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.

翻译：重复运动任务在机器人学中十分常见，但受环境变化及机器人磨损等因素影响，其性能会随时间逐渐下降。迭代学习控制（ILC）通过利用先前迭代中的信息来补偿未来迭代中的预期误差，从而提升系统性能。本研究将准周期高斯过程（QPGP）纳入预测性ILC框架，用以建模并预测跨迭代的扰动与漂移。通过采用近期提出的QPGP结构方程形式，所提方法能以$\mathcal{O}(p^3)$而非$\mathcal{O}(i^2p^3)$的复杂度实现高效推断，其中$p$表示单次迭代内的点数，$i$代表总迭代次数，该优势在$i$较大时尤为显著。此形式化表述还能实现无信息损失下的参数估计，使得在控制回路内进行持续的高斯过程学习在计算上成为可行。通过预测下一迭代的误差分布而非仅依赖历史误差，控制器实现了更快的收敛速度，并在时变扰动下保持该性能。我们在三个任务上对本方法与标准ILC及传统基于高斯过程（GP）的预测ILC进行了对比测试：自动驾驶车辆轨迹跟踪、三连杆机械臂仿真以及真实Stretch机器人实验。在所有案例中，所提方法均展现出更快的收敛速度，在注入扰动与自然扰动下保持鲁棒性，同时降低了计算成本。这凸显了该方法在多种重复动力系统中的实用性。