The main contribution of the authors is to present a Fast Marching based method as an advanced tool for underwater trajectory planning (Petres et al., 2007). With a similar complexity to classical graph-search techniques in Artificial Intelligence, the Fast Marching algorithm converges to a smooth solution in the continuous domain even when it is implemented on a sampled environment. This specificity is crucial to the understanding of the other contributions of our method:

• FM* algorithm: we develop a new algorithm called FM* that is a heuristically guided version of the Fast Marching algorithm. The FM* algorithm combines the efficiency of the A* algorithm (Hart, 1968) with the accuracy of the Fast Marching algorithm (Sethian, 1999).

• Curvature constrained trajectory planning: the FM* algorithm allows the curvature of the trajectory solution to be constrained, which enables us to take the turning radius of any mobile robot into account.

• Dynamic and partially-known domains: a dynamic version of the Fast Marching algorithm, called DFM, is proposed to deal with dynamic environments. DFM algorithm is then proved to be very efficient to recompute trajectories after minor changes in the robot perception of the world.

• Simulations and open water trials: a complete architecture has been designed, developed and tested for simulated and real AUV missions. In-water experiments are compared to simulation results to demonstrate the performance and usefulness of the DFM-based trajectory planning approach in the real world.

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