Geometric Control of an Autonomous Quadrotor UAV

Geometric Control of an Autonomous Quadrotor UAV Taeyoung Lee Mechanical and Aerospace Engineering Florida Institute of Technology

Geometric Control of an Autonomous Quadrotor UAV

1/9

Introduction

Computational Geometric Mechanics and Control Dynamics and Control Understand the behavior of physical systems under the interaction with their environment Create a control system that causes the system to behave in a desired manner Most of nonlinear dynamics and control problems are studied in a linear space. x˙ = f (t, x, u),

x ∈ Rn , u ∈ Rm , f : Rn+m+1 → Rn

Geometric Mechanics and Control Understand the structure of the equations of motion of a system in order to facilitate its analysis and design Analyze the evolution of a system and design controllers on a nonlinear manifold


2/9

Introduction

Computational Geometric Mechanics and Control Computational Geometric Mechanics and Control Develop computational algorithms which preserve the geometric properties of a mechanical system Robust and careful numerical implementation of geometric control theory to complex engineering systems

Importance Structure-preservation is critical for stability, accuracy, reliability and efficiency of numerical computations Yields a systematic framework to develop computational methods consistent with the underlying geometry of the problem Provides nontrivial maneuvers that are globally valid on a nonlinear configuration manifold Computational methods constructed by underlying physical principles


3/9

Introduction

Quadrotor Unmanned Aerial Vehicle Quadrotor UAV Two pairs of counter-rotating rotors and propellers Vertical take-off/landing, and hovering capability Simpler mechanical structures compared with general helicopters Envisaged for autonomous surveillance, mobile sensor network, and educational purposes

Existing Control Systems for Quadrotor UAVs Based on the linearized dynamics of a quadrotor UAV Singularities in representing complex maneuvers Fundamental restriction in tracking nontrivial trajectories


4/9

Introduction

Geometric Control of a Quadrotor UAV Proposed Geometric Tracking Control of a Quadrotor UAV Represent the dynamical of a quadrotor UAV globally using differential geometry Asymptotic stability is guaranteed for almost all initial conditions Provides extreme maneuverabilities to follow complex trajectories accurately

Control Input Structures Thrust at four rotors (f1 , f2 , f3 , f4 ) Total thrust magnitude and moment vector are controlled f4 f1

f3

~b1 f2

~e1 ~e3

~b3 ~b2

~e2


5/9

Introduction

Geometric Control of a Quadrotor UAV Three Flight Modes Attitude Controlled Mode: track an attitude command Rd (t) Position Controlled Mode: track a position command xd (t) and a heading direction b1d (t) Velocity Controlled Mode: track a velocity command vd (t) and a heading direction b1d (t)

Hybrid Control System Switching between several flight modes yields autonomous acrobatic maneuvers Robust to switching conditions xd

- Trajectory ~ b3d tracking ~b1 d 6 r -

f Attitude tracking

M

-

Quadrotor Dynamics

r -

Controller x, v, R, Ω Geometric Control of an Autonomous Quadrotor UAV

6/9

Introduction

Geometric Control of a Quadrotor UAV

Elliptic Helix


Double Flipping

7/9

Introduction

Hardward System Development FIT Quadrotor UAV Prototype UAV to demonstrate capabilities of geometric control experimentally, supported by ACITC grant Composed of a main controller, four motor speed controllers, an attitude sensor, WIFI communication, and a safety module Currently verifying control system codes before a flight test


8/9

Introduction

Benefits Research Explicit demonstration of unification between differential geometry in applied mathematics and autonomous systems in control engineering The outcome of this research will be presented at international conferences (IEEE CDC 2010, IFAC World Congress 2011).

Teaching Control system design procedure and test results have been incorporated into the following classes at FIT: MAE4242 MAE4014 MAE5690

Aircraft Stability and Control Control Systems Nonlinear Systems and Control

Human Resources Training two graduate students in developing a real-time embedded control system for a quadrotor UAV Advising their thesis projects directly related to embedded systems Geometric Control of an Autonomous Quadrotor UAV

9/9