  This paper studies a class of approach-evasion differential games, in which
one player aims to steer the state of a dynamic system to the given target set
in minimum time, while avoiding some set of disallowed states, and the other
player desires to achieve the opposite. We propose a class of novel anytime
computation algorithms, analyze their convergence properties and verify their
performance via a number of numerical simulations. Our algorithms significantly
outperform the multi-grid method for the approach-evasion differential games
both theoretically and numerically. Our technical approach leverages
incremental sampling in robotic motion planning and viability theory.
