Optimal navigation in a planar time-varying point-symmetric flow-field

This paper is concerned with time-optimal navigation for flight vehicles in a planar, time-varying point-symmetric flow-field - such as inside vortices or regions of eddy-driven upwelling/downwelling-where the objective is to find the fastest trajectory between initial and final points. The primary contribution of the paper is the observation that for time-optimality the rate of the steering angle has to be equal to one-half of the instantaneous vertical vorticity. Consequently, if the vorticity is zero, then the steering angle has to be constant. The result can be applied to find the time-optimal trajectories in practical control problems, by reducing the infinite-dimensional continuous problem to numerical optimization involving at most two unknown scalar parameters.