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

## TL;DR

This paper introduces a new robot calibration method combining adaptive wavelet networks and particle swarm optimization to improve positioning accuracy in industrial robots.

## Contribution

A novel PSO-driven neuro-symbolic state-space framework using adaptive wavelet networks for industrial robot calibration is proposed.

## Key findings

- The proposed method achieved a test RMSE of 0.73 mm on an ABB IRB 120 robot.
- It outperformed Levenberg–Marquardt by reducing RMSE by 40.16% and maximum error by 35.71%.
- The framework maintained high computational efficiency with convergence within 20.15 seconds.

## 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.