Feasibility of navigating a one-meter sailboat on the oceans for month
Boris Kogan (MAE, Cornell)

Can a one meter sailboat survive on the world oceans for years without human contact? The boat is slow and winds and currents can be large. So, simultaneously being pushed by and using the variety of changing winds and currents, can such a boat survive without crashing. We partially address this question using the controls concept of ‘reachability’.

For given current, and wind at a given location a given boat at that place has a set of speeds it can travel, one speed for each candidate direction. For example, if the boat is slow and the current large the possible net velocities are all close to the water current velocity. The oceans can be divided into regions: 1) regions where the boat can hold position; 2) regions where a boat can revisit any point in that region any number of times; 3) regions with one way passage between regions (2); 4) regions where survival is possible, but points cannot be revisited; 5) regions where crashes are inevitable. We develop and apply viability and reachability methods to investigate these regions using real ocean current data. The key result is that the surviving regions 1-4 can be substantial even if the boat speed is much less than the maximum water current. The various regions generalize familiar concepts from 2D dynamical systems theory (stable and unstable fixed points, limit cycles, etc).

This talk will cover the motivation for this work (environmental monitoring) and the problem formulation. Computation methods will be discussed and initial results towards answering the question at hand will be shown.