The main objective of this thesis is to solve the problem of balancing tasks in the Multi-robot Task Allocation problem domain. When allocating a large number of tasks to a multi-robot system, it is important to balance the load effectively across the robots in the system. In this thesis an algorithm is proposed in which tasks are allocated through clustering, investigating the effectiveness of agglomerative hierarchical clustering as compared to K-means clustering. Once the tasks are clustered, each agent claims a cluster through a greedy self-assignment. This thesis investigates the performance both when all tasks are known ahead of time as well as when new tasks are injected into the system periodically. To account for new tasks, both global re-clustering and greedy clustering methods are considered. Three metrics: 1) total travel cost, 2) maximum distance traveled per robot, and 3) balancing cost index are used to compare the performance of the overall system in environments both with and without obstacles. The results collected from the experiments show that agglomerative hierarchical clustering is deterministic and better at minimizing the total travel cost, especially for large numbers of agents, whereas K-means works better to balance costs. In addition to this, the greedy approach for clustering new tasks works better for frequently appearing tasks than infrequent ones
