Computation load-sharing across a network of heterogeneous robots is a promising approach to increase robots capabilities and efficiency as a team in extreme environments. However, in such environments, communication links may be intermittent and connections to the cloud or internet may be nonexistent. In this paper we introduce a communication-aware, computation task scheduling problem for multi-robot systems and propose an integer linear program (ILP) that optimizes the allocation of computational tasks across a network of heterogeneous robots, accounting for the networked robots' computational capabilities and for available (and possibly time-varying) communication links. We consider scheduling of a set of inter-dependent required and optional tasks modeled by a dependency graph. We present a consensus-backed scheduling architecture for shared-world, distributed systems. We validate the ILP formulation and the distributed implementation in different computation platforms and in simulated scenarios with a bias towards lunar or planetary exploration scenarios. Our results show that the proposed implementation can optimize schedules to allow a threefold increase the amount of rewarding tasks performed (e.g., science measurements) compared to an analogous system with no computational load-sharing.
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