טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentHayoun Shmuel Yonatan
SubjectCooperative Strategies and Capture Zones in Multi-Player
Pursuit-Evasion Games
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Tal Shima


Abstract

This research is concerned with the study of games-based solutions to interception engagements of a single target by either one or many interceptors. Main issues addressed are: exploration of alternative game formulations, assessment of the merits of utilizing a multiplicity of pursuers, investigation of the type and level of required cooperation in a given game, and finally development of optimal pursuit and evasion strategies. The framework of this study is limited to the endgame of planar engagements, in which linear motion and constant speeds are assumed. The adversaries' controls are bounded and a perfect information structure exists.


Initially, the investigation of an alternative game formulation for a scenario in which a missile with large lateral acceleration capability, but no endgame thrust capacity, intercepts an evading target which has thrust capacity, but limited lateral acceleration capability, is presented. The engagement is formulated as a two-person zero-sum pursuit-evasion game with a linear quadratic cost, where only the maneuverability of the evader is assumed bounded. A closed-form guidance law is formulated, consisting of the optimal saddle point strategies and three proposed variants when no saddle point solution exists. Linear and nonlinear simulations are performed, illustrating the advantages and performance of the proposed guidance algorithm in comparison with classical optimal and differential-game-based laws.


Next, a linear game of pursuit is considered with two pursuers vs. a single evader, all with bounded controls, for which a suitable cost function is proposed and validated. Construction and analysis of the game space is shown and the players' closed-form optimal controls are derived for the case of two "strong" pursuers. It is shown that adding a pursuer enlarges the capture zone and introduces a new singular zone to the game space, in which the pursuers can guarantee equal misses. It is concluded that in the regular zones the closed-form optimal pursuit strategies are non-cooperative, whereas a more complex optimal evasion strategy is obtained.


Wishing to examine the merits of using a multiplicity of pursuers, a linearized endgame interception scenario between a single evading target and n pursuers is considered. The adversaries' controls are bounded and have arbitrary-order dynamics. A capturability analysis is performed, presenting necessary and sufficient conditions for the feasibility of point capture for any admissible evader maneuver in "hit-to-kill" scenarios. It is shown that, regardless of the number of pursuers, the pursuing team is capable of guaranteeing point capture if and only if it includes at least one pursuer capable of independent capture. This condition cannot be relaxed by increasing the number of interceptors or by cooperation, in terms of coordinated motion, between pursuers.


Following this, the endgame of a linearized interception scenario is considered between an evading target and a single pursuing missile with bounded controls and arbitrary-order dynamics. The necessary and sufficient condition for the existence of a "hit-to-kill" capture zone is derived. An appropriate test is presented, which is later expressed as a function of the adversaries' arbitrary control dynamics. Explicit conditions are obtained for several previously studied cases, complimenting known results.