In this paper, we consider the problem of a swarm traveling between two points as fast as possible in an unknown environment cluttered with obstacles. Potential applications include search-and-rescue operations where damaged environments are typical. We present swarm generalizations, called SwarmCom, SwarmBug1, and SwarmBug2, of the classical path generation algorithms Com, Bug1, and Bug2. These algorithms were developed for unknown environments and require low computational power and memory storage, thereby freeing up resources for other tasks. We show the upper bound of the worst-case travel time for the first agent in the swarm to reach the target point for SwarmBug1. For SwarmBug2, we show that the algorithm underperforms in terms of worst-case travel time compared to SwarmBug1. For SwarmCom, we show that there exists a trivial scene for which the algorithm will not halt, and it thus has no performance guarantees. Moreover, by comparing the upper bound of the travel time for SwarmBug1 with a universal lower bound for any path generation algorithm, it is shown that in the limit when the number of agents in the swarm approaches infinity, no other algorithm has strictly better worst-case performance than SwarmBug1 and the universal lower bound is tight.

翻译：本文研究群体在未知环境中以最快速度穿越障碍物密集区域的问题。潜在应用包括典型受损环境下的搜索救援行动。我们提出了经典路径生成算法Com、Bug1和Bug2的群体泛化版本，分别称为SwarmCom、SwarmBug1和SwarmBug2。这些算法专为未知环境开发，所需计算能力和内存存储较低，从而为其他任务释放资源。我们展示了SwarmBug1算法中群体内首个代理到达目标点的最差情况旅行时间上界。对于SwarmBug2，研究表明其最差情况旅行时间性能劣于SwarmBug1。对于SwarmCom，我们证明存在一个平凡场景使算法无法终止，因此该算法无性能保证。此外，通过比较SwarmBug1的旅行时间上界与任意路径生成算法的通用下界，表明当群体中代理数量趋于无穷时，没有任何其他算法具有严格优于SwarmBug1的最差情况性能，且该通用下界是紧致的。