Quasi-Periodic Gaussian Process Predictive Iterative Learning Control

TL;DR

This paper introduces a novel predictive iterative learning control method using Quasi-Periodic Gaussian Processes to model disturbances, enabling faster convergence and robustness in repetitive robotic tasks with reduced computational complexity.

Contribution

It integrates QPGPs into ILC for efficient disturbance prediction and parameter estimation, improving convergence speed and robustness in dynamic environments.

Findings

Faster convergence compared to standard ILC and Gaussian Process-based methods.

Robust performance under natural and injected disturbances.

Reduced computational complexity enabling real-time application.

Abstract

Repetitive motion tasks are common in robotics, but performance can degrade over time due to environmental changes and robot wear and tear. Iterative learning control (ILC) improves performance by using information from previous iterations to compensate for expected errors in future iterations. This work incorporates the use of Quasi-Periodic Gaussian Processes (QPGPs) into a predictive ILC framework to model and forecast disturbances and drift across iterations. Using a recent structural equation formulation of QPGPs, the proposed approach enables efficient inference with complexity $\mathcal{O}(p^3)$ instead of $\mathcal{O}(i^2p^3)$, where $p$ denotes the number of points within an iteration and $i$ represents the total number of iterations, specially for larger $i$. This formulation also enables parameter estimation without loss of information, making continual GP learning computationally feasible within the control loop. By predicting next-iteration error profiles rather than relying only on past errors, the controller achieves faster convergence and maintains this under time-varying disturbances. We benchmark the method against both standard ILC and conventional Gaussian Process (GP)-based predictive ILC on three tasks, autonomous vehicle trajectory tracking, a three-link robotic manipulator, and a real-world Stretch robot experiment. Across all cases, the proposed approach converges faster and remains robust under injected and natural disturbances while reducing computational cost. This highlights its practicality across a range of repetitive dynamical systems.