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

Saeed Rafee Nekoo

Saeed Rafee Nekoo

Universidad de SevillaSpain
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Nekoo, Saeed Rafee
  
31. März 2025
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Online veröffentlicht: 31. März 2025
Seitenbereich: 17 - 32
Eingereicht: 10. Jan. 2024
Akzeptiert: 23. Juli 2024
DOI: https://doi.org/10.14313/jamris-2025-003
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© 2025 Saeed Rafee Nekoo, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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)
20 144.3912 911.3158
50 76.4762 345.8130
80 104.3379 388.0787
100 124.3148 427.7242
200 224.7471 630.6206
300 324.6205 827.9986
400 424.4897 1025.9861
500 524.4070 1223.8401

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

context Ref. 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‐follower this workthis workthis work 1,089, UAV45, mobile robot1,050, mobile robot
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