  As the number of uncontrollable objects in low earth orbit is rising, the
thread of collisions and thus the breakdown of working satellites becomes worth
analyzing. Consequently, projects on removing objects from the important orbits
are taken into account by the international space associations. This paper is
about the modelling and optimal path planning of a docking maneuver to an
uncontrollable tumbling target. After deriving the system dynamics, we
introduce boundary conditions to ensure a safe and realizable maneuver and a
general Bolza type cost functional to incorporate different optimization goals.
In order to solve the resulting problem, we transform the dynamics to a set of
differential algebraic equations which allow us to employ a direct optimization
method while perserving the energy of the system. The concluding simulation
results show the reliability and effectiveness of this approach.
