Toward a language-theoretic foundation for planning and filtering

TL;DR

This paper introduces procrustean graphs, a formal structure based on language theory, to model and analyze the impact of sensor and actuator degradations on robot planning and filtering capabilities.

Contribution

It presents a novel formal framework that unifies plans, planning problems, and filters into a single structure with semantics grounded in formal language theory.

Findings

Procrustean graphs generalize existing planning and filtering structures.

Operations on these graphs can determine the impact of hardware changes.

Connections to hybrid automata and combinatorial filtering are established.

Abstract

We address problems underlying the algorithmic question of automating the co-design of robot hardware in tandem with its apposite software. Specifically, we consider the impact that degradations of a robot's sensor and actuation suites may have on the ability of that robot to complete its tasks. We introduce a new formal structure that generalizes and consolidates a variety of well-known structures including many forms of plans, planning problems, and filters, into a single data structure called a procrustean graph, and give these graph structures semantics in terms of ideas based in formal language theory. We describe a collection of operations on procrustean graphs (both semantics-preserving and semantics-mutating), and show how a family of questions about the destructiveness of a change to the robot hardware can be answered by applying these operations. We also highlight the connections between this new approach and existing threads of research, including combinatorial filtering, Erdmann's strategy complexes, and hybrid automata.