Strategy Analysis and Design of Target-Attacker-Defender Game With Non-Zero Capture Radius for Attacker Vehicle

In the land warfare Target-Attacker-Defender (TAD) game, the Attacker vehicle seeks to capture the Target vehicle, while the Defender vehicle aims to intercept the Attacker vehicle and assist the Target vehicle in escaping capture before the Attacker succeeds. In practice, the Attacker usually has a non-zero capture radius and only need to explode in a specific area around the Target to hit it. However, at present, for TAD game where the speed of the Attacker with a non-zero capture radius is equal to the speed of the Defender, there is no design method for the barrier function for dividing the Attacker's winning zone and the Target-Defender's winning zone and the optimal feedback strategy on the Attacker's winning zone. Therefore, this paper delves into the TAD game with non-zero capture radius, and obtains the optimal feedback strategy and barrier function by studying its Game of Degree and Game of Kind, respectively. Firstly, we solved the optimal strategy using a two-point boundary value problem, and then proved that the designed value function satisfies the HJI equation, which the obtained optimal strategy is a state feedback Nash equilibrium. Then, based on the initial positions of the Defender and Attacker, and the Attacker's capture radius, the Attacker's ultimate interception curve is given. Using geometric methods, this paper presents a barrier function by determining whether there is an intersection between the Attacker's ultimate interception curve and the Apollonius oval formed by the Attacker-Target. Finally, the effectiveness of this paper was verified through simulation.