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Task allocation is an important problem for robot swarms to solve, allowingagents to reduce task completion time by performing tasks in a distributedfashion. Existing task allocation algorithms often assume prior knowledge oftask location and demand or fail to consider the effects of the geometricdistribution of tasks on the completion time and communication cost of thealgorithms. In this paper, we examine an environment where agents must exploreand discover tasks with positive demand and successfully assign themselves tocomplete all such tasks. We first provide a new discrete general model formodeling swarms. Operating within this theoretical framework, we propose twonew task allocation algorithms for initially unknown environments -- one basedon N-site selection and the other on virtual pheromones. We analyze eachalgorithm separately and also evaluate the effectiveness of the two algorithmsin dense vs. sparse task distributions. Compared to the Levy walk, which hasbeen theorized to be optimal for foraging, our virtual pheromone inspiredalgorithm is much faster in sparse to medium task densities but iscommunication and agent intensive. Our site selection inspired algorithm alsooutperforms Levy walk in sparse task densities and is a less resource-intensiveoption than our virtual pheromone algorithm for this case. Because theperformance of both algorithms relative to random walk is dependent on taskdensity, our results shed light on how task density is important in choosing atask allocation algorithm in initially unknown environments.

A Comparison of New Swarm Task Allocation Algorithms in Unknown Environments with Varying Task Density