Cobra aerobatic flight for quadrotors using θ-D nonlinear control

Abstract

The control design for the Cobra maneuver of quadrotors is presented based on quaternion dynamics. Cobra maneuver commands the quadrotor in ± π / 2 (rad) pitch angle such that the conventional hovering assumption for quadrotor flight is not applicable. The finite-time θ-D method is proposed to control the Cobra maneuver. Based on this technique, the intractable Hamilton–Jacobi–Bellman equation can be approximated by a differential Riccati equation and a series of state-dependent Lyapunov equations, which can be solved recursively and lead to the closed-form state feedback control law . This control law can achieve semi-global asymptomatic stability of the closed-loop system. Numerical simulations verify that the proposed technique is compared favourably with the finite-time state-dependent Riccati equation (SDRE) technique in terms of computation efficiency and control effort, and also shows faster recovery of the quadrotor after the Cobra maneuver compared with conventional dynamics without the derivative of the rotation matrix.