An efficient optimization method to deal with global RLV (ascent and branching) trajectories

Paper number

IAC-05-C1.P.18

Author

Mr. Julien Laurent-Varin, INRIA, France

Coauthor

Mr. Nicolas Berend, Office National d’Etudes et de Recherches Aérospatiales (ONERA), France

Coauthor

Mr. Christophe Talbot, Centre National d'Etudes Spatiales (CNES), France

Coauthor

Mr. Frédéric Bonnans, INRIA, France

Year

2005

Abstract

The talk is devoted to the optimisation of the multi-edge trajectory
of a future space launcher, using an interior-point algorithm,
combined with dedicated linear algebra solvers, as well as an
optimized refinement policy based on a precise control of integration
errors. We apply our tool to a simple model of re-entry and probably
on multi-edge trajectory.

Basically, the algorithm consists in Newton steps applied to the
primal-dual formulation of the optimality system with logarithmic
penalty of all inequality constraints. We adopted the so-called dogleg
procedure in order to globalize the algorithm.

Our linear algebra tool is based on the band structure of the
Jacobian, which (up to a doubling of bandsize) is compatible with the
QR factorization (that, since it is based on rotations, has strong
stability properties). Design parameters are dealt with a bilevel
procedure within the linear algebra procedure.

The interior-point methodology allows refinement at any stage of the
algorithm. This means that, for a given value of the logarithmic
penalty parameter, we may reach a given target on integration errors,
and hence, solve the penalized problem with a prescribed precision.

Finally, the refinement policy is (asymptotically) optimal since the
knowledge of error order allows to predict the decrease of errors
associated with a given refinement, and hence, it is possible to find
the optimal refinement allowing to reach a given target.

After the presentation of this method, we validate it successfully on
several reentry problems with an increasing level of difficult, by
adding path constraints and changing the cost function. Moreover, we
can see that with a minimum cpu-time for computation we obtain an
optimal trajectory where the error estimation is controled.

Abstract document

IAC-05-C1.P.18.pdf

Manuscript document

IAC-05-C1.P.18.pdf (🔒 authorized access only).

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