Multi-robot task assignment (allocation) involves assigning robots to tasks in or-der to optimize the entire team’s performances. Until now, one of the most useful non-domain-specific ways to coordinate multi-robot systems is through task alloca-tion mechanisms. This dissertation addresses the classic task assignment problems in which robots and tasks are eventually matched by forming a one-to-one mapping, and their overall performances (e.g., cost, utility, risk) can be linearly summed. At a high level, this research emphasizes two facets of the multi-robot task as-signment, including (1) novel extensions from classic assignment algorithms, and (2) completely newly designed task allocation methods with impressive new features. For the former, we first propose a strongly polynomial assignment sensitivity analysis algorithm as well as a means to measure the assignment uncertainties; af-ter that we propose a novel method to address problems of multi-robot routing and formation morphing, the trajectories of which are obtained from projections of aug-menting paths that reside in a new three-dimensional interpretation of embedded

Abstract — Although many approaches have been developed to form robot coalitions that can achieve a multirobot task, no general methods exist to execute these coalitions, especially when the coordination among the robots is tightly coupled. In this paper, we propose a coordination mechanism as the first step to address coalition execution; it provides a flexible method to reason about synergies with overlapping coalitions (thus enabling multi-tasking robots in multi-robot tasks), which not only improves efficiency, but also reduces resource requirements in task execution. This means that our approach enables tasks that cannot be easily handled before, especially when critical resources are rare but commonly required. Our approach is based on the concept of sensor constraint, which is introduced by the tight coupling (e.g., information sharing) between the robots. We show that our algorithm is sound and complete in finding a coordination solution given a few assumptions, and discuss a distributed implementation. Simulation results are provided to demonstrate the capabilities of this new approach. I.