Metrology-Driven Framework for Online Estimation of Anthropomorphic Robot End-Effector Position and Uncertainty

The online End Effector Positioning Estimation (EEPE) is a critical challenge for anthropomorphic robots typically used in industrial and medical applications. The online EEPE includes the evaluation of uncertainty, i.e. the EEPE is not a point, but it is a region of the space where the end effector can be with a given probability. The online EEPE is essential for developing suitable control programs, uncertainty-aware, with the aim to increase the reliability and the accuracy of robotic operations. To address this challenge, this paper proposes a unified metrology driven framework that starts with the metrological characteristics of the robot components and integrates analytical forward kinematics, Monte Carlo based uncertainty propagation, Jacobian covariance analysis, and fuzzy logic-based correction. Rather than replacing existing uncertainty propagation models in the Guide to the Expression of Uncertainty in Measurement (GUM), that for its complexity is not suitable for online EEPE, the proposed framework uses GUM as a theoretical reference and performs GUM compliant uncertainty budgeting by combining Type A and Type B evaluations. Numerical tests based on ground truth datasets derived from forward kinematics demonstrate that the proposed framework enables online EEPE to be compatible with GUM method and with a lower uncertainty with respect to other online EEPE methods present in literature. The present study demonstrates the framework via simulation to validate its metrological consistency, while the lightweight fusion and correction layers ensure online-capable deployment in future hardware implementations.