Savunma

System identification of a quadrotor UAV

Turgay Kale / Güleser Kalaycı Demir

Overview

Scope

Literature

My studies and goal

Basic concepts

Kinematics and dynamics

Simulink model

Things to do

Evaluation

Scope

Understanding the law and facts behind the flight of an UAV

Dynamic modelling of a quadrotor

Controlling of a rigid quadrotor plant

Building a Simulink model of the entire flight system

Evaluation of simulation test benchmark

Literature

Project owner University Control method Picture

Bauabdallah

ÉCOLE POLYTECHNIQUE

FÉDÉRALE DE LAUSANNE

Backstepping, PID,

Optimal control,

Sliding mode

Fower

Brigham Young University

Visual feedback

MD4-200R

Micro Drones

Gmbh

PI

Weng & Shukri

Universiti Teknologi

Malaysia

PID

Literature

Project owner University Control method Picture

Starmac

Stanford

University

Reinforcement

learning

Hanford

Pennysylvania

University

PI

HMX4

Micro Drones

Gmbh

Feedback

linearization

My studies & goal

Efforted in data correction of Sparkfun’s ultimate imu

Data acquisition & filtering effort with 9-dof Imu

Arduino platform

Open source libraries : SD card

Proper peripheral units for control

Worldwide support

Pololu IMU-9

9 degree-of-freedom

I²C support

Cheap cost & good feedbacks

Dynamic modelling effort in Matlab/simulink

To complete accurate simulink model (goal)

Basic concepts

Throttle (N) Roll (N.m)

Pitch (N.m) Yaw (N.m)

Quadrotor movements are ensured by controlling the rotational speeds of 4-rotors

Kinematics

Position and attitude vector with respect to E-frame

Linear position vector :

Angular attitude vector :

Generalized position vector w.r.t. E-frame

Kinematics

Rotations between E-frame and B-frame

Kinematics

Hence overall rotating matrice is

Velocity vectors with respect to B-frame

Linear velocity vector :

Angular velocity vector :

Generalized velocity vector w.r.t. B-frame

Kinematics

Thus it is possible that and where

As a result

and

Hence the equivalent form of statements becomes,

Dynamics

Newton-Euler formulation is adopted

Three assumptions are made to decrease the computation complexity

Inertia matrix is time-invariant (fundamental)

Origin of the body-fixed frame is assumed as the center of mass (COM)

In hovering condition, moment of inertia matrix I is approximately diagonal

From the Euler’s first axiom of the Newton’s second law ;

Dynamics

where

From Euler’s second axiom of the Newton’s second law ;

is body inertia matrix (in the body-fixed frame)

is torque vector w.r.t. E-frame

is quadrotor total mass

is rotation matrix derivative

is force vector w.r.t. E-frame

Dynamics

By associating two axioms, it is possible to define motion dynamics of rigid

body. Below equation shows the matrix formulation of dynamics.

(1)

Let’s define a generalized force (including torque) vector as;

where , means an identity matrix with dimension 3 times 3. First matrix in

equation is diagonal and constant.

Dynamics

Therefore it is possible to rewrite equation (1) in matrix form

where

is generalized acceleration vector w.r.t. B-frame

is system inertia matrix w.r.t. B-frame

is Coriolis-centripetal matrix w.r.t. B-frame

Dynamics

generalized force vector can be splitted into three components according

to the nature of quadrotor contributions.

First contribution is gravitational vector

Second contribution is gyroscopic effects produced by the propeller rotation.

Dynamics

where is total rotational moment of inertia.

Third contribution is aerodynamic effects produced by main movements. In this

phenomenon, forces and torques are assumed to be proportional to squared propeller’s

speed.

where is movement matrix

Dynamics

Hence, it is possible to describe the dynamics considering these last three

contributions according to equation (1) .

By re-arranging , it is possible to write equation (23) ;

Dynamics

Hybrid model

Generalized velocity vector in hybrid notation called H-frame ;

By rewriting in a matrix form based on H-frame ;

Dynamics

Dynamics

By re-arranging , it is possible to write ;

Hence it is possible to write system equations in hybrid system as below ;

Simulink model

task control

sensors

dynamics +

-

IMU 9-dof

IR

PI/PID

control

commands

quadrotor

plant

position

tracking states

Things to do

Complete simulink model

Benchmark test results & restorate model

Hardware implementation & tests (partialy optional)

Design 3D computer simulation model based on openGL (optional)

Port simulink model blocks to microsoft .net framework (optional)

End of defence