Distributed Algorithm Design for Multi-robot Generalized Task Assignment

We present a provably-good distributed algorithm for generalized task assignment problem in the context of multirobot system (MR-GAP), where a group of robots need to cooperate to complete a group of tasks. In MR-GAP, each robot has its own resource budget constraint, and needs to consume a certain amount of resource to obtain a payoff for each task. The overall objective is to find a maximum payoff assignment of tasks to robots such that each task is assigned to at most one robot while respecting robots’ resource budget constraints. MR-GAP is a NP-hard problem with various applications in multi-robot system, and is an extension of multi-robot linear assignment problem, in the sense that each task would consume different amount of resource from different robots (due to the heterogeneity of robots and tasks). The main contribution of our paper is that we designed a distributed algorithm specifically for multi-robot in-field applications with provable performance guarantee. We first present a decentralized auction-based iterative algorithm for MR-GAP, where each robot uses a knapsack algorithm as a subroutine to iteratively maximizes its own objective (using a modified payoff function based on an auxiliary variable, called price of a task). We then show that our iterative algorithm can be viewed as (approximate) best response assignment update rule of each robot to the temporary assignment of other robots at that iteration. We prove that our algorithm would eventually converge to an assignment at (approximate) equilibrium under the assignment update rule, with a provable approximate ratio for MR-GAP. We also indicate how to combine our algorithm with a message passing mechanism to remove the requirement of a shared memory and make our algorithm totally distributed. Finally, we present simulation results to depict the performance of our algorithm.