design of controllers for a quad-rotor uav using optical flow

126/03/09LIST – DTSI

Design of controllers for a quad-rotor UAV using optical flow

Bruno Hérissé

CEA ListFontenay-Aux-Roses, France

[email protected]

226th March 2009DTSI SRI-LIST

Introduction

Purpose : measurements of inertial data and visual optical flow for the design of controllers for a VTOL UAV.

Camera

IMU(inertial

measurments unit)


Model of the UAV

T

The system is nonlinear and under actuated.Definition of used frames.

I : Inertial frame attached to the earth

B : body-fixed frame attached to the vehicle’s center of mass.

Vehicle state: : position of the center of mass in I : speed of the center of mass in I : orientation matrix from B to I : rotational velocity in B

Inputs: : Global thrust in B : Control torque in B

Dynamic Model used :

Translational dynamics

Rotational Dynamics

Already controlled

vR

T

F=f(T,R)

Constant forces

High gain controller


Plan

The main object : elaboration of controllers for hovering flight, vertical landing and terrain following of a VTOL UAV above a textured target.

Optical flow computation Computation of the translational optical flow

A non-linear controller for the stabilization of the hovering flight.

A non-linear controller for a smooth vertical landing.

A non-linear controller for terrain following.


Kinematics of an image point under spherical projection

Optical flow from an image plane to a spherical retina.

Tp

p

ppI

P

Vpp

P

Pp

Optical Flow


I

T

d

Translational optical flow computation

RRRd

VR

d

vw

diag

RRRRQ

d

QVp

Ttt

T

Ttt

T

W

1

321 ,,

0

2

Known data :

η

Measured data :

, p

Rotational term Translational term


Schema of control

UAV dynamics

Controller

Camera

+

-

Environment

configuration

State : (ξ , v)

Optical flow : w

Set point : wc (P, PI)

(0 ou ω*)

Perturbations


For the stabilisation of the hovering flight define the error term,

The goal is the regulation of to zero :

The control law ensures the exponential

convergence of to zero (PI-type controller)

The UAV does not collide the obstacle

Stabilization of the hovering flight

t

IP wdkwkF0

td

vw

0w

dtd

vk

td

vkvm

t

IP

0

w

0

0

0

cw

v


Consider that , that is is the distance of the vehicle to the ground

Define for the control of the third component of the dynamics the error term,

Goal: and for all time

Proposition 1: Consider the control law , then for all , one can ensure the exponential convergence of to zero while keeping for all time.

Vertical landing control (1)

* zz wmkF

3' e

**~

h

hww z

hzd

tehhh

hw

*

0*0~

h 0th

0th

00lim ,vhkk

Smooth vertical landing

*

0

0

cw


Proof: Define , and , and

The third component of the dynamics is:

Integrating this equation, it yields

Differentiating L, it yields

Chosing klim such that and

It ensures that is bounded. Consequently, converges to zero with

as exponential decay constant.


mkz *

22

2 1

h

khL

0 0

02

L

k

h

h

hkhm

hh 22

2

1

2

1

hL

01

exp 00

tehhh

kh

h


Proposition 2: Consider the following control law, then for all it ensures the exponential convergence of to zero with as exponential decay constant while keeping for all time.


dwkwkFt

zIzPz 0

**

h * 0th

limkkP


Experimental setup

Drone:- Embeded attitude control from IMU data-running at 166Hz

Numerical transmission:- Transmision of the desired attitude to the drone- Transmission of IMU data to the ground station- 70 ms are required for the data transmission

Textured ground Ground station:Treatment of vision algorithms at 60 ms

Camera:-Focus: 2.1mm

Analogical transmission:-Transmission at 2.4GHz- Associate with an acquisition card, a new image is available each 50 ms


Experiments


Consider that

The goal is , or has to be set to a constant :

Control on the z axis and on the x axis Control on the x axis and on the z axis

Maintaining a constant forward thrust, the drag force opposite to the vehicle's direction of flight ensures that the forward velocity converges to a constant. Then, one can consider that is constant.

Terrain following (1)

00*cw

tdvtd

vx

x ** xv

0

0

*

cw

xv

d

dxv

**


The control law ensures the asymptotic convergence of to

The UAV does not collide the obstacle


0

0

*

cw

**

**

d

DP

vd

d

dk

d

ddkdm

dx vv

zDxP wkwkF *F

d

F d *d


Proof:


d

dkL

d

dgvkd

mL

D

dP

2

*2

2

d

P vk

L 0

0

0

*

cw



0

0

*

cw


Experiments


Conclusion

Computation of the translational optical flow over a textured flat target plane.

Rigorous non-linear controllers for hovering flight, vertical landing and terrain (or wall) following.

The UAV remains free from collision.

The control approach has been experimented on a quad-rotor UAV to demonstrate the performance of controllers.


Publications

[1] Herisse, B.; Russotto, F-X.; Hamel, T. & Mahony, R.Hovering flight and vertical landing control of a VTOL Unmanned Aerial Vehicle using Optical FlowIEEE/RSJ International Conference on Intelligent Robots and Systems, IROS'08, 2008

[2] Herisse, B.; Hamel, T.; Mahony, R. & Russotto, F-X.A nonlinear terrain-following controller for a VTOL Unmanned Aerial Vehicle using translational

optical flowIEEE International Conference on Robotics and Automation, ICRA'09, 2009

Tarek Hamel Robert MahonyFrançois-XavierRussotto


Acknowledgments

Projet NaviflowAssistance à la NAVIgation par FLux Optique

design of controllers for a quad-rotor uav using optical flow

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