Quantifying uncertainty in robotics trajectories: A time-dependent approach using polynomial chaos expansion

Abstract

In today’s industrial context, maintaining precision in automated systems, particularly in high-degree-of-freedom robotic manipulators, is critical for achieving optimal performance and computational efficiency. A research analysis seeks to improve manufacturing accuracy through the evaluation of trajectory optimization methods when faced with uncertain conditions. A comprehensive dataset comprising 5.5 × 105 samples is generated using a Gaussian process, where the desired trajectory is constructed based on mean values to represent nominal operational conditions. The Monte Carlo simulation provides highly accurate predictions to analyze deviation from the ideal path at the cost of intensive computation. To address this challenge, Polynomial Chaos Expansion (PCE) is proposed as a computationally efficient alternative, achieving over a 90% reduction in computation time while maintaining comparable prediction accuracy. In addition, neural networks and support vector regression models are also employed for performance comparison. Results demonstrate that PCE not only significantly reduces computational burden but also improves accuracy in trajectory prediction. These findings highlight the suitability of PCE for deployment in high-precision, real-time robotic applications, including automated assembly, quality control, and surgical robotics. Furthermore, the proposed methodology shows strong potential for extension to dynamic and uncertain industrial environments requiring adaptive reliability analysis.