A general, open-loop formulation for reach-avoid games

A reach-avoid game is one in which an agent attempts to reach a predefined goal, while avoiding some adversarial circumstance induced by an opposing agent or disturbance. Their analysis plays an important role in problems such as safe motion planning and obstacle avoidance, yet computing solutions is often computationally expensive due to the need to consider adversarial inputs. In this work, we present an open-loop formulation of a two-player reach-avoid game whereby the players define their control inputs prior to the start of the game. We define two open-loop games, each of which is conservative towards one player, show how the solutions to these games are related to the optimal feedback strategy for the closed-loop game, and demonstrate a modified Fast Marching Method to efficiently compute those solutions.