# Dynamic Path Planning for Unmanned Surface Vehicles with a Modified Neuronal Genetic Algorithm
## 3 Problem Formulation and Contribution  
Unmanned surface vehicle (USV) path planning refers to the procedure of establishing the most advantageous or efficient course for an autonomous surface vehicle to traverse a water body, which could be a lake, river, or ocean. This process aims to guide a USV from its current position to a predetermined destination. The central objective of path planning is to facilitate the USV's successful arrival at its target by steering clear of obstacles, accommodating dynamic environmental changes, and adhering to specific constraints. When the USV is in the environment, its task is to analyze the environment and determine where it is moving to and at what acceleration. Figure 2 shows the types of forces acting on the USV and the determination of movement decisions based on environmental detection [11].  
In this research, the target or goal of a USV (or an evolutionary algorithm, hereinafter referred to as an agent) is to achieve the expected fitness value. The fitness value can be achieved if the agent can move across a predetermined route and avoid obstacles or boundary walls. To carry out these tasks, the agent performs two maneuvers: moving straight and turning (right or left). Figure 3 shows a simple map of the experimental environment and the expected path (the black dotted line). The experiment is initiated from the bottom-left corner, as opposed to other starting locations. This choice is made because, from this starting point, the agent encounters an equal number of right and left turns in the first four movements. Starting from a different point with an uneven distribution of turns would make it easier for the agent to detect a specific turn, but it would lead to failure when the agent must navigate in a different direction.  
Figure 3: Simple map of the experimental environment and the expected path (the black dotted line).  
Figure 2: Types of forces acting on the USV (**a**) and the determination of movement decisions based on environmental detection (**b**).  
The best and most concise path does not collide with obstacles or boundaries and has a convergent path (i.e., it can be reused for the next iteration or round). We consider it to be used in the next round or iteration because in the case of a dynamic environment, the USV may not necessarily use the same path in the next round. These different paths are the result of adapting the USV to dynamic environments such as water surface waves. For the USV to generate the optimal path, it is essential to start from the initial position on \(x_{0}\), \(y_{0}\), and \(z_{0}\), and then transition to the trajectory using two maneuvers involving forward motion with an acceleration value represented as \(\alpha\), and a turning action (either to the right or left) with an angle value denoted as \(\theta\). These two maneuvers are produced by the neural network using the weight and bias parameters. The optimal weight and bias values obtained from the network play a pivotal role in determining the most effective maneuver for the USV. These values are instrumental in evaluating the USV's acceleration and the angle at which it turns during its movement. We optimize the weight and bias parameters using modified genetic algorithms.  
Through this research, we contribute to implementing the neuronal genetic algorithm (combining neural network parameters--weights and biases--as the input for the GA). For GA modification, we introduce a partially exponential-based fitness function to the neuronal genetic algorithm. We also add an inverse time variable to the fitness function. These two modifications aim to produce faster convergence. We implement the proposed methodology for both static and dynamic environments.