Optimal Feedback Control of an Active Drifter

Drifters are energy-efficient sampling platforms widely used in rivers, lakes, and oceans with pronounced flows. Passive drifters cannot exert control over their motion, so their motion is determined by the local flow structure. To overcome this limitation, we propose an active drifter with a thruster to generate propulsion and increase maneuverability. To retain the energy-efficient nature of drifters, application of the thruster must be carefully planned. In this paper we consider an optimal control problem for an active drifter with one degree-of-freedom, where its motion is governed by rudder-modulated drag and thruster propulsion. Despite the realistic and complex nonlinear dynamics, an analytical solution is developed using Pontryagin's Minimum Principle (PMP). Optimal solutions are back-propagated from the final state to find state-space locations where the optimal control switches. Such locations are parameterized by one of the costate variables and are related to the system's final state. These locations enclose regions in the state space where the optimal control is the same; thus the optimal control can be mapped to the state space to be used as a feedback control law that depends on the final state. The proposed approach is first illustrated in simulation, and the trade-off between thruster use and time taken is examined. The efficacy of the proposed approach is further demonstrated by results from field experiments conducted with an active drifter prototype.