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

To improve the defense ability of the spacecraft in orbit,an orbital pursuit-evasion-defense(PED)linearquadratic 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.