SLAM as a Stochastic Control Problem with Partial Information: Optimal Solutions and Rigorous Approximations

TL;DR

This paper formulates the active SLAM problem as a stochastic control task under partial information, introducing a new exploration cost and deriving near-optimal solutions with rigorous analysis.

Contribution

It presents a novel stochastic control formulation of active SLAM with a new exploration cost and provides rigorous approximations and numerical solutions.

Findings

The new exploration stage cost encodes environment geometry.

Rigorous analysis yields near-optimal approximate solutions.

Numerical study demonstrates effectiveness of learned policies.

Abstract

Simultaneous localization and mapping (SLAM) is a foundational state estimation problem in robotics in which a robot accurately constructs a map of its environment while also localizing itself within this construction. We study the active SLAM problem through the lens of optimal stochastic control, thereby recasting it as a decision-making problem under partial information. After reviewing several commonly studied models, we present a general stochastic control formulation of active SLAM together with a rigorous treatment of motion, sensing, and map representation. We introduce a new exploration stage cost that encodes the geometry of the state when evaluating information-gathering actions. This formulation, constructed as a nonstandard partially observable Markov decision process (POMDP), is then analyzed to derive rigorously justified approximate solutions that are near-optimal. To enable this analysis, the associated regularity conditions are studied under general assumptions that apply to a wide range of robotics applications. For a particular case, we conduct an extensive numerical study in which standard learning algorithms are used to learn near-optimal policies.