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Formation Control of Multi-agent Nonlinear Systems using The State-Dependent Riccati Equation

Journal of Automation, Mobile Robotics and Intelligent Systems
Volume 19 (2025): Issue 1 (March 2025)
By:
Open Access
|Mar 2025

Figures & Tables

Figure 1.

A schematic view of the multi-agent system, moving from an initial randomly-distributed form to a final desired shape with arranged agents in an environment with an obstacle. The 2D representation is intended to show more detail; its formation is general and could be applied to 3D formation as well.
A schematic view of the multi-agent system, moving from an initial randomly-distributed form to a final desired shape with arranged agents in an environment with an obstacle. The 2D representation is intended to show more detail; its formation is general and could be applied to 3D formation as well.

Figure 2.

The schematic view and axis definition of a quadrotor.
The schematic view and axis definition of a quadrotor.

Figure 3.

The schematic view and axis definition of a differential-wheel mobile robot.
The schematic view and axis definition of a differential-wheel mobile robot.

Figure 4.

The trajectories of the multi-agent system of 1,089 quadrotor UAVs.
The trajectories of the multi-agent system of 1,089 quadrotor UAVs.

Figure 5.

The error convergence of the multi-agent system of 1,089 quadrotor UAVs.
The error convergence of the multi-agent system of 1,089 quadrotor UAVs.

Figure 6.

The distance between the drones and the obstacle for the multi-agent system of 1,089 quadrotor UAVs.
The distance between the drones and the obstacle for the multi-agent system of 1,089 quadrotor UAVs.

Figure 7.

The collision distance between the drones for the multi-agent system of 1,089 quadrotor UAVs.
The collision distance between the drones for the multi-agent system of 1,089 quadrotor UAVs.

Figure 8.

The ds,j(t) parameter for the multi-agent system of 1,089 quadrotor UAVs. Samples are shown the axes instead of time as a result of the mesh presentation.
The ds,j(t) parameter for the multi-agent system of 1,089 quadrotor UAVs. Samples are shown the axes instead of time as a result of the mesh presentation.

Figure 9.

The position and orientation states for the 5th quadrotor UAV.
The position and orientation states for the 5th quadrotor UAV.

Figure 10.

The linear and angular velocity states for the 5th quadrotor UAV of the multi-agent system.
The linear and angular velocity states for the 5th quadrotor UAV of the multi-agent system.

Figure 11.

The angular velocities of the rotors for the 5th quadrotor UAV.
The angular velocities of the rotors for the 5th quadrotor UAV.

Figure 12.

The trajectories of the leader and 45 follower agents.
The trajectories of the leader and 45 follower agents.

Figure 13.

The errors of the leader and 45 follower agents.
The errors of the leader and 45 follower agents.

Figure 14.

The obstacle avoidance performance of the leader/follower system of mobile robots.
The obstacle avoidance performance of the leader/follower system of mobile robots.

Figure 15

The collision avoidance performance of the leader/follower system of mobile robots.
The collision avoidance performance of the leader/follower system of mobile robots.

Figure 16.

The input signals of the wheels for one of the agents.
The input signals of the wheels for one of the agents.

Figure 17.

The state information for one of the agents.
The state information for one of the agents.

Figure 18.

The migration of 1,050 mobile robots in leader-follower formation.
The migration of 1,050 mobile robots in leader-follower formation.

The error of the system under different ws values_

ws(mm)error leader (mm)error 5th follower (mm)
20144.3912911.3158
5076.4762345.8130
80104.3379388.0787
100124.3148427.7242
200224.7471630.6206
300324.6205827.9986
400424.48971025.9861
500524.40701223.8401

A detailed report on the population of agents in SDRE in previous, as literature compared to this work_

contextRef.No. of agents, type of agent
multi‐agentleader‐followerformation[37][38][40][41][42][43][44][45][46][47][39]5, single‐integrator2, mobile robot2, spacecraft5, single‐integrator2, spacecraft3, mobile robot2, aircraft3, spacecraft2, spacecraft2, satellite1024, satellite
consensus control[22]10, crane
cooperativemulti‐agents[48][49][50][19][51][52]2, manipulator2, manipulator3, spacecraft4, manipulator4, UAV3, mobile robot
multi‐agentsleader‐followerthis workthis workthis work1,089, UAV45, mobile robot1,050, mobile robot
DOI: https://doi.org/10.14313/jamris-2025-003 | Journal eISSN: 2080-2145 | Journal ISSN: 1897-8649
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Language: English
Page range: 17 - 32
Submitted on: Jan 10, 2024
Accepted on: Jul 23, 2024
Published on: Mar 31, 2025
Published by: Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP
In partnership with: Paradigm Publishing Services
Publication frequency: 4 times per year
Keywords:
Multi-agent,
Formation,
Control,
SDRE,
Robotics
Related subjects:
Computer sciences,
Artificial intelligence,
Engineering,
Electrical engineering,
Control engineering, metrology and testing,
Mechanical engineering,
Fundamentals of mechanical engineering

© 2025 Saeed Rafee Nekoo, published by Łukasiewicz Research Network – Industrial Research Institute for Automation and Measurements PIAP
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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