We consider a robotic vehicle tasked with gathering information by visiting a set of spatially-distributed data sources, the locations of which are not known a priori, but are discovered on the fly. We assume a first-order robot dynamics involving drift and that the locations of the data sources are Poisson-distributed. In this setting, we characterize the performance of the robot in terms of its sensing, agility, and computation capabilities. More specifically, the robot's performance is characterized in terms of its ability to sense the target locations from a distance, to maneuver quickly, and to perform computations for inference and planning. We also characterize the performance of the robot in terms of the amount and distribution of information that can be acquired at each data source. The following are among our theoretical results: the distribution of the amount of information among the target locations immensely impacts the requirements for sensing targets from a distance; performance increases with increasing maneuvering capability, but with diminishing returns; and the computation requirements increase more rapidly for planning as opposed to inference, with both increasing sensing range and maneuvering ability. We provide computational experiments to validate our theoretical results. Finally, we demonstrate that these results can be utilized in the co-design of sensing, actuation, and computation capabilities of mobile robotic systems for an information-gathering mission. Our proof techniques establish novel connections between the fundamental problems of robotic information-gathering and the last-passage percolation problem of statistical mechanics, which may be of interest on its own right.
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