  In this paper, a model predictive control (MPC) framework is employed to
realize autonomous rendezvous and docking (AR&D) with a tumbling target, using
the piecewise affine (PWA) model of the 3-D line-of-sight (LOS) dynamics and
Euler attitude dynamics. Consider the error between the predictions obtained by
the approximate linear model and the actual states of nonlinear dynamics, a
sampling-based PWA MPC is proposed to sample the predictions in the closer
neighborhood of the actual states. Besides, novel constructions of constraints
are presented to reduce the on-board computation cost and time-delay.
Furthermore, a singularity-free strategy is provided to realize crossing the
singularity of angle states smoothly. Then, the mission is achieved by
continuous 6-DOF pose (position and attitude) tracking of the target's docking
port, with the coupling between the position and attitude of the target's
docking port is taken into account. Finally, numerical results are presented to
demonstrate the above theories.
