Leader-follower formation control of quadcopter UAVs using a Mamdani fuzzy PID controller with performance evaluation under disturbance conditions

Vo Van An; Vo Van An

doi:10.3934/electreng.2026019

AIMS Electronics and Electrical Engineering

2026, Volume 10, Issue 3: 473-503. doi: 10.3934/electreng.2026019

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Leader-follower formation control of quadcopter UAVs using a Mamdani fuzzy PID controller with performance evaluation under disturbance conditions

Vo Van An ^,

Institute of Engineering Technology, Thu Dau Mot University, Ho Chi Minh City, Vietnam

Academic Editor: Mihailo Ristic

Received: 28 February 2026 Revised: 28 April 2026 Accepted: 15 May 2026 Published: 10 June 2026

This paper proposes and evaluates a triangular formation control method for unmanned aerial vehicles (UAVs) based on a leader-follower structure using a Mamdani fuzzy PID controller on a fully nonlinear 6-DOF dynamic model. The controller was designed with a fuzzy inference mechanism to adjust PID gains via a rule-based, nonlinear fuzzy gain-scheduling mechanism based on state deviations, thereby improving trajectory tracking quality under nonlinear conditions and disturbances. The system's performance was evaluated through transient metrics and energy error indicators (MSE, RMSE) in three scenarios: no noise, external noise, and external noise combined with wind disturbance. Simulation results in MATLAB/Simulink showed that under noise-free conditions, the fuzzy PID achieves a rise time of 2.03 s, a percentage overshoot of 50.30%, and a steady-state error of 0.0315 m, significantly improving upon the PID (3.29 s; 55.74%; 0.0365 m). When external noise is present, the overshoot decreases from 227.50% to 88.58%, and the steady-state error decreases from 1.0272 to 0.4060 m (approximately 60.5% improvement). In conditions with combined wind disturbance, MSE decreases by up to 87.49% along the z-axis, and RMSE decreases from 1.1538 to 0.4081, demonstrating superior disturbance rejection. Quantitative results confirm that fuzzy PID significantly enhances trajectory tracking accuracy, stability, and robustness of the multi-agent UAV system in uncertain environments.
- PID,
- fuzzy PID,
- leader-follower,
- UAV swarm,
- disturbance
Citation: Vo Van An. Leader-follower formation control of quadcopter UAVs using a Mamdani fuzzy PID controller with performance evaluation under disturbance conditions[J]. AIMS Electronics and Electrical Engineering, 2026, 10(3): 473-503. doi: 10.3934/electreng.2026019

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Abstract

This paper proposes and evaluates a triangular formation control method for unmanned aerial vehicles (UAVs) based on a leader-follower structure using a Mamdani fuzzy PID controller on a fully nonlinear 6-DOF dynamic model. The controller was designed with a fuzzy inference mechanism to adjust PID gains via a rule-based, nonlinear fuzzy gain-scheduling mechanism based on state deviations, thereby improving trajectory tracking quality under nonlinear conditions and disturbances. The system's performance was evaluated through transient metrics and energy error indicators (MSE, RMSE) in three scenarios: no noise, external noise, and external noise combined with wind disturbance. Simulation results in MATLAB/Simulink showed that under noise-free conditions, the fuzzy PID achieves a rise time of 2.03 s, a percentage overshoot of 50.30%, and a steady-state error of 0.0315 m, significantly improving upon the PID (3.29 s; 55.74%; 0.0365 m). When external noise is present, the overshoot decreases from 227.50% to 88.58%, and the steady-state error decreases from 1.0272 to 0.4060 m (approximately 60.5% improvement). In conditions with combined wind disturbance, MSE decreases by up to 87.49% along the z-axis, and RMSE decreases from 1.1538 to 0.4081, demonstrating superior disturbance rejection. Quantitative results confirm that fuzzy PID significantly enhances trajectory tracking accuracy, stability, and robustness of the multi-agent UAV system in uncertain environments.

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