Universal Plans: One Action Sequence to Solve Them All!

TL;DR

This paper proposes the concept of universal plans that can solve entire classes of planning problems without feedback, combining automata theory and number theory to achieve optimal solutions in discrete and continuous domains.

Contribution

It introduces the novel idea of universal plans, providing theoretical foundations and constructions for their existence and optimality across different planning problem categories.

Findings

Universal plans can solve all problems in a category regardless of obstacles or initial conditions.

They can be constructed using automata theory and number theory principles.

Simulation studies demonstrate their practical applicability.

Abstract

This paper introduces the notion of a universal plan, which when executed, is guaranteed to solve all planning problems in a category, regardless of the obstacles, initial state, and goal set. Such plans are specified as a deterministic sequence of actions that are blindly applied without any sensor feedback. Thus, they can be considered as pure exploration in a reinforcement learning context, and we show that with basic memory requirements, they even yield optimal plans. Building upon results in number theory and theory of automata, we provide universal plans both for discrete and continuous (motion) planning and prove their (semi)completeness. The concepts are applied and illustrated through simulation studies, and several directions for future research are sketched.