  Capturing disused satellites in orbit and their controlled reentry is the aim
of the DEOS space mission. Satellites that ran out of fuel or got damaged pose
a threat to working projects in orbit. Additionally, the reentry of such
objects endangers the population as the place of impact cannot be controlled
anymore. This paper demonstrates the modelling of a rendezvous szenario between
a controlled service satellite and an uncontrolled target. The situation is
modelled via first order ordinary differental equations where a stable target
is considered. In order to prevent a collision of the two spacecrafts and to
ensure both satellites are docked at the end of the maneuver, additional state
constraints, box contraints for the control and a time dependent rendezvous
condition for the final time are added. The problem is formulated as an optimal
control problem with Bolza type cost functional and solved using a full
discretization approach in AMPL/IpOpt. Last, simulation results for capturing a
tumbling satellite are given.
