Kabsch Marker Estimation Algorithm—A Multi-Robot Marker-Based Localization Algorithm Within the Industry 4.0 Context

Abstract

This paper introduces the Kabsch Marker Estimation Algorithm (KMEA), a new, robust multi-marker localization method designed for Autonomous Mobile Robots (AMRs) within Industry 4.0 (I4.0) settings. By integrating the Kabsch Algorithm, our approach significantly enhances localization robustness by aligning detected fiducial markers with their known positions. Unlike conventional methods that rely on a limited subset of visible markers, the KMEA uses all available markers, without requiring the camera’s extrinsic parameters, thereby improving robustness. The algorithm was validated in an I4.0 automated warehouse mockup, with a four-stage methodology compared to a previously established marker estimation algorithm for reference. On the one hand, the results have demonstrated the KMEA’s similar performance in standard controlled scenarios, with millimetric precision across a set of error metrics and a mean relative error (MRE) of less than 1%. On the other hand, KMEA, when faced with challenging test scenarios with outliers, showed significantly superior performance compared to the baseline algorithm, where it maintained a millimetric to centimetric scale in error metrics, whereas the other suffered extreme degradation. This was emphasized by the average reduced results of error metrics from 86.9% to 92% in Parts III and IV of the test methodology, respectively. These results were achieved using low-cost hardware, indicating the possibility of even greater accuracy with advanced equipment. The paper details the algorithm’s development, theoretical framework, comparative advantages over existing methods, discusses the test results, and concludes with comments regarding its potential for industrial and commercial applications by its scalability and reliability.

Keywords

• ArUco markers
• automated warehouse
• autonomous mobile robots
• fiducial markers
• ground truth system
• industry 4.0