TIME–OPTIMAL MANAGEMENT

BY SEVERAL AIRCRAFT FLOWS

IN POINT-MERGE SCHEMES1

S.I. Kumkov∗, S.G. Pyatko∗∗, M.M. Ovchinnikov∗

World ATM Congress 2016Madrid, Spain, March 08 – 10, 2016

The Frequentis Aviation Arenahttp://www.worldatmcongress.org/the-frequentis-aviation-arena

1 Supported by RFBR Grant 15-01-07909 and by NITA Llc Contract;∗ N.N. Krasovskii Institute of Mathematics and Mechanics, UrB RAS, Ekaterinburg,

Russia, kumkov@imm.uran.ru; ∗∗ NITA Llc., Sankt-Petersburg, Russia.

Topics of presentation

1. References

2. Aim of investigations

3. Standard ideology of merging the aircraft flows

4. Merging aircraft flows in point-merge schemes

5. Main problems and possible solutions of merging in point-

merge schemes

6. Conclusions

7. Demonstration: computer simulation of merging

in two point-merge schemes with different conditions

2

References

[1] Images for merge point.https://www.google.ru/search?q=merge-point&newwindow...

[2] Point Merge Integration of Arrival Flows Enabling Extensive RNAVApplication and Continuous Descent. Operation Services and EnvironmentDefinition. Report, July 2010. Eurocontrol Experimental Center, Bretigny-sur-Orge.http://www.eurocontrol.int/eec/gallery/content/public/

document/eec/report/2008/003_Point_Merge_OSED_V2.0.pdf

[3] Air Traffic Management Technology Demonstration–1 (ATD–1). NASAReport FS-2011-10-01-ARC.[4] Point Merge: improving and harmonising arrival operations with existingtechnology.http://www.eurocontrol.int/services/point-merge-concept

[5] Point Merge in Paris ACC.https://www.youtube.com/watch?v=3W-LECKDhtw

3

References

[6] Point Merge System - new regulations for air traffic at Oslo.https://www.youtube.com/watch?v=rC_X6t_Rbq4

[7] Point merge – a new approach to air traffic control at Dublin //EOLAS Magazine, February, 2012

[8] IRISH AVIATION AUTHORITY POINT MERGE - ICAO.www.icao.int/.../PBN%20and%20PANS%20OPS%20Imp%20Wkshp%2...

[9] Boursier L., Favennec B., Hoffman E.,Trzmiel A., Vergne F., and K.Zeghal. Merging Arrival Flows without Heading Instructions // Proceedingsof the USA/Europe Air Traffic Management R&D Seminar, Barcelona,Spain, July 2007.

[10] Dan Ivanescu, Chris Shaw, Constantine Tamvaclis (EUROCONTROLExperimental Centre, Bretigny–sur–Orge, France), Tarja Kettunen (ISASoftware, Paris, France). Models of Air Traffic Merging Techniques: EvaluatingPerformance of Point Merge.https://www.researchgate.net/.../256497459_Models_of_Air_Traffic_...

4

Aim of investigations

The global aim: creation of the Traffic Manager Adviser

algorithms and software for computer complexes of advanced

automated systems for control of merging the aircraft flows

arriving at airport of landing.

Investigations were performed on the basis of practically

meaning versions of point-merge schemes and trajectories

of aircrafts motions on approach and in aerodrome

zones [1–10].

5

Problem of merging aircraft flows

10_

10

x N, km ( )

20 30

10_

20_

10 z, km

( )E30_

40_

50_

60_

70_

90_

100_

110_

_50

_60

_70

_80

80_

Landing queue

ANITABELLA

ALINA

BIDDY

Flow 120

_

30_

40_

Flow 2 Flow 3

BONNY

DOLLY

DORIS

DENIS

HELEN GLORY

( )H3( )H2

(! at the same altitude )Hmrg

LOISEMerge point: MP

? | | >t t1 2 tmrg__

? | | >t t1 3 tmrg__

? | | >t t2 3 tmrg__

arrvarrv

arrv arrv

arrv arrv

6

Standard technology – delay (holding)on schemes of the “trombone” type

10_

10

x N, km ( )

20 30

10_

20_

10 z, km

( )E30_

40_

50_

60_

70_

90_

100_

110_

_50

_60

_70

_80

80_

Landing queue

ANITA

ALINA

BIDDY

Flow 120

_

30_

40_

Flow 2 Flow 3

BONNY

DOLLY

DORIS

DENIS

HELEN GLORY

BELLA

Delayscheme

( )H2 ( )H3

Delay scheme 2 ( )H2

Delay scheme 3 ( )H3

BETTY

FUNNY

(! at the same altitude )Hmrg

LOISEMerge point: MP

? | | >t t1 2 tmrg__

? | | >t t1 3 tmrg__

? | | >t t2 3 tmrg__

arrvarrv

arrv arrv

arrv arrv

7

Standard simple scheme. Aggravated situation undertwo flows merging. Manual managing and its difficulties.

ANITA

ANITAH

BELLAH

BONNYH

BELLA

BONNY

BELLAH

ALINAH

ALINA

BIDDY

Flow 1

Flow 2

BETTY

NAINA

(! at the same altitude )Hmrg

Merge point

? | | >t t1 2 tmrg__ arrvarrv

BELLAH

BELLAH

BIDDYH

BIDDYH

BIDDYH

t1del

t2del

t1

enter

t2

enter

8

Possible exclusion of inducted conflict situationsby a special two-level trombone (NITA Llc.)

ANITA

DH

Back turn at

tarrive

tenter

ANITAH

BELLAH

the altitude BELLAH

BELLAHBELLABETTY

BONNY

BONNYH

BONNYH

BONNYH

with descendingBack turn

to BONNYH

Lower

Upper

shoulder

shoulder

9

Possible exclusion of the inducted conflict situationsby preliminary holding scheme: special advancedtwo-level anteverted trombone (NITA Llc.) as a stepto the point-merge scheme on approach trajectories

2

13

4ANITADH

ANITAH

BELLAH

BELLA

BONNY

BONNYH

BONNYH

BONNYH

Lower

Upper

shoulder

shoulder

Partial turn atthe altitude BELLAH

Point of return

45 : 60_

with descendingBack turn

to BONNYH

the traceReturn onto

at BONNYH

BETTY

DOLLY

tarrive

tenter

10

Structure of a merge-point scheme for each flow

D

1

43

2

5

Altitude

D

D

D

D

Dof longitudinal

Markers

Horizontal zone of turn onto the starting barrier

of the “fan”

Starting barrier

Conic surface

z

x

of enter

DD

DD

y

Projection of

for visual checkD

L

L

-q

q

V

Finalpoint

Enter point

MP

MPhp

hwa

on “fan”

waiting arc

Waiting arc

separation

of descending

11

Structure of a merge-point scheme for two flows

h I

1

43

2

5

D

DD

DD

D

y

hII

D

D

D

D

DD

DD

DD

DD

DD

DD

DD

Fan II

Fan I

LII

LI

Horizontal zone of turn onto the starting barrier of fan II

Horizontal zone of turnonto the starting barrier of fan I

Starting barrier of descending on fan II

Starting barrier of descending on fan I

Waiting arc II

Waitingarc I

Altitudeof enter II

Altitude of enter I

FP II

FP I

EP II

EP I

of longitudinal

Markers

for visual check

separation

z

x

MP

MPhp

Flow I

Flow II

12

Profile of two-fan scheme for merging two flows

4 3 25 1

+

{

1

r1,2

y

x

h I

yMP

h II

2

-qI

qI

qII

-qII

LII

LI

Markers for visual check of longitudinal separation

MP

MPhp

Trajectoryof descending

on fan I

Trajectoryof descending

on fan II

Starting barrier of descending on fan II

Starting

descending Alt

itu

de

of

ente

r II

Alt

itu

de

of

ente

r I

Waiting arc II

Wai

tin

g a

rc I

barrier of

on fan ITrajectory

of turn

Trajectoryof turn

13

Building non-conflict queue on the two-fan point-mergescheme. Reliable algorithmic and visual check

D

4

3

5x

D

D

D

D

1

2

1

2

4

3

r D>3,4

_

r D>1,2_

r D>2,3

_

arc IWaiting

arc IIWaiting

Altitudeof enter II

Altitudeof enter I

Flow IFlow II

Starting barrier of descending on fan II Starting barrier of descending on fan I

of longitudinal

Markers

for visual check

separation

EP IIEP I3,4

R D>>

and different altitudes

14

Structure of a model complicated five-fan point-mergescheme for merging five (seven) flows

Model five-fan point-merge schemefor processing five main flows andtwo ones with missed landings andapproaches

++

++ +

+

Waiting arcs:

WA2 for Flows 2 and 5

+ + WA4 for Flow 4

+ + WA1 for Flow 11

+ + WA5 for Flow 6

Flow 2

N

E

Flow 2++

+

++++

++++

MP

+

DOLLY

++

++

+ +

Flow 6

+

For missed

FUNNY

BETTY

Flow 4

Flow 4

For missed

Flow 1 BELLA

Flow 7

Flow 3

Flow 7

++ + L1+

NELLY

WA3 for Flows 3 and 7

(0, 0) km

+

Flow 5

Flow 5

+

+

++

+

++++ 5-1

5-2

5-3

5-4

5-5 5-6

1-1

1-2

1-3

1-4

1-5 1-6

2-1

3-2

3-3

3-4

3-53-6

3-1

4-3

4-4

4-5 5-6

+2-2

2-3

2-4

2-5 2-6

4-2

4-1

+L2

+

++L4

L3

RWL5 L6

BONNY

+ALINA

+ADELL

+ANITA

+

HELEN

+

DORIS

+

x, km

z, km

landings

+

+

JANNY

FRANY

++

LILLY

LOISE

+ !?

!?approaches

15

Standard model of aircraft controllable motion

x′ = V cos θ cosψ,z′ = V cos θ sinψ,y′ = V sin θ,V ′ = au1,ψ′ = bu2/V,θ′ = cu3/V,a = const, |u1| ≤ 1,b = const, |u2| ≤ 1,c = const, |u3| ≤ 1,

where x, z, y are coordinates in the ATM system; ψ is theheading; θ is the velocity angle; V is the spacial velocity;a is an admissible value of the longitudinal acceleration ofaircraft; u1 is the control in the longitudinal channel; b is themaximal value of the lateral acceleration; u2 is the control inthe lateral channel; c is is the maximal value of the verticalacceleration; u3 is the control in the vertical channel.

16

Criteria of control (management)

It is necessary to provide:

– obligatory guarantee of the safe longitudinal time interval

τmrg between aircrafts on their trajectories and at the merge-

point;

– minimization of delay time of each aircraft from the instant

of the control beginning till passage of the merge-point with

maximal density of the landing queue;

– desirable: minimization of summary time-on-control

of all aircrafts’ managed groups in flows to be merged.

17

Problem formulation

It is formulated in the following engineering form:

to calculate and implement the minimal-necessary value

of delay (or acceleration) for each aircraft in each flow that

constructively guarantees the maximal density of the merged

flow under obligatory satisfaction of the safe longitudinal

time-interval τmrg between aircrafts in the landing queue.

18

The main approach to manage the aircraft merging.Special forecast of instants of arriving at the mergepoint in a model three flows scheme

0

Flow 2

. . .(2) (3) (4)(1) (15)(14)(13)(12)

0

Flow 3

(2) (3) (4)(1) (15)(14)(13)(12). . .

0

Flow 1

(2) (3) (4)(1) (15)(14)(13)(12). . .

. . .0 2 31 4544435 64 4240 41

Forecastassembly

withconflicts

tarive

nom

tarive

nom

tarive

nom

tarive

nom

19

Non-conflict merged queue

(2) (3) (4)(1) (15)(14)(13)(12)

. . .0

0

input

delayed

Flow 3

. . .

. . .

(2) (3) (4)(1) (15)(14)(13)(12)

0

0

input

delayed

Flow 2

0

input

0 (2) (3) (4)(1) (15)(14)(13)(12). . .

delayed

Flow 1

Merged flow

0

Delayedwithout conflicts.

instants

tmrg(landing queue)

2 31 4544435 64 4240 41in queuenumbers . . . . . .

tarrivenom

tarrivenom

tarrivenom

tarrive

del

tarrive

del

tarrive

del

tarrive

del

20

Special procedures for non-conflict merging

– computation of minimal necessary delays in the preliminary

holding zones or by acceleration/deceleration of aircrafts;

– computation of minimal necessary delays on the waiting

arcs;

– managing the cases of aircrafts with priority (alarm

or urgent ones);

– changing the aircraft sequence in the queue for

minimization of their time of arriving to the merge-point.

21

END of PRESENTATION:

Demonstration of work

of algorithms for

aircraft flows merging.

1. Alarm.avi with input density of 24 aircraft/hour.

2. Model04.avi with input density of 25 aircraft/hour.

22