Robust Flight Control of an Underactuated Quadrotor via Sliding Modes
An underactuated quadrotor has four actuators and six degrees of freedom to be controlled. Nevertheless, by deliberately controlling the velocities of the four propellers, the underactuated quadrotor can track the desired position trajectory and maintain
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Robust Flight Control of an Underactuated Quadrotor via Sliding Modes Chih-Chen Yih
Abstract An underactuated quadrotor has four actuators and six degrees of freedom to be controlled. Nevertheless, by deliberately controlling the velocities of the four propellers, the underactuated quadrotor can track the desired position trajectory and maintain the correct attitude during flight. To improve the robustness and performance of the underactuated quadrotor system, we propose two sliding mode control to deal with the parametric variations and the external disturbances. We first establish the quadrotor model in terms of the translational and rotational dynamics along with the disturbances and the model uncertainties. By specifying the desired pitch and roll angle as the virtual control, we then design dual sliding modes: one for the translational and the other for the rotational dynamics. Our Lyapunov-based stability analysis shows that the proposed control schemes can guarantee the asymptotical stability of the error dynamics for the position and attitude control of the underactuated quadrotor. Numerical simulations also indicate that the sliding mode control can effectively follow the desired trajectory and maintain the proper attitude in the presence of parametric variations and external disturbances. Keywords Quadrotor · Sliding mode · Underactuated systems · Robust control
Nomenclature B Pi Fw FB FPi RT p
≡ quadrotor body ≡ propeller i ≡ inertia world frame ≡ body frame ≡ ith propeller frame ≡ transform matrix from body angular rates to Euler ones ≡ position of B in Fω
C.-C. Yih (B) Department of Mechanical and Automation Engineering, I-Shou University, 84001 Kaohsiung, Taiwan e-mail: [email protected] © Springer Science+Business Media Singapore 2017 N. Derbel et al. (eds.), Applications of Sliding Mode Control, Studies in Systems, Decision and Control 79, DOI 10.1007/978-981-10-2374-3_5
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q ω RB B R Pi ωi ω Pi TPi ωB τB τ Pi τdi Ti τωi m I Pi IB kf km L g
C.-C. Yih
≡ Euler angle of B in Fω ≡ rotation matrix from FB to Fω ≡ rotation matrix from FPi to FB ≡ ith propeller spinning velocity about Z Pi ≡ angular velocity in the ith propeller frame ≡ force in the ith propeller frame ≡ angular velocity of B in FB ≡ torque in FB ≡ torque in FPi ≡ ith propeller air drag torque about Z Pi ≡ ith propeller thrust along Z Pi ≡ motor torque along Z Pi ≡ total quadrotor mass ≡ inertia of the ith propeller Pi ≡ inertia of the quadrotor body B ≡ propeller thrust coefficient ≡ propeller drag coefficient ≡ distance of FPi to FB ≡ gravity constant
5.1 Introduction In recent years, small quadrotors have attracted much attention in the field of research on unmanned aerial vehicles (UAV). Due to the simple mechanical structure, researchers have been using microprocessors and micro-electro-mechanical sensors to stabilize the attitude and the altitude of the quadrotor. With the aid of GPS or the lightweight camera, quadrotor UAVs can easily hover and delicately fly in indoor or outdoor environment. The control of the quadroto
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