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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.

DKP (Deterministic Kinodynamic Planning) is a bottom-up trajectory planner for robots with flatnessproperties. DKP builds an exploration tree of which the branches are spline trajectories. DKP employs an A * -like algorithm to select which branch of the tree to grow. The selected trajectories are then grown in a propagation process which respects the kinematic constraints, such as linear/angular speed limits or obstacle avoidance. In addition, DKP produces trajectories that are immediately executable by the robot. Various experiments are provided to show the ability of DKP to effectively handle complex environments with one or more robots. I. INTRODUCTIONComputing a trajectory that takes into account both kinematic and dynamic constraints is known as kinodynamic planning [5], and is proven to be PSPACE-hard [22].Decoupled approaches separate kinodynamic planning in two successive problems; first, compute a path taking into account a part of the problem constraints (classically obstacles) and, then, smooth this path with the remaining constraints to make the solution admissible by the robot. The efficiency of decoupled approaches, such as variants of Elastic Bands [23], is explained by the fact that they are generally customized for specific kinodynamic problems [15]. They also provide bounds on the computation time, allowing on-line planning, which explains their wide usage. However, decoupled approaches present difficulties to solve complicated problems, with many degrees of freedom. Moreover, they suffer from incompleteness issues: since the initial path is not guaranteed to be feasible by the robot, the path smoothing phase may fail to satisfy all kinodynamic constraints or fail to find a solution even if one exists.To solve these difficulties [18], we can distinguish two categories of hybrid approaches which incorporate a local motion planner (selection process) within a global path planner (propagation process) to ensure the respect of constraints. The first category contains heavily customized approaches: both local and global motion planner are then designed to generate complex local maneuvers [11] and/or improve the quality of the global path to be tracked. They successfully deal with very specific problems, such as [6] which integrates perception sensors in the local planner; or the multi resolution approaches like AD * [18].

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