**1. Introduction**

A piezoelectric nano-stepping motor [1] was presented in our previous research work. This article presents its latest enhancements. The device has two degree-of-freedoms (DOF), translation for 6 mm and rotation for endless 360◦. Its stepping resolution of translation and rotation are 100 nm and 0.04◦, respectively. As it is well-known, piezoelectric elements have inherent nanometer resolution if they work in scanning mode [2–4], i.e., driven by smoothly adjusting its voltage. Adding amplifying mechanisms [5–7] for piezoelectric elements extends the stroke. Switching between scanning and stepping modes [8–10], the proposed device features mm-level working range at nm-level resolution. Referring to Figure 1, the most significant design factor is the parallel arrangemen<sup>t</sup> of two piezoelectric elements. Translational or rotational stepping motions are generated when this pair of piezoelectric elements are driven by a sawtooth waveform [11] in-phase or anti-phase, respectively. Our parallel design avoids serial stacking and achieves multiple DOF within a stiffer and more compact structure. This is an important feature for precision nano-positioners, in order to reduce vibration and thermal expansion. In brief, stepping mode offers a theoretically infinite stroke with μm-level resolution; scanning mode offers several μm-level stroke with nm-level resolution. Bridging two modes in 2-DOF is the goal of this study. The proposed system is designed to achieve several mm-level stroke with sub-μm resolution. If a higher accuracy is expected, the device can be switched to scanning mode, which has been well investigated in [2].

The stick-slip principle [12–14] is the foundation of the proposed nano-stepping motor. The periodic high slew-rate sawtooth waveform drives piezoelectric elements to overcome the friction force. Therefore, the inertia motor [15,16], or so-called impact drive [17,18], accumulates a series of steps forward. However, the step size does not remain consistent, because the friction force varies due to the microscopic nature of the contacting surfaces. Since open loop control is impossible, a standard method to control 1-DOF inertia in stepping motors is adding displacement sensors to form a feedback system. In the case of 2-DOF, crosstalk or coupling may occur between sensors if they are not aligned properly. This article proposes an optically visual servo control system to solve the afore-mentioned problem. Similar piezoelectric motors are used to manipulate a phase plate [19] in a transmission electron microscope (TEM). This requires high resolution, long stroke, and does not allow the electromagnetic field to interfere with electron beams. TEM itself is a perfect 2-DOF motion sensor that can navigate the piezoelectric motor accurately, but only inside TEM itself. This research work extends the nano-stepping motor's applicability beyond the confines of a TEM. The instrumentation, image processing, control method, and validity are discussed in detail in the following sections. The experiments show that the proposed system functions effectively.

**Figure 1.** Photograph and schematic of a piezoelectric 2-DOF (degree of freedom) nano-stepping motor, which has a compact size of 5 cm × 5 cm × 3 cm. The fine screw presses the flexure spring and adjusts the clamping force between the V-groove guideway and the sliding block. The rotor can rotate around the cylinder. Translational or rotational stepping motions are generated when the pair of piezoelectric elements are driven in-phase or anti-phase, respectively.

#### **2. Instrumentation and Control**

#### *2.1. Microscopic Imaging System*

Based on our proposed nano-stepping motor [1], a microscopic imaging system is installed as in Figure 2. The camera (eco655CVGE, SVS-Vistek, Seefeld, Germany) has 2448 × 2050 pixels. Central 1000 × 1000 pixels are cropped for the following study. Two microscopic objectives (Plan 4× and 10×, Olympus) have resolutions of 1 μm/pixel and 0.38 μm/pixel, respectively. The relation between the physical distance and the image pixel count is correlated by an accurate laser displacement sensor (LK-H020, Keyence, Osaka, Japan), which has a 20 nm repeatability. The laser displacement sensor is not used in the following experiments because it only has 1-DOF and cannot measure rotation. The machine vision framework (Precise Eye 1-6044, Navitar, San Ramon, CA, USA) connects the camera and the objective together. The framework's coaxial illuminator provides suitable brightness for acquired images. The video stream is fed into an industrial computer (3.3 GHz, Intel i5 CPU) via Ethernet interface, and is then handled by LabVIEW (National Instrument, Austin, TX, USA). After image processing and decision making, the control signals are generated by a multifunction I/O interface (USB-6341, National Instrument, Austin, TX, USA), which provides two fast analog outputs for generating steep saw-tooth waveform, and at least one digital output for switching the

relay. The state of the relay decides whether the sawtooth waveform pair is in-phase for translation, or in anti-phase for rotation.

An atomic force microscope (AFM) [20] probe is small, lightweight, and can serve as a micromachining tool bit [21–23]. Therefore, an AFM probe (Tap300Al-G, BudgetSenors, Sofia, Bulgaria) is glued to the rotor as the marker for micro vision, as labeled in Figure 1. The original image of the AFM probe is acquired as Figure 3a, and then binarized into Figure 3b. Our image processing program detects the edges, which are drawn as green lines in Figure 3c. The intersection of the crossed green lines is defined as the rotor's position, the subject to be controlled in this research work.

**Figure 2.** Block diagram and the photograph of the proposed visual servo control system for a piezoelectric 2-DOF nano-stepping motor. The camera acquires microscopic motion video and feeds it into an industrial computer. The image processing and motion control program drive the motor via the multifunction I/O interface and the high voltage amplifier.

**Figure 3.** (**a**) The original, (**b**) the binarized, and (**c**) the edge-detected images of an AFM probe, which is treated as a micro marker of the proposed system. The width of above images is 1 mm.
