Minimally sufficient structures for information-feedback policies

TL;DR

This paper identifies minimal and sufficient internal structures and sensors needed for information-feedback policies in robotic tasks, ensuring effective task achievement with optimal resource use.

Contribution

It establishes necessary and sufficient conditions for the existence of internal systems and sensors that support information-feedback policies, including the uniqueness of minimal internal systems.

Findings

Necessary and sufficient conditions for internal systems and sensors.

Existence and uniqueness of minimal internal systems.

Application to distance-optimal navigation in polygons.

Abstract

In this paper, we consider robotic tasks which require a desirable outcome to be achieved in the physical world that the robot is embedded in and interacting with. Accomplishing this objective requires designing a filter that maintains a useful representation of the physical world and a policy over the filter states. A filter is seen as the robot's perspective of the physical world based on limited sensing, memory, and computation and it is represented as a transition system over a space of information states. To this end, the interactions result from the coupling of an internal and an external system, a filter, and the physical world, respectively, through a sensor mapping and an information-feedback policy. Within this setup, we look for sufficient structures, that is, sufficient internal systems and sensors, for accomplishing a given task. We establish necessary and sufficient conditions for these structures to satisfy for information-feedback policies that can be defined over the states of an internal system to exist. We also show that under mild assumptions, minimal internal systems that can represent a particular plan/policy described over the action-observation histories exist and are unique. Finally, the results are applied to determine sufficient structures for distance-optimal navigation in a polygonal environment.