SEQUENTIAL, HIERARCHICAL, AND ANALOGICAL PLAN TRANSFER IN ROBOTICS

Abstract

As robotic systems encounter increasingly complex domains, efficient plan transfer—within and across distinct planning contexts—becomes essential to achieving adaptability and operational efficiency. This dissertation formalizes task-level plan transfer by introducing a conceptual and mathematical framework based on category theory, defining three types of transfer: sequential, hierarchical, and analogical plan transfer. For sequential and hierarchical transfers, symmetric monoidal categories (SMCs) and string diagrams are used to provide a rigorous framework for coherent task composition. To enable analogical transfers, a new planning representation language that integrates structured knowledge through $\mathsf{C}$-sets and double-pushout (DPO) rewriting is introduced. Functorial data migrations are then used to align and preserve semantic structure during analogical plan transfer, circumventing the need to re-plan. The efficacy of this framework is demonstrated through case studies across several applications, from industrial automation to service robotics, illustrating the broad applicability of these methods. In doing so, this work contributes to the growing body of research demonstrating how category theory unifies heterogeneous representations across computer science. Ultimately, this work advances AI planning and robotics by establishing a principled foundation for task-level plan transfer that enhances the safety, flexibility, and interpretability of robotic task planning in complex and knowledge-rich environments.