A Distributed Augmenting Path Approach for the Bottleneck Assignment Problem

Khoo, Mitchell; Wood, Tony; Manzie, Chris; Shames, Iman

doi:10.48550/arxiv.2011.09606

Cited by 1 publication

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“…However, we will show that our safety objective is nonsubmodular and nonsupermodular. The aforementioned studies on auction-based approaches either do not propose any optimality guarantee, or when they do, their problems lie in the class of set partitioning problems with fixed task-robot pair costs (that is, additive/modular objective functions) [44,45] or submodular objective functions [24,26]. In terms of safety-oriented task allocation, there are studies where the objective is either the conditional value-at-risk cost [46,47], or the worst-case cost [48].…”

Section: Introductionmentioning

confidence: 99%

Multi-robot task allocation for safe planning against stochastic hazard dynamics

Lu¹,

Karaca²,

Kamgarpour³

2021

Preprint

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This paper considers the problem of multi-robot safe mission planning in uncertain dynamic environments. This problem arises in several applications including safety-critical exploration, surveillance, and emergency rescue missions. Computation of a multi-robot optimal control policy is challenging not only because of the complexity of incorporating dynamic uncertainties while planning, but also because of the exponential growth in problem size as a function of the number of robots. Leveraging recent works obtaining a tractable safety maximizing plan for a single robot, we propose a scalable two-stage framework to solve the problem at hand. Specifically, the problem is split into a low-level single-agent planning problem and a high-level task allocation problem. The low-level problem uses an efficient approximation of stochastic reachability for a Markov decision process to handle the dynamic uncertainty. The task allocation, on the other hand, is solved using polynomial-time forward and reverse greedy heuristics. The safety objective of our multi-robot safe planning problem allows an implementation of the greedy heuristics through a distributed auction-based approach. Moreover, by leveraging the properties of the safety objective function, we ensure provable performance bounds on the safety of the approximate solutions proposed by these two heuristics. Our result is illustrated through case studies.

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