Covariance Alignment for Dynamic Domain Adaptation in Robotic Trajectory Identification Under Variable Loading and Speed Regimes

Abstract

Industrial robotic trajectory condition monitoring under dynamic operating environments is constrained by covariate shift, where variations in end-effector payload mass and operational speed induce shifts in multi-sensor feature distributions. Supervised classifiers trained on a baseline operating state experience significant performance degradation when transferred to a different loading regime without adaptation. To address this discrepancy without target-domain labels or non-linear parameter estimation, this paper presents an unsupervised domain adaptation framework based on second-order Correlation Alignment (CORAL). The methodology is validated on an experimental parallel delta-robot platform equipped with multi-sensor acoustic and kinematic sensing across light and heavy payload states under low- and high-speed trajectory conditions. Information-theoretic and geometric evaluations show that covariance alignment reduces cross-domain divergence, achieving a 100% reduction in 2-Wasserstein optimal transport distance at both speeds, a reduction in Maximum Mean Discrepancy (MMD) of 59.3% at low speed and 91.5% at high speed, and a corresponding decrease in Domain Silhouette overlap score. Cross-domain trajectory classification accuracy for the decision-tree ensembles is restored from an unadapted baseline of 34.39% to above 98% post-alignment, with low variance across 10-fold cross-validation. These findings demonstrate that linear covariance alignment provides a computationally lightweight and mathematically grounded approach to mitigating payload-induced covariate shift in robotic trajectory monitoring