Discrete-Time Optimal Attitude Control of Swivelling Biplane Quadrotor

This article focuses on deriving a discrete-time optimal control law for the transition ma-noeuver, from its biplane mode to the quadrotor mode, of a swivelling biplane quadrotor, a hybrid vertical take-off and landing UAV. The problem is formulated in a discrete setting by discretizing the existing continuous-time model, setting up a measure of performance and then applying the discrete-time Pontryagin Maximum Principle (DMP) on Lie groups to obtain the first order necessary conditions for an optimal transition. A modified multiple shooting method is used to solve the necessary conditions and the proposed control law is validated by numerical experiments.