The multiplayer reach-avoid game plays an important role in the applications involving cooperative agents. Analyzing the defendable region for the multiplayer reach-avoid game is the prerequisite for designing the target assignment algorithms and the control laws for both sides of the teams. Since the attacker-defender velocity ratio could be different in different application scenarios, this paper studies the defendable region for the multiplayer reach-avoid game with free attacker-defender velocity ratio. That is to say, the velocity of attacker might be less than, equal to or greater than the velocity of the defender. In order to simplify the problem, the two-dimension one defender versus one attacker issue is first dealt with. Based on the attacker-defender moving time ratio, the concept of the breakthrough point is proposed in this paper. Then, the defendable region of the one versus one reach-avoid game is analyzed based on the concept of breakthrough point. And then the defendable region of the multiplayer reach-avoid game is considered and the defendable regions are classified as strongly defendable regions and weakly defendable regions according to whether the target assignment algorithm is necessary for the defenders. Finally, we illustrate our method by some simulation results.
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