Unmanned aerial vehicles (UAVs) have recently gained increasing attention. Self-positioning and integrated navigation are main aspects during a flight mission and rely on predefined trajectories. Current guidance and control systems provide real-time control laws to track desired trajectories given by the Embedded Flight Management System (E-FMS). Since some UAVs are highly non-linear systems with under-actuation properties from the control point of view, discontinuities in control inputs (coming from trajectories generated by E-FMS) can produce undesired vibrations causing aging and damages in the structure. In this paper, we propose a Recursive Smooth Trajectory generation algorithm (RST) that allows for finding a smooth \mathcal{C}^{\propto} polynomial path, and thus a close form trajectory satisfying any arbitrary dynamic limitations translated into kinematic constraints (e.g. position, velocity, acceleration, etc). Each kinematic constraint is recursively fulfilled, leading to a fast online implementation for the E-FMS. The storage requirements and execution time are therefore discussed in this paper. The effectiveness and suitability of the RST algorithm over a minimum-snap piecewise polynomial approach for highly nonlinear UAV flight is also analyzed.
