Optimal trajectories in energetic environment for underwater vehicles can be computed using a numerical solution of the optimal control problem (OCP). An underwater vehicle is modeled with the six dimensional nonlinear and coupled equations of motion, controlled by DC motors in all degrees of freedom. An energy performance index that should be minimized may be considered. This leads to a Two Point Boundary Value Problem (TPBVP). The resulting TPBVP is generally solved using iterative methods. In this paper, the applications of two different intelligent algorithms are briefly studied and compared versus the generally acceptable conjugate gradient penalty (CGP) method for the OCP. Genetic algorithm (GA) and particle swarm optimization (PSO) methods are applied to solve OCP. Two approaches for performance index minimization, using GA and PSO, are proposed. CGP method is used to solve the TPBVP, by applying Euler-Lagrange equation. The simulation results show that the trajectories obtained by the intelligent methods were better than that of conjugate gradient penalty. After analyzing the simple path planning problem, the problem energetic environments consisting some energy sources is propounded. The optimal paths are found using GA and PSO algorithms. The problem of collision avoidance in an energetic environment is solved and energy avoidance paths are computed.
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