Hybrid Neuro-Symbolic State-Space Modeling for Industrial Robot Calibration via Adaptive Wavelet Networks and PSO.

Overview

1. School of Sino-German Robotics, Shenzhen University of Information Technology, Shenzhen 518172, China
2. School of Software Engineering, Chengdu University of Information Technology, Chengdu 610225, China

Abstract

The absolute positioning accuracy of industrial manipulators is frequently bottlenecked by the interplay of geometric tolerances and complex, unmodeled non-geometric parameter drifts. Traditional static kinematic models, predicated on rigid-body assumptions, often struggle to characterize these state-dependent dynamic behaviors. To bridge this gap, this study introduces a PSO-Driven Neuro-Symbolic State-Space Framework incorporating Adaptive Wavelet Networks, drawing inspiration from two biological principles: the collective swarm intelligence observed in bird flocking and fish schooling, and the localized receptive field structure of mammalian visual cortex neurons. By reformulating calibration as a latent state estimation problem, we model kinematic parameters as stochastic states. Crucially, the observation model fuses symbolic Denavit–Hartenberg (D–H) predictions with an Adaptive Wavelet Network (AWNN). The AWNN utilizes Mexican Hat kernels, whose morphology mirrors the center-surround antagonism of cortical receptive fields, and leverages their precise time–frequency localization to effectively learn complex, configuration-dependent residuals. The framework employs a robust decoupled strategy. First, Particle Swarm Optimization (PSO) executes meta-optimization to autonomously determine hyperparameters, thereby mitigating initialization sensitivity. Second, a recursive inference engine estimates the hybrid states. Third, a global batch optimization refines the symbolic parameters against a frozen non-geometric error field. Experimental validation on an ABB IRB 120 robot (400 datasets) yielded a test RMSE of 0.73 mm. Compared to the standard Levenberg–Marquardt method, our approach reduced the RMSE by 40.16% and the maximum error by 35.71% (down to 0.99 mm). Moreover, it outperforms the state-of-the-art RPSO-DCFNN baseline by 12.05% while maintaining high computational efficiency (convergence within 20.15 s). These findings underscore the superiority of the proposed bio-inspired state-space fusion strategy for high-precision industrial applications.

Reproduced under the paper's license (CC BY), from the paper cited above.

Code

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Data

Datasets cited

• github.com/lizhibing1490183152/hsr-robotcali, at github.com; found in “Data Availability Statement”

Data Availability Statement

The cross-platform validation dataset HSR-RobotCali used in this study is publicly available at https://github.com/Lizhibing1490183152/HSR-RobotCali (accessed on 29 January 2026). The ABB IRB 120 experimental data supporting the reported results are available from the corresponding author upon reasonable request.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 3 funders, 24 references.

Cite

This paper

Mao, H., Lai, Z., & Li, Z. (2026). Hybrid Neuro-Symbolic State-Space Modeling for Industrial Robot Calibration via Adaptive Wavelet Networks and PSO. Biomimetics (Basel, Switzerland), 11(3), 171. https://doi.org/10.3390/biomimetics11030171

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