model based conflict detection & resolution · 2006-01-09 · model based conflict detection...
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Model based Conflict Detection & Resolution
& Coordination of approach manoeuvres demo
Yannis Lymperopoulos & Yannis Lygeros
Systems and Measurements Laboratory
University of Patras
(in collaboration with A. Lecchini, W. Glover and J. Maciejowski,University of Cambridge)
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Aircraft Trajectory Prediction(during take-off)
Formulation of the problemThe Aircraft ModelA first approach to the problemResults Future ideas
+DEMO: Coordination of approach manoeuvres using a “Roissy -Charles De Gaulle” set-up
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Formulation of the problem
While taking off, there is great uncertainty about the future position of the aircraft.
Sources of uncertaintyInitial mass of the aircraft (undisclosed information)Wind and wind perturbations/disturbances (forecasts are approximations and account for very large areas)FMS settings (e.g. max thrust settings)
also:Model inaccuraciesHuman factors (pilots, controllers)
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Improve on the prediction errors
When aircrafts are climbing or descending their future position is more unpredictable than when cruising
Uncertainty increases with look ahead time
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Improve by measuring the position
Measure the position of the aircraft (every 6 or 12 seconds) with a RADARThe acquired trajectory encapsulates information about the missing parameters and the windUse this information to improve on your current estimation of the future
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The aircraft model
Hybrid – combines continuous and discrete dynamicsConsiders the wind as a stochastic process, correlated in space and timeUses realistic flight plans from CFMUAcquires specific aircraft parameters from BADA (speed_profile, engine_type, mass, coefficients ...)Implements a Flight Management system (bank angle, flight path angle and thrust control)Includes nominal wind from RUC database.
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Block Diagram of the model
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State of the Aircraft Model
Continuous state (x)[Position (X1,X2,h)][True Airspeed V][Heading (psi)]
Inputs (u)Thrust (u1)Bank angle (phi)Flight path (gamma)
Discrete state FL: Flight LevelWP: Way point indexAM: Acceleration modeCM: Climb modeTrM: Troposphere modeSHM: Speed hold modeFP: Flight phaseRPM: Reduced power mode
CRM : Cruise mode
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Goal
Use this model to predict the future positionof an aircraft, given the:
initial position in the RUNWAY (0.0 , 0.0)first way-point before starting cruisingunknown: aircraft_mass, wind evolution
Another problem arises: Measurement inaccuracyThe scale of the radar error is
small (comparable to the size of the aircraft) and such a distance
is covered in a fraction of a second
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What is the current uncertainty?
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What is the current uncertainty?
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What is the current uncertainty?
Different scenarios give a maximum uncertainty of over 70.000 meters after 20 minutes from takeoff
Our prediction of aircraft position for more than 4 minutes breaks the line of safe separation(5nmi) by far and increasingly with time
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A first approach to the problem
Create an “actual” trajectory using specific parameters and store the wind componentsImpose a Gaussian noise on this trajectory to represent measurement errors (we assume a RADAR accuracy of 60 meters).Implement an algorithm that uses the measurements to construct the posterior distribution of trajectories
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Algorithm
I. Extract parameters: (m,w)(i) ~ g(m,w), i=1,...,N N=Number of configurations, m ~ Uniform, w ~ Gaussian
II. Simulate using (m,w)(i) to create a respective trajectory X(i)
III.Measure: Get a number of measurements Y1,...,YT, every 12 seconds, for the first 4 minutes (T=20) of the flight referring to the “actual” trajectory
IV.Weight each one of the trajectories to create the posterior:
P( X(i) | Y1:T ) => the probability, that this specific trajectory has
actually happened, given the measurements.
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Weight the trajectories
weight(i) = P( m(i), w(i) | Y1:T ) => the probability that these parameters were the actual ones, given the measurements
oc L(m,w | Y1,...,YT) g(m,w) = L(m,w | Y1) L(m,w | Y2)......L(m,w | YT) g(m,w)
Calculate L(m,w | YK) = P(YK | m,w) => the probability that we got measurement YK using the specific parameters. That is, the probability, our Gaussian noise (N(0,400)) gave an error YK-XK.
Calculate g(m,w) => the probability that our prior distribution provided us with those parameters.
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A possible problem - Degeneracy
Depending on the number of extractionsOne trajectory will have a huge weight, while all the others a weight close to zeroThis will be considered the most prominent to fit the actual trajectory, and the best prediction of future position available
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Results
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Horizontal and vertical distance
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Trajectory prediction
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Parameter identification
massestimated : 120800kgactual: 121940kg
wind initially there is informationon the effect of the wind fromthe measurements. As timeelapses and (1) no new measurements arrive, (2) thewind is less correlated to theprevious samples => the wind estimation worsens
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Future ideas
Acquire real aircraft trajectories, to compare withCreate an aircraft model that moves to its next state stochastically (currently deterministic)Define a two stage process that estimates the position and identifies the parameters
Best candidate:
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Sequential Monte Carlo Algorithm
I. Initialize X0(i) ~ P0(x0) i=1,...,N (set t = 1)II. Importance Sampling Step
I. Evolve X0:t(i) from X0:t-1
II. Evaluate the importance weights for each X0:t(i)
III.Selection StepI. Multiply/Discard particles with respect to high low
normalized importance weights to obtain N equally weighted particles X''0:t(i)
IV. Markov transition stepI. Sample X0:t(i) ~ M( X0:t(i) | X''0:t(i) ), where M( . | . ) is a
transition kernel of invariant distribution Pt(X0:t)II. Set t = t + 1 and go to step II
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Conclusions
Greater ATM complexity requires more advanced DSTs (Decision Support Tools)The current ability for prediction of future aircraft positions will soon become insufficientThe uncertainty is really high during climb or descend proceduresGoal: Predict with high accuracy the location of an aircraft given a small amount of measurements (2-4 minutes)
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Coordination of approach manoeuvres DEMO
A. Lecchini, W.Glover, J.Lygeros, J.MaciejowskiFind an optimal solution for the “trombone manoeuvre”
The method measures the performance of each of the feasible configurations (time of arrival)The constraint:
the trajectories should maintain safe separationthe aircraft must reach 1500ft before glide
MCMC simulation to achieve maximum performancegenerate trajectories for different parameters accept those that fit the constraint, with a probability for the ones with “superior performance”
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Roissy - Charles De Gaulle IAF
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Set-up for 2 aircrafts arriving simultaneously
nmi
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Optimal configurations
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Simulation DEMO
~interactive