Recent Advances in the Design, Modeling, and Control of Flexure-Based Nanopositioning Stages

Flexure-based nanopositioning stages have emerged as indispensable tools in advanced fields such as nanotechnology, semiconductor manufacturing, and biomedical engineering, where nanometer-scale precision is paramount. This paper presents a comprehensive review of the state-of-the-art in flexure-based nanopositioning, systematically examining the three critical and interconnected domains of geometric design, theoretical modeling, and advanced control strategies. This review begins by analyzing fundamental design principles, including motion decoupling, stiffness-range trade-offs, and various structural topologies (serial, parallel, and hybrid), highlighting how they achieve high precision and reject disturbances. It then delves into analytical and computational modeling techniques, from pseudo-rigid-body models and beam theory to finite element analysis, which are essential for predicting system behavior and guiding design optimization. A core section of this review is dedicated to control methodologies, providing a critical analysis of active resonant control for damping mechanical vibrations, classical and robust control for stability under uncertainties, and modern adaptive and learning-based techniques for handling nonlinearities and time-varying dynamics. Furthermore, this review addresses persistent challenges such as bandwidth limitations, performance trade-offs, and the integration of complex multi-axis systems. Finally, it outlines future research directions, emphasizing the promising potential of data-driven modeling, artificial intelligence-enhanced control, and a holistic mechatronic co-design approach to push the boundaries of precision, speed, and robustness in next-generation nanopositioning systems. This work aims to serve as a systematic reference and synthesis for researchers by integrating a vast body of literature and providing a clear perspective on the development of high-performance nanopositioning stages.