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

2026-04-23

AI Summary

This work addresses the challenge of exploration and mapping decisions in active SLAM under partial observability by formulating it as a stochastic control problem with incomplete information. The authors propose a non-standard partially observable Markov decision process (POMDP) framework that jointly integrates motion, perception, and map representation. A key innovation is the introduction of an exploration cost function that explicitly captures the geometric structure of the state space to quantify the value of information-gathering actions. Building upon this formulation, they develop a general stochastic control model and derive an approximately optimal policy with theoretical guarantees by combining stochastic control theory and reinforcement learning algorithms. Numerical experiments in representative environments demonstrate the effectiveness of the approach, successfully learning high-performance exploration strategies.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning with Markov Models (MDPs, POMDPs)
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• SLAM
• stochastic control
• partial information
• POMDP
• active perception

Innovation

• active SLAM
• stochastic control
• POMDP
• information gathering
• near-optimal approximation