Task allocation is an important problem for robot swarms to solve, allowing agents to reduce task completion time by performing tasks in a distributed fashion. Existing task allocation algorithms often assume prior knowledge of task location and demand or fail to consider the effects of the geometric distribution of tasks on the completion time and communication cost of the algorithms. In this paper, we examine an environment where agents must explore and discover tasks with positive demand and successfully assign themselves to complete all such tasks. We first provide a new discrete general model for modeling swarms. Operating within this theoretical framework, we propose two new task allocation algorithms for initially unknown environments -- one based on N-site selection and the other on virtual pheromones. We analyze each algorithm separately and also evaluate the effectiveness of the two algorithms in dense vs. sparse task distributions. Compared to the Levy walk, which has been theorized to be optimal for foraging, our virtual pheromone inspired algorithm is much faster in sparse to medium task densities but is communication and agent intensive. Our site selection inspired algorithm also outperforms Levy walk in sparse task densities and is a less resource-intensive option than our virtual pheromone algorithm for this case. Because the performance of both algorithms relative to random walk is dependent on task density, our results shed light on how task density is important in choosing a task allocation algorithm in initially unknown environments.

翻译：任务分配是群机器人系统需要解决的重要问题，使智能体通过分布式方式执行任务以缩短任务完成时间。现有任务分配算法通常假设任务位置和需求具有先验知识，或未能考虑任务几何分布对算法完成时间与通信成本的影响。本文研究智能体需通过探索发现具有正需求的任务，并自主分配以完成所有此类任务的环境。我们首先提出一种新的离散通用群集建模框架。在此理论框架下，针对初始未知环境提出两种新型任务分配算法——基于N位点选择算法与基于虚拟信息素算法。我们分别对两种算法进行理论分析，并评估其在密集与稀疏任务分布场景中的有效性。相比于被理论认为在觅食中具有最优性的列维行走策略，我们的虚拟信息素启发算法在稀疏至中等任务密度区域显著更快，但需消耗更多通信与智能体资源。我们所提出的位点选择启发算法在稀疏任务密度下同样优于列维行走，且在此场景中比虚拟信息素算法更具资源友好性。由于两种算法相对于随机游走的性能均取决于任务密度，本文揭示任务密度对初始未知环境中任务分配算法选择的关键影响。