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Large-Scale 3D En-Route Conflict Resolution

Cyril Allignol, Nicolas Barnier, Nicolas Durand,Alexandre Gondran and Ruixin Wang

allignol,barnier,durand,gondran,wangrx

@recherche.enac.fr

ATM 2017 – SeattleJune 28th, 2017

Introduction

Background

The Conflict Resolution ProblemResearch on automatic conflict resolution started in the 1980s

Many different models comply with existing resolution techniques

Research from ANSPs focused on realistic models, but not on resolutionmethodsOther approaches focused both on model (e.g. using uncertainty modelsand BADA) and resolution algorithm, but completely tailored to a giventraffic simulator (e.g. CATS)

→ prevents scientific community from comparing different methods

Many generic resolution algorithms able to deal with complex problems(e.g. simplex, Branch & Bound, metaheuristics...): should be testedand compared scientifically on the same instances

Conflict resolution: large-scale combinatorial problem

→ a common model needed to validate the comparison

Allignol, Barnier, Durand, Gondran, Wang (ENAC) 3D En-Route Conflict Resolution ATM 2017 1 / 19

Introduction

The Conflict Resolution Problem

A New Framework for Solving En-Route Conflicts [ATM 2013]

Trajectory maneuver options + prediction with uncertainties

Conflicts discrete detection → combinatorial optimization problem

Resolution solvers independent from models

Benchmark enables scientific comparison of algorithms (e.g. CP vs GA)

What’s New. . .

Scenarios 3D over several FLs with possible in-between waypoints

Maneuvers more versatile, including FL change

Uncertainties more taken into account

Instances larger (up to 100 aircraft)

Solver Memetic Algorithm: harder, better, faster, stronger!

Introduction

The Conflict Resolution Problem

A New Framework for Solving En-Route Conflicts [ATM 2013]

Trajectory maneuver options + prediction with uncertainties

Conflicts discrete detection → combinatorial optimization problem

Resolution solvers independent from models

Benchmark enables scientific comparison of algorithms (e.g. CP vs GA)

What’s New. . .

Scenarios 3D over several FLs with possible in-between waypoints

Maneuvers more versatile, including FL change

Uncertainties more taken into account

Instances larger (up to 100 aircraft)

Solver Memetic Algorithm: harder, better, faster, stronger!

Introduction

Contents

1 BenchmarkTrajectory PredictionConflict DetectionConflict Resolution Problem

2 ResolutionDataAlgorithmsResults

3 Conclusion

Benchmark Trajectory Prediction

Traffic

Initial TrajectoriesLevelled (in our scenarios, but could be climbing or descending)

Following a sequence of waypoints

Associated to a nominal aircraft speed

Sampled into time steps of duration τ (small enough, e.g. 3 s)

→ ready to be embedded in a traffic simulator

FL 310

FL 300

FL 290

Maneuver Model

ManeuversStarts at t0 and returns on initial trajectory after t1

Either change heading by α or change FL by δFL

For simplicity, heading and FL changes cannot be combined

parameter size typical valuesstart t0 n0 (= 4) 0,1,2,3 (min)

return t1 n1 (= 4) 5,6,7,8 (min)

horizontal α nα (= 6) -30,-20,-10,+10,+20,+30 (°)vertical δFL nFL (= 4) -20,-10,+10,+20 (FL)

Options per aircraft: nman = n0 × n1 × (nα + nFL) + 1 (= 161)

Maneuver Model

ManeuversStarts at t0 and returns on initial trajectory after t1

Either change heading by α or change FL by δFL

For simplicity, heading and FL changes cannot be combined

parameter size typical valuesstart t0 n0 (= 4) 0,1,2,3 (min)

return t1 n1 (= 4) 5,6,7,8 (min)

horizontal α nα (= 6) -30,-20,-10,+10,+20,+30 (°)vertical δFL nFL (= 4) -20,-10,+10,+20 (FL)

Options per aircraft: nman = n0 × n1 × (nα + nFL) + 1 (= 161)

Handling Uncertainties

Uncertainties on maneuvers and speed

parameter error typical values

start t0 εt0 ∈ [0, Et0 ] 10-30 s

return t1 εt1 ∈ [0, Et1 ] 10-30 s

angle α εα ∈ [−Eα, Eα] 1-3°

horizontal speed vh εvh ∈ [−Evh , Evh ] 2-6%

vertical speed vv εvv ∈ [−Evv , Evv ] 5-15%

beacon fly mode fm fm ∈ {Fb, Fo} {Fb, Fo}

Beacon Fly Mode

Fb: fly by

Fo: fly over

start t0 εt0 ∈ [0, Et0 ] 10-30 s

return t1 εt1 ∈ [0, Et1 ] 10-30 s

Reaction Time Uncertainty

Et0 : start error

Et1 : return error t0

t1 t1+ Et1

t0+ Et0

Beacon Fly Mode

Fb: fly by

Fo: fly over

start t0 εt0 ∈ [0, Et0 ] 10-30 s

return t1 εt1 ∈ [0, Et1 ] 10-30 s

Heading Change Uncertainty

Eα: angle errort0

α− Eαα+ Eα

Beacon Fly Mode

Fb: fly by

Fo: fly over

start t0 εt0 ∈ [0, Et0 ] 10-30 s

return t1 εt1 ∈ [0, Et1 ] 10-30 s

Speed Uncertainty

Evh : speed error

(1− Evh)vh t1

t0(1 + Evh)vh

(1 + Evh)vh

(1− Evh)vh

Beacon Fly Mode

Fb: fly by

Fo: fly over

start t0 εt0 ∈ [0, Et0 ] 10-30 s

return t1 εt1 ∈ [0, Et1 ] 10-30 s

Climb and Descend Uncertainty

Evv : vertical error

(1 + Evv)vv (1− Evv)vv

(1 + Evv)vv (1− Evv)vvNew FL

Beacon Fly Mode

Fb: fly by

Fo: fly over

start t0 εt0 ∈ [0, Et0 ] 10-30 s

return t1 εt1 ∈ [0, Et1 ] 10-30 s

Beacon Fly Mode

Fb: fly by

Fo: fly over

Trajectory Hull Model

Horizontal PlaneAt each time step, aircraft positionmodelled as the smallest convexhull containing all possible positions

Red: not maneuvered yet (εvh)

Green: being maneuvered (εt0 , εα)

Blue: returning (εt1)

Gray: smallest convex hull

Vertical PlaneFor simplicity, the 3D convex hull isapproximated by the smallest right “cylinder”(prism) containing all possible horizontal convexhulls according to εvv

alt.max

alt.min

alt.max

alt.min

alt.max

alt.min

Benchmark Conflict Detection

Conflict Matrix

Detection

Trajectories l of aircraft i and k of aircraft j are conflicting iff ∃t = k × τ :

distv(ch(l, t), ch(k, t)) < normv ∧ disth(ch(l, t), ch(k, t)) < normh

where ch(l,t) is the 3D convex hull (prism) of trajectory l at time t, andtypically normv = 1000 ft and normh = 5 NM

For all ordered pairs of aircraft and pairs of trajectories

∀(i, j) ∈ [1, n]2, i < j, ∀(k, l) ∈ [1, nman]2

Ci,j,k,l =

{true if trajectories k and l conflicts

false otherwise

Benchmark Conflict Detection

Conflict Matrix

Detection

Trajectories l of aircraft i and k of aircraft j are conflicting iff ∃t = k × τ :

distv(ch(l, t), ch(k, t)) < normv ∧ disth(ch(l, t), ch(k, t)) < normh

where ch(l,t) is the 3D convex hull (prism) of trajectory l at time t, andtypically normv = 1000 ft and normh = 5 NM

For all ordered pairs of aircraft and pairs of trajectories

∀(i, j) ∈ [1, n]2, i < j, ∀(k, l) ∈ [1, nman]2

Ci,j,k,l =

{true if trajectories k and l conflicts

false otherwise

Benchmark Conflict Resolution Problem

Combinatorial Optimization

Decision variables M = {mi, i ∈ [1, n]} with mi ∈ [1, nman]

All maneuver options associated with allowed tuples 〈t0, t1, α, δFL〉 arenumbered from 1 to nman

mi represents the maneuver of aircraft i

Size of the search space: nnman

Cost cost(M) =∑n

i=1 c(mi)

Increasing absolute values of parameter ? indexed by k? ∈ [1, n?]

Individual: c(mi) =

(n0 − k0)2 + k12 +

2 if α 6= 0(1 + kδ)

2 if δFL 6= 00 otherwise

where mi is described by the tuple 〈 k0 , k1 , kα , kδ 〉

Constraints ∀(i, j) ∈ [1, n]2 s.t. i 6= j ¬Ci,j,mi,mj

with Ci,j,k,l = maneuvers k of aircraft i and l of aircraft j conflicts

Cost cost(M) =∑n

i=1 c(mi)

Individual: c(mi) =

(n0 − k0)2 + k12 +

2 if α 6= 0(1 + kδ)

Cost cost(M) =∑n

i=1 c(mi)

Individual: c(mi) =

( 4 − 1 )2 + 3 2 +

{2 2 = 22 if α 6= 0(1 + kδ)

where mi is described by the tuple 〈0 min, 7 min, 20°, FL0〉

Cost cost(M) =∑n

i=1 c(mi)

Individual: c(mi) =

(n0 − k0)2 + k12 +

2 if α 6= 0(1 + kδ)

Benchmark

Available at clusters.recherche.enac.fr

Instance files: specified by matrix C for a given set of parameters

Current results: optimal solutions, lower and upper bounds

Currentlyn ∈ {5, . . . , 100}, nman = 161, 3 levels of uncertainty, 10 instances

A Small Sample From a Benchmark File