  This paper considers a reach-avoid differential game in three-dimensional
space with four equal-speed players. A plane divides the game space into a play
subspace and a goal subspace. The evader aims at entering the goal subspace
while three pursuers cooperate to prevent that by capturing the evader. A
complete, closed-form barrier for this differential game is provided, by which
the game winner can be perfectly predicted before the game starts. All possible
cooperations among three pursuers are considered and thus the guaranteed
winning for each team is a prior. Furthermore, an algorithm is designed to
compute the barrier for multiple pursuers of any numbers and any initial
configurations. More realistically, since the whole achieved developments are
analytical, they require a little memory without computational burden and allow
for real-time updates, beyond the capacity of traditional
Hamilton-Jacobi-Isaacs method.
