航天器追踪-逃逸-防御三方博弈均衡解

Equilibrium of orbital pursuit-evasion-defense three-sided game

为提高航天器在轨防御能力,对航天器追踪-逃逸-防御三方博弈场景进行了研究。博弈中,追踪航天器(追踪器)旨在拦截逃逸航天器(逃逸器),逃逸器旨在躲避追踪器,而防御航天器(防御器)通过主动拦截追踪器来保护逃逸器。由于防御器的存在,追踪器在接近目标时不得不规避防御器,而逃逸器和防御器之间也可以开展合作。对于这样的场景,综合能量和距离指标,建立了线性二次型微分对策模型,推导了三方博弈的纳什均衡条件,求解了追踪器的最优追踪制导律和逃逸器与防御器的最优合作逃逸-防御制导律。进一步考虑多防御器的场景,求解了三方多人博弈的纳什均衡解。仿真结果表明,防御器的存在提高了逃逸器的生存能力,二者可以在机动加速度劣势情况下共同抵御一个机动能力强的追踪器。处在绕飞护卫下的防御器的初始位置并非离追踪器或逃逸器越近越好,而是存在优势位置。

To improve the defense ability of the spacecraft in orbit,an orbital pursuit-evasion-defense(PED)linear-quadratic game is investigated.Three players are called the pursuer,evader,and defender,respectively.The pursuer aims to intercept the evader,while the evader tries to escape from the pursuer,accompanied by a defender who attempts to protect the evader by intercepting the pursuer actively.Due to the existence of the defender,the pursuer has to evade the defender when chasing the evader.Meanwhile,cooperation between the evader and the defender may decrease the difficulty of escape.For such a three-sided game,a linear-quadratic differential game model is established with a performance index combining three players′energy consumption and the distance.Then the necessary conditions for the Nash equilibrium of the three players are derived and the optimal pursuit guidance law and evasion-defense guidance law are obtained.Furthermore,the equilibrium solution is extended to a more general PED scenario with multiple defenders.Simulation results show that a defender can improve the survivability of the evader.Even with inferiority in maneuverability,they can win the pursuer cooperatively.Besides,an initial position close to the pursuer or evader is not the best choice for the defender who flies around the evader.The defender has favorable positions.