Geometric Optimal Controls for Flapping Wing UAV on a Lie Group

TL;DR

This paper develops a global Lie group-based optimal control framework for flapping-wing UAVs inspired by butterfly flight, enabling energy-efficient periodic motions and stabilization, applicable to general Lagrangian systems on Lie groups.

Contribution

It introduces a Lie group formulation for flapping-wing UAV dynamics and derives optimal control strategies for energy-efficient periodic motions, avoiding local coordinate singularities.

Findings

Derived a Lie group-based model for flapping-wing UAVs.

Identified energy-minimizing periodic motions.

Formulated optimal control for stabilization of periodic flight.

Abstract

Inspired by flight characteristics captured from live Monarch butterflies, an optimal control problem is presented while accounting the effects of low-frequency flapping and abdomen undulation. A flapping-wing aerial vehicle is modeled as an articulated rigid body, and its dynamics are developed according to Lagrangian mechanics on an abstract Lie group. This provides an elegant, global formulation of the dynamics for flapping-wing aerial vehicles, avoiding complexities and singularities associated with local coordinates. This is utilized to identify an optimal periodic motion that minimizes energy variations, and an optimal control is formulated to stabilize the periodic motion. Furthermore, the outcome of this paper can be applied to optimal control for any Lagrangian system on a Lie group with a configuration-dependent inertia.