**1. Introduction**

With the rapid development of nanoscience and technology, precise positioning platforms and related technologies with micron motion range and nanoscale positioning accuracy have been widely applied in various fields, such as micromechanical systems, atomic force microscopy, and biomedical science [1–3]. In nanopositioning technology, system processing and measurement accuracy are increasingly demanding, so the resolution of nanopositioning needs to be achieved for the positioning system. Piezoelectric actuators are widely used in devices to achieve precise positioning because of their small sizes, simple structure, and high resolution. However, it cannot achieve long-distance motion owing to its limited motion range. Therefore, infinite stroke motion can be achieved by combining the piezoelectric actuator principle and the frictional inertia principle. The piezoelectric stick-slip actuator with high resolution and long stroke has advantages that other types of actuators do not have. The introduction and review of other types of actuators can be discovered in the

literature [4]. The development and research of piezoelectric rod-slip actuators have been a very active field for several decades. A large number of studies on precision positioning stages based on rod-slip actuators have been carried out at home and abroad.

In the process of the stick-slip actuator, it is often affected by a variety of factors, such as the electrical and hysteresis characteristics of the piezoelectric element, dynamic characteristics of the piezoelectric stack, the mechanical structure, and friction characteristics between slider and drive rod. By analyzing the motion law of the main influencing factors, some non-significant nonlinear factors can be appropriately simplified in the process of establishing the model. Peng et al. proposed an end-effector model considering the linear dynamics and hysteresis characteristics of the piezoelectric stick-slip actuator, as well as the friction of the end-effector. However, the model is suitable for piezoelectric stick-slip actuators with horizontal movement of the end-effector. The effect of gravity should be taken into account in subsequent model studies [5]. The structure of the piezoelectric stick-slip actuator is simple, but since the system relies on the frictional drive for long-distance positioning, there are uncertainties and disturbances. To achieve great motion characteristics, the control requirements of the system are extremely important. The control method is mainly divided into open-loop control and closed-loop control. The open-loop control is often used to compensate for the influence of hysteresis characteristics, and the adjustment and control method is used to realize positioning and tracking. Song et al. proposed feedforward control based on the Preisach model to eliminate the hysteresis characteristics [6]. Li et al. proposed a parasitic-type piezoelectric actuator, and this control strategy was used in scanning mode (high precision motion) to improve the positioning accuracy simply and effectively [7].

In the past few decades, a lot of research has been conducted on the modeling and control of hysteresis nonlinearity of piezoelectric actuators. In this paper, we plan to focus on the piezoelectric stick-slip actuator. Section 2 introduces various models and modeling methods under different characteristics of piezoelectric stick-slip actuators and summarizes the overall comprehensive model including each sub-model. Section 3 reviews various control schemes of the piezoelectric stick-slip actuator, including open-loop control and closed-loop control, and presents its limitations and related challenges. Finally, summarizes the problems in modeling and control of the piezoelectric stick-slip actuator and the future development direction in Section 4.
