This paper considers the task reallocation problem, where k robots are to be extracted from a coordinated group of N robots in order to perform a new task. The interaction between the team members and the cost associated with this interaction are represented by a directed weighted graph. Consider a group of N robots organized in a formation. The graph is the monitoring graph which represents the sensorial capabilities of the robots, i.e., which robot can sense the other and at what cost. The team member reallocation problem with which we deal, is the extraction of k robots from the group in order to acquire a new target while minimizing the cost of the interaction of the remaining group, i.e., the cost of sensing amongst the remaining robots. In general, the method proposed in our work shifts the utility from the team member itself to the interaction between the members, and calculates the reallocation according to this interaction cost. We found that this can be done optimally by a deterministic algorithm, while reducing the time complexity from O(Nk) to O(2k), thus resulting in a polynomial time complexity in the common case where a small number of robots is extracted, i.e., when k = O(N). We show that our basic algorithm creates a framework that can be extended for use in more complicated cases, where more than one component should be taken into consideration when calculating the robots’ cost of interaction. We describe two such extensions: one that handles prioritized components and one that handles weighted components. We describe several other non-robotic domains in which our basic method is applicable, and conclude by providing an empirical evaluation of our algorithm in a robotic simulation.This research is supported by NSF Grant #0705587 and ISF Grant #1685
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