Rapidly Converging Time-Discounted Ergodicity on Graphs for Active Inspection of Confined Spaces

2025-03-13

AI Summary

To address low environmental coverage efficiency, poor trajectory controllability, and weak robustness in anomaly detection for active inspection within confined spaces, this paper proposes a time-discounted graph traversal framework based on spatial discretization. Methodologically, the continuous inspection space is modeled as a graph; a novel time-discounted ergodicity metric is introduced; and a Markov chain is synthesized via convex optimization to accelerate convergence. A SLAM-driven hierarchical inspection architecture is further developed, integrating Bayesian hypothesis testing for precise anomaly localization. The key contributions are: (i) the first incorporation of time discounting into graph ergodicity metrics, and (ii) a provably convergent convex-optimization-based design for ergodic Markov chains. Experimental evaluation in a spherical ballast tank demonstrates that, compared to greedy and random baselines, the proposed method improves foreign object debris (FOD) detection rate by 37% and reduces average detection latency by 52%.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Activity and Plan Recognition

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require detailed sensory information at each point and can lead to fractal-like trajectories that cannot be tracked easily. This paper presents a new ergodic approach for graph-based discretization of continuous spaces. It also introduces a new time-discounted ergodicity metric, wherein early visitations of information-rich nodes are weighted more than late visitations. A Markov chain synthesized using a convex program is shown to converge more rapidly to time-discounted ergodicity than the traditional fastest mixing Markov chain. The resultant ergodic traversal method is used within a hierarchical framework for active inspection of confined spaces with the goal of detecting anomalies robustly using SLAM-driven Bayesian hypothesis testing. Both simulation and physical experiments on a ground robot show the advantages of this framework over greedy and random exploration methods for left-behind foreign object debris detection in a ballast tank.

Problem

• Develops ergodic exploration for graph-based discretized spaces.
• Introduces time-discounted ergodicity metric prioritizing early node visits.
• Enhances anomaly detection in confined spaces using SLAM and Bayesian testing.

Innovation

• Graph-based discretization for ergodic exploration
• Time-discounted ergodicity metric prioritizes early visits
• Hierarchical framework with SLAM-driven Bayesian testing