Surveillance Planning with Bézier Curves

Abstract

This paper concerns surveillance planning for an Unmanned Aerial Vehicle (UAV) that is requested to periodically take snapshots of areas of interest by visiting a given set of waypoint locations in the shortest time possible. The studied problem can be considered as a variant of the combinatorial traveling salesman problem in which trajectories between the waypoints respect the kinematic constraints of the UAV. Contrary to the existing formulation for curvature-constrained vehicles known as the Dubins traveling salesman problem, the herein addressed problem is motivated by planning for multi-rotor UAVs which are not limited by the minimal required forward velocity and minimal turning radius as the Dubins vehicle, but rather by the maximal speed and acceleration. Moreover, the waypoints to be visited can be at different altitudes, and the addressed problem is to find a fast and smooth trajectory in 3D space from which all the areas of interest can be captured. The proposed solution is based on unsupervised learning in which the requested 3D smooth trajectory is determined as a sequence of Bézier curves in a finite number of learning epochs. The reported results support feasibility of the proposed solution which has also been experimentally verified with a real UAV.