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In this paper, we consider a network of agents that has to self-assign a setof tasks while respecting resource constraints. One possible formulation is theGeneralized Assignment Problem, where the goal is to find a maximum payoffwhile satisfying capability constraints. We propose a purely distributedbranch-and-price algorithm to solve this problem in a cooperative fashion.Inspired by classical (centralized) branch-and-price schemes, in the proposedalgorithm each agent locally solves small linear programs, generates columns bysolving simple knapsack problems, and communicates to its neighbors a fixednumber of basic columns. We prove finite-time convergence of the algorithm toan optimal solution of the problem. Then, we apply the proposed scheme to ageneralized assignment scenario in which a team of robots has to serve a set oftasks. We implement the proposed algorithm in a ROS testbed and provideexperiments for a team of heterogeneous robots solving the assignment problem.

Generalized Assignment for Multi-Robot Systems via Distributed Branch-And-Price