Automation for Separation with CDOs: Dynamic Aircraft Arrival Routes Tatiana Polishchuk, LiU Raúl Sáez, UPC Valentin Polishchuk, LiU Xavier Prats, UPC Christiane Schmidt, LiU
Motivation ๏ Air transportation grows: ‣ Beneficial for growing global economy ‣ Increased complexity for air traffic controllers (ATCOs) ‣ Environmental effects ๏ Terminal Maneuvering Areas (TMAs) most congested ➡ Optimization of arrival and departure procedures is needed: ‣ Lessen ATCO workload ‣ Mitigate environmental impact Our solution: ๏ Automatically temporally separated arrivals to reduce complexity and ATCO’s workload ๏ Aircraft fly according to optimal continuous descent operations (CDOs): ‣ Promising solution to mitigate environmental effects, according to ICAO and EUROCONTROL: CDOs "allow aircraft to follow a flexible, optimum flight path that delivers major environmental and economic benefits— reduced fuel burn, gaseous emissions, noise and fuel costs—without any adverse effect on safety” NTKt, October 23, 2019 � 2
CDOs CDOs have shown important environmental benefits w.r.t. conventional (step-down) approaches in TMAs Figure source: Performance comparison between TEMO and a typical FMS in presence of CTA and wind uncertainties, by Ramon Dalmau, Xavier Prats, Ronald Verhoeven and Nico de Gelder, DASC 2016 NTKt, October 23, 2019 � 3
Previous Work • LiU-LFV: • Optimal standard arrival routes (STARs) • Time-separated demand-weighted arrival routes (dynamic, for pre-tactical planning), assuming unit edge traversal time • UPC: CDO-enabled optimized arrival procedures (engine-idle, low noise) • Here: Automated time-separated demand-weighted CDO- enabled optimized arrival routes NTKt, October 23, 2019 � 4
Grid-based MIP Formulation NTKt, October 23, 2019 � 5
Input Ent 1 • Location and direction of the airport runway • Locations of the entry points to Ent 3 the TMA Ent 2 • Aircraft arrival times at the entry points for a fixed time period RWY • Cruise conditions (altitude, true airspeed, distance to entry point + path distance inside TMA) and aircraft type for CDO profile generation Ent 4 NTKt, October 23, 2019 � 6
Output Ent 1 Optimal arrival tree that: • Merges traffic from the entries to the runway Ent 3 • Ensures safe aircraft separation Ent 2 for the given time period ⇨ A set of time-separated CDO- RWY RWY enabled tree-shaped aircraft trajectories optimized w.r.t. the traffic demand during the given period Ent 4 NTKt, October 23, 2019 � 7
Operational Requirements ๏ No more than two routes merge at a point: in-degree ≤ 2 ๏ Merge point separation: distance threshold L ๏ No sharp turns: angle threshold α , minimum edge length L ๏ Temporal separation of all aircraft along the routes ๏ All aircraft fly energy-neutral CDO: idle thrust, no speed brakes (noise avoidance) ๏ Smooth transition between consecutive trees when switching NTKt, October 23, 2019 � 8
Grid-based MIP Formulation Ent 1 • Square grid in the TMA • Snap locations of the entry points and the runway into the grid Ent 3 • Grid cell side of the length L Ent 2 (separation parameter) RWY Ent 4 NTKt, October 23, 2019 � 9
Grid-based MIP Formulation Ent 1 • Square grid in the TMA • Snap locations of the entry points and the runway into the grid Ent 3 • Grid cell side of the length l Ent 2 (separation parameter) • Every node connected to its 8 RWY neighbours Ent 4 NTKt, October 23, 2019 � 10
Grid-based MIP Formulation Ent 1 • Square grid in the TMA • Snap locations of the entry points and the runway into the grid Ent 3 • Grid cell side of the length l Ent 2 (separation parameter) • Every node connected to its 8 RWY neighbours • Problem formulated as MIP • Based on flow MIP formulation for Steiner trees Ent 4 NTKt, October 23, 2019 � 11
MIP Formulation VARIABLES - decision variable - indicates whether edge e participates in arrival tree - gives the flow on edge e = (i, j) , non-negative OBJECTIVES Short flight routes for aircraft Demand-weighted path length: Total tree weight: Arrival tree should “occupy little space” NTKt, October 23, 2019 � 12
Constraints ๏ Flow constraints ๏ Degree constraints ๏ Turn angle constraints ๏ Auxiliary constraints to prevent crossings ๏ Temporal separation of all aircraft along the routes ๏ Realistic CDO speed profiles ๏ Consistency between trees of different time periods NTKt, October 23, 2019 � 13
T. Andersson, T. Polishchuk, V. Polishchuk, C. Schmidt. Automatic Design of Aircraft Arrival Routes with Limited Turning Angle. ATMOS 2016, Aarhus, Denmark. 8 Flow from all entry points reaches runway P i = R k ∈ EP κ k > < X X Flow of #a/c leaves each entry point f ki − f ij = i ∈ EP (1) − κ i k :( k,i ) ∈ E j :( i,j ) ∈ E > 0 i ∈ V \ {EP ∪ R } Flow conservation : f e (2) Edges with positive flow are in STAR x e ≥ ∀ e ∈ E |EP| f e ≥ 0 (3) ∀ e ∈ E Flow non-negative x e ∈ { 0 , 1 } (4) ∀ e ∈ E Edge decision variables are binary Degree constraints: X x ki ≤ 2 ∀ i ∈ V \ {EP ∪ R } Outdegree of every vertex at most 1, maximum k :( k,i ) ∈ E (5) indegree is 2. X x ij ≤ 1 ∀ i ∈ V \ {EP ∪ R } Runway only one ingoing, entry points only one j :( i,j ) ∈ E outgoing edge. (6) X x kR = 1 (7) k :( k,R ) ∈ E X x Rj ≤ 0 (8) j :( R,j ) ∈ E a e = | A e | X x ki ≤ 0 ∀ i ∈ EP (9) k :( k,i ) ∈ E X x ij = 1 ∀ i ∈ EP (10) j :( i,j ) ∈ E If an edge x e the angle to the consecutive X a e x e + (11) x f ≤ a e ∀ e ∈ E segment of a route is never smaller than 𝞫 f ∈ A e NTKt, October 23, 2019 � 14
Constraints Auxiliary Constraints to Prevent Crossings Why? Temporal Separation may enforce paths that are not shortest, hence, crossings may appear For all points except last column, last row, entries and rwy : For different entry point locations : J. Dahlberg, T. Andersson Granberg , T. Polishchuk, C. Schmidt, L. Sedov. Capacity-Driven Automac Design of Dynamic Aircraft Arrival Routes. DASC 2018, London, UK. NTKt, October 23, 2019 � 15
Constraints J. Dahlberg, T. Andersson Granberg , T. Polishchuk, C. Schmidt, L. Sedov. Capacity-Driven Automatic Design of Dynamic Aircraft Arrival Routes. DASC 2018, London, UK. Temporal Aircraft Separation Assumption: unit time u to cover a single edge More variables : - binary, shows a/c a at node j at time t - binary: edge e in the route from entry point b Connect to plus several other constraints Aircraft arriving at entry point b Set: Time when aircraft a arrives at entry point b Forward the Not linear information on the ⟹ we linearise using a new variable z a,j,k,b,t times at which a arrives at nodes along the route from b to the rwy Temporal separation: 𝞃 - separation parameter NTKt, October 23, 2019 � 16
Constraints ๏ Flow constraints ๏ Degree constraints ๏ Turn angle constraints ๏ Auxiliary constraints to prevent crossings ๏ Temporal separation of all aircraft along the routes ๏ Realistic CDO speed profiles ๏ Consistency between trees of different time periods NTKt, October 23, 2019 � 17
Realistic CDO Speed Profiles • The state vector x represents the fixed initial conditions of the aircraft: TAS v, altitude h and distance to go s • To achieve environmentally friendly trajectories, idle thrust is assumed and speed- brakes use is not allowed throughout the descent → energy-neutral CDO • The flight path angle is the only control variable in this problem → control vector u NTKt, October 23, 2019 � 18
Realistic CDO Speed Profiles • A point-mass representation of the aircraft reduced to a “gamma-command” is considered, where vertical equilibrium is assumed → Dynamic constraints f • Path constraints h are enforced to ensure that the aircraft airspeed remains within operational limits, and that the maximum and minimum descent gradients are not exceeded • Terminal constraints 𝜔 fix the final states vector Dynamic constraints Path constraints Terminal constraints NTKt, October 23, 2019 � 19
Realistic CDO Speed Profiles • The trajectory is divided in two phases: the latter part of the cruise phase prior the top of descent (TOD) and the idle descent • The original cruise speed is not modified after the optimization process, so the two-phases optimal control problem can be converted into a single-phase optimal control problem • BADA V4 is used to model the aircraft performance Sáez, R., Dalmau, R., & Prats, X. (2018 , Sep). Optimal assignment of 4D close-loop instructions to enable CDOs in dense TMAs. Proceedings of the 37th IEEE/AIAA Digital Avionics Systems Conference (DASC) NTKt, October 23, 2019 � 20
Constraints ๏ Flow constraints ๏ Degree constraints ๏ Turn angle constraints ๏ Auxiliary constraints to prevent crossings ๏ Temporal separation of all aircraft along the routes ๏ Realistic CDO speed profiles ๏ Consistency between trees of different time periods NTKt, October 23, 2019 � 21
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