Analyzing Uncertainties in Cost: Mitigating Centralization in Multi-Robot Task Allocation∗

We consider the problem of finding the optimal assignment of tasks to a team of robots when the costs associated with the tasks may vary. This arises often because robots typically update their cost estimates and re-compute task assignments to deal with dynamic situations (e.g., the addition of new robots to the team, arrival of new tasks, or the revelation of new information). This paper describes a way to compute a sensitivity analysis that characterizes how costs may alter from current estimates before the optimality of the present assignment is violated. Using this analysis, robots are able to avoid unnecessary re-assignment computations. By exploiting this analysis, we propose multiple methods that help reduce global communication and centralized computations. First, given a model of how costs may evolve, we develop an algorithm that partitions a team of robots into several independent cliques, which can maintain global optimality by communicating only amongst themselves. Second, we propose a method for computing the worst-case cost sub-optimality if robots persist with the initial assignment and perform no further communication and computation. Lastly, we develop an algorithm that assesses whether cost changes affect the optimality ∗This paper is an extended version of [1]. †Both authors are with the Department of Computer Science and Engineering at Texas A&M University, College Station, Texas, USA. {cjnam,dshell} at cse.tamu.edu of the current assignment through a succession of local checks. Experimental results show that our proposed methods reduce the degree of centralization needed by a multi-robot system.