Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/7.
Aspec s Rega ding Fly Con ol o Quadcop e
End owednes Kuan ama
Enginee ing Doc o al School
Uni e si y o O adea
1 Uni e si ăţii S ., O adea, Romania
end owedne[email p o ec ed]m
Ioan Ta ca1, Radu Ta ca2, Dan C aciun3
Mecha onics Depa men
Uni e si y o O adea
1 Uni e si ăţii S ., O adea, Romania
1nelu @uo adea. o, 2 a ca@uo adea. o,
3danc [email protected]
Abs ac —Quadcop e is one o Unmanned Ae ial Vehicle
(UAV) which has wo pai s o iden ical ixed pi ched o o
p opelle s. I can ly au onomously based on p e-p og ammed
ligh o manually con olled by a emo e, and e e y mo emen
achie ed by a ying he speed o each o o independen ly. The
o ien a ion o quadcop e axes ela i e o a e e ence line and i s
di ec ion o mo ion a e known as a i ude. Fly con ol ac o s a e
a ec ed by a i ude de e mina ion which can be calcula ed om
3 possible angles using combined measu emen . Gy oscope and
accele ome e a e p ima y senso s o con ol quadcop e
a i ude, bu magne ome e senso and GPS also used o enhance
he s abili y du ing ligh . This pape will ocus on de ails o
unc ion and ma hema ical o mula o e e y ac o ega ding ly
con ol and compa a i e da a o 2 ypes o o ien a ion senso
used in his sys em.
Keywo ds—quadcop e ; a i ude; gy oscope; ly con ol;
o ien a ion senso
I. INTRODUCTION
Quadcop e is classi ied as Unmanned Ae ial Vehicle
which is li ed by 4 o o s, as i s name sugges . I s mo emen
can be di ec ed by con olling he angula speed o each o o .
The o o s a e connec ed wi h he p opelle s, and he each pai
o opposed simila p opelle a e o a ing in he same di ec ion
( wo clockwise and wo coun e clockwise). The mos
impo an aspec s needed o be conside ed when designing
quadcop e a e ela ed o i s ligh s abili y: wha ac o s a e
a ec ing i and how hey in luence he s abili y. Main opics
ega ding quadcop e s a e ela ed o hei a i ude;
ma hema ical o mulas and ligh con ol aim o con ol hei
a i ude.
A i ude is a posi ion o he body (ine ial ame) o he
o ien a ion o quadcop e axes ela i e o a e e ence line and
i s di ec ion o mo ion. Quadcop e a i ude can be measu ed
using MEMS (Mic o Elec o Mechanical Sys em) senso . This
senso canno accomplish same accu acy as Kalman il e o
complemen a y usion algo i hms which a e used o p o ide
mo e accu a e and eliable in o ma ion in he MEMS a i ude
de e mina ion sys ems [1]. Senso sys em is a undamen al
pa o UAV, including quadcop e , ha ing hei ole in
calcula ing accu a e a i ude by measu ing h ee angles, using
combined measu emen s such as he gy oscope/gy o a e,
accele ome e and magne ome e [2]. These senso s measu e
h ee-axis angula a es, h ee-axis appa en accele a ion, and
Ea h’s magne ic ield wi h espec o he quadcop e ’s body
ame. In o de o achie e he bes e alua ion o a i ude
angles om hese senso s, i is essen ial o use hese
measu emen s in a seamless manne while conside ing he
di e ence be ween each senso ’s signal speci ica ions. I is
possible o use a a e gy o o ob ain a i udes, by in eg a ing
he igid body's kinema ic equa ions, while accele ome e s
p o ide g a i y di ec ion. Wi h high quali y gy oscope and
app op ia e ini ial alues, hese assessmen s can be e y
accu a e o e long pe iods o ime. On he o he hand,
accele ome e s signals p esen di ec alues o il angles [3].
When quadcop e shi s om one posi ion o he o he , he
wing on espec i e side will slan sligh ly in he mo ing
di ec ion as seen on Fig.1. The esul ed angle is an impo an
ac o in de e mining he quadcop e s abili y. Each
mo emen ’s angle has o be con inuously moni o ed by he
o ien a ion senso un il he s abili y is achie ed. Wi h he
ligh con ol senso s' help, quadcop e will adjus i s posi ion
acco dingly, e en in he case o na u al dis u bances o
p opelle ai low. These aspec s e eal he impo ance o
quadcop e ligh con ol.
Fig. 1. Illus a ion o a i ude quadcop e mo emen
II. ATTITUDE PARAMETERIZATION AND
REPRESENTATION
P ope es ima ion o a i ude angles and posi ion o
quadcop e a e he mos impo an ac o in ligh con ol
na iga ion. De e mina ion o ligh a i ude also in ol es he
compu a ion o quadcop e ’s pi ch angle, oll angle, and
heading angle. Bo h pi ch angle and oll angle can be
compu ed by measu ing accele a ions and body a es om
accele ome e s and a e gy os, while heading angle can be
measu ed by calcula ing he magne ic heading. Ha ing known
he accele a ion on h ee axes (pi ch, oll, and yaw a e
in o ma ion), he pi ch and oll angles can also be de e mined
ei he by compu ing he g a i a ional accele a ion componen s
Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/7.
on he body axes, o by using he Eule qua e nion me hod.
The la e me hod, howe e , p o ides low noise con en s and
as esponse o changes in he inpu signals, bu ends o d i
wi h ime due o gy o bias e o s [4].
The absolu e linea posi ion o he quadcop e is de ined in
he ine ial ame x, y, z axes wi h Eule (£). The a i ude is
de ined in he ine ial ame wi h h ee Eule angles: Pi ch
angle (θ) de e mines he o a ion o he quadcop e a ound he
y-axis, while Roll angle (ɸ) a ound he x-axis and Yaw angle
(ψ) a ound z-axis. Using concep o kinema ic mo ing ame,
quadcop e mo emen om ini ial posi ion o desi ed posi ion
can be calcula ed as seen on Fig. 2.
Fig. 2. Illus a ion o quadcop e o ien a ion
The Eule o mula (1) can be used o calcula e he o a ion o
he quadcop e ame h oughou each axis as well as he
ma ix mul iplica ion esul o R oll, Rpi ch, Ryaw:
(1)
Whe e symbol ‘s’ ep esen sine and ‘c’ ep esen cosine. To
ge he desi ed quadcop e mo emen (based on each
mo emen angle), he angula mo emen o e e y o o mus
gene a e app op ia e h us . The h us mo emen in (2) is
p oduced by each o o h ough he o que applied by o o
which d i en by elec onic speed con olle s. The o o speed
is ωi and he li cons an o quadcop e is b ha depends on
he ai densi y a ound p opelle .
(2)
Fly con ol, especially he a i ude measu emen senso , holds
an essen ial pa o moni o e e y a i ude and o ien a ion o
quadcop e in o de o i o ly s able e en h ough
dis u bance.
III. QUADCOPTER FLY CONTROL MEASUREMENT
In e ms o quadcop e a i ude, o ien a ion and mo emen
posi ion ha e o be moni o ed con inuously using o ien a ion
measu emen such as accele ome e and gy oscope senso .
Accele ome e is used o measu e accele a ion om
quadcop e mo emen , whe eas gy oscope is used o measu e
he angula a e as seen in diag am block on Fig. 3.
Magne ome e and GPS as posi ion senso s a e used o
imp o e he accu acy o o a ion and posi ion o quadcop e .
By using hese senso s, one can p ecisely e alua e quadcop e
speed, posi ion and o ien a ion and help s abilizing quadcop e
mo emen .
Fig. 3. Quadcop e ligh con ol uni
Accele ome e and gy oscope as o ien a ion senso s a e called
s ap down sys em in which he ine ial senso s a e di ec ly
a ached o he ehicle ame. These senso s unc ion as he
ull dynamic mo ion o he ehicle. The ela ionship be ween
he body- ixed ame and he na iga ional ame mus be
main ained compu a ionally on boa d.
A. Quadcop e a i ude es ima ion based on Accele ome e
Accele a ion is he a e o eloci y change wi h ime o he
a e o change o dis ance wi h squa ed ime. To de e mine
speci ic accele a ion, an accele ome e is used. As a measu e
senso , accele ome e can calcula e he di e ence be ween
ehicle’s accele a ion and g a i y accele a ion. To be able o
de e mine h ee-dimensional accele a ion ec o , accele a ion
can be calcula ed based on New on’s second law o mo ion
which ela es o ce (F), mass (m), and accele a ion (a).
Accele ome e is going o be used in ine ial na iga ion;
he e o e, accele a ion wi h espec o he ine ial ame is
needed. The ou pu o accele ome e is measu emen o he
di e ence be ween he ac ual ehicle accele a ion (a) and he
g a i a ional accele a ion (g)
(3)
In (3), F is he speci ic o ce. I is necessa y o know he
magni ude and o ien a ion o he g a i y ec o g wi h espec
o he accele ome e inpu axis in o de o compu e he
accele a ion componen s om he accele ome e ou pu s. The
ou pu o accele a ion on a igid body is he e o e gi en by
(4).
(4)
Whe e am is he measu ed accele a ion and Fg is he o ce due
o g a i y and F is he ex e nal o ce. One can use (4) o
calcula e he g a i a ional e ec when he ex e nal o ces
equals o ze o. I is assumed ha he axes o he accele ome e
a e aligned wi h he body- ame axes and ha he
accele ome e has been p ope ly calib a ed o emo e
misalignmen e o s and c oss-axis sensi i i y.
Y
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Angula Ra e
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Na iga ion
Algo i hm
A i ude ( ad)
Veloci y (m/s)
Posi ion (m)
Magne ome e
& GPS
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Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/7.
In he h ee axis accele ome e , (ax, ay, az) ep esen he
accele a ion measu ed in he body ame axes. In he ine ial
ame, he o ce o g a i y is in z-axis. Using (4) and he o ce
o g a i y, he accele a ion in he body ames is gi en by (5).
(5)
The symbol Ri ep esen he o a ion ma ix om he ine ial
o he body- ixed e e ence ame, which come om
calcula ion be ween Pi ch and Roll (Rx, Ry), as in (1). Since
he accele a ions in s able ligh egimes a e usually small
compa ed o he g a i y accele a ion, neglec ing he linea
accele a ion is a classical assump ion [5]. No malizing he
ec o o accele a ion measu emen s acili a es o exp ess he
oll and pi ch angles as (6).
(6)
Whe e ϕ is he oll angle and θ is he pi ch angle ela i e o he
g ound. Quadcop e s a e di e en om g ound ehicles
because o he h us equi ed o keep hem ai bo ne. The
accele ome e s in s ap down sys ems measu e he esul an o
g a i a ional and o he accele a ions ac ing on he body o
which he senso s a e a ached. The idea o his me hod is o
ega d he accele ome e s as inclinome e s, which p o ide an
absolu e e e ence o he a i ude by ela ing he body
o ien a ion o he g a i y ec o . I is assumed ha he body is
no mo ing o is mo ing a cons an speed, so ha he
accele a ion due o he ea h’s o a ion is negligible and he
g a i y is he only sou ce o accele a ion, also known as
Co iolis accele a ion [6]. The accele ome e s can p o ide e y
accu a e measu emen s o a i ude, bu he accele ome e -
based a i ude is sensi i e o ex e nal accele a ion and
ib a ion.
B. Quadcop e a i ude es ima ion based on gy oscope
Gy oscope is he angula a e senso which is used o
measu e he a e o o a ion a ound he senso axis in
quadcop e . Theo e ically, when in eg a ing he signal om
he gy oscope, one can acqui e he angula change o e a
pe iod o ime. In Fig. 2 can be seen he illus a ion o
quadcop e ’s o ien a ion and posi ion, he e e ence ame X,
Y, and Z is aligned wi h he p incipal (main) axis o he body.
In s ap down sys ems, gy oscopes measu e he angula a es
o h ee axes o he body wi h espec o he ine ial coo dina e
ame. Wi h hese measu emen s o angula a es in body
coo dina es, he a i ude o he quadcop e can be de i ed by
in eg a ing he igid body kinema ic equa ions, s a ing om a
known ini ial a i ude a a gi en poin in ime. The a i ude o a
body wi h espec o he ine ial coo dina e ame is de ined by
Eule o mula. Examina ion o small changes in each Eule
angle and he e ec s on he angula ec o a e based on
kinema ic mo ing ames heo em. The con inuous ime
nonlinea igid body kinema ic equa ion in s a e space
ep esen a ion is shown in (7) and (8).
(7)
(8)
Whe e p, q, a e he angula a es measu ed by gy oscopes
in he body coo dina e ame. Using his equa ion, he
measu emen esul om gy o senso will be compa ed wi h
desi ed a i ude o quadcop e .
C. Quadcop e a i ude es ima ion based on magne ome e
Magne ome e s a e commonly used o measu e Ea h’s
local magne ic ield ec o hus de e mine he di ec ion in
which magne ic no h lies. A 3 axis magne ome e can
measu e magne ic ield in ensi y in 3 dimensions. These poin s
a e e e ed o as he magne ic poles. Magne ic ield lines a y
bo h in s eng h and di ec ion abou he ace o he ea h. The
di ec ion and s eng h o he ea h’s magne ic ield (H) can be
ep esen ed by he h ee axis alues Hx, Hy, and Hz. The Hx
and Hy in o ma ion can be used o de e mine compass
headings in e e ence o he magne ic poles.
The a i ude is es ima ed by wo successi e qua e nion
o a ions. The i s o a ion is he one be ween magne ic ield
ec o measu ed by he magne ome e in i s e e ence sys em
and he ea h’s magne ic ield ec o es ima ed by a model.
The second o a ion is by sub ac ing he cen ipe al
accele a ion om he accele a ion measu ed by he
accele ome e [8]. The magne ome e -based a i ude
de e mina ion is widely used o spacec a as well as
quadcop e [9]. In quadcop e , hese me hods a e based on he
qua e nions a i ude ep esen a ion. The in o ma ion abou oll
and pi ch angle can be ex ac ed om g a i y poin s which
head o he local e ical down di ec ion.
The magne ome e is used o measu e quadcop e ’s
magne ic ield in ensi y in 3 dimensions. The declina ion (δ)
and inclina ion (Ƞ) a e modeled and p o ided by he Wo ld
Magne ic Model (WMM) o he Na ional Geophysical Da a
Cen e (NGDC). F om his model, he magne ic ec o , which
is exp essed in local na iga ion ame, can be known. In
addi ion, he yaw, pi ch, and oll angle is de e mined by he
magne ome e measu emen s. The g a i y ec o o he ea h
is always poin ing o a local e ical down di ec ion. In
con as , he di ec ion o he magne ic ec o o he ea h
a ies wi h posi ion on he ea h. In yaw mo emen , he
di ec ion o he magne ic ec o is exp essed by he
declina ion and inclina ion o he local na iga ion ame in
Fig. 4.
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Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/7.
Fig. 4. Magne ic ec o o he ea h on local na iga ion ame
The magne ome e -based yaw angle in quadcop e is
de e mined wi h he Ea h’s magne ic ield. Ho izon al
di ec ion o he Ea h’s magne ic ield is poin ing owa d he
magne ic no h o he Ea h. Magne ic no h is de ia ed om
ue no h. I s de ia ion is e e ed as a declina ion angle and
a ies wi h i s posi ion on he Ea h. The yaw angle
de e mina ion om he magne ome e measu emen is
conduc ed as shown in (9) and (10):
(9)
(10)
Whe e Hb is he magne ome e measu emen ec o in body
ame and δ is he declina ion angle o he ea h’s magne ic
ield. The angle ψ can be calcula ed using he equa ion abo e
based on illus a ion in Fig. 4. Ob iously, he e o o oll and
pi ch angle a ec s he accu acy o he de e mined yaw angle.
The e o e, he magne ome e -based yaw aiding me hod should
be applied wi h a alid oll and pi ch angle in o ma ion.
Example o magne ic oll angle de e mina ion can be seen in
Fig. 5.
Fig. 5. Magne ic oll angle de e mina ion
The heading-down plane and he X, Y, and Z plane a e
iden ical, and H ep esen s he p ojec ed magne ic ec o on
his plane. Angle ȠT can be calcula ed by ans o ming he
magne ic ec o om he magne ic ield model o he heading-
down ame. Angle λ is de e mined by he magne ome e
measu emen s, which a e ans o med om he body ame o
he X’, Y’, and Z’ ame. Likewise, he oll angle can be
de e mined by sub ac ing ȠT om λ. This p ocess is gi en by
(11): (11)
The accu acy o magne ic ec o is limi ed o abou 1o in oo
mean squa e by he modeling esolu ion, a ia ion abou ime
and ex e nal dis u bances [10]. The magne ic ield is easily
dis u bed by he en i onmen , hus he magne ome e -based
a i ude me hod should be applied wi h an app op ia e
calib a ion and dis u bance de ec ion. The λ and ȠT angle can
be calcula ed using igonome y o kinema ic mo ing ame
heo em.
D. GPS-based a i ude
GPS holds an impo an ole in a i ude es ima ion because
o i s long- e m accu acy in eading quadcop e ’s posi ion and
eloci y. La ge e o s in low-cos ine ial senso s can be
coun e balanced by da a upda es acqui ed om GPS. Fo
small scaled o a y-wing ai c a , an a i ude es ima ion
me hod using he eloci y measu emen s wi h single an enna
GPS was p oposed; he ime lag o he es ima ed a i ude was
compensa ed wi h he help o measu emen s om gy oscopes
by using he complemen a y il e [11].
A GPS ecei e calcula es i s posi ion by using a me hod
called T ila e a ion which is shown in Fig. 5. Many
ila e a ion algo i hms ha e been p oposed o de e mine
loca ion accu a ely. GPS ecei e calcula es he posi ion,
eloci y and ime based on he da a om he GPS Sa elli e.
Fig. 6. T ila e a ion
The 3D mul i-la e a ion uses he ollowing s anda d equa ions:
(12)
Whe e,
(13)
F om his heo y o ila e a ion, he syn hesized a i ude is
called he pseudo-a i ude. I consis s o an equi alen oll
angle abou he eloci y ec o o he quadcop e , an
equi alen pi ch angle de ined as he ho izon al ligh pa h
angle and an equi alen yaw angle de ined as he e ical
ligh pa h angle. S anda d equa ion usage and qua e nion o
quadcop e a e wo o he mos popula app oaches which a e
used o calcula e pseudo a i ude. The qua e nion and Eule
angles a e bo h common ep esen a ions o he a i ude. The
qua e nion, which ep esen s a o a ion abou a speci ic axis, is
de ined in e ms o ou pa ame e s in a column ec o as seen
in (14). (14)
One essen ial cons ain o he qua e nion in he applica ion is
ha i s no m should be equal o uni y. The qua e nion uni s
om q1 o q3 a e called he ec o pa o he qua e nion, while
H
δ
Ƞ
X
Y
ϕ
ȠT
H
λ
Y
Z
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Recen Inno a ions in Mecha onics (RIiM) Vol. 3. (2016). No. 1-2.
DOI: 10.17667/ iim.2016.1-2/7.
q0 is he scala pa . The inpu s a e he angula a es measu ed
by he gy oscopes and he eloci y wi h espec o g ound in
No h-Eas -Down di ec ion coo dina es acqui ed om he
GPS ecei e , and he ou pu s a e he es ima ed oll angle,
pi ch angle, and yaw angle, compu ed om he qua e nion
es ima ed o he Eule angles can be de i ed by using: [12]
(15)
IV. ATTITUDE AND ORIENTATION SENSOR
The o ien a ion senso s compa ed in his esea ch a e he
GP9 and UM7 senso . They use hei own a i ude es ima ion
in conjunc ion wi h he onboa d accele ome e s, in o de o
measu e changes in eloci y. These eloci y es ima es a e hen
compa ed o eloci ies epo ed by he GPS and p essu e
senso s. Since a i ude inaccu acy is a majo sou ce o eloci y
measu emen e o , i is possible o measu e a i ude by
compa ing he accele ome e -based eloci y wi h GPS-based
eloci y. In Table 1 de ail in o ma ion o GP9 and UM7
AHRS elec onic sys em can be seen.
TABLE I. COMPARISON BETWEEN TWO ATTITUDE SENSOR
Compa ison
GP9
UM7
Powe consump ion
< 150mA a 5.0V
du ing GPS seek.
< 100mA a 5.0V
wi h GPS lock
50mA a 5.0V
Ope a ing empe a u e
-40C o +85C
-40 o +85 C
Communica ion
3.3V TTL UART
3.3V TTL UART,
SPI bus
Ra e o measu es o ien a ion,
eloci y, and posi ion
500 Hz
500 Hz
S a ic pi ch/ oll accu acy
+/- 2 deg ee
+/- 2 deg ee
Dynamic pi ch/ oll accu acy
+/- 1 deg ee
+/- 4 deg ee
S a ic yaw accu acy
+/- 5 deg ee
+/- 5 deg ee
Dynamic yaw accu acy
+/- 1 deg ee
+/- 8 deg ee
Resolu ion
< 0.01 deg ees
0.01 deg ee
Da a ou pu a e
0 o 255 Hz,
selec able da a
0 Hz o 255 Hz
(bina y packe s)
1 Hz o 100 Hz
(NMEA packe s)
I can be concluded ha GP9 has highe le el o sensi i i y o
dynamic mo emen wi h less powe consump ion. Da a ou pu
a e in he o m o accele a ion, angula a es, magne ic ield,
ba ome ic p essu e, GPS al i ude, posi ion, eloci y, a i ude
(qua e nion, Eule Angle). Bo h senso and p ocessing yield
excellen gy o bias s abili y o e empe a u e. Adjus able low-
pass il e and Kalman il e se ings p o ide cus omizable
pe o mance o a ious applica ions. S a es and senso da a
synch onized o GPS posi ion and eloci y using op ional
ex e nal GPS module allows o alignmen calib a ion and
hi d-o de bias and scale ac o empe a u e compensa ion o
accele ome e s, gy os, and magne ome e . Magne ome e so
and ha d-i on calib a ion can be pe o med h ough he se ial
in e ace so wa e.
V. CONCLUSION
Fligh con ol plays an indispensable ole in managing
quadcop e ligh s abili y. Gy oscope and accele ome e a e
jus enough o moni o quadcop e ’s posi ion and mo emen
o ien a ion, bu o coun e he e o ac o and ou side
dis u bance, addi ional senso s such as magne ome e and
GPS a e needed. While gy oscope compa es he angle
be ween he ini ial posi ion and he desi ed posi ion,
magne ome e compa es each ini ial and al e ed angle wi h
ea h magne ic ield in o de o ge he changes in angle. Wi h
his da a, he esul om gy o and magne ic senso can be
compa ed o ge be e eading. GPS has accu a e eading on
quadcop e posi ioning and mo emen . Senso o ien a ion GP9
has highe p ecision on a i ude changes eading, compa ed o
UM7.
ACKNOWLEDGMENT
This wo k has been unded unde he LEADERS - E asmus
Mundus G an (ag eemen numbe 2014-0855/001-001) by
Eu opean Commission, h ough he Educa ion, Audio isual
and Cul u e Execu i e Agency, in he Ac ion Plan 2 o he
yea s 2014-2018.
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Illinois: Ame ican Ins i u e o Ae onau ics and As onau ics.
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