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.

翻译：本文引入了通用规划的概念，其执行时保证能解决某一类别中的所有规划问题，无论障碍物、初始状态和目标集如何。此类规划被定义为确定性的动作序列，无需任何传感器反馈即可盲目执行。因此，它们可被视为强化学习背景下的纯粹探索，并且我们证明，在基本的内存要求下，它们甚至能产生渐近最优的规划。基于数论和自动机理论的成果，我们为离散和连续（运动）规划提供了通用规划，并证明了它们的（半）完备性。通过仿真研究应用和阐释了这些概念，并概述了未来研究的若干方向。