Swarm Bug Algorithms for Path Generation in Unknown Environments

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, SwarmBugl, and SwarmBug2, of the classical path generation algorithms Com, Bugl, 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 SwarmBugl. For SwarmBug2, we show that the algorithm underperforms in terms of worst-case travel time compared to SwarmBugl. 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 SwarmBugl 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 SwarmBugl and the universal lower bound is tight.