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This brief presents a real-time, feasible trajectory generation algorithm for unmanned air vehicles (UAVs) flying through a sequence of waypoints. The algorithm produces extremal trajectories that transition between straight-line path segments in a time-optimal fashion. In addition, the algorithm can be configured so that the dynamically feasible trajectory has the same path length as the straight-line waypoint path. Implementation issues associated with the algorithm are described in detail. Simulation studies show the effectiveness of the proposed method.