Quantitative Evaluation and Comparison of Motion Discrepancy Analysis Methods for Enhanced Trajectory Tracking in Mechatronic Systems

Pre-defined motion command profiles enable precise positioning and dynamic control in mechanical and mechatronic systems, maximizing efficiency and reliability. Real-world applications introduce dynamic factors like mechanical compliance, friction, and external disturbances that significantly impact system performance. Understanding these influences improves motion control strategy accuracy, robustness, and system stability. This study emphasizes the role of systematic and stochastic disturbances in improving motion control and accuracy. It introduces a structured method for evaluating system behavior under realistic operational conditions using advanced vibration analysis and spatio-temporal similarity measures. Using vibration indicators like amplitude, frequency content, phase relationships, crest factor, and acceleration root mean square (RMS) values, a comprehensive framework is created to quantify motion profile deviations. These indicators identify resonant frequencies, transient disturbances, and system inconsistencies, improving compensation strategies and predictive maintenance. A key contribution of this research is the comparison of quantification methods for motion precision and robustness integrating vibration diagnostics and advanced motion similarity analysis to improve motion control and assessment. Multi-faceted motion deviation characterization is achieved by combining displacement, velocity, and acceleration measurements with statistical and mathematical analysis. To assess motion consistency, spatio-temporal similarity measures like Dynamic Time Warping (DTW), Hausdorff distance, and discrete Fréchet distance capture spatial alignment and temporal progression. These measures allow a more nuanced evaluation of motion quality than traditional error metrics, especially in variable-speed dynamics, sampling rate inconsistencies, and complex motion patterns. Frequency-domain methods like FFT and wavelet transforms detect oscillatory behaviors to improve motion analysis reliability. The study uses spectral analysis and time–frequency domain techniques to detect motion inconsistencies that may cause mechanical wear, instability, or energy waste. Crest factor analysis and phase relationship assessment can also detect misalignment, structural resonance, and transient perturbations that conventional metrics miss.