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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

  1. At most airports predesigned standard routes for departure and arrival: Standard Instrument Departures (SIDs) and Standard Terminal Arrival Routes (STARs) AD 2–ESSA–4–21 STOCKHOLM/ARLANDA AERODROME AD 2–ESSA–4–5 STOCKHOLM/ARLANDA AERODROME AIP-SVERIGE/SWEDEN RWY 01L AIP SWEDEN RWY 01L/01R FMS/RNAV SID STAR Instrument 017° 30’ 018° 00’ 018° 30’ HOLDING 17° 00’ 17° 30’ 18° 00’ 18° 30’ DVOR/DME HMR VOR RESNA KOGAV HAMMAR HMR 112.60 HMR Holding 60° 60° 0 73X elev 102 ft VAR 3.5°-4.5° E 2005 1 See inset figure 00’ 00’ 0 601645.5N 0182329.7E t k 2 1900 2 0 0 E 1 3 0 K 0 2 n O 1 ° – i G S m A 5 085° 265° R L 012° V A F 3 - 5 I C ° . M RESNA 3 C (RESN 3C) 4 1700 2200 X 1 ( K O A N G R M M A 355° 3 A C ) (003.4° T) V HMR 2 < 31.2 > 9 MSA 25 NM ARL VOR 9 ° M ( < 3 0 2 2 4 7 6 . . 7 7 19° 00’ 2 ° R > T 1 60° ) 60° A – 359° M R 00’ 00’ M R A M H H NDB SA403 ERKEN 2 MAX IAS 230 kt 8 6 ERK 383 ° 595346.4N 0182012.8E VOR/DME 1.5 min 2 5 (003.4° T) NORTEL MNM FL 100 DME VOR/DME NTL 116.30 A NORTEL 110X elev 68 ft R ARL 2 L R – 2 3 NTL 116.30 8 6 594459.3N 0184600.6E 110X elev 68 ft < 6.8 > DME ELTOK ARL R–286 594459.3N 0184600.6E ANW 112.05 359° SA402 SA422 57Y elev 163 ft 594247.8N 0175109.2E H M R M E 3 2 N O R T E L 3 C ( N T L 3 C ) D ° T ) 0 7 9 . 9 ELTOK 6M SA401 7 6 ° ( 0 LNA QDM 156° DME 0 8 6 ° ( 0 9 0 . 3 ° T ) ASE 114.45 2 > < 6 . 5 < 1 8 . 7 > 91Y elev 141 ft . 3 1 593813.9N 0175726.5E XILAN DVOR/DME 006° (010.4° T) MAX IAS 230 kt DVOR/DME AROS 056° < 4.0 > DME ARLANDA SA850 ARS 112.80 ARL 116.00 3 ANE 113.30 1 min MNM FL 90 22 1 75X elev 50 ft < 6.2 > 80X elev 108 ft 107X elev141 ft 0 (252.6° T) – 593510.3N 0163901.4E SID 593912.4N 0175451.9E R SA851 594138.3N 0180335.6E R–056 SA701 SA421 27.7 4 9 ° XILAN 3 M 2 > B . 0 4 BABAP 3 C (BABA 3C) 153° (157.1°T) E < (ARL DME 1.3) ° 2 6 1 T TEB R–069 STAR MAX IAS 170 kt XILAN (224.1° T) Holding DME 1 min DVOR/DME ASE 114.45 See inset MNM 2500 AROS 91Y elev 141 ft figure DME ARS 112.80 IAF 221° > 1 ° ASW 113.75 593813.9N 0175726.5E 0 8 75X elev 50 ft 5 MAX IAS 230 kt 4 . 59° 59° ) 84Y elev 232 ft IAF < T Stockholm, 593510.3N 0163901.4E MNM 2500 AROS 4 C (ARS 4C) TEB R–178 178° ° 593515.7N 0174910.9E DVOR/DME DVOR/DME 30’ 30’ 3 > 1 min < 27.5 > < 21.5 > NDB TEBBY . 9 ° T ) 7 . ARLANDA 2 6 3 ° ( 2 6 6 SA723 0 9 Stockholm, LENA TEB 117.10 . ARL 116.00 1 7 LNA 330 ( 107X elev141 ft 118X elev197 ft < 194° 593220.3N 0172130.0E 593154.1N 0181212.0E 593912.4N 0175451.9E SA702 DVOR/DME <2.2> RWY 01L TEBBY 115° TEB 117.10 45 (118.4° T) 118X elev197 ft SA724 RWY 01L/01R < 6.9 > 593154.1N 0181212.0E SA703 59° 59° 218° (221.9° T) 30’ 30’ 0 9 5 ° ( 0 9 9 . 3 ° T ) < 25.4 > < 2 TEB R–178 8 . 7 > MENGA 1 C (MENA 1C) MENGA DUNKER 4C (DKR 4C) < 3 . 0 > BABAP NTL DME 44 LEGEND BABAP See GEN 2.3 M 1 DVOR/DME 1 0 59° 2 59° DVOR TROSA G – 1 U R DUNKER 4 Fly-over wpt TRS 114.30 00’ L 00’ 1 DKR 116.80 I L ° 90X elev 213 ft N T (145.7°) N 591225.8N 0170043.5E 585616.5N 0173008.0E < 30.6 > Fly-by wpt DME 44.2 TEB R–188 MAX IAS 230 kt R–215 Description of ELTOK, NILUG and XILAN TROSA 4 C (TRS 4C) 180° (183.1° T) MNM 5000 1.5 min 215° see AD 2–ESSA–4–6 ) T ° 3 . 9 9 < 35.2 > 1 Tracks are in MAG. NILUG MAX IAS 210 kt ( > ° LEGEND MNM-MAX/Time 6 Tracks within brackets are in True. 6 9 . 8 FL 70-90/1.0 min 1 See GEN 2.3 2 ELEV and ALT in ft MSL MAX IAS 230 kt < 8 8 ° 1.0 min ) NEKLA C 1 8 BRG are MAG MNM FL 100 – 8 4 1 R INITIAL CLIMB CLEARANCE ELEV and ALT in ft MSL L S 18° 30’ 19° 00’ O Common to all SIDs published on this chart. N MAR ( Unless otherwise specified, climb to 5000 ft. HOLDING C 114.70 km 10 0 10 20 30 km 6 XILAN 5 4 1 2 8 . I – L 3 R S E TEB R–069 R O M NM 5 0 10 20 NM A D N M k t 3 0 N 872 2 DVOR/DME A S e X I m M A X / T i TROSA TEB DME 27.7 A n M - M m i N . 5 TRS 114.30 M 5 1 / 2 4 0 0 - L 1 90X elev 213 ft F 069° 585616.5N 0173008.0E NOSLI 58° 58° 30’ 30’ 17° 00’ 17° 30’ 18° 00’ 017° 30’ 018° 00’ 018° 30’ AIRAC AMDT 5/2012 23 AUG 2012 AMDT 80 29 SEP 2005 LFV CHANGE: New STAR NILUG 1M. Deleted TRS 3M, VAR, pagina Swedish Civil Aviation Authority CHANGE: SID to ARS, DKR, NOSLI and TRS 4 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  2. SIDs/STARs: 5 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  3. SIDs/STARs: • Designed manually 5 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  4. SIDs/STARs: • Designed manually • No optimal routes for any specific criteria 5 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 optimal STAR merge trees 5 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  6. Optimal STAR merge trees 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  7. Optimal STAR merge trees Input: 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  8. Optimal STAR merge trees Input: locations of the entry points to the TMA 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  9. Optimal STAR merge trees Input: locations of the entry points to the TMA location and direction of the airport runway 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  10. Optimal STAR merge trees Input: locations of the entry points to the TMA location and direction of the airport runway Output: 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  11. Optimal STAR merge trees 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, 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  12. Optimal STAR merge trees 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 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  13. Optimal STAR merge trees 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) 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  14. Optimal STAR merge trees 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 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  15. Optimal STAR merge trees 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 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  16. Optimal STAR merge trees 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 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  17. Optimal STAR merge trees 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 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  18. Optimal STAR merge trees 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: 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  19. Optimal STAR merge trees 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, 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  20. Optimal STAR merge trees 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) 6 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  21. Optimal STAR merge trees Objective function: 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  22. Optimal STAR merge trees Objective function: ๏ Short flight routes for aircraft 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  23. Optimal STAR merge trees Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  24. Optimal STAR merge trees Objective function: ๏ Short flight routes for aircraft ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  25. Optimal STAR merge trees 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 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  26. Optimal STAR merge trees Objective function: ๏ Short flight routes for aircraft paths length ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  27. Optimal STAR merge trees Objective function: ๏ Short flight routes for aircraft paths length ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges tree weight 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  28. Optimal STAR merge trees Objective function: ๏ Short flight routes for aircraft paths length ➡ Minimize total length of the routes ๏ STAR tree should "occupy little space" ➡ Minimize total length of the edges 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) 7 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  29. Grid-based IP formulation 8 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  30. Grid-based IP formulation 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  31. Grid-based IP formulation ๏ Square grid in the TMA 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  32. Grid-based IP formulation ๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  33. Grid-based IP formulation ๏ Square grid in the TMA ๏ Snap locations of the entry points and the runway onto the grid ๏ P: set of (snapped) entry points 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  34. Grid-based IP formulation ๏ 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 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  35. Grid-based IP formulation ๏ 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) 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  36. Grid-based IP formulation ๏ 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): 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  37. Grid-based IP formulation ๏ 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 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  38. Grid-based IP formulation ๏ 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 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  39. Grid-based IP formulation ๏ 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: 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  40. Grid-based IP formulation ๏ 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) 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  41. Grid-based IP formulation ๏ 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) 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  42. Grid-based IP formulation ๏ 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 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  43. Grid-based IP formulation ๏ 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 ๏ IP formulation is based on flow IP formulation for Steiner trees (Min Cost Flow Steiner arborescence) 9 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  44. Grid-based IP formulation 10 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  45. Grid-based IP formulation decision variables: edge e participates in the STAR. x e 10 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  46. Grid-based IP formulation decision variables: edge e participates in the STAR. x e f e flow variables: gives the flow on edge e = (i, j) (i.e., from i to j ) 10 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  47. Grid-based IP formulation decision variables: edge e participates in the STAR. x e f e flow variables: gives the flow on edge e = (i, j) (i.e., from i to j ) 8 |P| i = r > < X X i ∈ P f ki − f ij = − 1 > k :( k,i ) ∈ E j :( i,j ) ∈ E i ∈ V \ {P ∪ r } 0 : x e ≥ f e ∀ e ∈ E N f e ≥ 0 ∀ e ∈ E x e ∈ { 0 , 1 } ∀ e ∈ E 10 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  48. Grid-based IP formulation Objective functions: X min (1) ` e f e e ∈ E X min (2) ` e x e e ∈ E 11 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  49. Grid-based IP formulation Objective functions: X min (1) ` e f e paths length e ∈ E X min (2) ` e x e e ∈ E 11 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  50. Grid-based IP formulation Objective functions: X min (1) ` e f e paths length e ∈ E X tree weight min (2) ` e x e e ∈ E 11 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  51. Grid-based IP formulation Degree constraints: X x ki ≤ 2 ∀ i ∈ V \ {P ∪ r } k :( k,i ) ∈ E X ∀ i ∈ V \ {P ∪ r } x ij ≤ 1 j :( i,j ) ∈ E X x kr = 1 k :( k,r ) ∈ E X x rj ≤ 0 j :( r,j ) ∈ E X x ki ≤ 0 ∀ i ∈ P k :( k,i ) ∈ E X ∀ i ∈ P x ij = 1 j :( i,j ) ∈ E 12 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  52. Grid-based IP formulation Turn angle constraints: 13 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  53. Grid-based IP formulation Turn angle constraints: A e 13 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  54. Grid-based IP formulation Turn angle constraints: A e a e = | A e | 13 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  55. Grid-based IP formulation Turn angle constraints: A e a e = | A e | X a e x e + x f ≤ a e ∀ e ∈ E f ∈ A e 13 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  56. Grid-based IP formulation SID constraints: We disallow STAR edges to intersect SID edges within distance d from the runway. 14 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  57. Experimental Study: Arlanda Airport 15 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  58. Experimental Study: Arlanda Airport Stockholm TMA: 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  59. Experimental Study: Arlanda Airport Stockholm TMA: ๏ Arlanda’s runway 19L 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  60. Experimental Study: Arlanda Airport Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  61. Experimental Study: Arlanda Airport Stockholm TMA: ๏ Arlanda’s runway 19L ๏ Four main entry points: NILUG, XILAN, HMR, and ARS ๏ Square grids of size 14x20 and 25x30 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  62. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  63. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  64. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  65. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  66. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  67. Experimental Study: Arlanda Airport 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: 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  68. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  69. Experimental Study: Arlanda Airport 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 16 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  70. Experimental Study: Arlanda Airport 17 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  71. Experimental Study: Arlanda Airport 234 Pareto 232 frontier: 230 Tree Weight 228 226 224 222 286 288 290 292 294 296 298 300 302 304 Paths Length 18 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  72. Experimental Study: Arlanda Airport 234 Pareto 232 frontier: 230 Tree Weight 228 226 224 222 286 288 290 292 294 296 298 300 302 304 Paths Length Pareto optimal solutions: 18 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  73. Experimental Study: Arlanda Airport Obstacle avoidance: 19 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  74. Experimental Study: Arlanda Airport Obstacle avoidance: 19 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  75. Experimental Study: Arlanda Airport Obstacle avoidance: 19 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  76. Experimental Study: Arlanda Airport Obstacle avoidance: 19 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  77. Experimental Study: Arlanda Airport Increased Number of Entry Points: 20 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

  78. Experimental Study: Arlanda Airport Increased Number of Entry Points: paths length 20 ATMOS, 25.08.2016 Automatic Design of Aircraft Arrival Routes with Limited Turning Angle

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