In this work we study the problem of landing a quadrotor on an inclined moving platform. The aerial robot employs an forward looking on-board camera to detect and observe the landing platform, which is carried by a mobile robot moving independently on an inclined surface. The platform may also be tilted with respect to the mobile robot. The overall goal is to design the aerial robot's control inputs such that it initially approaches the platform, while maintaining it within the camera's field of view and finally lands on it, in a way that minimizes the errors in position, attitude and velocity, while avoiding collision. Owing to the inclined ground and landing surface, the desired final state of the aerial robot is not an equilibrium state, which complicates significantly the control design. In that respect, a discrete-time non-linear model predictive controller was developed that optimizes both the trajectories and the time horizon, towards achieving the aforementioned objectives while respecting the input constraints as well. Finally, an extensive experimental study, with a Pioneer mobile robot and a Parrot ARDrone quadrotor, clarifies and verifies the theoretical findings.