Task Insertion and Reassignment in Networked Robots for Topological Morphing

This paper considers a particular form of incremental assignment problem that can be used to achieve efficient topological morphing in a network of robots. The assignment problem arises from a task-allocation formulation in which destination locations for newly deployed robots are added as tasks to an existing allocation. We adapt the bipartite matching variant of the Hungarian algorithm—originally designed to solve the optimal assignment problem—to perform path routing by showing that there is a three-dimensional spatial interpretation of the Hungarian graph. The assignment is globally reallocated in an efficient manner when new agent-task pairs are inserted. The algorithm uses a parameter to adjust the optimization criterion: from minimizing global time (or energy, or distance), to minimizing disruption (i.e., obtaining the fewest number of robot reassignments), and mixtures in-between. The algorithm can be directly applied to wirelessly networked robot systems in which graph edges reflect robots whose signal strength can be measured and used for gradient-based traversal from a particular node. The adjustable optimization criterion permits the degree to which potentially unreliable long traversals are favored over more costly short traversals to be tuned. Our results suggest that the algorithm works well for sparse graphs making it well-suited to networks of robots with limited communication.