Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution with Time Constraints inTrajectory-Based Arrival Management
A. Valenzuela1 D. Rivas1 R. Vázquez1
I. del Pozo2 M. Vilaplana2
1Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Spain
2Boeing Research and Technology Europe, Madrid, Spain
The Second SESAR Innovation DaysBraunschweig, Germany, 27-29 November 2012
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 1 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 2 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 3 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Introduction
Arrival management involves two high-level functions at the strategic level:
tra�c management: performs runway assignment, sequencing and scheduling.separation management: synthesizes intents that meet the tra�cmanagement schedule and ensures that the arrival plan is con�ict free.It relies on the combination of TP, CD, and CR functions.
Objective of this work: development of a CR algorithm to generatee�cient, con�ict-free trajectories that meet the scheduled times of arrival,using parametric optimization theory.
Hard constraint: to maintain safe separation.Primary objective: to meet the schedule (or at least to be as close as possible).Secondary objective: to minimize the deviation from the intended trajectories.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 4 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Resolution algorithm
Centralized and strategic.
Based on the parameterization of the �ight intents (prede�nedtrajectory patterns). Advantages:
simplicity: intents described in terms of a small number of parameters.�yability: standard airline procedures and ATC regulations are considered.
The CR problem is formulated as a multivariable optimization problemsubject to constraints. It is solved in three steps:
1 avoidance,2 recovery, and3 optimization.
Trajectory modeling: dynamic, nonlinear point-mass model with variablemass.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 5 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 6 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Trajectory Patterns
They are �ight intents that can be described in terms of a small number ofparameters. Some parameters are �xed, whereas others are free.
The optimization is performed on the set of free parameters.
They model both the vertical pro�le and the lateral pro�le.
Two types of trajectory patterns are considered:
Nominal trajectory patterns: which model the aircraft intended (preferred)trajectories.Resolution trajectory patterns: which model the aircraft resolutiontrajectories. They are modi�cations of the nominal trajectory patterns.
Each aircraft can have a di�erent resolution trajectory pattern assigned.
Simpli�cations: instantaneous heading, path-angle and thrust changes.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 7 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Nominal Trajectory Pattern (Vertical Pro�le)
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 8 / 29
constant M, constant h cruise,
horizontal deceleration to reach Md ,
idle Mach/CAS descent until 10000 ft,
horizontal deceleration to reach 250 kt,
constant CAS descent until glide-pathinterception altitude,
standard �nal approach.
Introduction T Patterns T Prediction CD CR Results Summary & FW
Resolution Trajectory Patterns
Lateral pro�le: waypoint changes (vectoring) between the TMA entry pointand the IAF, keeping �xed the total number of waypoints.
Vertical pro�le: speed changes above 10000 ft: cruise Mach (Mc), descentMach (Md) and descent CAS (CASd).
Di�erent patterns are considered depending on the �ight phase the aircraftis �ying when it enters the TMA:
Pattern A: the aircraft enters TMA while cruising.Pattern B: the aircraft enters TMA while cruising, between CSR and TODpoints.Pattern C: the aircraft enters TMA while descending, �ying theconstant-Mach descent segment.Pattern D: the aircraft enters TMA while descending, �ying the constant-CASdescent segment.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 9 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Resolution Trajectory Pattern A (Vertical Pro�le)
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 10 / 29
Free parameters: x=[λk ,ϕk ,M
∗c ,M
∗d ,CAS
∗d
].
x de�nes the aircraft trajectory: given x, thetrajectory y(x) can be computed.
New �ight segment: horizontal acel./decel.from Mc to M∗c .
Pattern constraints, cTP(x)≤ 0:
• |M∗c −Mc | ≤ 0.1Mc ,∣∣M∗d −Md
∣∣≤ 0.1Md ,∣∣CAS∗d −CASd
∣∣≤ 0.1CASd
• M∗d ≤M∗c• CAS∗d ≥ 250kt
• 10000ft≤ hTR(M∗d ,CAS
∗d
)≤ hCR Transition altitude between 10000 ft and the
cruise altitude
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 11 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Trajectory Prediction
Scalar equations considered for �ight in a vertical plane (heading angle χA):
mdVdt
= T −D(V ,h,L)−mg sinγ
mVdγ
dt= L−mg cosγ
dmdt
=−c(V ,h)T
(RE +h)dϕ
dt= V cosγ cosχA
(RE +h)cosϕdλ
dt= V cosγ sinχA
dhdt
= V sinγ
G1 (V ,γ,m,ϕ,λ ,h,T ,L,t) = 0
G2 (V ,γ,m,ϕ,λ ,h,T ,L,t) = 0
DAE system reduced to ODE system through the explicit utilization of the �ightconstraints.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 12 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 13 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Detection
Horizontal distance is measured (along a great circle):
dij = RE cos−1 [sinϕi sinϕj + cosϕi cosϕj cos(λj −λi )]
The separation minimum considered, ds , depends on the wake turbulenceseparation minima:
Preceding aircraftHeavy Medium Light
Succeeding Heavy 4 3 3aircraft Medium 5 3 3
Light 6 5 3
ICAO DOC-4444
dij is measured at discrete times:
tk = t0 +k∆t
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 14 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 15 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution: 2-step Algorithm
2-step Algorithm
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 16 / 29
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Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution: 2-step Algorithm
2-step Algorithm
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Phase 1: sequential, aircraft areprocessed according to the land-ing sequence.While aircraft i is processed,the only con�icts considered arethose with the i−1 previous air-craft.
Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution: 2-step Algorithm
2-step Algorithm
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 16 / 29
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Phase 1: sequential, aircraft areprocessed according to the land-ing sequence.
Avoidance: a con�ict-freetrajectory is randomlyobtained. It satis�es
cTPi (xi )≤ 0(dij )min ≥ ds,ij , ∀j = 1, . . . , i −1
tETA,i > tSTA,i−1
where
(dij )min = dmin(yi (xi ),yj (xj ))tETA,i = tETA(yi(xi ))
Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution: 2-step Algorithm
2-step Algorithm
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 16 / 29
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Phase 1: sequential, aircraft areprocessed according to the land-ing sequence.
Avoidance: a con�ict-freetrajectory is randomlyobtained.
Recovery: minimizes thedeviation with tSTA,i .
minimize f (xi ) = (tETA,i − tSTA,i )2
subject to cTPi (xi )≤ 0(dij )min ≥ ds,ij , ∀j = 1, . . . , i −1tETA,i > tSTA,i−1
Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution: 2-step Algorithm
2-step Algorithm
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 16 / 29
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Phase 1: sequential, aircraft areprocessed according to the land-ing sequence.
Avoidance: a con�ict-freetrajectory is randomlyobtained.
Recovery: minimizes thedeviation with tSTA,i .
Phase 2: global.
Optimization: minimizesthe lateral deviation.
minimize f (x1, . . . ,xn) =1
n
√q
∑k=1
[(λk −λ
0
k
)2+(ϕk −ϕ
0
k
)2]subject to cTPi (xi )≤ 0 ∀i = 1, . . . ,n
(dij )min ≥ ds,ij ∀i , j = 1, . . . ,n, j 6= i
tETA,i − t1ETA,i = 0 ∀i = 1, . . . ,n
Introduction T Patterns T Prediction CD CR Results Summary & FW
Con�ict Resolution: 3-step Algorithm
3-step Algorithm
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 17 / 29
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Avoidance: no change.
Recovery: no change.
Optimization: sequential,minimizes the lateraldeviation.
minimize f (xi ) =
√qi
∑k=1
[(λk −λ
0
k
)2+(ϕk −ϕ
0
k
)2]subject to cTPi (xi )≤ 0
(dij )min ≥ ds,ij ∀j = 1, . . . , i −1tETA,i − t1ETA,i = 0
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 18 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Results
Matlab environment:
randn (normally distributed pseudorandom numbers),fmincon (sequential quadratic programming, SQP).
Aircraft models based on BADA 3.6.
Con�ict detection time step ∆t = 0.1s.
Two di�erent scenarios.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 19 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Scenario 1 (I)
Nominal Trajectories
TMA of Canarias with 3 entry points.30 medium aircraft arriving in 1 hour, ahead of schedule, and landing every2 minutes.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 20 / 29
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
FAYTA
CANIS
BETAN
λ [deg]
ϕ[deg]
t = 2600 s
Max deviation time: 148.0 s.Mean deviation time: 61.3 s.No. of con�icts: 12.
Introduction T Patterns T Prediction CD CR Results Summary & FW
Scenario 1 (II)
Resolution trajectories: with 2-step algorithm.
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 3500 s
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 3500 s
Phase 1 Phase 2
Indicator Value
Objective function value after phase 1, f1 [deg] 0.1324Objective function value after phase 2, f2 [deg] 0.0048Maximum deviation time, [s] 0.10
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 21 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Scenario 1 (III)
Resolution trajectories: with 3-step algorithm.
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 4000 s
Phase 1
Indicator Value
Objective function value, f [deg] 0.0488Maximum deviation time, [s] 0.28
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 22 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Scenario 2 (I)
Nominal trajectories
TMA of Canarias with 4 entry points.35 medium (red) and heavy (blue) aircraft arriving in 60 minutes, ahead ofschedule, and landing every 2 minutes.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 23 / 29
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 2600 s
Max deviation time: 630.8 s.Mean deviation time: 274.2 s.No. of con�icts: 30.
Introduction T Patterns T Prediction CD CR Results Summary & FW
Scenario 2 (II)
Resolution Trajectories: with 3-step algorithm.
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 2200 s
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 3500 s
Indicator Value
Objective function value, f [deg] 0.0873Maximum deviation time, [s] 38.47
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 24 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Scenario 2 (III)
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]
ϕ[deg]
t = 4500 s
−16 −15.5 −15 −14.5 −14 −13.5 −13 −12.5 −12
27.5
28
28.5
29
29.5
30
30.5
LZR
LTE
FTV
GDV
LPC
TERTO
RUSIK
ENETA
FAP WPT1
WPT2
FAYTA
CANIS
BETAN
WPT3
λ [deg]ϕ[deg]
t = 5000 s
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 25 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Outline
1 Introduction
2 Trajectory Patterns
3 Trajectory Prediction
4 Con�ict Detection
5 Con�ict Resolution
6 Results
7 Summary and Future Work
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 26 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Summary
A method to generate e�cient, con�ict-free trajectories that meet (whenpossible) the scheduled times of arrival have been presented.
It is based on the parameterization of the aircraft intents (prede�nedtrajectory patterns), and on the use of parametric optimization theory.
The resolution method is formed by 3 steps: avoidance, recovery, andoptimization.
Two algorithms have been presented:
2-step algorithm: in which the optimization step is applied globally. Adequatefor scenarios which are not very demanding.3-step algorithm: in which the optimization step is applied locally. Adequatefor very demanding scenarios.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 27 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Future Work
Departing aircraft and locked aircraft (whose trajectories cannot bemodi�ed).
Altitude changes in the resolution patterns.
Di�erent route structures.
Other tra�c conditions:
mixture of early and late aircraft,schedules with more incoming aircraft.
Uncertain tra�c: analysis of delay propagation.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 28 / 29
Introduction T Patterns T Prediction CD CR Results Summary & FW
Acknowledgements
This work has been funded by Boeing Research and Technology Europe andthe Spanish Comisión para el Desarrollo Tecnológico e Industrial (CDTI),through the Project ATLANTIDA/Cenit 2007.
Valenzuela et al. (U. Sevilla & BRTE) CR with Time Constraints SID 2012 29 / 29