Optimal guidance strategy for the defense of a non-manoeuvrable target in 3-dimensions

摘要

An engagement scenario involving the defence of a non-manoeuvrable agent, called the Target, is considered. A pursuing agent, engages the non-manoeuvrable Target while a defending agent, which aims at intercepting the Pursuer to protect the Target, is considered in 3-dimensions. A zero-sum differential game is formulated where the objective of the Defender is to capture the Pursuer and maximise the terminal Pursuer-Target range at final time; while the Pursuer aims at minimising the terminal Pursuer-Target range at final time. The terminal time is not fixed and is determined by the interception of the Pursuer by the Defender. The saddle point state-feedback strategies for the Pursuer and the Defender are obtained using a gradient-based minimisation routine. A comparison of the saddle point strategy against a heuristic approach, Pure Pursuit, is conducted. The comparison demonstrates that poorer performance is achieved by players who deviate from the optimal saddle point strategy; and, as a result, the saddle point strategies outperform the heuristic method.