**Search for lost targets**

The minimum time search problem consists in determining the best sequence of actions (observations) to find a target (object) with uncertain location in the minimum time possible. In more colloquial way we can pose the following question: where do we have to look to find a lost object as soon as possible? I propose a Bayesian approach to efficiently find the target using several moving agents with constrained dynamics and equipped with sensors that provide information about the environment. The whole task involves two processes: the target location estimation using the information collected by the agents, and the planning of the searching routes that the agents must follow to find the target. The agents trajectory planning is faced as a sequential decision making problem where, given the a priori target location estimation, the best actions that the agents have to perform are computed. For that purpose, three Bayesian strategies are proposed: minimizing the local expected time of detection, maximizing the discounted time probability of detection, and optimizing a probabilistic function that integrates a heuristic that approximates the expected observation. The minimum time search problems are found inside the core of many real applications, such as search and rescue emergency operations (e.g. shipwreck accidents).