This paper addresses the problem of path planning in strong current fields. In such situations, existing approaches are subject to incorrectness and incompleteness issues. That is, they may return physically infeasible paths or no path at all, even if a feasible path exists. That is why we propose here a new approach called the sliding wavefront expansion. This algorithm, which combine an appropriate cost function and continuous optimization techniques, guarantees the existence of a path with an arbitrary precision. The validity and the global optimality of the path are theoretically proven. Simulation results on realistic environments, which is based on actual wind charts, are also provided.

Numerous approaches have been proposed for path planning in dynamic current fields, for a fixed departure time. However, in many applications, the departure time is not necessarily known in advance, but can vary in a time window. In this context, the choice of a good departure time is a critical issue. That is why we introduce in this paper a new approach, called symbolic wavefront expansion, determining both the path and the departure time minimizing the travel time of the vehicle. The key idea of this approach is to propagate and compose functions instead of numerical values, with appropriate operators.

The wavefront expansion is commonly used for path planning tasks and appreciated for its efficiency. However, the existing extensions able to handle currents are subject to incorrectness and incompleteness issues when these currents become strong. That is, they may return physically infeasible paths or no path at all, even if a feasible path exists. This behavior endangers the robot, especially in a dynamic replanning context. That is why we propose a new extension called sliding wavefront expansion. This algorithm, combining an appropriate cost function and continuous optimization techniques, guarantees the existence of a path with an arbitrary precision.

The concept of wavefront expansion was introduced in order to build a collision-free path between two points among obstacles, minimizing a criterion. In this paper, we propose a new concept, called wavefront collision, in order to do the same for all possible paths between n waypoints. It consists in expanding simultaneously one wavefront by waypoint, until they collide. Using this concept, all paths can be computed thanks to one multiple wavefront expansion instead of n - 1, hence dividing the computational effort by about 3.5.