Structure Aware Probabilistic Inference and Belief Space Planning with Performance Guarantees

Intelligent autonomous agents and robots are increasingly utilized across various domains, impacting our daily lives in significant ways. From robotic surgery to automated warehousing, these agents are often expected to operate reliably and efficiently despite facing limited environmental knowledge and uncertainty. Uncertainty arises from various factors, including noisy or restricted observations due to physical constraints, imprecise action execution, and unpredictable events in dynamic environments. In such scenarios, a truly autonomous agent should be able to perform both inference, which involves maintaining a belief over the high-dimensional state based on available information, and decision making under uncertainty, also known as Belief Space Planning (BSP). In BSP, the agent autonomously determines its optimal next actions while considering the future evolution of beliefs. However, solving bot these problems is computationally expensive and practically infeasible in real-world autonomous systems, where the agent is required to operate in real time, using inexpensive hardware and limited resources.

In our research, we utilize both topological structures, induced from graph representations of posterior beliefs, and specific structures of posterior distributions, to efficiently perform inference and BSP in high dimensional state spaces. Specifically, for BSP, we introduce a novel concept that leverages topological signatures to approximate the solution. We establish analytical bounds for this approximation to ensure performance and empirically quantify its computational efficiency. In perceptually aliased environments, where data association is not solved and posterior distributions are multi modal, we leverage the structure of posterior distributions to bound the information loss when pruning hypotheses. This enables us to efficiently solve nonmyopic BSP problems without compromising on the quality of the solution. Finally, we introduce an innovative method for incremental nonparametric probabilistic inference. Our approach leverages slices from high-dimensional surfaces to efficiently approximate posterior distributions of any shape.