Optimal guidance of the Isotropic Rocket in a partially uncertain flow field

In this paper, we address the problem of characterizing the optimal strategy for guiding the so-called Isotropic Rocket to a fixed target in the presence of a partially known flowfield. We reformulate the guidance problem into an equivalent two-player pursuit evasion game, where the evader has a modified vectogram. First, we characterize the optimal strategies for both players, assuming that the evader is capturable. Then, we derive the necessary condition for capture, and visualize the capturability envelope using numerical simulations in which we compute the level sets of the optimal value function (isochrones). In addition, we consider a more general case of the game, where the pursuer is affected by friction (or drag). In that case, we identify the capture zones from geometric properties of the isochrones.