## 2 Materials and Methods  
### Genetic Path Planner  
This section describes the architecture of the genetic planner designed for autonomous IG applications in marine environment. The main purpose of the proposed GPP is to find the optimal path to be followed by the AUV by maximising a performance function, called 'utility function', which involves the path informativeness and other variables assessing the path performance. Within the specific application, the planner has to generate collision-free trajectories, compliant with the AUV manoeuvrability, to carry out PO inspection and monitoring tasks. A GP is employed to model the presence of PO and the resulting uncertainty in its estimate is used to compute the information acquired along the path. Typically, high uncertainties will be obtained in borders between PO meadow and sand, and zones not yet explored by the robot. Therefore, the planner should focus on those uncertain areas, where the robot can acquire data to increase the knowledge about the environment. In designing the GPP, the following assumptions were made:  
1. **The presence of PO is considered time-invariant during all the planning task**. The assumption is reasonable as the typical endurance of an AUV is limited to few hours while the variations in PO meadows usually occur over several months. 2. **The boundaries of the area to be explored and the presence of obstacles are considered a priori known**. The assumption results appropriate as PO monitoring is carried out periodically in the same geographical areas to assess its spread and health state. 3. **A two-dimensional scenario is considered** to represent a path using North and East coordinates referred to the NED frame. The vertical coordinate is beyond the aim of the proposed planner. The considered application of PO monitoring is usually based on optical cameras. The vertical coordinate is thus usually controlled to ensure the AUV to maintain a desired altitude with respect to the sea bottom to guarantee good acquisition conditions. According to assumptions 2 and 3, \(X_{free}\subset\mathbb{R}^{2}\) represents the space free from obstacles of the area in which the vehicle can move, expressed in North and East coordinates. The AUV paths generated by the GPP strategy are described using chromosomes and genes, essential elements of general genetic algorithms (more details in Appendix A.2). In particular, a chromosome represents a path, and it is composed of \(m\) genes, each of which describes a step of the path. Within this work, a gene has been characterised as a tuple \(\eta=(\alpha,d)\), where \(\alpha\) represents the increment of the AUV heading angle and \(d\) the length of the step of the path. The \(\alpha\) angle follows a Gaussian distribution \(\alpha\sim\mathcal{N}(0,\sigma_{\alpha}^{2})\) with zero mean and with standard deviation \(\sigma_{\alpha}\), while \(d\) is sampled over an uniform distribution with a range \([d_{min},d_{max}]\) scaling with the size of the area to inspect. Figure 1 shows an example of a chromosome along with its genes. Note that paths composing of genes characterised by small values for the angle \(\alpha\) better approximate smooth paths, which are crucial to reduce energy consumption and survey duration. Indeed, they can be performed by the AUV without stopping. This is related to the AUV manoeuvrability, which mostly depends on its speed and shape. Typically, AUVs can be categorised, according to their geometry, such as high-manoeuvrable or torpedo-shape. On the one hand, the high-manoeuvrable AUVs are usually stocky and provided with several motors to move and rotate in almost all directions [37; 38]. This category of underwater vehicles is able to perform rapidly big changes in direction by rotating on the spot, but their manoeuvrability reduces with the increase of their speed. On the other hand, torpedo-shaped vehicles are slender and usually equipped with a propeller on the stern and a rudder, or lateral thrusters, to make turns [39; 40].