Time-optimal feedback control for the game of two Isotropic Rockets

Abstract

In this paper, the problem of computing feedback solutions for time-optimal pursuit-evasion between two Isotropic Rockets is considered. The classical version of the game involves an Isotropic Rocket chasing a simple velocity bounded kinematic evader. Here a modified and more general version, with both players as Isotropic Rockets, is investigated using the recently developed technique of containment of continuous subsets of reachable sets. Under a suitable assumption on the initial conditions, a complete characterisation of capture is first provided using these special subsets. The geometry of these sets is then used to compute the feedback policy, through the solution of a quartic equation at each instant of time. Fortunately, quartic equations can be solved analytically or numerically in an efficient manner. Thus the feedback law can be implemented in real time. Simulation results are given to show the agreement of the proposed laws with the numerical results obtained using an available algorithm for computing open loop representations of min-max policies.