Tunable routing solutions for multi-robot navigation via the assignment problem: A 3D representation of the matching graph

In scenarios in which new robots and tasks are added to a network of already deployed, interchangeable robots, a trade-off arises in minimizing the 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 parametrizable 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 a task-allocation formulation in which the destinations of newly deployed robots are added to an existing allocation. We adapt the graph matching variant of the Hungarian algorithm-originally designed to solve the optimal assignment problem in complete graphs-to construct routing paths by showing that there is an interpretation of the sparse Hungarian bipartite graph in three dimensions. When new agent-task pairs are inserted, the assignment is reallocated in an incremental fashion in linear time (assuming traversal choices are limited in number). The algorithm is studied systematically in simulation and also validated with physical robots.