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...prove thessmoothness of the trajectories; Philippsen [41] introduces an interpolated Navigation Function,sbut with trajectories too close to obstacles and without smooth properties; and Petres et al. =-=[40]-=-sintroduce efficient path-planning algorithms for Underwater Vehicles that take advantage ofsunderwater currents. They developed an algorithm called , which is a continuous version ofsthesalgorithm ba...

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...s, as the majority of underwater vehicles are propeller-driven, short-duration (< 24 hr) AUVs. A shared downside to these planners is the assumption that the vehicle thrust is assumed constant (e.g., =-=[22]-=-, [23] and [24]). This condition is restricting in the case of a general AUV, however this is precisely the situation for a glider. On the other hand, all of these works assume that the vehicle can ch...

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...Vehicles (AUVs), which are generally small or slow, the impact of (air or water) currents is significant. In this context, several extensions of the original wavefront expansion have been proposed [5]=-=[7]-=-, but they become incorrect in presence of strong currents. That is to say, they may provide a path which is not physically feasible by the robot. This behavior is due to the use of invalid cost funct...

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...a different variety of sensors. Thessystem is also extendable. Some examples of this extendibility have been recently shown in parallelsworks, where trajectory constraints based on vehicle kinematics =-=[6]-=- and localisation uncertainties [28]sare added to the system to improve its capability of adaptation within a changing environment. Moresextensions assessing changes in higher levels of plan abstracti...

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...ing done at the level of trajectory planning. Trajectory planning algorithms have become quite mature and efficient algorithms for continuous adaptation of vehicle trajectory are now state of the art =-=[4]-=-. As new applications and more complicated tasks are required for autonomous vehicles, this decision making must be extended to make changes to the mission itself. A planning algorithm may be used pre...

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...ath corridors along great circle routes using A ∗ . This algorithm finds path corridors that satisfy path constraints such as minimum depth, desired depth, maximum depth, width and fuel resources. In =-=[8]-=-, Petres et al, introduce an algorithm called Fast Marching (FM) and extensions to it to deal with underwater currents. In this algorithm, they can specify the curvature of the final path which allows...

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... [1], [2], [11] can now produce current forecasts at time scales and resolutions sufficient to inform glider plans. While a growing body of work addresses path planning in a static current field [9], =-=[5]-=-, [7], currents in the glider scenario vary on time scales much shorter than the mission duration. Dynamic currents of the Slocum glider domain demand true spatiotemporal path planning. Advances in th...

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... trajectories than classic discrete search approaches. This fast marching methods are capable of dealing with uncertainty, dynamic objects and kinematics of the vehicle during the adaptation process (=-=Pêtrès et al. 2007-=-). A real application of these techniques in the underwater environment is shown in Fig. 8. Mission planning Single platform Current mission plan solutions for underwater platforms are procedural and ...

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...r or water) currents is significant, and cannot be neglected. Specific path planning approaches have been proposed to handle currents, based on evolutionary computation [1][9], wavefront expansion [4]=-=[8]-=-[10] or optimization techniques [5][7][11]. These approaches determine the path taking at most profit of currents, i.e. they maximize the parts of the path where the vehicle and the currents point in ...