# An Approach to Multi-Objective Path Planning Optimization for Underwater Gliders
## 1 Introduction
### Underwater Glider Path Planning  
Ocean gliders are torpedo-shaped vehicles that make use of a highly energy efficient propulsion system: They modify their buoyancy and pitch angle by means of an artificial swim bladder operation combined with internal batteries displacement. The induced descend-ascend movement is transformed into effective horizontal displacement by the interaction between the water column and the vehicle hydrodynamics, resulting in a saw-tooth like trajectory profile similar to the one shown in Figure 1. Typically, the vehicle performs two or three down-up cycles, called _yo-yo's_, between pre-defined max- and min-depths before returning to surface to start a new sequence or _stint_ each 6-8 h. As energy consumption is mainly associated with the activation of the electric pump, which is responsible for the buoyancy control at inflection points, extremely long-term missions are possible with these vehicles. During a glider mission, the control centre relies on satellite communication to upload commands to the glider when at the surface, including target waypoints or depth limits, for example. The surfacing period has to be kept as short as possible to avoid collisions with surface vessels, reduce biofouling, and decrease vehicle's drift. After the surfacing, the glider submerges again to perform another set of stints. Although major deviations from expected trajectories occur generally at surface (due to strong currents), when the glider dives, its location can only be estimated using its on-board sensors, producing errors that grow with time. In order to reduce this uncertainty, as the ocean is a very dynamic and unknown environment, researchers have developed different strategies. [PERSON] et al. [4], for example, use a doppler velocity log with promising results on predicting glider position underwater; [PERSON] et al. [5] propose a dynamic model-aided localization scheme that proved to be able to improve significantly the precision in the estimation of the vehicle position. The main drawback of (passive) ocean gliders is that they can only reach low horizontal speeds (around 0.25 m/s). To optimize their operation, factors such as bathymetry, marine traffic or, remarkably, ocean currents, have to be anticipated, so that suitable paths are well planned in advance. Figure 1: Example of a 3D generic saw–tooth glider trajectory (10 stints). As this constitutes a 4D problem (latitude, longitude, depth, and time), with variable environment conditions, the process is not so trivial. From the traditional path planning, the strategies to achieve the best path for gliders kept evolving. An A* search procedure was done by [PERSON] et al. (2016), in areas with different length scale eddies and currents with varying intensities. However, the authors considered the usage of constant thrust power to navigate the vehicle. They also tested different start and end points across the simulation area, to find the best paths and best locations to achieve their objectives. The usage of Lagrangian coherent structures carried out by ([PERSON] et al., 2016) showed how those can be used to find near optimal trajectories in dynamic environments, considering a 2D glider kinematic model. They used ocean current velocities collected with an HF radar system to calculate the optimal trajectories for the vehicle. A fast marching based approach (called FM*) was used by [PERSON] et al. (2016) in order to extract a continuous path from a discrete representation of the environment. The authors considered underwater currents, with the vehicle turning radius being added as a constraint. The backward study of a particle tracking equation provided an optimal path in ([PERSON] et al., 2016), with the authors stating that the system can easily handle forbidden regions (such as strong currents areas) and real obstacles that affect the ocean flow and consequently the vehicle pathway.