  In this article, we present a control strategy for the problem of safe
autonomous docking for a planar floating platform (Slider) that emulates the
movement of a satellite. Employing the proposed strategy, Slider approaches a
docking port with the right orientation, maintaining a safe distance, while
always keeping a visual lock on the docking port throughout the docking
maneuver. Control barrier functions are designed to impose the safety,
direction of approach and visual locking constraints. Three control inputs of
the Slider are shared among three barrier functions in enforcing the
constraints. It is proved that the control inputs are shared in a conflict-free
manner in rendering the sets defining safety and visual locking constraints
forward invariant and in establishing finite-time convergence to the visual
locking mode. The conflict-free input-sharing ensures the feasibility of a
quadratic program that generates minimally-invasive corrections for a nominal
controller, that is designed to track the docking port, so that the barrier
constraints are respected throughout the docking maneuver. The efficacy of the
proposed control design approach is validated through various simulations.
