  In this paper, the trajectory planning problem for autonomous rendezvous and
docking between a controlled spacecraft and a tumbling target is addressed. The
use of a variable planning horizon is proposed in order to construct an
appropriate maneuver plan, within an optimization-based framework. The involved
optimization problem is nonconvex and features nonlinear constraints. The main
contribution is to show that such problem can be tackled effectively by solving
a finite number of linear programs. To this aim, a specifically conceived
horizon search algorithm is employed in combination with a polytopic constraint
approximation technique. The resulting guidance scheme provides the ability to
identify favourable docking configurations, by exploiting the time-varying
nature of the optimization problem endpoint. Simulation results involving the
capture of the nonoperational EnviSat spacecraft indicate that the method is
able to generate optimal trajectories at a fraction of the computational cost
incurred by a state-of-the-art nonlinear solver.
