This paper deals with large-scale decentralised task allocation problems for multiple heterogeneous robots with monotone submodular objective functions. One of the significant challenges with the large-scale decentralised task allocation problem is the NP-hardness for computation and communication. This paper proposes a decentralised Decreasing Threshold Task Allocation (DTTA) algorithm that enables parallel allocation by leveraging a decreasing threshold to handle the NP-hardness. Then DTTA is upgraded to a more practical version Lazy Decreasing Threshold Task Allocation (LDTTA) by combining a variant of Lazy strategy. DTTA and LDTTA can release both computational and communicating burden for multiple robots in a decentralised network while providing an optimality bound of solution quality. To examine the performance of the proposed algorithms, this paper models a multi-target surveillance scenario and conducts Monte-Carlo simulations. Simulation results reveal that the proposed algorithms achieve similar function values but consume much less running time and consensus steps compared with benchmark decentralised task allocation algorithms.
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