Finite-Time Suboptimal Control Design for Aerobatic Maneuver of Variable-Pitch Quadrotor

Abstract

The variable-pitch quadrotors can perform aggressive maneuvers such as aerobatic flip by varying the thrust in both positive and negative vertical directions via the blade pitch, which can provide an additional degree of freedom as opposed to the fixed-pitch quadrotor that only changes the rotational rate of motors. However, an inevitable challenge exists when designing an operative controller for the aerobatic flip due to the resultant singularity of the rotation matrix. In this paper, a finite-time suboptimal control design strategy named finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta -D$</tex-math></inline-formula> algorithm combined with the geometric control technique is proposed for the aerobatic maneuver control of the variable-pitch quadrotor. Based on this scheme, the singularity issue can be circumvented. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta -D$</tex-math></inline-formula> control design provides a closed-form suboptimal control law by offline solving a differential Riccati equation and a set of linear Lyapunov equations analytically, which does not require complex online numerical and iterative solutions compared with the similar finite-time state dependent Riccati equation technique. Simulation results demonstrate that the proposed geometric finite-time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta -D$</tex-math></inline-formula> method provides an effective and efficient control of the variable-pitch quadrotor.