Automatic Design of Aircraft Arrival Routes with Limited Turning - - PowerPoint PPT Presentation

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Automatic Design of Aircraft Arrival Routes with Limited Turning - - PowerPoint PPT Presentation

Feb 13, 2024 340 likes •1.57k views

Automatic Design of Aircraft Arrival Routes with Limited Turning Angle Tobias Andersson Granberg, Ta0ana Polishchuk, Valen0n Polishchuk, Chris&ane Schmidt Introduction: Air transportation, SIDs + STARs Grid-based IP formulation Experimental

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Tobias Andersson Granberg, Ta0ana Polishchuk, Valen0n Polishchuk, Chris&ane Schmidt

Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 2

Introduction: Air transportation, SIDs + STARs Grid-based IP formulation Experimental Study: Arlanda Airport Conclusion/Outlook

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

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SLIDE 7

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
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SLIDE 8

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
  • In Air Traffic Management (ATM): humans-in-the-loop!
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SLIDE 9

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
  • In Air Traffic Management (ATM): humans-in-the-loop!

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs)

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SLIDE 10

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
  • In Air Traffic Management (ATM): humans-in-the-loop!

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs) ๏ Safe separation between aircraft

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
  • In Air Traffic Management (ATM): humans-in-the-loop!

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs) ๏ Safe separation between aircraft ➡ Route design should:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
  • In Air Traffic Management (ATM): humans-in-the-loop!

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs) ๏ Safe separation between aircraft ➡ Route design should: ๏ lead to traffic patterns with “low complexity”

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 3

Air transportation:

  • Significant growth over the last decades
  • International Air Transport Association (IATA) projected that the

number of passengers will double to reach 7 billion/year by 2034

  • Terminal Maneuvering Area (TMA), i.e., the area surrounding one or

more neighboring aerodromes, is particularly affected by congestion

  • Design Arrival and Departure procedures ➜ higher throughput
  • In Air Traffic Management (ATM): humans-in-the-loop!

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs) ๏ Safe separation between aircraft ➡ Route design should: ๏ lead to traffic patterns with “low complexity” ๏ avoid creating conflict points

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 4

At most airports predesigned standard routes for departure and arrival:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 4

At most airports predesigned standard routes for departure and arrival: Standard Instrument Departures (SIDs) and Standard Terminal Arrival Routes (STARs)

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 4

017° 30’ AMDT 80 29 SEP 2005 CHANGE: SID to ARS, DKR, NOSLI and TRS Swedish Civil Aviation Authority AD 2–ESSA–4–21 RWY 01L AIP-SVERIGE/SWEDEN STOCKHOLM/ARLANDA AERODROME FMS/RNAV SID 018° 00’ 60° 00’ 59° 30’ 018° 00’ 017° 30’ 59° 30’ 60° 00’ 018° 30’ 018° 30’ K O G A V 3 C ( K O G A 3 C ) ( 3 2 . 7 ° T ) < 2 6 . 2 > SA403 RESNA 3 C (RESN 3C) KOGAV SA850 BABAP DKR 116.80 DVOR DUNKER 591225.8N 0170043.5E NOSLI LEGEND See GEN 2.3 Tracks are in MAG. Tracks within brackets are in True. ELEV and ALT in ft MSL VAR 3.5°-4.5° E 2005 Fly-over wpt Fly-by wpt INITIAL CLIMB CLEARANCE Common to all SIDs published on this chart. Unless otherwise specified, climb to 5000 ft. 585616.5N 0173008.0E TROSA DVOR/DME TRS 114.30 90X elev 213 ft 593510.3N 0163901.4E AROS DVOR/DME ARS 112.80 75X elev 50 ft 594138.3N 0180335.6E ANE 113.30 80X elev 108 ft 594247.8N 0175109.2E DME ANW 112.05 57Y elev 163 ft 593515.7N 0174910.9E DME ASW 113.75 84Y elev 232 ft 594459.3N 0184600.6E NORTEL VOR/DME NTL 116.30 110X elev 68 ft DME 593154.1N 0181212.0E TEBBY DVOR/DME TEB 117.10 118X elev197 ft 593912.4N 0175451.9E ARLANDA DVOR/DME ARL 116.00 107X elev141 ft RESNA (003.4° T) < 31.2 > SA401 ( 7 9 . 9 ° T ) < 6 . 2 > ( 9 . 3 ° T ) < 1 8 . 7 > SA402 N O R T E L 3 C ( N T L 3 C ) (003.4° T) < 6.8 > (010.4° T) < 4.0 > SA421 (ARL DME 1.3) SA851 < 4 . > < 6.2 > SA723 < 4 . 5 > (224.1° T) AROS 4 C (ARS 4C) SA701 2 6 3 ° ( 2 6 6 . 9 ° T ) MENGA 1 C (MENA 1C) ( 9 9 . 3 ° T ) < 2 8 . 7 > TROSA 4 C (TRS 4C) 180° (183.1° T) < 35.2 > ( 1 9 7 . 3 ° T ) < 7 . > (118.4° T) < 6.9 > SA702 SA703 BABAP NEKLA < 30.6 > (145.7°) 593813.9N 0175726.5E DME ASE 114.45 91Y elev 141 ft 2 9 9 ° 359° 359° 7 6 ° 006° 2 4 9 ° (252.6° T) 221° 1 4 1 ° 9 5 ° 115° 194° 8 6 ° SA422 MENGA BABAP 3 C (BABA 3C) 153° (157.1°T) < 21.5 > < 3 . > < 27.5 > DUNKER 4C (DKR 4C) 218° (221.9° T) < 25.4 > <2.2> N O S L I 4 C ( N O S L 4 C ) 1 9 6 ° ( 1 9 9 . 3 ° T ) < 2 8 . 6 > SA724

At most airports predesigned standard routes for departure and arrival: Standard Instrument Departures (SIDs) and Standard Terminal Arrival Routes (STARs)

AIRAC AMDT 5/2012 23 AUG 2012 CHANGE: New STAR NILUG 1M. Deleted TRS 3M, VAR, pagina LFV AD 2–ESSA–4–5 RWY 01L/01R AIP SWEDEN STOCKHOLM/ARLANDA AERODROME STAR Instrument LEGEND See GEN 2.3 BRG are MAG ELEV and ALT in ft MSL km 10 0 10 20 30 km NM 5 0 10 20 NM Description of ELTOK, NILUG and XILAN see AD 2–ESSA–4–6 V A R 4 °
  • 5
° E 2 1 17° 00’ 17° 30’ 18° 30’ 19° 00’ 18° 00’ 17° 00’ 17° 30’ 18° 00’ 18° 30’ 19° 00’ 58° 30’ 60° 00’ 59° 30’ 59° 30’ 59° 00’ 60° 00’ 59° 00’ 58° 30’ HOLDING HMR VOR 593154.1N 0181212.0E TEBBY DVOR/DME TEB 117.10 118X elev197 ft 585616.5N 0173008.0E TROSA DVOR/DME TRS 114.30 90X elev 213 ft 593912.4N 0175451.9E ARLANDA DVOR/DME ARL 116.00 107X elev141 ft LNA 330 NDB LENA 593220.3N 0172130.0E 601645.5N 0182329.7E HAMMAR DVOR/DME HMR 112.60 73X elev 102 ft HMR M A X I A S 2 3 k t 1 . 5 m i n M N M F L 1 R – 1 2 012° XILAN TEB R–178 178° MAX IAS 230 kt 1 min MNM 2500 HMR Holding See inset figure XILAN Holding See inset figure A R L R – 2 8 6 2 8 6 ° MAX IAS 230 kt 1.5 min MNM FL 100 R–056 056° MAX IAS 230 kt 1 min MNM FL 90 MAX IAS 170 kt 1 min MNM 2500 2 6 1 ° R–215 215° MAX IAS 230 kt 1.5 min MNM 5000 069° M A X I A S 2 3 k t M N M
  • M
A X / T i m e F L 1
  • 2
4 5 / 1 . 5 m i n ELTOK 8 1 ° XILAN 3 M TEB R–069 27.7 IAF ELTOK 6M LNA QDM 156° 22 45 T E B R – 1 3 1 3 . 5 H M R D M E 3 2 H M R R – 1 7 7 3 2 H A M M A R 4 M MAR 114.70 N 872 TEB DME 27.7 TEB R–069 M A R R – 2 1 6 D M E 3 8 . 5 HOLDING XILAN IAF 594459.3N 0184600.6E NORTEL VOR/DME NTL 116.30 110X elev 68 ft 593510.3N 0163901.4E AROS DVOR/DME ARS 112.80 75X elev 50 ft ERK 383 NDB ERKEN 595346.4N 0182012.8E 593813.9N 0175726.5E DME ASE 114.45 91Y elev 141 ft DME ARL 2 5 ARL R–286 MSA 25 NM ARL VOR 1900 085° 265° 355° 2200 1700 MAX IAS 210 kt MNM-MAX/Time FL 70-90/1.0 min MAX IAS 230 kt 1.0 min MNM FL 100 R – 1 8 8 1 8 8 ° NTL DME 44 TEB R–178 N T L R – 2 1 N I L U G 1 M NILUG TEB R–188 DME 44.2

STAR Stockholm, RWY 01L/01R SID Stockholm, RWY 01L

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 5

SIDs/STARs:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 5

SIDs/STARs:

  • Designed manually
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 5

SIDs/STARs:

  • Designed manually
  • No optimal routes for any specific criteria
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 5

SIDs/STARs:

  • Designed manually
  • No optimal routes for any specific criteria
  • here: mathematical programming framework for finding
  • ptimal STAR merge trees
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway,

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
  • 2. Merge point separation: distance threshold L
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
  • 2. Merge point separation: distance threshold L
  • 3. No sharp turns: angle threshold 𝛽, minimum edge length L
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
  • 2. Merge point separation: distance threshold L
  • 3. No sharp turns: angle threshold 𝛽, minimum edge length L
  • 4. Obstacle avoidance
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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
  • 2. Merge point separation: distance threshold L
  • 3. No sharp turns: angle threshold 𝛽, minimum edge length L
  • 4. Obstacle avoidance
  • 5. STAR–SID separation:
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SLIDE 34

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
  • 2. Merge point separation: distance threshold L
  • 3. No sharp turns: angle threshold 𝛽, minimum edge length L
  • 4. Obstacle avoidance
  • 5. STAR–SID separation:

STAR–SID crossings far from the runway,

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SLIDE 35

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

6

Input: locations of the entry points to the TMA location and direction of the airport runway Output: arrival tree that merges traffic from the entries to the runway, i.e., a tree that has the entries as leaves and the runway as the root (arborescence oriented differently than usual)

  • 1. No more than two routes merge at a point: in-degree ≤ 2
  • 2. Merge point separation: distance threshold L
  • 3. No sharp turns: angle threshold 𝛽, minimum edge length L
  • 4. Obstacle avoidance
  • 5. STAR–SID separation:

STAR–SID crossings far from the runway,

where arriving and departing planes sufficiently separated vertically (difference of descend and climb slopes)

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function:

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space"

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges paths length

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges paths length tree weight

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Optimal STAR merge trees

7

Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges paths length tree weight Pareto frontier of multicriteria optimization problem: set of Pareto optimal solutions (cannot be improved with respect to one of the objectives without sacrificing on the other)

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 8

Grid-based IP formulation

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points

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SLIDE 49

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway

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ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation)

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SLIDE 51

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E):

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SLIDE 52

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors

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SLIDE 53

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ G is bi-directed

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SLIDE 54

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ G is bi-directed ๏ Only exceptions:

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SLIDE 55

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ G is bi-directed ๏ Only exceptions: ๏ Entry points (no incoming edges)

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SLIDE 56

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ G is bi-directed ๏ Only exceptions: ๏ Entry points (no incoming edges) ๏ r (no outgoing edges)

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SLIDE 57

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ G is bi-directed ๏ Only exceptions: ๏ Entry points (no incoming edges) ๏ r (no outgoing edges) ๏ length of an edge (i, j)

`i,j

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SLIDE 58

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

9

๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points ๏ r: runway ๏ Side of the grid pixel: L (➜merge point separation) ๏ G = (V,E): ๏ Every grid node connected to its 8 neighbors ๏ G is bi-directed ๏ Only exceptions: ๏ Entry points (no incoming edges) ๏ r (no outgoing edges) ๏ length of an edge (i, j) ๏ IP formulation is based on flow IP formulation for Steiner trees (Min Cost Flow Steiner arborescence)

`i,j

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SLIDE 59

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

10

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SLIDE 60

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

10

decision variables: edge e participates in the STAR.

xe

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SLIDE 61

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

10

decision variables: edge e participates in the STAR. flow variables: gives the flow on edge e = (i, j) (i.e., from i to j )

xe fe

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SLIDE 62

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

10

decision variables: edge e participates in the STAR. flow variables: gives the flow on edge e = (i, j) (i.e., from i to j )

xe fe

X

k:(k,i)∈E

fki − X

j:(i,j)∈E

fij = 8 > < > : |P| i = r −1 i ∈ P i ∈ V \ {P ∪ r} xe ≥ fe N ∀e ∈ E fe ≥ 0 ∀e ∈ E xe ∈ {0, 1} ∀e ∈ E

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SLIDE 63

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

11

Objective functions: min X

e∈E

`efe (1) min X

e∈E

`exe (2)

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SLIDE 64

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

11

Objective functions: min X

e∈E

`efe (1) min X

e∈E

`exe (2)

paths length

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SLIDE 65

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

11

Objective functions: min X

e∈E

`efe (1) min X

e∈E

`exe (2)

paths length tree weight

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SLIDE 66

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

12

Degree constraints:

X

k:(k,i)∈E

xki ≤ 2 ∀i ∈ V \ {P ∪ r} X

j:(i,j)∈E

xij ≤ 1 ∀i ∈ V \ {P ∪ r} X

k:(k,r)∈E

xkr = 1 X

j:(r,j)∈E

xrj ≤ 0 X

k:(k,i)∈E

xki ≤ 0 ∀i ∈ P X

j:(i,j)∈E

xij = 1 ∀i ∈ P

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SLIDE 67

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

13

Turn angle constraints:

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SLIDE 68

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

13

Turn angle constraints:

Ae

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SLIDE 69

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

13

Turn angle constraints:

Ae

ae = |Ae|

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SLIDE 70

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

13

Turn angle constraints: aexe + X

f∈Ae

xf ≤ ae ∀e ∈ E

Ae

ae = |Ae|

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SLIDE 71

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Grid-based IP formulation

14

SID constraints:

We disallow STAR edges to intersect SID edges within distance d from the runway.

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SLIDE 72

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 15

Experimental Study: Arlanda Airport

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SLIDE 73

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA:

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SLIDE 74

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L

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SLIDE 75

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS

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SLIDE 76

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30

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SLIDE 77

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with

slide-78
SLIDE 78

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions

slide-79
SLIDE 79

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions ❖ Degree constraints

slide-80
SLIDE 80

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions ❖ Degree constraints ❖ Turn Angle constraints

slide-81
SLIDE 81

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions ❖ Degree constraints ❖ Turn Angle constraints ๏ 8 grid directions

slide-82
SLIDE 82

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions ❖ Degree constraints ❖ Turn Angle constraints ๏ 8 grid directions ๏ Postprocessing for smoother paths:

slide-83
SLIDE 83

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions ❖ Degree constraints ❖ Turn Angle constraints ๏ 8 grid directions ๏ Postprocessing for smoother paths: shortcuts by removing vertices as long as the turn angle constraint is not violated

slide-84
SLIDE 84

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

16

Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 ๏ Solve IP with ❖ Both objective functions ❖ Degree constraints ❖ Turn Angle constraints ๏ 8 grid directions ๏ Postprocessing for smoother paths: shortcuts by removing vertices as long as the turn angle constraint is not violated

slide-85
SLIDE 85

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

17

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SLIDE 86

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

18

222 224 226 228 230 232 234 286 288 290 292 294 296 298 300 302 304

Tree Weight Paths Length

Pareto frontier:

slide-87
SLIDE 87

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

18

222 224 226 228 230 232 234 286 288 290 292 294 296 298 300 302 304

Tree Weight Paths Length

Pareto frontier: Pareto optimal solutions:

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SLIDE 88

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

19

Obstacle avoidance:

slide-89
SLIDE 89

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

19

Obstacle avoidance:

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SLIDE 90

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

19

Obstacle avoidance:

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SLIDE 91

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

19

Obstacle avoidance:

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SLIDE 92

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

slide-93
SLIDE 93

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length

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SLIDE 94

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length

slide-95
SLIDE 95

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length

slide-96
SLIDE 96

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length

slide-97
SLIDE 97

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

slide-98
SLIDE 98

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

slide-99
SLIDE 99

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

slide-100
SLIDE 100

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

slide-101
SLIDE 101

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight serve the airlines’ request for short trajectories best

slide-102
SLIDE 102

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight serve the airlines’ request for short trajectories best quite dense network

  • f routes ➜
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SLIDE 103

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight serve the airlines’ request for short trajectories best quite dense network

  • f routes ➜

hard to control the traffic

slide-104
SLIDE 104

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight most merge points are located close to TMA boundary serve the airlines’ request for short trajectories best quite dense network

  • f routes ➜

hard to control the traffic

slide-105
SLIDE 105

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight most merge points are located close to TMA boundary serve the airlines’ request for short trajectories best quite dense network

  • f routes ➜

hard to control the traffic

➜helpful to use linear combination of these two functions

slide-106
SLIDE 106

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

➜helpful to use linear combination of these two functions

slide-107
SLIDE 107

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

➜helpful to use linear combination of these two functions

Solutions for large number of entry points could be used to suggest the number and location

  • f entry points for a

design from scratch.

slide-108
SLIDE 108

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

➜helpful to use linear combination of these two functions

Solutions for large number of entry points could be used to suggest the number and location

  • f entry points for a

design from scratch. 2 entry points

slide-109
SLIDE 109

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

20

Increased Number of Entry Points:

paths length tree weight

➜helpful to use linear combination of these two functions

Solutions for large number of entry points could be used to suggest the number and location

  • f entry points for a

design from scratch. 2 entry points 16 entry points

slide-110
SLIDE 110

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

21

SID constraints:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Each tree: within approximately 2 CPU hours (105 B&B nodes)

slide-111
SLIDE 111

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

22

SID constraints:

200 210 220 230 240 250 260 270 280 290 1 2 3 4 5 6 7 8 9 10 11 12 13

Paths Length Radius

slide-112
SLIDE 112

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

22

SID constraints:

200 210 220 230 240 250 260 270 280 290 1 2 3 4 5 6 7 8 9 10 11 12 13

Paths Length Radius

d 1

slide-113
SLIDE 113

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

Experimental Study: Arlanda Airport

22

SID constraints:

200 210 220 230 240 250 260 270 280 290 1 2 3 4 5 6 7 8 9 10 11 12 13

Paths Length Radius

d 1

slide-114
SLIDE 114

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 23

Conclusion/Outlook

slide-115
SLIDE 115

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

slide-116
SLIDE 116

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle

slide-117
SLIDE 117

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle Easily integrates constraints from the departure routes

slide-118
SLIDE 118

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle Easily integrates constraints from the departure routes Static obstacles, e.g., no-fly zones, can be added

slide-119
SLIDE 119

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle Easily integrates constraints from the departure routes Static obstacles, e.g., no-fly zones, can be added Might choose to minimize weighted version: minimize the sum of trajectory lengths flown by all arriving aircraft (easily integrated by changing right-hand side of first equation)

slide-120
SLIDE 120

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle Easily integrates constraints from the departure routes Static obstacles, e.g., no-fly zones, can be added Might choose to minimize weighted version: minimize the sum of trajectory lengths flown by all arriving aircraft (easily integrated by changing right-hand side of first equation) Outlook:

slide-121
SLIDE 121

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle Easily integrates constraints from the departure routes Static obstacles, e.g., no-fly zones, can be added Might choose to minimize weighted version: minimize the sum of trajectory lengths flown by all arriving aircraft (easily integrated by changing right-hand side of first equation) Outlook: Simultaneous design of both SIDs and STARs

slide-122
SLIDE 122

ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle 24

Proof of concept for our grid-based IP approach for finding aircraft arrival routes with limited turning angle Easily integrates constraints from the departure routes Static obstacles, e.g., no-fly zones, can be added Might choose to minimize weighted version: minimize the sum of trajectory lengths flown by all arriving aircraft (easily integrated by changing right-hand side of first equation) Outlook: Simultaneous design of both SIDs and STARs 3D routes