Adaptive Bayesian Optimization for High-Precision Motion Systems

TL;DR

The paper tackles real-time safe online tuning of low-level controller gains for high-precision motion systems, where expensive Bayesian optimization hinders runtime use. It presents a Modified GoOSE that removes input discretization and employs multi-task Gaussian Processes to model performance $f(x)$ and safety $q(x)$, enabling online adaptation under the constraint $q(x) \le c$. The method alternates active and passive phases, uses a lower confidence bound acquisition, and couples with parallel schemes (ParaGoOSE and LookupGoOSE) to deliver fast, safe exploration. Validation on a real nanometer-precision motion axis shows faster adaptation and robust safety compared to baseline GoOSE and interpolated LPV methods, highlighting practical viability for semiconductor-grade precision motion systems. Overall, the work advances real-time, data-driven adaptive control by delivering safe, scalable Bayesian optimization for high-speed motion applications.

Abstract

Controller tuning and parameter optimization are crucial in system design to improve closed-loop system performance. Bayesian optimization has been established as an efficient model-free controller tuning and adaptation method. However, Bayesian optimization methods are computationally expensive and therefore difficult to use in real-time critical scenarios. In this work, we propose a real-time purely data-driven, model-free approach for adaptive control, by online tuning low-level controller parameters. We base our algorithm on GoOSE, an algorithm for safe and sample-efficient Bayesian optimization, for handling performance and stability criteria. We introduce multiple computational and algorithmic modifications for computational efficiency and parallelization of optimization steps. We further evaluate the algorithm's performance on a real precision-motion system utilized in semiconductor industry applications by modifying the payload and reference stepsize and comparing it to an interpolated constrained optimization-based baseline approach.

Figures (8)

• Figure 1: The BO-based run-to-run controller tuning setting considered in this work.
• Figure 2: Parallel computation scheme to run the modified GoOSE. 1. ParaGoOSE: A horizon of the next m tasks is sampled and fed to the queue. LookupGoOSE: Corresponding to the next task, a neighborhood of tasks within the grid is selected and fed to the queue. 2. The optimization processes pick the entries in the task queue and calculate the corresponding optimizers/optima according to algorithm \ref{['alg:adaptive_control_goose']} 3. The optimizers/optima are returned to the manager thread to be executed. 4. The $\mathcal{GP}^f$ and $\mathcal{GP}^q$ are updated with $f(x^*)$ and $q(x^*)$.
• Figure 3: Top panel: Simplified controller architecture in the experimental study. Top panel. The cyan blocks contain control parameters optimized in this work. Bottom panel: Positioning system by Schneeberger Linear Technology AG.
• Figure 4: Simulation: Comparison of the modified GoOSE with one accounting for the drift term as a task parameter and the other without. The plots show the achieved cost and constraint value with respect to stepsize after convergence of the algorithm. It is evident that the GoOSE without the drift term has difficulty achieving optimality due to the presence of the artificial drift.
• Figure 5: Simulation: The achieved optimum cost over the iterations is depicted for the modified GoOSE with the drift term. It is able to compensate for the drift by constantly modifying the controller gains and thus to keep the cost at the optimum.