Minimum effort intercept of a maneuvering target with multiple obstacle avoidance

This paper presents a guidance law for the interception of a maneuvering target in an environment with several static obstacles. The guidance law is derived from the solution of an linear quadratic optimal control problem that minimizes the guidance effort subject to the constraint that the separation between missile and each obstacle is larger than a given minimum range. Using linearized engagement kinematics, the general solution of the optimal control problem for multiple obstacles case is first devised. Subsequently, it is applied to the case of two obstacles and this case is also illustrated in a few numerical simulation experiments. The proposed guidance laws have a form similar to that of augmented proportional navigation guidance with some additional bias term that account for the required maneuvers to avoid the obstacles.