Optimal Control of a Self-propelled Particle in a Fluid Flow Field

This work presents a solution for the fuel-optimal navigation problem of an AUV given a fixed final time and free end states. The formulation of the problem assumes a self propelled particle in a two dimensional horizontal flow field. A closed form solution for the fuel-optimal control inputs of the thrust vectors are obtained. This is done through analytically solving the two point boundary value problem of the Euler-Lagrange equations. Subsequently, a feedback form of control is derived allowing the particle to navigate a flow field with disturbance. Finally, the concept of changing the cost weights of the optimal cost formulation in situ has been explored and viable applications such as obstacle avoidance has been presented.