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Research and utilization of quadrotor helicopter in many areas is increasing because of its special flight performance. It is not easy to control a quadrotor whose dynamic characteristics are nonlinear, multivariable and stronglycoupled. A novel method is proposed to solve this problem, which adopts a MIMO RBF-ARX model to represent the nonlinear dynamics of quadrotor, and then based on a locally linearized ARX model that is obtained from the RBF-ARX model at a working-point, the state-feedback control law with LQR approach is proposed to control the quadrotor. The results of real-time control on a quadrotor helicopter illustrate the feasibility and efficient performance of the modeling and control approach presented in this paper. And this successful application to the quadrotor helicopter confirms the validity of the RBF-ARX model.