Minimally sufficient structures for information-feedback policies

TL;DR

The paper addresses how to identify minimally sufficient internal structures and sensing for information-feedback policies in robotics by formalizing an Information Transition System (ITS) framework. It introduces sufficiency and quotient ITS concepts via I-maps and derives necessary and sufficient conditions for ITSs and sensor mappings to support given policies, including minimal refinements and uniqueness under fullness. The work extends to multiple tasks by taking joins of task-specific policies and demonstrates the approach on distance-optimal navigation in polygonal environments using Gap Navigation Trees as minimal structures. Overall, the framework provides a principled design methodology for minimal sensing and filtering in planning under partial observability with implications for autonomous navigation and cognitive robotics.

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.

Figures (2)

• Figure 1: Internal $({\cal I}, Y, {\phi})$ and external $(X, U, f)$ systems coupled through coupling functions $h$ and $\pi$, the sensor mapping and the information-feedback policy, respectively.
• Figure 2: (a) Skewed tetromino environment. (b)Labels attributed by ${\kappa}_\pi$ with labels $u_1$ (blue), $u_2$ (orange), $u_3$ (green), and $\xi$ (red). (c) $S$ is the quotient of $S_{hist}\mathord{\upharpoonright}_{\pi_{hist}}$ by ${\kappa}$.

Theorems & Definitions (21)

• definition thmcounterdefinition: Information Transition System
• definition thmcounterdefinition: State-relabeled ITS
• definition thmcounterdefinition: External System
• definition thmcounterdefinition: Sufficiency
• definition thmcounterdefinition: Refinement of an Imap
• definition thmcounterdefinition: History ITS
• definition thmcounterdefinition: Set of attainable histories
• lemma thmcounterlemma
• definition thmcounterdefinition: Feasible Policy
• lemma thmcounterlemma