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In several scenarios in which new robots and tasks are added to a network of already deployed, interchangeable robots, a trade-off arises in seeking to minimize cost to execute the tasks and the level of disruption to the system, This paper considers a navigation-oriented variant of this problem and proposes a parameterizable method to adjust the optimization criterion: from minimizing global travel time (or energy, or distance), to minimizing interruption (i.e., obtaining the fewest number of robot reassignments), and mixtures in-between. Paths are computed by task-allocation formulation in which destination locations of newly deployed robots are added as tasks to an existing allocation. We adapt the graph matching variant of the Hungarian algorithmâ€”originally designed to solve the optimal assignment problem in complete graphsâ€”to construct routing paths by showing that there is a three-dimensional spatial interpretation of the Hungarian bipartite graph. When new agent-task pairs are inserted, the assignment is globally reallocated in an incremental fashion so it requires only linear time when the robotsâ€™ traversal options have bounded degree. The algorithm is studied systematically in simulation and also validated with physical robots.
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