| Summary: | We study an informative path planning problem where the goal is to minimize the time required to learn a spatial field. Specifically, our goal is to ensure that the mean square error between the learned and actual fields is below a predefined value. We study three versions of the problem. In the placement version, the objective is to minimize the number of measurement locations. In the mobile robot version, we seek to minimize the total time required to visit and collect measurements from the measurement locations. A multi-robot version is studied as well where the objective is to minimize the time required by the last robot to return back to a common starting location called depot. By exploiting the properties of Gaussian Process regression, we present constant-factor approximation algorithms that ensure the required guarantees. In addition to the theoretical results, we also compare the empirical performance using a real-world dataset with other baseline strategies. === M. S. === We solve the problem of measuring a physical phenomenon accurately using a team of robots in minimum time. Examples of such phenomena include the amount of nitrogen present in the soil within a farm and concentration of harmful chemicals in a water body etc. Knowing accurately the extent of such quantities is important for a variety of economic and environmental reasons. For example, knowing the content of various nutrients in the soil within a farm can help the farmers to improve the yield and reduce the application of fertilizers, the concentration of certain chemicals inside a water body may affect the marine life in various ways. In this thesis, we present several algorithms which can help robots to be deployed efficiently to quantify such phenomena accurately. Traditionally, robots had to be teleoperated. The algorithms proposed in this thesis enable robots to work more autonomously.
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