  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 asymptotically 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.
