Autonomous river navigation using the Hamilton-Jacobi framework for underactuated vehicles

Motorized floating sensors have distinct advantages over their non-actuated counterparts. A motorized unit can prevent the sensor from washing ashore or heading into dangerous areas, expanding the mission regions in which they can be feasibly operated. In this article, we present a control frame work and describe the physically realized system used to prove its effectiveness. The controller uses two minimum-time-to-reach (MTTR) functions-one giving the time to reach the center of the river and one giving the time to reach the shoreline. The MTTR functions are constructed from solutions to Hamilton Jacobi-Bellman-Isaacs (HJBI) Equations. Contours along these functions are used to define the state transition thresholds for an on-off controller. The first MTTR function is also used to construct the optimal bearing to travel back to the center of the river. We investigate the effectiveness of the controller using a software-in-the-loop (SIL) simulator. Using prototypes built at UC Berkeley, results from a field operational test in the Sacramento-San Joaquin River Delta are then presented to validate the simulation results.