Dynamics and Control ofQuadrotor UAV

Moncrief-O’Donnell Chair, UTA Research Institute (UTARI)The University of Texas at Arlington, USA

F.L. Lewis, NAI

Director, Key Laboratory of Autonomous Systems and Network Control, MoESouth China University of Technology, Guangzhou

Hai-Long Pei

and

Moncrief-O’Donnell Chair, UTA Research Institute (UTARI)The University of Texas at Arlington, USA

and

F.L. Lewis, NAI

Talk available online at http://www.UTA.edu/UTARI/acs

Dynamics and Control ofQuadrotor UAV

Qian Ren Consulting Professor, State Key Laboratory of SyntheticalAutomation for Process Industries

Northeastern University, Shenyang, China

Supported by :NSF AFOSR EuropeONR – Marc SteinbergUS TARDEC

Supported by :China NNSFChina Project 111

AR Drone Parrot

Crazyflie

3D Robotics Octocopter

Position –navigational states

Angular position –attitudes

The Quadrotor States

Roll

Pitch

yaw

xyz

X

Body AxesVs. earth‐fixed axes

Control distribution from 4 actuator rotors to lift and torques

Lift

torques

u

Position –navigational states

Angular position –attitudes

The Quadrotor States

Roll

Pitch

yaw

xyz

X

Lift

torques

u

The Quadrotor Controls

6 states and 4 controls = under‐actuated system

xyz

Position states‐ navigation states Attitude states

Quadrotor equations of motion

Position subsystem

Angle subsystem

00 Fmg

sincos sincos cos

F u

Virtual control input for position subsystem 

Position subsystem

Attitude subsystem

uxyz

torques

lift

attitudes

positionAttitudesubsystem Position 

subsystem

00 Fmg

Backstepping Control Design

00 ( )d dF F Fmg

00 dm F Fmg

dF F F And force mismatch is

Where ideal virtual force input is dF

00 dm F Fmg

Backstepping Control Design

1. Pick desired virtual force          to make position dynamics track desired positionsdF

2. Pick actual control – the torques         ‐ to make force error         go to zero  F

d

Given          find required attitude angles and liftdF

define

then

So that

Then compute

Note that        is not involved here!

An Inverse Kinematics problam

Inputs are desired position and yaw (heading)

Backstepping Controller‐ 2 loops