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
22
Embed
DITAN: A TOOL FOR OPTIMAL SPACE TRAJECTORY DESIGN - ESA
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
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
Outline
Introduction to DITAN
Study Cases What’s new? Final Remarks
Agenda
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 (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.
Introduction to DITAN
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
• 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
Introduction to DITAN
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: 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
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
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
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
Direct Transcription by FET
• 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 ˙
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
Direct Transcription by FET
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
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
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
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
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.
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
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
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
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
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
Europa
• 6000-7000 variables and constraints for the NLP problem
• 14 swingbys
• resonant orbits
• variable thrust
• Variable reference frames
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
Pluto Probe
• 1000-7000 variables and constraints for the NLP problem