Genetic Algorithm for Coupled RLV Trajectory & Guidance Optimization

VERNIS Philippe - FERREIRA Eugénio – Guidance & Control Department

MORIO Vincent – LAPS/CNRS Bordeaux

Astrium Space Transportation

Genetic Algorithm

for

Coupled RLV Trajectory & Guidance Optimization

VERNIS Philippe - FERREIRA Eugénio – Guidance & Control Department

MORIO Vincent – LAPS/CNRS Bordeaux


Genetic Algorithms Overview

The Hypersonic Re-entry Design Problem

GAGHARIN Toolbox

Application to a high L/D Vehicle

Conclusion

OVERVIEW


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09/02/07 p3

Objectives

1st step

optimal reference trajectory

(parametric optimization)

3rd step

Update of Guidance data

(Monte-Carlo process,

100 runs)

Classical operating mode for re-entry Guidance studies

Objectives

4th step

Final GNC performances report

(Monte-Carlo process,

1000 runs)

2nd step

Guidance data settings

(iterative handmade process)

To mix steps 2 to 4 in order to rely on a robust and one-shot method enabling:

the design of the nominal guided re-entry trajectory

the setting of all mission/internal Guidance data

the compliance of the GNC performances with all mission requirements on a given set of

off-nominal flight conditions

Input: entry gate, targeted point, path and final constraints, off-nominal flight conditions

GNC chain (full closed-loop algorithm, or simplified performances models)

Output: Guidance settings, nominal guided entry path & GNC performances

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09/02/07 p4

Genetic Algorithms Overview (1)

Background

1859 Charles Darwin‘s theory of evolution

1866 Gregor Mendel‘s experiments concerning vegetables hybridization

1975 John Holland‘s first GA formal model

GAs have to be understood as neo-Darwinism based algorithms

union of evolution theory and modern genetics

typical applications

in each environment, only the best adapted species are favored in the struggle for life

in each specie, the renewal of populations is esentially due to the best individuals through

reproduction process

Genetic algorithms are based on a biological metaphor

PID fine tuning

travelling salesman problem applied to Flight Management ... Design of optimal hypersonic entry trajectories

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09/02/07 p5

ind

ivid

ua

ls

genes


basic genetic transformation: selection, crossover, mutation, reinsertion

Population, individuals, chromosomes…

at a given time, a population is defined by individuals, individuals by chromosomes,

chromosomes by genes, and genes by bits with binary or real-valued encoding

evolution

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09/02/07 p6


evaluation of offspring

mutation

recombination

fitness assigment

selection

Initialization:

• creation of initial population

• evaluation of individuals

yes

Generate

new

populationreinsertion

no

migration

competition

Optimization criteria OK?

start stop

extended multi-population GA

Principles

an encoding process for each individual of a population

a mechanism to generate the initial population

some genetic operators (selection, crossover, mutation, …)

sizing parameters (number of individuals, of generations, …)

objective to look for the extrema of a function defined on a data space

key elements

best individuals

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09/02/07 p7


seems to be well adapted to treat complex optimization problems

GAs differ substantially to traditional search and optimization methods:

search a population of points in parallel, not just a single point

do not require derivative information or other auxiliary knowledge only the objective

function and corresponding fitness levels influence the directions of search

use probabilistic transition rules, not deterministic ones

generally more straightforward to apply because no restriction for the definition of

the objective function exists

evolutionary algorithms can provide a number of potential solutions to a given

problem

performances of the GA strongly depend on the initial population

for complex processes, it may be necessary to parallelize computations

GAs vs. classical optimization methods

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09/02/07 p8

path constraints

• heat flux, heat load

• load factor

• dynamic, total pressure

• no-skip

The Hypersonic Re-entry Design Problem (1)

off-nominal flight conditions

• entry gate dispersions

• aerologic disturbances

• vehicle design

GNC performances

• nominal guided entry path

• off-nominal trajectories & sizing cases

• final miss-ranges

• margins left on design constraints

final constraints

• miss-range at Mach 2 gate

• heading at Mach 2 gate

End-to-End global optimization

• entry gate

• Mach 2 gateenvironment

• atmosphere model

• gravity field

Statement of the problem

Guidance settings

• D-V profile waypoints

• dynamic pressure triggering threshold

• open-loop bank angle

• D-V tracking command gains

• route angle corridor width

• a.o.a command gains (if modulation)

GC constraints

• roll reversal strategy

• flyable D-V profile

• flyable a.o.a corridor

Control

• roll rate limitation

• 2nd order model (bank angle)

• a.o.a offset

Guidance

• downrange: D-V profile tracking

• cross-range: roll reversal

Navigation

• Linear piecewise profile wrt.altitude

• IMU, GPS and DDA during black-out

Guidance settings

• D-V profile waypoints

• dynamic pressure triggering threshold

• open-loop bank angle

• D-V tracking command gains

• route angle corridor width

• a.o.a command gains (if modulation)

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09/02/07 p9

Re-entry Guidance scheme

NAVIGATION

a.o.a entry profile

a.o.a

Mach

EGC

Qmax

Gmax

Fmax

Drag

Velocity

DV profile update

Dstr = 1 Dref

KD-V

CONTROL

EGC

Qmax

Gmax

Fmax

Fref

Dref

D45

D12

Df

V12 V23 Vt34 Vt45 Vtf

Drag

Velocity

Reference DV profile

1

2 3 4

5

Drag

EGC

Qmax

Gmax

Fmax

Velocity

DV profile tracking

route angle

roll reversal technique

Velocity


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09/02/07 p10

V23 = f(V12,D12,D23)

Vt34 = f(Vt45, Vtf, D23,D45, Df)

Phase 1 Phase 2

Phase 3Phase 4 Phase 5

D-V profiles drawings

to rely on a flyable D-V profile meeting design & extra smoothness constraints

dedicated process to generate the sets of compliant Di-Vi waypoints


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09/02/07 p11

Mission constraints

Design constraints

Extra constraints

Objective functions and fitness

missrange at TAEM handover[ ]( )2offset1M rangemaxOBJ =

no-skip trajectory[ ]( ) 0hwithhmaxOBJ2

5M >D= &

max. dynamic pressure[ ]( ) [ ]

=

-=

otherwise0OBJ

QQmaxifQQmaxOBJ

2M

maxesti2

maxesti2M

[ ]( ) [ ]

=

GGG-G=

otherwise0OBJ

maxifmaxOBJ

4M

maxesti

2

maxesti4M max. load factor

max. heat flux[ ]( ) [ ]

=

FFF-F=

otherwise0OBJ

maxifmaxOBJ

3M

maxesti

2

maxesti3M

D-V profile tracking cost

-= dtDDmaxOBJ

fT

0

refesti1A

bank angle consumption

m= dtmaxOBJ

fT

0

esti2A

AoA consumption (if AoA modulation)

a= dtmaxOBJ

fT

0

esti3A

Global cost KK +++++=2A2A1A1A2M2M1M1Mglob OBJKOBJKOBJKOBJKOBJ


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09/02/07 p12

GAGHARIN Toolbox (1)

GAGHARIN 78 M-files, 23450 lines of code

SITHAR 172 files, 17500 lines of code

Genetic Algorithm for Guided Hypersonic Atmopsheric Re-entry desIgN

■ mission data: vehicle, mission, constraints, …

■ GA data: genetic operators, objective functions, …

■ run data (SITHAR tool)

■ GA outputs: static/dynamic 2D or 3D displays, ….

Matlab toolbox enabling the choice of

simulation core: SITHAR (Fortran end-to-end pseudo 6 dof simulation tool)

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09/02/07 p13


Graphical User Interface

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09/02/07 p14

GAGHARIN dynamic displays (examples)

individuals

chromosomes

value

generations

individuals

objective

function


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09/02/07 p15

Application to a high L/D Vehicle (1)

mass 2000 kg

reference area 9 m2

length 5.9 m

wing span 3.2 m

max roll rate 15 deg/s

L/D 1.1 to 2.2

ARES-H vehicle and mission

demoflight mission

Z= 120.0 km

V= 7593.0 m/s

g = -1.34 dega.o.a

Mach 5 Mach 2

40 deg

12 deg

L/D = 1.1L/D = 2.2

TSTO 1:5 sub-scale

max g-load 5 g

max heat flux 500 kW/m2

footprint

downrange= 7025 km

cross-range= -213 km

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09/02/07 p16


Input/Output data

■ D-V profile Fref,Di-Vi, i = 2,5

■ command gains parameters xi, w1,i, w2,i, i =

1,2

■ route angle corridor width DYi, i = 1,5

■ Guidance triggering QON

chromosomes

population 20 individuals, 50 generations

GA tuning

closed-loop D-V tracking w/o a.o.a modulation down to Mach 2 gate

limitation to 5 roll reversals (nose-up), with no roll reversal engaged below 30 km altitude

GPS & DDA & IMU Navigation scenario

■ authorised transient violation of EGC boundary

■ generation gap 0.9

■ linear ranking with selective pressure SP = 2

■ exponential scaling with a 0.1scaling rate

■ roulette wheel selection

■ extended line recombination, with a 0.7 crossover rate

■ real-valued mutation with 0.025 mutation rate

■ fitness-based reinsertion with a 0.7 reinsertion rate

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09/02/07 p17


Final Monte-Carlo results

parameter requirement worst case

heat flux < 500 kW/m2 465 kW/m2

g-load < 5 g 2.7 g

miss-range < 25 km 11.3 km

min F.P.A < 0 deg -0.06 deg

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09/02/07 p18

Conclusion (1)

Using only heuristic considerations, GAs are able to provide rather quickly

quasi-optimal solutions to a given complex optimization problem

A dedicated tool relying on Genetic algorithms has been developed to design

the nominal guided entry path while tuning the Guidance mission/internal data

in a one-shot process with D-V profile margins update capability

A multi-objective management using Pareto optimality instead of a single global

scalar objective could improve GA performances by exploring more efficiently

the search space and thus finding quickly optimal solutions closer to the global

optimum

GAs will quite always find a solution, but with a possible handmade refinment

Beside a classical handmade tuning, GAs user may loose physical meaning

of what he’s doing

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09/02/07 p19

Conclusion (2)

environment

vehicle design

nominal entry path

mission & path constraints

drawing process

nominal D-V profile

GAGHARIN toolbox = intelligent and cooperative slot machine dedicated to robust

and one-shot design of hypersonic re-entry problem

but improvements have still to be done…

Technology

Genetic Algorithm for Coupled RLV Trajectory & Guidance Optimization