Comparison of Eulerian and Hamiltonian circuits for evolutionary-based path planning of an autonomous surface vehicle for monitoring Ypacarai Lake

Abstract

An evolutionary-based path planning is designed for an autonomous surface vehicle (ASV) used in environmental monitoring tasks. The main objective is that the ASV covers the maximum area of a large mass of water such as the Ypacarai Lake while taking water samples for sensing pollution conditions. Such coverage problem is transformed into a path planning optimization problem through the placement of a set of data beacons located at the shore of the lake and considering the relationship between the distance traveled by the ASV and the area of the lake covered. The optimal set of beacons to be visited by the ASV has been modeled through two different approaches such as Hamiltonian and Eulerian circuits. When Hamiltonian circuits are used, all the beacons should be visited only once. In the case of Eulerian circuits, the only limitation is that repeated routes cannot exist between two beacons. Both models have important implications on the possible trajectories of ASV throughout the lake. In this paper, we compare the application of both models for the optimization of the proposed evolutionary-based path planning. Due to the complexity of the optimization problem, a metaheuristic technique like a Genetic Algorithm (GA) is used to obtain quasi-optimal solutions in both models. The models have been compared by simulation and the results reveal that the Eulerian circuit approach can achieve an improvement of 2% when comparing to the Hamiltonian circuit approach.