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INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
MANAGEMENT & APPLIED SCIENCE (IJLTEMAS)
ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue VI, June 2026
Enhancing Formation Control of Multi Agent Systems Using Ann Based
Technique
Akaninyene M . Joshua
1
& Chukwuagu M. Ifeanyi
2
1
Department Electrical and Electronic Engineering, Enugu State University of Science and Technology.
2
Department of Electrical and Electronic Engineering Caritas University Amorji-Nike, Emene, Enugu
State
DOI:
https://doi.org/10.51583/IJLTEMAS.2026.150600001
Received: 20 June 2026; Accepted: 25 June 2026; Published: 02 July 2026
ABSTRACT
The persistent power failure that paralyzed business activities were caused by these factors that could not attain
threshold, Inter-agent spacing error (RMS), Maximum formation shape error, Relative position estimation error
,Formation centroid tracking error , Relative velocity mismatch , Formation convergence time , Communication
latency and Energy consumption deviation . This constant power failure observed in the country led to
introduction of enhancing formation control of multi agent systems using ANN based technique. To perfectly
achieve this, it was done in this manner, formation control of multi agent systems was characterized and the
causes of poor formation control of multi agent systems was established and a conventional SIMULINK model
for formation control of multi agent systems was designed. Then ANN was trained in the causes of poor
formation control of multi agent systems for an effective reduction of the causes of poor formation control of
multi agent systems and an algorithm was developed to implement the process. However, a SIMULINK model
for enhancing formation control of multi agent systems using ANN based technique was designed and the results
obtained were validated and justified. The results obtained were the conventional Inter-agent spacing error
(RMS) that causes poor formation control of multi agent systems was 0.4 m. On the other hand, when ANN
based technique was integrated into the system, it automatically changed 0.2 m. and the conventional Energy
consumption deviation that causes poor formation control of multi agent systems was 27%. Meanwhile, when
ANN based technique was integrated into the system, it drastically reduced to 20 %.Finally, with these results
obtained the percentage enhancement formation control of multi agent systems when an ANN was integrated in
to it was7%.
Keywords: enhancing, formation, control, multi agent, systems, ANN based, technique
INTRODUCTION
Multi-Agent Systems (MAS) have become an important area of research in control engineering, robotics,
artificial intelligence, and autonomous systems due to their ability to perform complex tasks through cooperation
among multiple intelligent agents. A multi-agent system consists of multiple autonomous entities that interact
and coordinate with one another to achieve common objectives that may be difficult or impossible for a single
agent to accomplish independently (Olfati-Saber et al., 2007). Applications of multi-agent systems include
autonomous vehicle platooning, unmanned aerial vehicle (UAV) swarms, robotic exploration, environmental
monitoring, military surveillance, and intelligent transportation systems. One of the fundamental challenges in
multi-agent systems is formation control, which refers to the coordination of multiple agents to maintain a
desired geometric arrangement while moving collectively toward a common goal. Effective formation control
ensures that agents maintain specific relative positions and distances despite disturbances, environmental
uncertainties, communication delays, and dynamic changes in operating conditions (Ren & Beard, 2008). The
ability to sustain stable formations is critical in applications such as search-and-rescue operations, cooperative
transportation, and swarm robotics, where coordinated movement directly influences system performance and
mission success. Traditional formation control approaches, including leader-follower, behavior-based, virtual
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INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue VI, June 2026
structure, and graph-theoretic methods, have demonstrated considerable success in coordinating multiple agents
(Fax & Murray, 2004). However, these conventional techniques often rely on accurate mathematical models of
agent dynamics and predefined control parameters. In real-world environments, uncertainties such as sensor
noise, actuator nonlinearities, external disturbances, and varying communication topologies can significantly
degrade the performance of these control methods. Consequently, maintaining robust and adaptive formation
control remains a major challenge in modern multi-agent systems. Recent advances in artificial intelligence and
machine learning have introduced new opportunities for addressing the limitations of traditional control
strategies. Artificial Neural Networks (ANNs), inspired by the structure and functionality of biological neural
systems, possess powerful learning and approximation capabilities that enable them to model complex nonlinear
relationships and adapt to changing environments (Haykin, 2009). ANNs have been widely applied in prediction,
optimization, pattern recognition, and intelligent control systems because of their ability to learn from data and
improve performance through experience. In the context of formation control, ANN-based techniques can
enhance the adaptability and robustness of multi-agent systems by learning agent dynamics, compensating for
uncertainties, and optimizing control actions in real time. Unlike conventional model-based controllers, ANN
controllers can approximate unknown nonlinear functions and adjust control parameters dynamically, thereby
improving formation accuracy and stability under uncertain operating conditions (Lewis et al., 2013).
Furthermore, ANN-based approaches can facilitate decentralized control architectures, where individual agents
make intelligent decisions based on local information while maintaining overall formation objectives. The
growing complexity of modern autonomous systems has increased the need for intelligent control mechanisms
capable of handling nonlinear dynamics and unpredictable environments. Researchers have demonstrated that
integrating neural network-based learning with formation control algorithms can improve convergence speed,
reduce tracking errors, and enhance fault tolerance in cooperative multi-agent operations (Wang et al., 2020).
Despite these advancements, challenges remain in developing ANN-based formation control techniques that are
computationally efficient, scalable, and capable of guaranteeing stability in large-scale multi-agent networks.
Therefore, this study focuses on enhancing the formation control of multi-agent systems using an Artificial
Neural Network-based technique. The study aims to develop an intelligent control framework that improves
coordination performance, increases robustness against uncertainties, and maintains stable formations under
varying environmental conditions. The findings of this research are expected to contribute to the advancement
of intelligent autonomous systems and provide practical solutions for applications requiring reliable cooperative
control among multiple agents.
METHODOLOGY
To characterize and establish the causes of poor formation control of multi agent systems
Table 1: characterized and established causes of poor formation control of multi agent systems
S/
N
Formation
Control
Metric
S.I.
Unit
Good
Performanc
e
Degraded
Performanc
e
Poor
Formatio
n Control
Threshold
Typical
Cause(s)
1
Inter-agent
spacing error
(RMS)
m
< 0.05 m
0.05–0.20 m
> 0.20 m
Sensor
inaccuracies,
localization
errors,
controller gain
mismatch
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2
Maximum
formation
shape error
m
< 0.10 m
0.10–0.50 m
> 0.50 m
Communicatio
n delays,
external
disturbances
3
Relative
position
estimation error
m
< 0.05 m
0.05–0.15 m
> 0.15 m
GPS
degradation,
poor state
estimation
4
Formation
centroid
tracking error
m
< 0.10 m
0.10–0.50 m
> 0.50 m
Navigation
errors, leader
tracking failure
5
Relative
velocity
mismatch
m·s⁻
¹
< 0.05
0.05–0.20
> 0.20
Inconsistent
actuator
response,
delayed
updates
6
Formation
convergence
time
s
< 5 s
5–15 s
> 15 s
Improper
controller
tuning,
insufficient
connectivity
7
Communicatio
n latency
s
< 0.02 s
0.02–0.10 s
> 0.10 s
Network
congestion,
limited
bandwidth
8
Energy
consumption
deviation
J
< 10%
deviation
10–25%
> 25%
Uneven task
allocation,
inefficient
routing
To design a conventional SIMULINK model for formation control of multi agent systems
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Fig 1 designed conventional SIMULINK model for formation control of multi agent systems
The results obtained were as shown in figures 6 and 7
To train ANN in the causes of poor formation control of multi agent systems for an effective reduction of the
causes of poor formation control of multi agent systems
Fig 2 trained ANN in the causes of poor formation control of multi agent systems for an effective reduction
of the causes of poor formation control of multi agent systems
Transfer Fcn 3
4
s +6s +9 s+12
3 2
Transfer Fcn 2
4
s +6s +9 s+12
3 2
Transfer Fcn 1
4
s +6s +9 s+12
3 2
Transfer Fcn
4
s +6s +9 s+12
3 2
Relative velocity mismatch
In 1
In 2
Out1
Relative posit ion estimation error
In 1
In 2
Out1
Maximum formation shape error
In1
In2
Out1
Inter -agent spacing error (RMS)
In 1
In 2
Out1
Formation convergence time
In 1
In 2
Out1
Formation centroid tracking error
In 1
In 2
Out1
Energy consumption deviation
In 1
In 2
Out1
Display 8
27
Display 7
0.3
Display 6
16
Display 5
0.4
Display 4
0.7
Display 3
0.18
Display 2
0.8
Display 1
0.5
Display
0.1106
Communication latency
In 1
In 2
Out1
CONVENTIONAL
1
CONTROLLER
In1
Out1
Out2
CONTROL PANNEL
In 1
Out1
Out2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
W(i,1)
W(i,2)
ENHANCING FORMATION CONTROL OF MULTI AGENT SYSTEMS USING ANN BASED TECHNIQUE
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In figure 2 ANN was trained twenty times in 8 causes of poor formation control of multi agent systems 20 x 8
= 160 to give hundred and sixty neurons that looked like human brain.
Fig 3 results obtained in trained ANN in the causes of poor formation control of multi agent systems for
an effective reduction of the causes of poor formation control of multi agent systems.
To develop an algorithm that will implement the process
1.Characterize and establish the causes of poor formation control of multi agent systems
2. Identify Inter-agent spacing error (RMS) that did not attain threshold
3.Identify Maximum formation shape error that did not attain threshold
4. Identify Relative position estimation error that did not attain threshold
5. Identify Formation centroid tracking error that did not attain threshold
6.Identify Relative velocity mismatch that did not attain threshold
7.Identify Formation convergence time that did not attain threshold
8.Identify Communication latency that did not attain threshold
9. Identify Energy consumption deviation that did not attain threshold
10. Design a conventional SIMULINK model for formation control of multi agent systems and integrate 2
through 9.
11. Train ANN in the causes of poor formation control of multi agent systems for an effective reduction of the
causes of poor formation control of multi agent systems
12. Integrate 11 into 10.
14.Did causes of poor formation control of multi agent systems reduce and attain threshold when 11 was
integrated into 10?
15. IF NO go to 12
16. IF YES go to 17
17. Enhanced formation control of multi agent systems
18.Stop
y{1}
x{1}
Input 1
Neural Network
x{1}
y {1}
Display
1.82
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18.End
To design a SIMULINK model for enhancing formation control of multi agent systems using ANN based
technique
Fig 4 designed SIMULINK model for enhancing formation control of multi agent systems using ANN
based technique
The results obtained were as shown in 5 and 6.
To validate and justify the percentage improvement in the reduction of causes of poor formation control of multi
agent systems with and without ANN based technique
To find percentage improvement in the reduction of Inter-agent spacing error (RMS) causes of poor formation
control of multi agent systems with ANN based technique
Conventional Inter-agent spacing error (RMS) =0.4 m
y{1}
x{1}
Input 1
Transfer Fcn 3
4
s +6s +9s+12
3 2
Transfer Fcn 2
4
s +6s +9s+12
3 2
Transfer Fcn 1
4
s +6s +9s+12
3 2
Transfer Fcn
4
s +6s +9s+12
3 2
Relative velocity mismatch
In 1
In 2
Out1
Relative position estimation error
In 1
In 2
Out1
Neural Network
x{1}
y {1}
Maximum formation shape error
In1
In2
Out1
Inter -agent spacing error (RMS )
In 1
In 2
Out1
Formation convergence time
In 1
In 2
Out1
Formation centroid tracking error
In 1
In 2
Out1
Energy consumption deviation
In 1
In 2
Out1
Display 9
1.82
Display 8
20 .01
Display 7
0.2224
Display 6
11.86
Display 5
0.2965
Display 4
0.5189
Display 3
0.1334
Display 2
0.593
Display 1
0.2965
Display
0.2013
Communication latency
In 1
In 2
Out1
CONTROLLER
In1
Out1
Out2
CONTROL PANNEL
In 1
Out1
Out2
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ANN based technique Inter-agent spacing error (RMS)=0.2 m
%improvement in the reduction of Inter-agent spacing error (RMS) causes of poor formation control of multi
agent systems with ANN based technique=
Conventional Inter-agent spacing error (RMS)- ANN based technique(RMS) x 100%
Conventional Inter-agent spacing error (RMS 1
%improvement in the reduction of Inter-agent spacing error (RMS) causes of poor formation control of multi
agent systems with ANN based technique= 0.4 m - 0.2m x 100%
0.4 m 1
%improvement in the reduction of Inter-agent spacing error (RMS) causes of poor formation control of multi
agent systems with ANN based technique=50%
To find percentage improvement in the reduction of Energy consumption deviation causes of poor formation
control of multi agent systems with ANN based technique
Conventional Energy consumption deviation =27%
ANN based technique Energy consumption deviation =20%
%improvement in the reduction of Energy consumption deviation causes of poor formation control of multi
agent systems with ANN based technique=
Conventional Energy consumption deviation - ANN based technique ECD
%improvement in the reduction of Energy consumption deviation causes of poor formation control of multi
agent systems with ANN based technique= 27% - 20%
%improvement in the reduction of Energy consumption deviation causes of poor formation control of multi
agent systems with ANN based technique=7%
RESULT AND CONCLUSION
Table 4 comparison of conventional and ANN based technique Inter-agent spacing error (RMS) that causes
poor formation control of multi agent systems(m )
Time(months
Conventional Inter-agent
spacing error (RMS) that
causes poor formation control
of multi agent systems(m )
ANN based technique Inter-
agent spacing error (RMS) that
causes poor formation control
of multi agent systems(m )
1
0.4
0.2
2
0.4
0.2
3
0.4
0.2
4
0.4
0.2
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Fig 5 comparison of conventional and ANN based technique Inter-agent spacing error (RMS) that causes
poor formation control of multi agent systems(m )
The conventional Inter-agent spacing error (RMS) that causes poor formation control of multi agent systems was
0.4 m. On the other hand, when ANN based technique was integrated into the system, it automatically changed
0.2 m.
Table 5 comparison of conventional and ANN based technique Energy consumption deviation that causes poor
formation control of multi agent systems(m )
Time(months
Conventional Energy
consumption deviation that
causes poor formation control
of multi agent systems(% )
ANN based technique Energy
consumption deviation that
causes poor formation control
of multi agent systems(% )
1
27
20
2
27
20
3
27
20
4
27
20
Fig 6 comparison of conventional and ANN based technique Energy consumption deviation that causes
poor formation control of multi agent systems
1 1.5 2 2.5 3 3.5 4
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
spacing error (RMS) that causes poor formation control of multi agent systems(m )
Time (months)
Conventional Inter-agent spacing error (RMS) that causes poor formation control of multi agent systems(m )
ANN based technique Inter-agent spacing error (RMS) that causes poor formation control of multi agent systems(m
1 1.5 2 2.5 3 3.5 4
20
21
22
23
24
25
26
27
sumption deviation that causes poor formation control of multi agent systems(dB )
Time (months)
Conventional Energy consumption deviation that causes poor formation control of multi agent systems(dB )
ANN based technique Energy consumption deviation ) that causes poor formation control of multi agent systems(dB )
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The conventional Energy consumption deviation that causes poor formation control of multi agent systems was
27%. Meanwhile, when ANN based technique was integrated into the system, it drastically reduced to 20
%.Finally, with these results obtained the percentage enhancement formation control of multi agent systems
when an ANN was integrated in to it was7%.
CONCLUSION
The random power failure in the country which had paralyzed business activities was overcame by introducing
enhancing formation control of multi agent systems using ANN based technique. To perfectly achieve this, it
was done in this manner, formation control of multi agent systems was characterized and the causes of poor
formation control of multi agent systems was established and a conventional SIMULINK model for formation
control of multi agent systems was designed. Then ANN was trained in the causes of poor formation control of
multi agent systems for an effective reduction of the causes of poor formation control of multi agent systems and
an algorithm was developed to implement the process. However, a SIMULINK model for enhancing formation
control of multi agent systems using ANN based technique was designed and the results obtained were validated
and justified. The results obtained were the conventional Inter-agent spacing error (RMS) that causes poor
formation control of multi agent systems was 0.4 m. On the other hand, when ANN based technique was
integrated into the system, it automatically changed 0.2 m. and the conventional Energy consumption deviation
that causes poor formation control of multi agent systems was 27%. Meanwhile, when ANN based technique
was integrated into the system, it drastically reduced to 20 %.Finally, with these results obtained the percentage
enhancement formation control of multi agent systems when an ANN was integrated in to it was7%.
REFERENCES
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2. Haykin, S. (2009). Neural networks and learning machines (3rd ed.). Pearson Education.
3. Lewis, F. L., Vrabie, D., & Syrmos, V. L. (2013). Optimal control (3rd ed.). Wiley.
4. Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and cooperation in networked multi-
agent systems. Proceedings of the IEEE, 95(1), 215–233.
5. Ren, W., & Beard, R. W. (2008). Distributed consensus in multi-vehicle cooperative control: Theory and
applications. Springer.
6. Wang, X., Zhang, Y., & Lewis, F. L. (2020). Adaptive neural-network-based formation control for multi-
agent systems with uncertainties. IEEE Transactions on Cybernetics, 50(8), 3508–3519.