This paper presents a semi-analytical trajectory planning method for quadrotor UAVs. These trajectories are analytically defined, are constant in speed and sub-optimal with respect to a weighted quadratic cost function of the translational and angular velocities. A technique for concatenating the trajectories into multi-segment paths is demonstrated. These paths are smooth to the first derivative of the translational position and pass through defined waypoints. A method for detecting potential collisions by discretizing the path into a coarse mesh before using a numerical optimiser to determine the point of the path closest to the obstacle is presented. This hybrid method reduces the computation time when compared to discretizing the trajectory into a fine mesh and calculating the minimum distance. A tracking controller is defined and used to show that the paths are dynamically feasible and the typical magnitudes of the controller inputs required to fly them.
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