Resumen
The aim of this research paper is to propose a framework to model, simulate and control the motion of a small spacecraft in the proximity of a space station. In particular, rendezvous in the presence of physical obstacles is tackled by a virtual potential theory within a modern manifold calculus setting and simulated numerically. The roto-translational motion of a spacecraft as well as the control fields are entirely formulated through a coordinate-free Lie group-type formalism. Likewise, the proposed control strategies are expressed in a coordinate-free setting through structured control fields. Several numerical simulations guide the reader through an evaluation of the most convenient control strategy among those devised in the present work.