Reactivity and statefulness: Action-based sensors, plans, and necessary state

Typically to a roboticist, a plan is the outcome of other work, a synthesized object that realizes ends defined by some problem; plans qua plans are seldom treated as first-class objects of study. Plans designate functionality: a plan can be viewed as defining a robot's behavior throughout its execution. This informs and reveals many other aspects of the robot's design, including: necessary sensors and action choices, history, state, task structure, and how to define progress. Interrogating sets of plans helps in comprehending the ways in which differing executions influence the interrelationships between these various aspects. Revisiting Erdmann's theory of action-based sensors, a classical approach for characterizing fundamental information requirements, we show how plans (in their role of designating behavior) influence sensing requirements. Using an algorithm for enumerating plans, we examine how some plans for which no action-based sensor exists can be transformed into sets of sensors through the identification and handling of features that preclude the existence of action-based sensors. We are not aware of those obstructing features having been previously identified. Action-based sensors may be treated as standalone reactive plans; we relate them to the set of all possible plans through a lattice structure. This lattice reveals a boundary between plans with action-based sensors and those without. Some plans, specifically those that are not reactive plans and require some notion of internal state, can never have associated action-based sensors. Even so, action-based sensors can serve as a framework to explore and interpret how such plans make use of state.