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Automation for Separation with CDOs: Dynamic Aircraft Arrival Routes Tatiana Polishchuk, LiU Ral Sez, UPC Valentin Polishchuk, LiU Xavier Prats, UPC Christiane Schmidt, LiU Motivation Air transportation grows: Beneficial for

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Automation for Separation with CDOs: Dynamic Aircraft Arrival Routes

Raúl Sáez, UPC Xavier Prats, UPC Tatiana Polishchuk, LiU Valentin Polishchuk, LiU Christiane Schmidt, LiU

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Motivation

2

๏ 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”

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CDOs

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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

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Previous Work 4

  • 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

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Grid-based MIP Formulation

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Input

  • Location and direction 

  • f the airport runway
  • Locations of the entry points to

the TMA

  • Aircraft arrival times at the entry

points for a fixed time period

  • Cruise conditions (altitude, true

airspeed, distance to entry point + path distance inside TMA) and aircraft type for CDO profile generation

6

Ent 3 Ent 2

RWY

Ent 1 Ent 4

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Output

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Ent 3 Ent 2

RWY

Ent 4 Ent 1

Optimal arrival tree that:

  • Merges traffic from the entries to

the runway

  • Ensures safe aircraft separation

for the given time period ⇨ A set of time-separated CDO- enabled tree-shaped aircraft trajectories optimized w.r.t. the traffic demand during the given period

RWY

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Operational Requirements

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๏ 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

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Grid-based MIP Formulation

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Ent 3 Ent 2

RWY

Ent 1 Ent 4

  • Square grid in the TMA
  • Snap locations of the entry points

and the runway into the grid

  • Grid cell side of the length L

(separation parameter)

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Grid-based MIP Formulation

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Ent 3 Ent 2

RWY

Ent 1 Ent 4

  • Square grid in the TMA
  • Snap locations of the entry points

and the runway into the grid

  • Grid cell side of the length l

(separation parameter)

  • Every node connected to its 8

neighbours

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Grid-based MIP Formulation

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Ent 3 Ent 2

RWY

Ent 1 Ent 4

  • Square grid in the TMA
  • Snap locations of the entry points

and the runway into the grid

  • Grid cell side of the length l

(separation parameter)

  • Every node connected to its 8

neighbours

  • Problem formulated as MIP
  • Based on flow MIP formulation for

Steiner trees

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MIP Formulation

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VARIABLES OBJECTIVES

Demand-weighted path length: Total tree weight:

  • decision variable - indicates whether edge e participates in arrival tree
  • gives the flow on edge e = (i, j), non-negative

Short flight routes for aircraft Arrival tree should “occupy little space”

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Constraints

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๏ 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

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Flow from all entry points reaches runway Flow of #a/c leaves each entry point Flow conservation Edges with positive flow are in STAR Flow non-negative Edge decision variables are binary Degree constraints: Outdegree of every vertex at most 1, maximum indegree is 2. Runway only one ingoing, entry points only one

  • utgoing edge.

ae = |Ae|

X

k:(k,i)∈E

fki − X

j:(i,j)∈E

fij = 8 > < > : P

k∈EP κk

i = R −κi i ∈ EP i ∈ V \ {EP ∪ R} (1) xe ≥ fe |EP| ∀e ∈ E (2) fe ≥ 0 ∀e ∈ E (3) xe ∈ {0, 1} ∀e ∈ E (4) X

k:(k,i)∈E

xki ≤ 2 ∀i ∈ V \ {EP ∪ R} (5) X

j:(i,j)∈E

xij ≤ 1 ∀i ∈ V \ {EP ∪ R} (6) X

k:(k,R)∈E

xkR = 1 (7) X

j:(R,j)∈E

xRj ≤ 0 (8) X

k:(k,i)∈E

xki ≤ 0 ∀i ∈ EP (9) X

j:(i,j)∈E

xij = 1 ∀i ∈ EP (10) aexe + X

f∈Ae

xf ≤ ae ∀e ∈ E (11)

  • T. Andersson, T. Polishchuk, V. Polishchuk, C. Schmidt. Automatic Design of Aircraft Arrival Routes with

Limited Turning Angle. ATMOS 2016, Aarhus, Denmark.

If an edge xe the angle to the consecutive segment of a route is never smaller than 𝞫

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Constraints

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Auxiliary Constraints to Prevent Crossings

Why? Temporal Separation may enforce paths that are not shortest, hence, crossings may appear

  • J. Dahlberg, T. Andersson Granberg , T. Polishchuk, C. Schmidt, L. Sedov. Capacity-Driven Automac

Design of Dynamic Aircraft Arrival Routes. DASC 2018, London, UK. For all points except last column, last row, entries and rwy: For different entry point locations:

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Constraints

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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 Set:

Forward the information on the times at which a arrives at nodes along the route from b to the rwy

  • J. Dahlberg, T. Andersson Granberg , T. Polishchuk, C. Schmidt, L. Sedov. Capacity-Driven

Automatic Design of Dynamic Aircraft Arrival Routes. DASC 2018, London, UK.

Aircraft arriving at entry point b Time when aircraft a arrives at entry point b

Temporal separation: 𝞃 - separation parameter Not linear ⟹ we linearise using a new variable za,j,k,b,t

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Constraints

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๏ 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

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Realistic CDO Speed Profiles

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  • 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
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Realistic CDO Speed Profiles

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Dynamic constraints Path constraints Terminal constraints

  • 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
  • perational limits, and that the maximum and minimum descent gradients are not exceeded
  • Terminal constraints 𝜔 fix the final states vector
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Realistic CDO Speed Profiles

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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)

  • 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

  • ptimal control problem
  • BADA V4 is used to model the aircraft performance
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Constraints

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๏ 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

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Constraints

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Integration of CDO-enabled Realistic Speed Profiles

Substitute: with - binary, indicates whether a/c a using speed profile p occupies the n-th vertex j at time t. Compute l(b) - path length from b to the rwy For each a/c a arriving from b we pick the speed profile from S(a) that has the length l(b), i.e., we want: l(b) is a variable ⟹ We use auxiliary binary variables and constraints to achieve this. Separation constraint: 𝞃 - separation parameter Substitute the corresponding equations with: Set of all speed profiles (different lengths) for aircraft a

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Constraints

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Consistency between trees of consecutive time periods

Define: - edge indicators for current and previous periods U - limits the number of differing edges in the two trees

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Experimental Study: Stockholm Arlanda Airport

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Experimental Airport: Stockholm Arlanda Airport

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๏ Data: Stockholm Arlanda airport arrivals during one hour of

  • peration

๏ Source: EUROCONTROL DDR2, BADA 4 ๏ High-traffic scenario on October 3, 2017, time: 15:00 - 16:00 ๏ Solved using GUROBI ๏ Run on a powerful Tetralith server, provided by SNIC, LIU: Intel HNS2600BPB nodes with 32 CPU cores and 384 GiB RAM

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CDO profiles inside TMA

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๏ Cruise conditions are obtained from DDR2 ๏ TOD position and descent phase are

  • ptimized

๏ Same time at the entry point for different path lengths inside TMA

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CDO profiles inside TMA

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๏ A set of realistic alternative speed profiles for different possible route lengths inside TMA ๏ Generated for all a/c types arriving to Arlanda during the given period ๏ Used as input to MIP

Example of A320 speed profiles for different path lengths inside TMA

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Results: Stockholm Arlanda Airport

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Tree 1: time: 15:00 - 15:30 (10 a/c) Tree 2: time: 15:30 - 16:00 (7 a/c)

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Results: Stockholm Arlanda Airport

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๏ Tree 1: time: 15:00 - 15:30 (10 a/c) ๏ Tree 2: time: 15:30 - 16:00 (7 a/c) ๏ Optimized for 30 min intervals (longer periods may be sub-optimal. Note: time within TMA 5-18 min) ๏ U = 23 provides consistency between the trees ๏ Separation: 2 min, ~6 nm ๏ 17 out of 22 arrivals scheduled ๏ 5 filtered out, because of:

  • Initial violation of separation at entry points
  • Potential overtaking problem
  • In general, about 10-15% are not scheduled
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Comparison against historical trajectories (Open Sky Network)

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Time Schedule

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t = 15:00

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t = 15:03

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t = 15:04

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t = 15:05

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t = 15:07

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t = 15:08

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t = 15:09

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t = 15:10

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t = 15:11

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t = 15:12

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t = 15:13

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t = 15:14

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t = 15:15

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t = 15:16

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t = 15:17

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t = 15:18

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t = 15:19

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t = 15:20

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t = 15:21

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t = 15:22

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t = 15:23

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t = 15:24

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t = 15:25

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t = 15:26

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t = 15:27

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t = 15:28

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t = 15:29

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t = 15:30

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t = 15:30

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t = 15:30

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t = 15:30

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t = 15:30

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t = 15:31

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t = 15:32

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Conclusions and Future Work

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Conclusions and Future Work

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๏ Flexible optimization framework for dynamic route planning inside TMA ๏ Automated spatial and temporal separation ๏ Environmentally-friendly speed profiles (CDO) ๏ Applicable to any other realistic speed profiles ๏ May be used for TMA capacity evaluation ๏ Account for uncertainties due to variations in arrival times ๏ Solve overtaking problem (allow non-optimal profiles, or route stretching) ๏ Consider fleet diversity ๏ Elaborate on implementation possibilities, link to the future operational enablers (data links, technologies) for air-ground synchronisation (EPP)

Conclusions Future Work

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THANKS.