In this paper, we formulate and solve the intermittent deployment problem, which yields strategies that couple \emph{when} heterogeneous robots should sense an environmental process, with where a deployed team should sense in the environment. As a motivation, suppose that a spatiotemporal process is slowly evolving and must be monitored by a multi-robot team, e.g., unmanned aerial vehicles monitoring pasturelands in a precision agriculture context. In such a case, an intermittent deployment strategy is necessary as persistent deployment or monitoring is not cost-efficient for a slowly evolving process. At the same time, the problem of where to sense once deployed must be solved as process observations yield useful feedback for determining effective future deployment and monitoring decisions. In this context, we model the environmental process to be monitored as a spatiotemporal Gaussian process with mutual information as a criterion to measure our understanding of the environment. To make the sensing resource-efficient, we demonstrate how to use matroid constraints to impose a diverse set of homogeneous and heterogeneous constraints. In addition, to reflect the cost-sensitive nature of real-world applications, we apply budgets on the cost of deployed heterogeneous robot teams. To solve the resulting problem, we exploit the theories of submodular optimization and matroids and present a greedy algorithm with bounds on sub-optimality. Finally, Monte Carlo simulations demonstrate the correctness of the proposed method.
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