Large-scale scenarios such as search-and-rescue operations, agriculture, warehouse, surveillance, and construction consist of multiple tasks to be performed at the same time. These tasks have non-trivial spatial distributions. Robot swarms are envisioned to be efficient, robust, and flexible for such applications. We model this system such that each robot can service a single task at a time; each task requires a specific number of robots, which we refer to as 'quota'; task allocation is instantaneous; and tasks do not have inter- dependencies. This work focuses on distributing robots to spatially distributed tasks of known quotas in an efficient manner. Centralized solutions which guarantee optimality in terms of distance travelled by the swarm exist. Although potentially scalable, they require non-trivial coordination; could be computationally expensive; and may have poor response time when the number of robots, tasks and task quotas increase. For a swarm to efficiently complete tasks with a short response time, a decentralized approach provides better parallelism and scalability than a centralized one. In this work, we study the performance of a weight-based approach which is enhanced to include spatial aspects. In our approach, the robots share a common table that reports the task locations and quotas. Each robot, according to its relative position with respect to task locations, modifies weights for each task and randomly chooses a task to serve. Weights increase for tasks that are closer and have high quota as opposed to tasks which are far away and have low quota. Tasks with higher weights have a higher probability of being selected. This results in each robot having its own set of weights for all tasks. We introduce a distance- bias parameter, which determines how sensitive the system is to relative robot-task locations over task quotas. We focus on evaluating the distance covered by the swarm, number of inter- task switches, and time required to completely allocate all tasks and study the performance of our approach in several sets of simulated experiments.

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