The underwater world is a very demanding environment for trajectory planning algorithms. Great efforts are currently being made to develop autonomous systems as underwater technology becomes more mature. Several key issues for the three dimensional underwater trajectory planning problem have been addressed in this chapter. Reliability of trajectory planners has been improved by introducing the Fast Marching algorithm as a new basis for sampling based trajectory planning methods in the continuous domain.
First, we have introduced the trajectory planning framework and the basic concepts shared by all the deterministic sampling based planning algorithms. The Fast Marching method, as one of these trajectory planning technique is similar in spirit to classical grid-search algorithms such as the A* algorithm. This led us to develop a new algorithm, called FM*, that combines the exploration efficiency of the A* algorithm with the accuracy of the Fast Marching method. For these reasons, the FM* algorithm opens new possibilities for planning trajectories in wide and continuous underwater environments.
Second, even if they are implemented on a discretized perception of the world, Fast Marching based planning methods have the property to extract derivable trajectories. By applying mathematical tools from differential geometry, it has been proved that smoothing input data results in smoother trajectories. A technique has been proposed that insures the feasibility of a trajectory for a mobile robot with a given turning radius. This technique iteratively smoothes input data until a formal criterion is satisfied. The method is efficient because the Fast Marching algorithm is eventually launched only when input data are compliant with the curvature constraints of the vehicle.
Third, another approach has been developed to speed up the exploration process in the case of partially-known or dynamic environments. A dynamic version of the Fast Marching algorithm, called DFM, has been presented that is able to reuse information of previous searches. Compared to A*, FM, FM* and D* Lite algorithms, the DFM algorithm is very efficient when changes happen randomly in the vehicle's perception of the world. Eventually, a complete architecture has been designed, developed and tested for real AUV missions. Performance and usefulness of the DFM based trajectory planning approach in partially-known domains have been demonstrated using the experimental prototype of the Ocean Systems Laboratory.
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