Kinematic Characterization of a Target-Defense Problem With an Interception and Expelling Strategy

This paper considers a target-defense problem of one defender and one adversary (or called intruder), in which the defender tries to approach a desired interception-position between the intruder and the target to intercept the intruder and expel it from the target. The defender adopts this interception and expelling strategy since the defender is assumed to not capture or destroy the intruder. An expelling-decay exponent is introduced to characterize the expelling-decay rate on the intruder. The system is nonlinear, with distinct physical meaning and rich kinematics. The main concern in this paper is the analysis of the kinematic properties. First, two motion patterns of the system are characterized with respect to different values of the system parameters. Then, the stability and the transition condition of the two motion patterns are provided. Finally, the optimal interception of the defender is provided, which interestingly coincides with the transition condition for the two motion patterns. The interpretations for the physical meaning of the optimal interception are also provided.