Planning Under Uncertainty: Informative and Stochastic Path Planning via Gaussian Processes

Abstract

Autonomous systems operating in real-world environments often face uncertainty due to incomplete or noisy information about their surroundings. Effective planning under such conditions requires models that can represent uncertainty and support informed decision-making. This thesis addresses planning under uncertainty in environments characterized by spatially correlated stochastic processes. We model the agent's belief over these environments using Gaussian Processes (GPs), enabling Bayesian inference from sparse observations by capturing spatial correlations. We study two problems. The first is informative path planning (IPP) in continuous space, where an agent collects measurements along a trajectory to reduce uncertainty about an unknown spatial field, subject to budget and obstacle constraints. We propose a hierarchical framework that integrates global graph-based planning with local continuous trajectory optimization to improve scalability and performance. The second problem is stochastic path planning in random fields (SPPRF), where an agent seeks to minimize expected traversal cost in an environment with uncertainty induced by a stochastic process. The agent maintains a GP-based belief over the cost field and adapts its plan through belief updates as new data becomes available. Our solutions to these problems combine methods and tools from stochastic processes, path planning, and trajectory optimization. In summary, the contributions of this thesis extend the planning capabilities of autonomous agents in environments governed by spatially correlated uncertainty, encompassing both informative exploration and uncertainty-aware planning.