2009/3/28

ENRI International Workshop on ATM/CNS. Tokyo, Japan. (EIWAC 2009)

Trajectory Optimization for
Safe, Clean and Quiet Flight
Shinji Suzuki, Takeshi Tsuchiya andAdriana Andreeva
Dept. of Aeronautics and Astronautics
The University of Tokyo

Trajectory Optimization
Trajectory Optimization isformulated as an optimalcontrol problem that finds thesolution that maximizes orminimizes an objective function
within constrained boundaries.

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Calculus of variations
Find the curve between two points
that is covered in the least time by abody that starts at the first point withzero speed.
AB
Johann Bernoulli

Brachistochrone curve

Numerical Optimization
Pontryagin's Minimum Principle
Bellman’s Dynamic Programming
Direct Numerical Optimization Method

Minimize : Jtfg ( x, u )dth(t f )

Subject to : dx / dt f ( x, u )x(t 0 ) x 0 , x(t f )xf

t0a ( x, u )022009/3/28

Air Trafic Manegement
NextGenTrajectory Management: Trajectory
management includes any function that
affects aircraft trajectory. These functions
include trajectory optimization andnegotiation with air traffic management,
navigation algorithms, delegated aircraft
separation applications, or trajectory
constraints to avoid weather. The
integration of these functions is key to
NextGen aircraft functionality.
FAA, “Aircraft and Operator Requirements Solution Set Smart Sheet”

Flight Trajectory Optimization
Safe Trajectory
Trajectory Generation for Emergency
Landing

Quiet Trajectory
Low Noise Trajectory Generation for
Helicopter Landing Approach

Clean Trajectory
Flight Management of Multiple Aircraft
for Co2 Reduction3

2009/3/28

Real-time Optimizationin Emergency Landing Approach

Ref: Y. Sakai, S. Suzuki., M. Miwa, T. Tsuchiya, and K. Maui,and H. Tomita, “Flight Test Evaluation of Non-Linear DynamicInversion Controller”, 46th AIAA Aerospace Sciences Meetingand Exhibit, Reno, NV/USA, 2008.1.8.

PurposeIn an emergency, as part of a faulttolerant flight control system,
generate an optimal flight trajectory
to the nearest airport in real time.

Funded by the Ministry of Economy, Trade, and Industry (METI)
and organized by the Society of Japanese Aerospace Companies.
Joint Research Between the Univ of Tokyo and JAXA

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Real-Time Trajectory Optimization method
Flight initiation

Stage 1

Initial condition
Leading path
Acquisition ofPrecise trajectory
flight environment
and aircraft condition
Rough trajectoryDense nodes

Sparse nodes

Terminal condition

Real-Time Trajectory Optimization method
Stage 1

Update offlight environment
and aircraft condition

Stage 2Sparse nodes

Precise trajectory
Dense nodes
Rough trajectory
Terminal condition5

2009/3/28

Real-Time Trajectory Optimization method
Stage 2

Stage 3Sparse nodes
Update offlight environment
Rough trajectory
and aircraft condition
Precise trajectory
Dense nodes
Terminal condition

Real-Time Trajectory Optimization method
Stage 3

Stage 4

Dense nodes

Initial condition
Update offlight environment
and aircraft condition

Precise trajectory

Terminal condition

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Real-Time Trajectory Optimization method
Stage 4Terminal condition

Flight-test results
1000-16000

Flight initiation-12000Wind

Altitude [m]800-14000

600
400
200

-10000

00100

-8000
y[m]
-2000

300

400

200
Time [sec]

300

400

74
72
Airspeed [m/s]

-6000

-4000

200
Time [sec]

70
68
66
64
62

-12000 -10000

-8000

-6000
x[m]

-4000

-2000

00

Actualflight60
0
Optimalsolution100
Indicated airspeed

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Flight-test results
1000-16000

Flight initiation-12000Wind

Altitude [m]800-14000

600
400
200

-10000

00100

-8000
y[m]
-2000

300

400

200
Time [sec]

300

400

74
72
Airspeed [m/s]

-6000

-4000

200
Time [sec]7068666462-12000 -10000

-8000

-6000

-4000

-2000

x[m]

00Actualflight
600
Optimalsolution100
Indicated airspeed

Flight Testing168

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Auto Pilot + Auto Throttle
using 4D Navigation
Indicated and Tracking Flight Path
Indicated path
Tracking result

700
600
500
m

400
300

0

200
5000
100
10000

00-2000

-4000

-6000

-8000

-10000-12000

15000

mmc

pc

e

Yc

c

qc

a

Zc

c

rc

Xc

SlowX
YZ

MediumrFastp

FlightDynamics

qr

Fault Tolerant Flight Control
Neural Network can learn the changeof dynamic characteristic due to failurein flight.

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Flight Demonstration

Small Electric Power UAV・Takeoff weight 2 kg
・Automatic Flight Capability
Developed by U of Tokyo and Mitsubishi Electric Co.

Ground Noise Reduction inHelicopter Landing Approach

Ref: T. Tsuchiya, H. Ishii, J. Uchida, H. Ikaida, H. Gommi, N.
Matayoshi, and Y. Okuno, “Flight Trajectory Optimization toMinimize Ground Noise in Helicopter Landing Approach”, J.
Guidance, Control and Navigation (to appear)10

2009/3/28

Introduction
A major problem in helicopter operations is noise.
Operation limit due to the noiseReduction of the ground noise of aircrafts
Designing silent aircrafts
Flying the existing aircrafts silently
Flight reducing the noise generation
Flight-path decision regarding land usePurpose
Optimizing helicopter flight trajectories
to reduce ground noise in the landing
approach

Trajectory optimization(University of Tokyo)

Flight demonstration(JAXA)

Collaborative Research11

2009/3/28

Flight test fieldTaiki Multi-Purpose
Aeronautical Park

Problem definition
Runwayx04
5yTerminal

1 NM32
2 NM

1Initial

3 NM
Measurement Point

noise measurement points 1NM=1.852km

The Pacific Ocean

Find optimal trajectories minimizing the noise levels
measured at the five measurement points
The optimal trajectories are computed before flight,
and a pilot tracks it manually.

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Helicopter dynamics model
Horizontal-velocity limit

Thrust50

horizontal velocity 100 [kt]Climb rate limit

hclimb rate
Velocity800 [fpm]（Altitude h480 [ft] ）5h [fpm]3（Altitude h480 [ft] ）Acceleration limit

0xGravityyhorizontal acceleration

1.5 [kt/sec]

vertical acceleration

100 [fpm/sec]

Roll angle limit

3DOF (point-mass model)roll angle

Define the constraint conditions
from pilot comments

15 [deg]

JAXA Simulator

Noise source model

Noise level Lref [dB]microphone

10098969492908886848280
78-209080-15-10-595

85
90085
510-30-20-100102030

Microphone array system

The level at a distance of 100 m from the helicopter

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Attenuation model

Distance absorption
attdist ( r ) = 20 log

r [m ]
100[m ]

[dB]

Atmospheric absorption
Sound level [dB]Distance r [m]Frequency [Hz]Altitude [m]Flight-test results
Case 1
Free ascent flight
Case 2
No ascent flight
Case 3
Normal approach

800
700
600
500
400
300
200
100
0-5423-4

51-3-2-10-6-5-4-3-2-1

014

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Flight-path angle [deg]Airspeed [m/sec]

Flight-test results
Case 1
Free ascent flight
Case 2
No ascent flight
Case 3
Normal approach

55
50
4540
35
30
25
20
10
50-5-10-15
-20

020

40

60

100 12080Flight time [sec]

140

160

180

200

Flight scene15

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Flight scene

Noise-reduction result

Temporal-mean noise level LA [dB]70

Test results(Measurement)

65

60

55

5065.6 dB

Noise reduction
9.9 dB

Optimal solutions59.3 dB(Simulation)
55.7 dB
54.1 dB
53.9 dB

Case 1
Free ascent flight

Case 2

Case 3

No ascent flight Normal approach1516

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Multiple Aircraft Descent
Trajectory Optimization with Air
Traffic Constraints for Minimal
Fuel Consumption
Adriana Hristova Andreeva,
Shinji Suzuki (Univ of Tokyo)
Eri Itoh (ENRI)
Ref: A. Andreeva, S. Suzuki, and E. Ito, “Multiple Aircraft
Descent Trajectory Optimization with Air Traffic Constraints
for Minimal Fuel Consumption”, International Conference
on Mathematical Problems in Engineering, Aerospace andsciences, ICNPAA-2008, Genoa, 2008.

Optimal Decent Trajectory of Single Aircraft

4x 10

4M(1): OBJECTIVE FUNCTION
3.5

Waypoint i position：(x(i), y(i), z(i))

Top Of Descentz(1)= 33000 ft

32.5

Sequential Qudratic
Programming（SQP）

2max = 3 deg
1.5

MATLAB®

1z(N+1)= 5000 ft

x(N+1)-x(1)= 130nm
0.5

M (N+1): dependent on aircraft type
0020

40

60

80

100

120

140

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Optimal Decent Trajectory of Single Aircraft

Higher for longer

4x 10Descent Trajectory of B747

43.5g0 16.5 hKT R

1Altitu de [ft]

32.5
2
1.5
1

1000 T0

0.5020406080

100120140x [nm]M

fuel _ B 747

M

initialM

finalttotal _ B 747

12065 lb

1530.2 s
35

Two Aircraft Case36

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Two Aircraft Case
1.64x 10

4

Fixed Time of Arrival + Separation 60 sec

1.62

Total Mfuel

1.6

1.58

1.56

1.54

1.52
st

1.5
1350

1400

1450

1500
1550
1600
st
Flight Time of the 1 Aircraftnd

1 B747 2 B737
stnd1 B737 2 B747
1650
1700
1750

37Summary
A numerical method for trajectory
optimization problem
Application to real flights
Ground noise reduction in helicopter
landing approach
Trajectory generation in emergency
landing approach

Air traffic management

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