Sensor placement and Informative Path Planning (IPP) are fundamental problems that frequently arise in various domains. The sensor placement problem necessitates finding optimal sensing locations in an environment, enabling accurate estimation of the overall environmental state without explicitly monitoring the entire space. Sensor placement is particularly relevant for problems such as estimating ozone concentrations and conducting sparse-view computed tomography scanning. IPP is a closely related problem that seeks to identify the most informative locations along with a path that visits them while considering path constraints such as distance bounds and environmental boundaries. This proves useful in monitoring phenomena like ocean salinity and soil moisture in agricultural lands—situations where deploying static sensors is infeasible or the underlying dynamics of the environment are prone to change and require adaptively updating the sensing locations.
This thesis provides new insights leveraging Bayesian learning along with continuous and discrete optimization, which allow us to reduce the computation time and tackle novel variants of the considered problems. The thesis initially addresses sensor placement in both discrete and continuous environments using sparse Gaussian processes (SGP). Subsequently, the SGP-based sensor placement approach is generalized to address the IPP problem. The method demonstrates efficient scalability to large multi-robot IPP problems, accommodates non-point FoV sensors, and models differentiable path constraints such as distance budgets and boundary limits. Then the IPP approach is further generalized to handle online and decentralized heterogeneous multi-robot IPP. Next, the thesis delves into IPP within graph domains to address the methane gas leak rate estimation and source localization problem. An efficient Bayesian approach for leak rate estimation is introduced, enabling a fast discrete optimization-based IPP approach. Lastly, the thesis explores sensor placement in graph domains for wastewater-based epidemiology. A novel graph Bayesian approach is introduced, facilitating the placement of sensors in wastewater networks to maximize pathogen source localization accuracy and enable efficient source localization of pathogens.