TY - JOUR
T1 - Intelligent tracking control of CRA cluster via back-stepping and RBFNN strategy
AU - Wei, Yiran
AU - He, Ming
AU - Pan, Zhenhua
AU - Wu, Haoyu
AU - Liu, Chengzhuo
AU - Jing, Peiliang
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2026.
PY - 2026/9
Y1 - 2026/9
N2 - To enhance the intelligent collaborative execution capability of tasks by Coaxial-Rotor-Aircraft (CRA) cluster, the problems of rapid response and stability maintenance need to be addressed. This study investigates a decentralized adaptive tracking control method based on a leader-follower coordination strategy, capable of achieving both the rapid formation tracking response and flight stability of each CRA simultaneously. Specifically, the mathematical model of CRA is established and extended to the CRA cluster system. Then, the intelligent formation tracking control scheme is proposed, guided by the virtual leader strategy, and the control system is divided into a position subsystem and an attitude subsystem. The position subsystem maintains formation by adjusting the relative position of each CRA, and the attitude subsystem is responsible for changing the attitude of each CRA to the desired stable state. The position controller is developed using the back-stepping control strategy, while the attitude tracking controller is created by an adaptive radial basis function neural network (RBFNN) based on the position model. The stability of these controllers is mathematically proven with Lyapunov theory. In the verification section of this work, numerical simulations and software-in-the-loop (SITL) simulations of intelligent tracking are conducted. The obtained trajectories of CRAs are smooth and continuous, demonstrating excellent position response and minimal amplitude vibration.
AB - To enhance the intelligent collaborative execution capability of tasks by Coaxial-Rotor-Aircraft (CRA) cluster, the problems of rapid response and stability maintenance need to be addressed. This study investigates a decentralized adaptive tracking control method based on a leader-follower coordination strategy, capable of achieving both the rapid formation tracking response and flight stability of each CRA simultaneously. Specifically, the mathematical model of CRA is established and extended to the CRA cluster system. Then, the intelligent formation tracking control scheme is proposed, guided by the virtual leader strategy, and the control system is divided into a position subsystem and an attitude subsystem. The position subsystem maintains formation by adjusting the relative position of each CRA, and the attitude subsystem is responsible for changing the attitude of each CRA to the desired stable state. The position controller is developed using the back-stepping control strategy, while the attitude tracking controller is created by an adaptive radial basis function neural network (RBFNN) based on the position model. The stability of these controllers is mathematically proven with Lyapunov theory. In the verification section of this work, numerical simulations and software-in-the-loop (SITL) simulations of intelligent tracking are conducted. The obtained trajectories of CRAs are smooth and continuous, demonstrating excellent position response and minimal amplitude vibration.
KW - Back-stepping control
KW - Coaxial rotor aircraft
KW - Intelligent tracking
KW - RBFNN
UR - https://www.scopus.com/pages/publications/105048868543
U2 - 10.1007/s13042-026-03215-0
DO - 10.1007/s13042-026-03215-0
M3 - Article
AN - SCOPUS:105048868543
SN - 1868-8071
VL - 17
JO - International Journal of Machine Learning and Cybernetics
JF - International Journal of Machine Learning and Cybernetics
IS - 9
M1 - 445
ER -