AUV rendezvous trajectories generation for underwater recovery

For many years, autonomous underwater vehicles (AUVs) have been developed and employed for a myriad of tasks. Their ability to accurately collect and monitor oceanic conditions makes them a valuable asset for a variety of naval missions. Deploying and recovering AUVs, however, is currently largely limited to surface vessels or swimmers. The purpose of this paper is to demonstrate that by using a mathematical technique called a direct method of calculus of variations, it is possible for an AUV to autonomously compute and execute a trajectory that will allow for recovery by a submerged mobile recovery system (another AUV, submarine, etc.). The algorithm ensures that a smooth trajectory is produced that, while not traditionally optimal, is realistic and still close to the optimal solution. Also, using this technique allows the trajectory to be computed very rapidly allowing it to be recomputed every couple of seconds to accommodate sudden changes, possible adjustments and different disturbances, and therefore to be used in the real life.