This paper focuses on path planning problem for a single beacon vehicle supporting a team of autonomous underwater vehicles (AUVs) performing surveying missions. Underwater navigation is a challenging problem due to the absence of GPS signal. The positioning error grows with time even though AUVs nowadays are equipped with onboard navigational sensors like compass for dead reckoning. One way to minimize this error is to have a moving beacon vehicle equipped with high accuracy navigational sensors to transmit its position acoustically at strategic locations to other AUVs. When it is received, the AUVs can fuse this data with the range measured from the travel time of acoustic transmission to better estimate their own positions and minimize the error. In this work, we address the beacon vehicle's path planning problem which takes into account the position errors being accumulated by the supported survey AUVs. The resultant path will position the beacon AUV at the strategic locations during the acoustic signal transmission. We formulate the problem within a Markov Decision Process (MDP) framework where the path planning policy is being learned through Cross-Entropy (CE) method. We show that the resultant planned path using the policy learned is able to keep the position error of the survey AUVs bounded throughout the simulated runs.
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