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This work deals with trajectory optimization for a robotic sensor network sampling a spatio-temporal random field. We examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories. This is a high-dimensional, multimodal, nonsmooth optimization problem, known to be NP-hard even for static fields and discrete design spaces. Under an asymptotic regime of near-independence between distinct sample locations, we show thatdoi:10.1109/tac.2011.2178332 fatcat:6imlgnjvzjhslhhhpborj4h2jy