Path planning in games

Path planning is one of the fundamental problems in games. The path planning problem can be defined as finding a collision-free path, traversed by a unit, between a start and goal position in an environment with obstacles. The variant we study is the problem of finding paths for one or more groups of units, such as soldiers or tanks in a real-time strategy game, all traversing the same (static) environment. Each group has its own start and goal position (or area), and each unit will traverse its own path. The objective is to find the paths that minimize the average arrival times of all units. Our main contribution is that we propose an efficient solution based on techniques from integer linear programming for the path planning problem with groups. Here we do not care about possible interference of paths; this will be taken care of by a collisionavoidance algorithm. Our solution can be used to handle difficult situations which typically occur near bottlenecks (e.g. narrow passages) in the environment. Initially, we restrict ourselves to the situation in which each unit has the same width and speed; we will address the consequences of relaxing this assumption later. Moreover, we will also discuss how we can use our approach in a game environment.