Formulation of a Cooperative-Confinement-Escape problem of multiple cooperative defenders against an evader escaping from a circular region

In this paper, we propose and formulate the Cooperative-Confinement-Escape (CCE) problem of multiple cooperative defenders against an evader escaping from a circular region, in which the defenders are moving on the circle with attempt to prevent possible escape of a single evader who is initially located inside the circle. The main contributions are summarized as follows: (1) we first provide an effective formulation of the CCE problem, which is an emphasis of this paper, with design of two nonlinear control strategies for the cooperative defenders and the adversarial evader, respectively. Particularly, we consider to include a proper interaction between each pair of the nearest-neighbor defenders, and an adaptive trajectory prediction mechanism in the strategies of the defenders to increase the chance of successful confinement. (2) For the first attempt on analyzing the CCE dynamics which is unavoidably strongly nonlinear, we analyze the minimum energy of the evader for possible escape. (3) For understanding of the behaviors of the system under different parameters, (i) we illustrate the effectiveness of the confinement strategy using the adaptive trajectory prediction mechanism, and (ii) the physical roles of the system parameters with respect to the system dynamics, some of which may be unexpected or not straightforward. A separate paper will be presented for systematic analysis of the agents' behaviors with respect to the large intervals of the parameter settings.