, the
difference here is that upon aggregating in formation (i.e.
the initial agreement condition |λ−1| ≤ εis satisfied) the
dispersion behavior becomes active. This causes the robots
to smoothly disperse to the new clearance dλand then finally
continue on the user specified trajectory.
VII. DISCUSSION
Having presented our problem statement and the solution
to the problem, we now highlight the differences and benefits

of our approach with respect to the previous works. As
mentioned in the introduction of this paper our approach is
founded on the results previously obtained in [1] and [4]. In
this sense, both our work and the one presented by Listmann
et al. in [4] use the generic artificial potential force model (6)
and the accompanying assumptions introduced by Gazi et al.
in [1]. However, in respect to aggregation a first fundamental
difference is that both [1] and [4] model the repulsive
magnitude as an unbounded exponential function of the inter-
neighbor distances. This in turn produces an asymmetric
total force response around a unique clearance distance. In
contrast, we model the repulsive term as a bounded logistic
like function, given in (9), which produces a symmetric total
force response with regards to the unique clearance distance.
A second fundamental difference is that while avoiding inter
member collisions in [1], [4] is accomplished at an increased
control effort due to the unbounded repulsive magnitude
response, our approach allowed for the seamless integration
of a collision avoidance rule while maintaining the symmetry
and boundness of the magnitude in question. Consequently,
this means that our approach does not generate arbitrary high
responses while integrating similar avoidance characteristics,
whereby equal control efforts in both attraction and repulsion
magnitudes are outputted. Moreover, a third fundamental
difference is that our decentralized control law exploits a
discontinuous strategy which yields bounded control inputs,
i.e. uiand ωi, in respect the total generated force. This allows
the user to directly apply our controller in real-world settings
by fine tuning its parameters to the robot specifications,
i.e. kuVmax in (12) and kα,dsin (15). Conversely, both
[1], [4] exploit continuous control strategies that generate
unbounded control inputs. Thus, these strategies can not be
directly applied to real world robots and require some form
of normalization, e.g. [5]. However, in the general case it is
hard to determine a suitable normalizer.
A first major benefit resulting from the above differences
is that a team of robots running our controller exhibits
both aggregation and dispersion emergent behaviors in a
decentralized manner. Moreover, in the course of dispersing
in an environment the robots present a smooth velocity
profile that is symmetric to its aggregation counter part. As
such our controller can be used in more complex applications
where teams of robots are required to perform both flocking
and area coverage tasks, e.g. exploration or search and
rescue. Additionally, a second major benefit is that the user
can easily configure the controller in order to account for
physical limitation of the robot actuators. Hence, it is more
tractable to be used in real world settings. Furthermore,
a third benefit is that the typical high frequency chatter
phenomenon associated with arbitrary unbounded responses
is eliminated. Thus, in addition to the smooth velocity profile
the control effort can be limited within bounds of real robots
capabilities, especially in the context of dispersion.
To illustrate these benefits we conducted a dispersion
experiment with the controller in [4] and our proposed
controller given in (12). The results of this experiment are
presented in Figure 6 and Figure 7, respectively.
Fig. 6. Top – Four robot dispersion with the controller in [4] (Grid – major:
1 m, minor 20 cm); Bottom – Root mean square error (ERMS) versus time.
Fig. 7. Top – Four robot dispersion our controller (Grid – major: 1 m,
minor 20 cm); Bottom – Root mean square error (ERMS) versus time.

In both instances four robots were used with identical
initial configurations given in standard units as follows:
x= [−0.5,−0.5,0.5,0.5],y= [0.5,−0.5,−0.5,0.5]and
θ= [−π/4,π/4,3π/4,−3π/4]where the control parame-
ters are equally identical, namely: ud=0.05 m/s, θd=0 rad,
Vmax =0.02 m/s ds=0.2 m, ku=kα=1 and dλ=2 m. For
the dispersion behavior presented in Figure 6 the controller
in [4] exhibits high frequency chatter, especially when the
robots are closer to one another. This, of course, is due to
the unbounded repulsive response that continously generates
high control inputs which are limited only by the maximum
achievable physical velocities. Thus, the behavior of the
robots in this case is seemingly unstable and it typically
leads to actuator wear down (c.f. [19]). In contrast, the result
obtained with our controller, presented in Figure 7, shows
that it performs significantly better, whereby the robots
exhibit a smooth behavior that is devoid of chatter.
VIII. CONCLUSION
In this paper we proposed a distributed formation control
approach based on the interplay between attractive and repul-
sive potentials that enables a team of non-holonomic robots
to both aggregate and disperse at user defined clearance dis-
tances. While its design is rooted in the work originally done
Gazi et al. in [1] and Listmann in [4] there are fundamental
differences that sets our work apart. First, our controller is
based on non-smooth stabilization which neither of [1], [4]
exploit. Second, the model for our repulsive potential force is
symmetric around a user defined clearance. This, in turn, is
a critical property that enables a team of robots running our
proposal controller to exibit a smooth emergent dispersion
behavior. Whereas, in the case of [1], [4] asymmetric models
are introduced in order to guarantee collision avoidance
among team members. And third, the total potential force
generates a bounded response in regard to the same user
defined clearance. That is, the controller generates finite
responses in relation to local pool of disagreement allowing
the user to configure the controller such that it meets the
psychical specifications of the various non-holonomic robot
units. Furthermore, while the symmetry and boundness of
the total response also means that team members may collide
while aggregating in formation, the model of our repulsive
force allowed us to seamlessly integrate a weighting factor
in order to avoid such collisions.
Finally, in light of the conducted swarm cohesiveness
analysis running the controller on a team of unicycle mobile
robots guarantees asymptotic stability.
ACKNOWLEDGMENT
This work was partially supported by grant
PN-III-P2-2.1-BG-2016-0425.
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