On Plans With Loops and Noise

TL;DR

This paper extends Levesque's formal framework for plan correctness to stochastic environments by incorporating noise and degrees of belief, enabling analysis of probabilistic plans in robotics.

Contribution

It introduces a new specification for plan correctness in noisy, uncertain settings based on a belief reasoning extension of the situation calculus.

Findings

The extended framework can analyze plans with noise and sensing uncertainty.

Application to example plans demonstrates its effectiveness.

Provides a foundation for synthesizing robust plans in stochastic environments.

Abstract

In an influential paper, Levesque proposed a formal specification for analysing the correctness of program-like plans, such as conditional plans, iterative plans, and knowledge-based plans. He motivated a logical characterisation within the situation calculus that included binary sensing actions. While the characterisation does not immediately yield a practical algorithm, the specification serves as a general skeleton to explore the synthesis of program-like plans for reasonable, tractable fragments. Increasingly, classical plan structures are being applied to stochastic environments such as robotics applications. This raises the question as to what the specification for correctness should look like, since Levesque's account makes the assumption that sensing is exact and actions are deterministic. Building on a situation calculus theory for reasoning about degrees of belief and noise, we revisit the execution semantics of generalised plans. The specification is then used to analyse the correctness of example plans.