Three-Dimensional Curvature-Constrained Trajectory Planning Based on In-Flight Waypoints

This paper proposes an efficient algorithm with a novel procedure for trajectory planning of unmanned aerial vehicles in three-dimensional space. This work has been motivated by a challenge to develop a fast trajectory planning algorithm for autonomous unmanned aerial Vehicles through the midcourse waypoints. The waypoints that are defined as a preflight or in-flight procedure are described in a five-dimensional configuration: the position in three dimensions plus desired crossing heading and flight-path angles. For achieving the waypoints, the Dubins path is extended to three-dimensional applications by using the geometrical concepts. In addition, the trajectory planning algorithm is represented as a set of ordinary differential equations called optimal-constrained-trajectory kinematics by applying the differential geometry concepts. Optimal-constrained-trajectory kinematic is a closed-loop guidance law that generates the guidance commands based on the waypoint configuration and minimum turning radius and is solved in a real-time manner. The proposed algorithm includes an operational framework that leads to gradually generating the smooth three-dimensional trajectory, aimed at reaching the midcourse targets and final target so that they are smoothly connected to each other. Finally, the simulation results show the capability of the algorithm in dynamic trajectory planning in low computational burden.