The isotropic rocket—A surveillance evasion game

Abstract

AbstractIn this paper the problem is considered of a vehicle, with bounded speed and the capability of instantaneous turns, that tries to escape from a circular region (such as from a radar) attached to a pursuer who has a bounded magnitude of acceleration, but who has the capability to direct the acceleration in any direction instantaneously. The central question is under what circumstances, i.e. for which parameter values and initial conditions, can the pursuer keep the vehicle (also called the evader) forever under surveillance. A subset of the state space will be given from where the evader cannot escape. The state space for this problem is three-dimensional and the problem has analogies with the famous isotropic rocket game treated by Isaacs and Bernhard. The efforts to locate the (permanent) region of surveillance will be described and the phenomena associated with this region, such as barriers, envelope barriers, leaking corners, as well as a correlation with the homicidal chauffer surveillance game, will be discussed