Dynamic Position Estimation and Flocking Control in Multi-Robot
Systems
Jonatan Alvarez
1 a
and Assia Belbachir
2 b
1
IPSA, 63 Bd de Brandebourg, Ivry-sur-Seine, France
2
NORCE, Grimstad, Norway
Keywords:
AVT, Networked Control, Flocking, Terrestrial Robots.
Abstract:
This paper presents a novel approach to improve flocking algorithms for terrestrial Multi-Robot Systems
(MRS) featuring defective or inaccurate sensors by using the Adaptive Value Tracking (AVT) algorithm. The
idea behind the usage of the AVT is to estimate the positions of robots with poor GPS connectivity. Such esti-
mation is then furnished as an input for the flocking controller, which is a method ensuring the movement even
when some robots lack of GPS data. The proposed framework is tested in simulation using several robots, and
found that the AVT effectively preserves accurate positioning and consequently flocking behavior.
1 INTRODUCTION
Flocking (He et al., 2018), inspired by the collec-
tive behavior observed in natural systems such as
bird flocks and fish schools, has been used in recent
years, particularly within the field of multi-agent sys-
tems. This phenomenon, where individual agents fol-
low simple rules based on the positions and veloci-
ties of their neighbors, results in emergent, collective
behavior that holds big potential for applications in
robotics, autonomous vehicles, and distributed sens-
ing networks.
Despite the progress made in developing flocking
algorithms, several challenges remain, particularly in
ensuring scalability, real-world applicability, commu-
nication efficiency, energy optimization, robustness,
and decentralization. These challenges needs the de-
velopment of more sophisticated and practical ap-
proaches to enhance the functionality and deployment
of multi-agent systems.
Reza Olfati-Saber (Olfati-Saber, 2006) introduced
fundamental algorithms for flocking in both free-
space and constrained environments, setting the stage
for subsequent research. Recent advancements have
seen the emergence of innovative strategies, such
as hybrid metric-topological interactions (He et al.,
2018), which enhance the flexibility and convergence
properties of flocking algorithms. Additionally, vari-
a
https://orcid.org/0000-0003-1038-6800
b
https://orcid.org/0000-0002-1294-8478
ous optimal flocking strategies have been used to spe-
cific objectives and environmental constraints, aiming
to optimize energy consumption, ensure spatial cov-
erage, and navigate complex terrains.
However, these advancements also introduce a set
of challenges. Ensuring scalability while maintain-
ing practical computational constraints is a significant
challenge. Moreover, the integration of theoretical in-
sights with practical considerations remains a critical
area of focus to develop robust, efficient, and scalable
flocking algorithms.
This paper addresses the aforementioned chal-
lenges by proposing novel solutions and methodolo-
gies that advance the theoretical foundations of flock-
ing and facilitate practical implementation in real-
world settings. Specifically, we present a framework
for improving robot positioning in flocking, focusing
on the synchronized movement of autonomous agents
with no GPS connection in open space. Our approach
uses the Adaptive Value Tracking (AVT) for dynamic
adjustment and tracking, enabling efficient communi-
cation and coordination among agents equipped with
different sensor capabilities.
Through theoretical analyses and numerical sim-
ulations, we show the benefits of using the AVT
method for the flocking control of multi-robot sys-
tems evolving in open but complex environments.
The outline of the paper is as follows. Section
2 presents the related works. Section 3 explains the
different methods used for achieving flocking behav-
ior in multi-agent systems. Section 4 describes our
Alvarez, J. and Belbachir, A.
Dynamic Position Estimation and Flocking Control in Multi-Robot Systems.
DOI: 10.5220/0012927200003822
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 21st International Conference on Informatics in Control, Automation and Robotics (ICINCO 2024) - Volume 1, pages 269-276
ISBN: 978-989-758-717-7; ISSN: 2184-2809
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
269

proposed framework, including the integration of the
AVT for position estimation of GPS-denied agents.
Section 5 presents the obtained results from our sim-
ulation studies, demonstrating the effectiveness of our
approach. Section 6 concludes the paper, summariz-
ing the key improvements and future research impli-
cations.
2 RELATED WORK
The study of flocking algorithms in multi-agent dy-
namic systems has evolved significantly over the
years, with numerous contributions advancing our un-
derstanding and application of these algorithms. One
of the foundational works in this field is the paper by
Reza Olfati-Saber (Olfati-Saber, 2006). This work ex-
plores flocking behavior in both free-space and envi-
ronments with multiple obstacles, introducing three
specific algorithms: two for free-flocking and one
for constrained flocking. The extensive analysis of
the first two algorithms reveals their incorporation of
Reynolds’ rules of flocking, addressing critical issues
such as fragmentation in flocking behavior. The au-
thors also proposes a “universal” definition of flock-
ing, supported by various simulation results demon-
strating the effectiveness of the algorithms in scenar-
ios such as 2-D and 3-D flocking, split/rejoin ma-
neuvers, and squeezing maneuvers for hundreds of
agents. This work has significantly advanced the un-
derstanding of multi-agent systems and their potential
applications in robotics and autonomous vehicle sys-
tems.
Building upon these foundational concepts, more
recent research has continued to refine and improve
flocking algorithms. Other researchers (He et al.,
2018) study on a flocking algorithm for multi-agent
systems that emphasizes connectivity preservation
under hybrid metric-topological interactions. This al-
gorithm utilizes a range-limited Delaunay graph for
interaction topology, reducing the cost of information
exchange among agents while increasing the flexibil-
ity of the flocking algorithm. This approach allows
the multi-agent system to converge to a more reg-
ular quasi-lattice formation without additional con-
straints on sensing range or desired distances between
agents. Implemented in a distributed manner, this al-
gorithm leverages local information for each agent to
construct its neighbor set. Theoretical and numeri-
cal analyses have demonstrated the superiority of this
approach compared to traditional disk and Delaunay
graph-based algorithms.
Further advancements in optimal flocking have
been explored, with various methodologies address-
ing specific objectives and environmental constraints.
For instance, Ergodic Trajectories Flocking ensures
agents cover a spatially distributed area evenly over
time, though it requires periodic information sharing,
which can be challenging in large swarms (Beaver
and Malikopoulos, 2020). Optimal Shepherding for
Flock Influencing is useful for steering real flocks of
birds away from hazards, but its complexity increases
with flock size and environmental factors (Lee, 2013).
Constraint-Driven Flocking focuses on minimizing
energy consumption and avoiding collisions, neces-
sitating sophisticated sensing and computation ca-
pabilities (Beaver and Malikopoulos, 2020). Dy-
namic Peloton Formation optimizes aerodynamic ef-
fects for energy efficiency, primarily validated in sim-
ulations, raising questions about real-world effective-
ness (Beaver and Malikopoulos, 2020). Line Flock-
ing with Model Predictive Control maximizes veloc-
ity matching and upwash benefits but is designed for
idealized conditions (Zhan and Li, 2013). Pareto
Front Selection in Multi-objective Control effectively
balances multiple objectives but requires significant
computational resources (Kesireddy and Medrano,
2024).
Despite these work, several challenges persist in
the field of flocking algorithms for multi-agent sys-
tems. Scalability remains a significant issue, as man-
aging large numbers of agents presents numerous lo-
gistical and computational hurdles. The real-world
application of these algorithms often reveals a gap
between simulation results and practical effective-
ness. Communication overhead is another critical
challenge, as ensuring effective communication in
large swarms without saturating the network is es-
sential for cohesive flock behavior. Balancing energy
efficiency, particularly the costs of communication,
computation, and movement, is a persistent concern.
Robustness is crucial, as maintaining performance in
the face of environmental uncertainties and system
failures is paramount. Additionally, developing algo-
rithms that allow for decentralized decision-making
and autonomy while ensuring cohesive flock behav-
ior poses a complex challenge. Embedding these ap-
proaches necessitates reducing computational time,
emphasizing the need for efficient and practical im-
plementations.
Our proposed framework aims to address these
challenges by integrating the AVT for dynamic posi-
tion estimation, particularly for GPS-denied agents.
This innovation enhances the ability of multi-agent
systems to maintain flocking behavior under vary-
ing conditions and sensor capabilities, for more ro-
bust and efficient flocking algorithms suitable for real-
world applications.
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3 PRELIMINARIES
3.1 Graph Theory for MRS
In this work, the MRS is described via the graph
theory. An undirected graph is defined as G =
{V ,ξ}, such that V represents the group of robots
(nodes), where V = {1, 2, ..., N}. ξ is a collection
of communication channels (edges), represented as
ξ = (i, j) ∀ i, j ∈ V . Furthermore, ξ is employed to
characterize the connectivity of multi-robot systems.
(i, j) implies that there exists a communication chan-
nel between robot i and robot j. The neighborhood
group of vehicle i is given as
N
α
i
= {j ∈V
α
: (i, j) ∈ξ}= {j ∈V
α
: ||q
j
−q
i
||< r}
(1)
with r > 0 is the interaction range between robots and
||.|| stands for the Euclidean norm. q
i
and q
j
are the
Cartesian coordinates of robots i and j, respectively.
3.2 Flock Modelling
Flocking refers to the coordinated movement and for-
mation of multiple agents, where each agent follows
simple rules based on the positions and velocities of
its neighbors, resulting in emergent, collective behav-
ior. Using the flocking control algorithm allows each
agent to apply a force input, embodying the collec-
tive dynamics of the flock through interactions with
its surroundings and neighboring agents.
Consider a set of n agents evolving in a m dimen-
sional space (m = 2 in our case), with the following
dynamics
˙q
i
= v
i
˙v
i
= u
i
i = 1,2,... , n
(2)
where q
i
,v
i
,u
i
∈ R
m
are the position, velocity and
control input of the agent i. The geometric forma-
tion, which is a quasi α-lattice pattern (Olfati-Saber,
2006), can be expressed as
||q
j
−q
i
|| = d ∀j ∈ N
α
i
(3)
with d representing the distance between neighbors
i and j. To avoid the singularity caused when q
i
=
q
j
, the control in (Olfati-Saber, 2006) is based on the
σ−norm which maps R
m
→ R
+
and is expressed as
∥z∥
σ
=
1
ε
(
p
1 + ε∥z∥
2
−1). Its gradient is given by
σ
ε
(z) =
z
√
1+ε∥z∥
2
=
z
1+ε∥z∥
σ
. Furthermore, let a
i j
(q)
be elements of an adjacency matrix A(q), defined as
a
i j
(q) =
(
0 i = j
ρ
h

∥q
j
−q
i
∥
σ
/r
α

j ̸= i
(4)
AVT
(Algorithm 1)
&
Multilateration
(eq. (18))
Sensor
Distance
sensor
GPS
Position estimation
Communication
Distance
perception
Own distance
perception
Multi-Robot System (MRS)
Robot System i
Flocking controller
(eq. (21))
Robot
System j
Robot System j position
Position
eq. (14)
Actuators
Figure 1: Illustration of the developed Multi-Robot System
(MRS) framework.
where ρ
h
: R → [0,1] is a bump function to obtain
smooth interaction for a
i j
(q) in the MRS with h ∈
(0,1) and r
α
= ∥r∥
σ
. ρ
h
(z) is defined as
ρ
h
(z) =





1 z ∈ [0,h)
1
2

1 + cos

π
z−h
1−h

z ∈ [h,1]
0 otherwise
(5)
The set of neighboring obstacles (β−agents) of
node i (robot i), can be expressed by
N
β
i
= {k ∈V
β
: ||ˆq
i,k
−q
i
|| < r
′
} (6)
Thus, additionally to (3), the desired formation in-
cludes the interaction between agents and obstacles,
given by
||ˆq
i,k
−q
i
|| = d
′
∀k ∈N
β
i
(7)
where r
′
and d
′
are the interaction range and the dis-
tance between an α−agent i and a β−agent k and
ˆq
i,k
is the estimated position of the closest point from
robot i to obstacle k. Consequently, the elements
b
i,k
of a heterogeneous adjacency matrix B(q) is ex-
pressed as
b
i,k
(q) = ρ
h

∥ˆq
i,k
−q
i
∥
σ
/d
β

(8)
where d
β
= ∥d
′
∥
σ
represents the distance between an
α-agent and an obstacle. Then, recalling the flocking
control from (Olfati-Saber, 2006), this is developed as
u
pi
= u
α
pi
+ u
β
pi
+ u
γ
pi
(9)
Such a design ensures that the MRS is capable of
avoiding obstacles while maintaining a quasi α-lattice
configuration pattern (Olfati-Saber, 2006). The term
u
α
pi
is responsible for maintaining an inter-distance be-
tween α−agents, u
β
pi
is a term comprising an obstacle
avoidance algorithm for α and β-agents, and u
γ
pi
is the
navigation feedback term, which drives the group to-
wards a collective objective. The terms are then given
as
u
α
pi
=
∑
j∈N
α
i
φ
α
(∥q
j
−q
i
∥
σ
)n
i j
+
∑
j∈N
α
i
a
i j
(v
j
−v
i
) (10)
Dynamic Position Estimation and Flocking Control in Multi-Robot Systems
271

u
β
pi
=K
β
1
∑
k∈N
β
i
φ
β
(∥ˆq
i,k
−q
i
∥
σ
) ˆn
i,k
+ K
β
2
∑
j∈N
β
i
b
i,k
(q)( ˆv
i,k
−v
i
)
(11)
u
γ
i
= −c
1
(q
i
−q
d
) −c
2
(v
i
−v
d
) (12)
where
• q
d
and v
d
are the desired position and velocity,
respectively
• ˆv
i,k
is the velocity between robot i and obstacle k
• v
i
is the linear velocity of robot i
• K
β
1
,K
β
2
> 0 are constant gains
• ˆn
i j
= σ
ε

q
j
−q
i

, ˆn
i,k
= σ
ε

ˆq
i,k
−q
i

• φ
α
(z) =
1
2
ρ
h
(z/d
α
)[(a + b)σ
1
(z + e) + (a −b)]
• φ
β
(z) = ρ
h
(z/d
β
)(σ
1
(z −d
β
) −1) is a repulsive
action function
• σ
1
(z) = z/
√
1 + z
2
• 0 < a ≤b and e = |a −b|/
√
4ab
• c
1
,c
2
> 0 are the navigation gains
4 PROPOSED FRAMEWORK
Consider a set of terrestrial robots embedding differ-
ent sensors (e.g., GPS, ultrasonic sensors). To per-
form a collective navigation, the communication be-
tween the agents is crucial. In this vein, every mem-
ber group embedding a GPS device will share with
its neighbors its position, which will be used by a
distributed controller (in our case the flocking algo-
rithm). Then, if a member group does not feature
a GPS device or this one is defective, one method
should be applied to determine the position.
Considering the cited issue, this work proposes the
usage of the AVT algorithm as a distance estimator
followed by a multilateration method for position es-
timation. As an example, agent i may have a GPS
and can estimate the distance to agent j, while agent
j might only have distance sensing capabilities and
no GPS. Then, the AVT retrieves the measured noisy
distances and processes them to obtain values closer
to the real ones. The output signal is then used by
the multilateration method to estimate the global po-
sition, which is employed as an input for the flocking
strategy of robot j.
In the next subsections, we carefully explain the
proposed framework. For this, we briefly present the
mathematical model of the used robots, followed by
the distance estimation using the AVT. Robot position
estimation and the control of the MRS is explained
later, completing the loop for the proposed frame-
work. Fig. (1) presents a block-diagram showing the
interaction between the elements of our proposed ar-
chitecture.
4.1 Multi-Robot System
Consider a multi-robot system composed by N unicy-
cle robots. (x
i
,y
i
) ∈ R
2
and θ
i
represent the Cartesian
positions and orientations w.r.t. the i-th robot. r and e
are the radius of the wheels and the distance between
these ones, respectively, see Figure 2. The equations
Figure 2: Wheeled mobile robot.
of motion for the i-th robot, containing the nonholo-
nomic constrains are expressed as
˙q
i
=


˙x
i
˙y
i
˙
θ
i


=


cosθ
i
0
sinθ
i
0
0 1



v
i
ω
i

(13)
with q
i
= (x
i
,y
i
,θ
i
)
T
the state vector of the robot i. v
i
and ω
i
stand for the linear and angular velocities.
For control purposes, let us redefine the system
output at an offset point l, where l ̸= 0, see Figure 2.
With this, the new position output is as follows
q
li
=

x
li
y
li

=

x
i
+ l
i
cosθ
i
y
i
+ l
i
sinθ
i

(14)
By differentiating (14) w.r.t. time and using (13),
it is possible to obtain
˙q
li
=

˙x
li
˙y
li

=

cosθ
i
−l sin θ
i
sinθ
i
l cosθ
i

v
i
ω
i

= Λ(θ
i
)v
i
(15)
Therefore, det(Λ(θ
i
)) ̸= 0. Solving for the auxil-
iary input, the following is obtained
v
i
=

cosθ
i
−l sin θ
i
sinθ
i
l cosθ
i

−1

u
xi
u
yi

= Λ
−1
(θ
i
)u
i
(16)
With the latter, (15) can be approximated to a sim-
ple integrator model, given as
˙q
li
= u
pi
(17)
where u
pi
= (u
xi
,u
yi
)
T
∈R
2N
the control input vector,
with N the number of agents conforming in the multi-
robot system.
ICINCO 2024 - 21st International Conference on Informatics in Control, Automation and Robotics
272

4.2 Drone Ranging Estimation Using
Adaptive Value Tracking (AVT)
Adaptive Value Tracking (AVT) (Yildirim and
G
¨
urcan, 2014) is a technique used to find and track
a dynamic value within a given search space as effi-
ciently as possible. This method has been success-
fully implemented in various scientific and industrial
projects (Belbachir and Pasin, 2019; Belbachir et al.,
2018; Belbachir et al., 2019; Agliamzanov et al.,
2015; Yildirim and G
¨
urcan, 2014; G
¨
urcan, 2013).
From the perspective of software engineering, an
AVT is a software component that implements a ro-
bust and efficient search algorithm in order to search
and track a dynamic value v
∗
(Yildirim and G
¨
urcan,
2014) (see Figure 3).
AVT Environment
Adaptive Value Tracker (AVT)
v
min
v
max
v
t
v
t+1
D
t+1
f "
f "
D
t+2
v
t+2
➊ ➋
➌
➍ ➎
➏
➐
D
t+3
f #
➑
➒
v
t+3
[...]
Figure 3: Interaction between an AVT and its environ-
ment (Yildirim and G
¨
urcan, 2014).
The search algorithm requires information about
the search space:
[v
min
,v
max
] ⊂ R
where v
min
is the lower boundary and v
max
is the up-
per boundary for the searched value v
∗
. At any time
t, the owner component can interact with the AVT
to obtain the current proposed value v
t
and guide the
search direction, ensuring convergence to v
∗
by pro-
viding feedback: INCREASING (↑), DECREASING (↓),
or PRESERVING (≈). The AVT adjusts its proposed
value by ∆t based on the feedback, where
∆t ∈ [∆
min
,∆
max
]
∆
min
represents the minimum adjustment step and is
considered the precision, ensuring |v
t
−v
∗
|≤∆
min
. ∆t
represents the adjustment value.
In scenarios where a vehicle loses GPS coverage,
it initiates an adaptive localization protocol (ALP)
with the first critical step being ranging estimation.
Here, the vehicle communicates with nearby infras-
tructure to estimate its relative distances, treating
ranging as a search process using AVT to increase the
robustness against noise measurements.
Algorithm 1: Ranging Estimation Algorithm.
1: Obtain a new range estimate
ˆ
d using any ranging
method
2: error = avt.getValue() −
ˆ
d
3: if error < 0 then
4: avt.ad just( f ↑)
5: else if error > 0 then
6: avt.ad just( f ↓)
7: else
8: avt.ad just( f ≈)
9: end if
In this algorithm, the distance estimate
ˆ
d taken
from a different sensor is compared to the AVT’s pro-
posed value. Depending on whether the estimate is
higher or lower, the AVT adjusts the feedback to con-
verge to the actual distance. This iterative process en-
sures that the estimated distance stabilizes over time,
allowing the vehicle to accurately determine its rela-
tive distance despite noisy measurements.
By using AVT in ranging estimation, vehicles can
maintain accurate localization, even in the absence of
GPS signals, enhancing the overall robustness of the
navigation system.
4.3 Multilateration Method
As it was previously stated, the multi-robot system
embeds different sensors (e.g., GPS, ultrasonic sen-
sors). Thus, within the group of robots, consider
agents featuring only distance sensors. The multi-
lateration strategy allows to these robots to estimate
their positions ( ˆx
i
, ˆy
i
), if these ones have a set of m
reachable neighborhoods featuring GPS signal with
information (x
j
,y
j
,d
j
), where (x
j
,y
j
) is the location
of the neighborhood j and d
j
is the measured distance
to it. Thus, by minimizing the difference between the
measured noisy distances and the estimated Euclidean
distances, it is possible to obtain the minimum mean
square estimate (MMSE). The computation, with the
form y = bX , outputs the location estimation ( ˆx
i
, ˆy
i
)
by employing the matrix solution for MMSE (Sav-
vides et al., 2001), given as
b =

ˆx
i
ˆy
i

= (X
T
X)
−1
X
T
Y (18)
where
X =




2(x
1
−x
2
) 2(y
1
−y
2
)
2(x
1
−x
3
) 2(y
1
−y
3
)
.
.
.
.
.
.
2(x
1
−x
m
) 2(y
1
−y
m
)




(19)
Dynamic Position Estimation and Flocking Control in Multi-Robot Systems
273

Y =





δ −x
2
2
−y
2
2
−d
2
2
δ −x
2
3
−y
2
3
−d
2
3
.
.
.
δ −x
2
m
−y
2
m
−d
2
m





; δ = x
2
1
+ y
2
1
+ d
2
1
(20)
4.4 MRS Distributed Control
Consider the position output q
li
in (13), such that the
i-th robot can be treated as a simple integrator system,
given in (17). Then, the control signal computed by
the flocking algorithm is modified as follows:
u
pi
=u
α
pi
+ u
β
pi
+ u
γ
pi
u
α
pi
=
∑
j∈N
α
i
(K
α
p
φ
α
(∥q
l j
−q
li
∥
σ
)n
i j
+ K
α
i
Z
φ
α
(∥q
l j
−q
li
∥
σ
)n
i j
dt)
u
β
pi
=K
β
p
(
∑
k∈N
β
i
φ
β
(∥ˆq
i,k
−q
li
∥
σ
)ˆn
i,k
+
∑
j∈N
α
i
∑
k∈N
β
j
φ
β
(∥ˆq
j,k
−q
l j
∥
σ
)ˆn
j,k
)
u
γ
pi
= −sat(K
γ
p
(q
li
−q
d
))
(21)
where K
α
p
,K
α
i
> 0 are gradient-based consensus
gains, K
β
p
> 0 and sat(∗) is a saturation function, such
that
sat(z) =



sat(z
1
)
.
.
.
sat(z
n
)



;sat(z
i
) =





z
imin
z
i
≤ z
imin
z
i
z
imin
< z
i
< z
imax
z
imax
z
i
≥ z
imax
(22)
Additionally, K
γ
p
> 0 is a gain for the navigation
feedback force. u
α
pi
is a PI decentralized control law of
the gradient-based term from the flocking algorithm.
Such a term was originally proposed as a PID con-
troller for double integrator systems in (Saif et al.,
2019). u
β
pi
is the term comprising the obstacle avoid-
ance algorithm initially proposed by (Olfati-Saber,
2006) and then modified in (Koung et al., 2020),
which is the approach used for this work. u
γ
pi
is the
navigation feedback term, which drives the group to-
wards a collective objective. The saturation function
allows to control the navigation term weight. Hence,
this one does not dominate over the other compo-
nents, specially when the desired position is far away
from the formation’s barycenter.
In summary, the multi-robot system considered in
this work consists of a group of nonholonomic terres-
trial robots. The main objective is to perform a trajec-
tory tracking mission while maintaining the quasi α-
lattice formation considering the communication lim-
itations coming from the sensors.
5 SIMULATION RESULTS
The current presents the tests of the proposed strategy
using the Matlab/Simulink
®
environment. The sim-
ulation consists of six terrestrial robots performing a
trajectory-tracking mission while maintaining a quasi
α-lattice formation using the proposed architecture.
5.1 Simulation Scenario
The simulation scenario focuses on a trajectory track-
ing mission involving a set of robots. The objec-
tive is to evaluate the effectiveness of the Adaptive
Value Tracking (AVT) algorithm for inaccurate mea-
surements (GPS signal lost), working in conjunction
with the flocking controller.
Initially, the group of robots start at random po-
sitions within the simulation environment, ensuring
a spread-out initial configuration to avoid clustering.
Then, a desired trajectory is generated and the flock-
ing controller is activated to self-organize the agents
into the desired pattern. The set of parameters used
for the simulation are given in Table 1
Table 1: Simulation parameters for MRS formation control
with obstacle avoidance.
Parameter Value Parameter Value
a,b 1.0 x
∗
,y
∗
[m] 1.75
ε 0.1 d [m] 0.41
h 0.2 d
′
[m] 0.45
K
α
p
5.5 r [m] 0.6
K
α
i
0.5 l [m] 0.01
K
β
p
0.3
˙
φ
max
[rad/s] π
K
γ
p
0.4
˙
φ
min
[rad/s] −π
The complete mission includes the trajectory,
which is given by a circular pattern of 4m radius.
Then, at t = 850s, a final desired position q
d
=
(−4,4)
T
m is provided. In our experiments, Robot 6 is
not equipped with a GPS device, providing an initial
challenge for the AVT algorithm. Likewise, Robot 3
embeds a GPS device, however the signal is lost at
t = 600s, switching to the AVT estimation.
5.2 Simulation Results
Fig. (4) shows the trajectories performed by the dif-
ferent robots during the simulation. We can see that
the MRS reaches the formation and avoids the obsta-
cle. The completion of the mission is confirmed in
Fig. (5), where we can visualize how the positions
of the robots keep constant once they have reached
the final position. Due to the loss of the GPS signal
ICINCO 2024 - 21st International Conference on Informatics in Control, Automation and Robotics
274

(Robot 3 at t = 600s), the MRS adapts the formation
as disturbances appear because of the switching to the
AVT estimation.
-5 0 5
-5
-4
-3
-2
-1
0
1
2
3
4
5
Start
Finish
Figure 4: Performed trajectories.
0 200 400 600 800 1000 1200
-5
0
5
0 200 400 600 800 1000 1200
-5
0
5
Figure 5: Linear trajectories for x and y-axis, respectively.
Fig. (6) depicts examples of the measured dis-
tances and estimated distances by the AVT from
robots 6 to 1 and 4 and 3 to 2 and 5. Such examples
were chosen since they correspond to the defective
robots featuring the AVT estimation. Additionally, we
can visualize the effectiveness of the estimation as it
reduces the noise coming from the embedded distance
sensors.
The inter-distances are shown in Fig. (7). The
curves confirm how the formation adapts after the loss
of the GPS signal coming from robot 3. It is impor-
tant to remember that the flocking controller works
for undirected graphs, implying that every robot must
know the positions of its neighbors. Likewise, if one
of the members is disturbed, such disturbance will af-
fect the rest of the group.
Fig. (8) and Fig. (9) show the trajectories per-
formed by the robots as well as the inter-distances
when the AVT algorithm is not applied. The flocking
0 200 400 600 800 1000 1200
0
0.5
1
1.5
860 870 880
0.6
0.7
0.8
0 200 400 600 800 1000 1200
0.2
0.4
0.6
0.8
1
1.2
950 960 970
0.35
0.4
Figure 6: [Top] Inaccurate and estimated distances from
Robot 6 to Robots 1 and 4, respectively. [Bottom] Inac-
curate and estimated distances from Robot 3 to Robots 2
and 5, respectively.
0 200 400 600 800 1000 1200
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Figure 7: Robots inter-distances during the simulation.
controller manages to carry out part of the mission,
however, for the last part, the formation disseminates
and robot 3 diverges because of the noisy sensors and
the disturbances. Thus, we can conclude that the pro-
posed framework provides a robust performance for
MRS.
-8 -6 -4 -2 0 2 4
-4
-3
-2
-1
0
1
2
3
4
5
Start
Figure 8: Performed trajectories without AVT estimation.
Dynamic Position Estimation and Flocking Control in Multi-Robot Systems
275

0 200 400 600 800 1000 1200
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Figure 9: Robots inter-distances during the simulation with-
out AVT estimation.
6 CONCLUSIONS
This paper has proposed a novel framework aiming
at improve the robustness and scalability of flocking
algorithms in multi-agent systems. Particularly focus-
ing on scenarios where agents lose GPS connectivity.
The integration of Adaptive Value Tracking (AVT) for
dynamic position estimation in GPS-denied environ-
ments represents a significant advancement. This ap-
proach enables agents to estimate their positions ac-
curately using ranging information from neighboring
agents, thereby maintaining synchronized movement
and safe flocking behavior.
Through theoretical analysis and numerical sim-
ulations, we have demonstrated the effectiveness of
our framework for MRS featuring defective sensors
and evolving in complex environments. By using the
AVT, our approach not only enhances the reliability
of multi-agent systems but also lays the groundwork
for future developments in autonomy and collective
intelligence.
Future research directions include further opti-
mization of communication protocols and integration
of additional sensor versatility. Additionally, the real-
time implementation of the proposed strategy, as well
as performance comparisons with the Kalman filter
and observers.
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