Distributed Optimal Assignment Algorithm for Collective Foraging *

We consider the problem of collectively transporting multiple objects by multiple agents. The objective is to find the optimal matching between the objects and agents that minimizes the energy of the overall system. We show that combining a proximal gradient method with continuous relaxation yields a distributed algorithm which converges to a near-optimal solution for the associated optimization problem. Furthermore, by using this solution as an initial solution, a distributed negative-cycle canceling algorithm, which monotonically decreases the matching cost at each step, provides the globally optimal solution for the problem. Numerical simulations demonstrate the performance on practical problems.