Air Traffic Complexity: An Input-Output Approach - ATM Seminar · Input-Output Approach (3) Def1:...

Air Traffic Complexity: An Input-Output Approach

Amy R Pritchett, Keumjin Lee and Eric JM Feron

School of Aerospace Engineering

Georgia Tech

2

Motivation

� Efforts to balance air traffic demand and airspace capacity� Traffic Flow Management (TFM):

Regulate traffic flows based on current and future traffic configuration

� Dynamic Airspace Configuration (DAC): Reconfigure the airspace in accordance with the users’demands and the traffic complexity

� Free Flight:While aircraft can ‘go any where’, may still need to prevent aircraft from entering any locally complex areas

All these methods require ability to assess ‘air traffic complexity’ in an operationally relevant manner

3

Previous Efforts

■ Combination of factors ■ Perceived levels of the complexity

We build upon these methods by examining the control impact required within an airspace configuration

■ Air traffic complexity metric

4

Input-Output Approach

Air traffic inside sector:

?No uncertainty

?Uncertainty

Reference Inputs Signal of interest :

Environment :

Air route structure

Air traffic inside sector:

No uncertainty

Uncertainty

An additional aircraft

Signal of interest :Control activity

Control architecture:

?Minimum control activityControl architecture:

Minimum control activity

Environment :Weather

Sector boundary closure

5

Input-Output Approach (2)

� Model airspace as a closed loop system� Build a map of the system’s response to all

possible instances of the reference signal

� Describe air traffic complexity from the input-output response

� Extensibile� Different airspace models

� External environmental factors

6


� Def1: Reference input is any hypothetical aircraft entering the sector of interest at any heading and location

� Def2: Air traffic complexity is a measure of the control activity required to accept a hypothetical aircraft entering into the sector. � “Absolute” complexity is based on optimal (minimum) control activity� “Relative” complexity specific to a sub-optimal controller denotes the

additional complexity

7


Def 3: The entering aircraft position angle defines the entry position of the aircraft into the sector as an angle representing its position relative to the sector center

Def 4: The entering aircraft bearing defines the relative track of an entering aircraft with respect to the line connecting the aircraft to the center of the sector

Nominal aircraft

Entering aircraft position angle

Entering aircraft bearing angle

Sector boundary

Entering aircraft

8

Details Of The System

� Detail of the plant used in our examples� Safety regions around each aircraft� Horizontal motion of aircraft� Only one impulsive turn� Constant velocity

� Control architecture� Ref: Pallottino, L., Feron, E., and Bicchi, A., “ Conflict

resolution problems for air traffic management systems solved with mixed integer programming”, IEEE, Trans. Intelligent Transportation System, Vol.3, No.1, 2002

� Does not preclude more extensive models

9

Details Of The System (2)

� Conflict geometry� Relative velocity vector V2/1

should point outsideforbidden area

2V

1V

1/2V

Safety region

Forbidden Area

10

Comparing Two Traffic Situations

−30 −20 −10 0 10 20 30

−20

−15

−10

−5

0

5

10

15

20

intruder position & heading angle

x−axis (nmi)

y−ax

is (

nmi)

Traffic Situation No. 1

−30 −20 −10 0 10 20 30

−20

−15

−10

−5

0

5

10

15

20


x−axis (nmi)

y−ax

is (

nmi)

Traffic Situation No. 1Traffic Situation 1

−30 −20 −10 0 10 20 30

−20

−15

−10

−5

0

5

10

15

20


x−axis (nmi)

y−ax

is (

nmi)

Traffic Situation No. 2

−30 −20 −10 0 10 20 30

−20

−15

−10

−5

0

5

10

15

20


x−axis (nmi)

y−ax

is (

nmi)

Traffic Situation No. 2Traffic Situation 2

Both are conflict free airspace right now – can measure complexity as result in an entering aircraft

11

Complexity Map of Traffic Situation #1

■ Contours of minimum control activity required to accept entering aircraft

Intruder position angle (deg)

Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)

Entering aircraft position angle (deg)

En

teri

ng

air

craf

t b

eari

ng

(d

eg)


Ent

erin

g ai

rcra

ft be

arin

g (d

eg)

12

Complexity Map of Traffic Situation #1 (2)

■ Particular entering aircraft (Position=120°, Bearing=20°)

● Heading change

● Entry position

● Uncertainty

■ Special attention on some parts of the sector boundary


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


En

teri

ng

air

craf

t b

eari

ng

(d

eg)


Ent

erin

g ai

rcra

ft be

arin

g (d

eg)

0/CC

0/C

CC/0C/0

13

Complexity Map of Traffic Situation #2

■ Contours of minimum control activity required to accept entering aircraft


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)

Minimum heading changes required (deg)


Intr

uder

bea

ring

angl

e (d

eg)



En

teri

ng

air

craf

t b

eari

ng

(d

eg)

Ent

erin

g ai

rcra

ft be

arin

g (d

eg)


14

Scalar Measures of Air Traffic Complexity

� Many possible scalar measures� Worst-case value

• Sensitivity to inputs

� Average value• Overall input-output response

� The area enclosed on a complexity map• How often aircraft need to be controlled

� Many other methods are possible

15

Comparing Two Complexity Maps

■ Traffic situation 1: Larger maximum control activity

■ Traffic situation 2: Larger range of entering aircraft position and bearing angles require control activity of at least 10 degrees


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)


En

teri

ng

air

craf

t b

eari

ng

(d

eg)


Ent

erin

g a

ircra

ft b

earin

g (

deg

)


Intr

uder

bea

ring

angl

e (d

eg)


Intr

uder

bea

ring

angl

e (d

eg)



Intr

uder

bea

ring

angl

e (d

eg)



En

teri

ng

air

craf

t b

eari

ng

(d

eg)

Entering aircraft position angle (deg)E

nter

ing

airc

raft

bea

ring

(d

eg)

16

Partially Closed Sector Boundary

■ Partial closure of sector’s boundary due to dynamic airspace management restrictions

-30 -20 -10 0 10 20 30

-20

-15

-10

-5

0

5

10

15

20

x-axis (nmi)

y-ax

is (

nmi)

A closed part of the sector boundary

Traffic situation 3

17

Complexity Map: No Boundary Closure

intruder position angle (deg)

intru

der h

eadi

ng a

ngle

(deg

)

J(sum of heading) vs intruder position & heading angle

55

45

5

2525

35

55

35

55

15

5

15

15

15

5

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80

intruder position angle (deg)intruder position angle (deg)

intru

der h

eadi

ng a

ngle

(deg

)


55

45

5

2525

35

55

35

55

15

5

15

15

15

5

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80

Required heading changes : nominal case


Intru

der b

earin

g an

gle

(deg

)


intru

der h

eadi

ng a

ngle

(deg

)


55

45

5

2525

35

55

35

55

15

5

15

15

15

5

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80

Required heading changes : nominal case


Intru

der b

earin

g an

gle

(deg

)


intru

der h

eadi

ng a

ngle

(deg

)

55

45

5

2525

35

55

35

55

15

5

15

15

15

5

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80


Ente

ring

airc

raft

bear

ing

(deg

)


Ent

erin

g ai

rcra

ft be

arin

g (d

eg)

18


intru

der h

eadi

ng a

ngle

(deg

)


75

5

8575

75

5565

45

1535

15 5

555

4565

6565

55

5

25

35

35

15

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80

Required heading changes : Sector closed


Intru

der b

earin

g an

gle

(deg

)


intru

der h

eadi

ng a

ngle

(deg

)


75

5

8575

75

5565

45

1535

15 5

555

4565

6565

55

5

25

35

35

15

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80


intru

der h

eadi

ng a

ngle

(deg

)


75

5

8575

75

5565

45

1535

15 5

555

4565

6565

55

5

25

35

35

15

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80



Intru

der b

earin

g an

gle

(deg

)


intru

der h

eadi

ng a

ngle

(deg

)


75

5

8575

75

5565

45

1535

15 5

555

4565

6565

55

5

25

35

35

15

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80


intru

der h

eadi

ng a

ngle

(deg

)


75

5

8575

75

5565

45

1535

15 5

555

4565

6565

55

5

25

35

35

15

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80



Intru

der b

earin

g an

gle

(deg

)


intru

der h

eadi

ng a

ngle

(deg

)

75

5

8575

75

5565

45

1535

15 5

555

4565

6565

55

5

25

35

35

15

5

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

80


Ente

ring

airc

raft

bear

ing

(deg

)


Ent

erin

g ai

rcra

ft be

arin

g (d

eg)

Complexity Map: Partially Closed Boundary

67% increase on the average value

19

Comparing Scalar Measures Across Situations

85.2361.3845.5170.10Worst-case(deg)

13.227.904.325.00Average (deg)

Traffic #3 (P)Traffic #3 (N)Traffic #2Traffic #1

67% increase

39% increase

N: Nominal sector with no boundary closure

P: Sector with partially closed boundary

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Conclusion

� Proposed input-output approach� Define air traffic complexity as the closed-loop response

of the airspace against reference inputs� Complexity map displays the effective complexity of the

traffic situation in a manner suitable for minute-by-minute decisions

� Scalar measures provide succinct measures of traffic situation

� Can evaluate a number of effects� Impact of near-term decisions (e.g., aircraft acceptance)� (on-going) Use to evaluate airway structures within

airspace� (on-going) Use in a predictive manner

21

Thank you very much for listening

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Air Traffic Complexity: An Input-Output Approach - ATM Seminar · Input-Output Approach (3) Def1:...

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