Six degree of freedom optimal trajectories for satellite rendezvous

A method is developed for computing the minimum fuel trajectory for a satellite that moves between two different positions and orientations using a sequence of impulsive burns. The method makes use of the linear Clohessy-Wiltshire equations to describe translational motions, Euler's equations of rigid body motion for describing the attitude motions, and a sequential quadratic programming optimization code. Initial solutions are found assuming no coupling between the translational and rotational motions and with no imposed constraint on the time of the rendezvous. Further solutions are then found by varying the vehicle center of gravity location along one axis, thereby coupling the rotational motions into two axes of translation thrusters, and by imposing time limits on the rendezvous. A discussion of the impact that these parameters have on the optimal solutions for two different models of the satellite thruster systems is then presented.