A Novel Monte-Carlo Compressed Sensing and Dictionary Learning Method for the Efficient Path Planning of Remote Sensing Robots

2025-07-24

AI Summary

To address the challenges of excessive path length and high reconstruction error in remote-sensing robotic environmental perception, this paper proposes a joint optimization framework integrating compressive sensing (CS) measurement matrix design with robot trajectory planning. For the first time, structural constraints of the CS measurement matrix are embedded directly into robotic path design, enabling a Monte Carlo–driven co-optimization that simultaneously minimizes traversal distance and reconstruction error. Furthermore, a data-driven dictionary learning strategy is incorporated to enhance signal sparsity, thereby jointly reducing the number of required measurements and reconstruction distortion. In experiments reconstructing NO₂ pollution maps, the robot traverses less than 10% of the distance required for full coverage, while achieving over fivefold higher reconstruction accuracy compared to conventional DCT- or polynomial-based dictionaries, and doubling the accuracy of state-of-the-art information-driven path planning methods. The approach significantly improves both sparse sensing efficiency and reconstruction fidelity.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

In recent years, Compressed Sensing (CS) has gained significant interest as a technique for acquiring high-resolution sensory data using fewer measurements than traditional Nyquist sampling requires. At the same time, autonomous robotic platforms such as drones and rovers have become increasingly popular tools for remote sensing and environmental monitoring tasks, including measurements of temperature, humidity, and air quality. Within this context, this paper presents, to the best of our knowledge, the first investigation into how the structure of CS measurement matrices can be exploited to design optimized sampling trajectories for robotic environmental data collection. We propose a novel Monte Carlo optimization framework that generates measurement matrices designed to minimize both the robot's traversal path length and the signal reconstruction error within the CS framework. Central to our approach is the application of Dictionary Learning (DL) to obtain a data-driven sparsifying transform, which enhances reconstruction accuracy while further reducing the number of samples that the robot needs to collect. We demonstrate the effectiveness of our method through experiments reconstructing $NO_2$ pollution maps over the Gulf region. The results indicate that our approach can reduce robot travel distance to less than $10%$ of a full-coverage path, while improving reconstruction accuracy by over a factor of five compared to traditional CS methods based on DCT and polynomial dictionaries, as well as by a factor of two compared to previously-proposed Informative Path Planning (IPP) methods.

Problem

• Optimizing robot path planning for efficient environmental data collection
• Reducing signal reconstruction error in compressed sensing frameworks
• Minimizing robot travel distance while maintaining high reconstruction accuracy

Innovation

• Monte Carlo optimized CS measurement matrices
• Dictionary Learning for sparsifying transform
• Minimizes robot path and reconstruction error