A Lie group formulation of multirotor aerial vehicle dynamics with applications to trajectory generation and optimal control

Abstract

This thesis presents a Lie group-based dynamics for general winged and wingless multirotor aerial vehicles (MAVs), and suggests optimal control using this. We deal with the dynamics of the MAVs with arbitrary sets of positions, axes, and coordinates of rotors or wings with no generic assumptions. From the large category of MAVs dynamics, we can make more simple dynamics equation by introducing the commonly used assumptions one after the other. In particular, we present an optimal control method of quadrotor as an application to this Lie group dynamics. This Lie group formulation can express all of the dynamics of any existing winged or wingless MAVs model, and we present the analytic gradient of the optimization problem, making it easy to plan trajectory and optimize various objective functions.