OPTEC - K.U.Leuven Center of Excellence: Optimization in Engineering

" Spacecraft Trajectory Optimization in a Project Environment "
Sven Erb (ESA - TEC/ECM , Netherlands)

It is one of the core competencies of the Dynamics and Mathematical
Analysis Unit TEC/ECM at the European Space Agency ESA to conduct
trajectory planning and related analysis services for ESA projects. The
activities range from advanced launch vehicle ascent and re-entry
trajectories and sizing of the vehicle, to spacecraft planetary transfers,
and interplanetary travel. It is common practice to employ optimization
techniques for such tasks. The preferred approach at TEC/ECM for solving
such problems is based on non-linear programming. The standard software is
GESOP/ASTOS, a graphical environment for simulation and optimization that
features NLP solvers, such as SNOPT and SOCS.

The primal problems with continuous controls and optimizable parameters is
transcribed into non-linear programming problems and subsequently solved
by means of NLP solvers. A typical example is the re-entry of a winged
vehicle into the earth atmosphere, where the angle of attack and the
sideslip angle are optimizable.

From the perspective of a practitioner, who uses the optimization software on heterogeneous tasks, robustness, flexibility, user friendliness and
precision are driving criteria for the usefulness of the algorithm. It is
an asset, if the user can stay close to the real world during the
optimization, with established physical properties, and does not have to
deal with costates, arising from indirect solution methods.

The range of optimization problems and sizes is illustrated through a
number of current spacecraft projects. Typical missions are, for instance,
launch vehicles, where the ascent trajectory has to satisfy a multitude of
constraints with very different character; or low-thrust transfer
trajectories, where the problem description can easily go beyond 100.000
parameters.