Automating Transfer of Robot Task Plans using Functorial Data Migrations

TL;DR

The paper presents a formal framework based on functorial data migrations to automate robot task plan transfer across planning domains, eliminating the need for replanning when ontologies differ. It uses a translation functor $F: \mathsf{D}' \rightarrow \mathsf{D}$ and a plan transfer functor $\Delta_F$ to map source plans from $\mathsf{D}$-Set to $\mathsf{D}'$-Set, with delta migrations guaranteeing valid transfers by preserving pushouts. A case study transferring a Blocksworld-inspired plan to a Kitchenworld (AI2-THOR) domain demonstrates how domain ontologies, maps, and generated actions can be formalized and executed, while highlighting the limitations and potential for lossy translations. The work also outlines patterns of use, integration strategies within planning architectures, and a proposed set of benchmarks and metrics to evaluate transfer quality, explainability, and feasibility. Overall, the approach provides a principled, scalable pathway to reuse symbolic plans across diverse robotic environments, with future work focusing on benchmarking, scaling, and deeper analysis of conjunctive migrations.

Abstract

This paper introduces a novel approach to ontology-based robot plan transfer by leveraging functorial data migrations, a structured mapping method derived from category theory. Functors provide structured maps between planning domain ontologies which enables the transfer of task plans without the need for replanning. Unlike methods tailored to specific plans, our framework applies universally within the source domain once a structured map is defined. We demonstrate this approach by transferring a task plan from the canonical Blocksworld domain to one compatible with the AI2-THOR Kitchen environment. Additionally, we discuss practical limitations, propose benchmarks for evaluating symbolic plan transfer methods, and outline future directions for scaling this approach.

Figures (5)

• Figure 1: A conceptual illustration of transferring a plan from ColorBlocksworld to AI2-THOR Kitchenworld, using an ontology map to formalize the translation between planning domains and automatically transfer a valid plan to the target domain.
• Figure 2: Example of translation functors for a delta data migration (top) and a conjunctive query data migration (bottom).
• Figure 3: Schematic of plan transfer, $\Delta_F: \mathsf{D}\text{-}\mathsf{Set} \rightarrow \mathsf{D^{\prime}}\text{-}\mathsf{Set}$, for the ontology map, $F: \mathsf{D^{\prime}} \rightarrow \mathsf{D}$. The top (blue) sequence represents a plan in $\mathsf{D}\text{-}\mathsf{Set}$. The bottom (yellow) sequence represents a plan in $\mathsf{D^{\prime}}\text{-}\mathsf{Set}$. Rectangles in the schematic correspond to actions within each plan. Arrows emerging from the left side of the rectangles are match morphisms. Dotted arrows emerging from the right side of the rectangles point to the resultant state after each action is applied.
• Figure 4: Illustration of plan transfer from the ColorBlocksworld domain to the Kitchenworld domain. The domain ontologies are drawn as directed graphs where the nodes of the graphs are the types and the directed edges of the graph are predicates. The source of the edge is the first argument of the predicate and the target of the edge is the second argument.
• Figure 5: Schematic of the four patterns of functorial plan transfer: (i) abstract-to-specific, (ii) specific-to-specific, (iii) specific-to-abstract-to-specific, and (iv) abstract-to-abstract.

Theorems & Definitions (4)

• Definition 1
• Definition 2
• Definition 3
• Definition 4