Assessing optimal assignment under uncertainty: An interval-based algorithm

Abstract

We consider the problem of multi-robot task-allocation when robots have to deal with uncertain utility estimates. Typically an allocation is performed to maximize expected utility; we consider a means for measuring the robustness of a given optimal allocation when robots have some measure of the uncertainty (e.g., a probability distribution, or moments of such distributions). We introduce a new O(n4) algorithm, the Interval Hungarian algorithm, that extends the classic Kuhn-Munkres Hungarian algorithm to compute the maximum interval of deviation (for each entry in the assignment matrix) which will retain the same optimal assignment. This provides an efficient measurement of the tolerance of the allocation to the uncertainties, for both a specific interval and a set of interrelated intervals. We conduct experiments both in simulation and with physical robots to validate the approach and to gain insight into the effect of location uncertainty on allocations for multi-robot multi-target navigation tasks.