DITAN: A TOOL FOR OPTIMAL SPACE TRAJECTORY DESIGN - ESA

University of Glasgow,Department of Aerospace Engineering, James Watt Building, Glasgow G12 8QQ, Tel. +44-141-330-6465 mail: [email protected]

Introduction What’s new?Study Cases Final Remarks

DITAN: A TOOL FOR OPTIMAL SPACE TRAJECTORY DESIGN

Massimiliano Vasile

Department of Aerospace Engineering, Glasgow University, Glasgow

Ruediger Jehn

ESA/ESOC



Outline

Introduction to DITAN

Study Cases What’s new? Final Remarks

Agenda



•DITAN (direct Interplanetary Trajectory Analysis) is a general purpose tool for the solution of optimal control problems.

•It implements a Direct Finite Elements Transcription (DFET) of the optimal control problem into a nonlinear programming problem (NLP)

•The solution of the resulting NLP is performed by the sparse SQP optimiser SNOPT

•The specific optimal control problem implemented in DITAN allows to design low-thrust multiple gravity assist trajectories.




• Developed under ESA/ESOC contract for low-thrust multiple gravity assist trajectories

• Open system for general trajectory design based on Direct Finite Element Transcription (DFET) and SSQP

• Fortran 77 code has SNOPT (source code) as NLP engine

• Several dynamic models, constraints and objectives can be implemented

• Automatic mesh grid adaptivity is included




DITAN: Software Logic

Dynamic Model

Algebraic

Constraints

Objective Function

DFET

Discretisation

Phase

Assembly

Boundary Constraints

NLP Solver

NLP Problem

First Guess OutputInput Post Processing

user

s/w core

external



Direct Transcription by FET

• The Time domain is decomposed in finite elements leading to a polynomial development of the solution on spectral basis (Gauss Points)

t

x

t

xs

xbf

xbi

ts

Gauss

Point

Boundary

Nodes

Boundary gap b

),(11 iii

N

ittDD




• Differential constraints are expressed in weak form leading to discontinuities at boundaries

• High Integration order 2n = 2k+2

t

x

t

xs

xbf

xbi

ts

Gauss

Point

Boundary

Nodes

Boundary gap b

ft

t

bT

ft

t

T dt0

0

)( xxwFxw ˙




Optimal Control

ProblemDFET

NLP Problem

min J(y)

wherey=[x,u,ti ,tf]

T SSQP

Sparse Sequential

Quadratic

Programming

( )

l u

c y 0

b y b

l

iisiss

b

j

Tb

j

T

p

j

is

T

ikis

T

iki

q

i

l

t

!

˙

0)),(),((

02

)()()()(

)(

111

1

uxG

xwxwFwxw

yc



Parametric Optimisation

f

i

t

t

f

b

f

b dtLtJ ),,(),,,( 0 puxpxx

0),,,( tpuxFx

0),,,( tpuxG

0),,,(0

0

ft

t

b

f

b tpxx

)J( min y

ul byb

yc 0)(

y=[xs,us,xb

0,xb

f,t0,tf,p]

DITAN allows the inclusion of a general set of real parameters and related constraint and objective functions



Multiphase Approach

),,( tJ l ux

Interphase-link Constraints

),,( tluxFx

0),,( tluxG

0))(()(

)()(

1

1

1

l

f

bll

i

b

l

f

l

i

l

f

bl

i

b

tt

tt

tt

xx

xx

),,,( l

f

l

i

l

f

l

i

l

link ttxx

Phase l

Assembly

NLP Solver0),,,(

0

ft

t

b

f

b

i

l tpxx

DITAN allows the solution of problems with a finite number of discontinuities, multiple reference frames, multiple dynamic models and multiple objectives, through a multiphase decomposition of the trajectory. Phases can be sequential or parallel.



Examples of Applications

• Multiple swing-by low-thrust Trajectories:

– SOLO

– Bepi Colombo

– Europa

– Mars Exobiology

– Pluto Probe

– NEO Rendezvous

• Robustness Optimisation

– Optimal NEO interception and deviation

• Multiobjective and Pursuit-Evasion Problems

• Mars free-return Trajectories

• Moon WSB Transfers



SOLO and BepiColombo

• 3000 variables and constraints for the NLP problem

• 4 to 7 swingbys

• resonant orbits

• more than 20 switching points

Example of Matlab output for a BepiColombo Trajectory



Europa

• 6000-7000 variables and constraints for the NLP problem

• 14 swingbys

• resonant orbits

• variable thrust

• Variable reference frames



Pluto Probe

• 1000-7000 variables and constraints for the NLP problem

• parallel phases• multiple objectives• Multiple swingbys

Interplanetary trajectoryTwo parallel phases at Jupiter passage



NEO Rendezvous

• 1000-3000 variables ad constraints.

• Variable thrust and variable Isp

• Mean orbital elements for multispiral escape from the Earth



Robustness Optimisation

• 1000-2000 variables and constraints

• multiple objectives• minimisation of the

uncertainties and of the expected value of the objective



Multiobjective and Pursuit-Evasion Problems

• Zero-sum differential game

• Multiple objectives

• Reconstruction of the correct lagrangian multipliers of the optimal control problem



Mars free-return Trajectories and Low-thrust Cyclers


• 1-14 swingbys

• Impulsive and low-thrust



Moon WSB Transfers


• Highly nonlinear and unstable dynamics

• Impulsive manoeuvres



New Features

New features:

Improved user interface: easier editing of the input files

New graphical user interface for trajectory representation

Transfer coast arcs can be analytically propagated: faster solution of MGA with chemical propulsion

Transfer arcs can be imported and edited



New Features

New features:

Extended database of celestial bodies: asteroids and comets database, updatable

New sets of boundary conditions: numerically or analytically propagated orbits

New set of objective functions: orbit insertion v with gravity losses, staging.

Atmospheric legs: aerocapture

Restricted three-body dynamics



Final Remarks

DITAN has been effectively applied to the solution of many mission design problems.

A limitation exists on the maximum dimension of the problems that can be solved.

An improved NLP solver is required and it is under development at present

Since many problems have a hybrid structure (mixed integer-real variables) the new NLP is conceived to tackle hybrid problems.

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DITAN: A TOOL FOR OPTIMAL SPACE TRAJECTORY DESIGN - ESA