Cameras are rapidly becoming the choice for on-board sensors towards space rendezvous due to their small form factor and inexpensive power, mass, and volume costs. When it comes to docking, however, they typically serve a secondary role, whereas the main work is done by active sensors such as lidar. This paper documents the development of a proposed AI-based (artificial intelligence) navigation algorithm intending to mature the use of on-board visible wavelength cameras as a main sensor for docking and on-orbit servicing (OOS), reducing the dependency on lidar and greatly reducing costs. Specifically, the use of AI enables the expansion of the relative navigation solution towards multiple classes of scenarios, e.g., in terms of targets or illumination conditions, which would otherwise have to be crafted on a case-by-case manner using classical image processing methods. Multiple convolutional neural network (CNN) backbone architectures are benchmarked on synthetically generated data of docking manoeuvres with the International Space Station (ISS), achieving position and attitude estimates close to 1% range-normalised and 1 deg, respectively. The integration of the solution with a physical prototype of the refuelling mechanism is validated in laboratory using a robotic arm to simulate a berthing procedure.