## 1 Introduction  
Piezoelectric materials are suitable for developing automatized systems on millimetric or microscopic scales, including roboticized grippers, thanks to their fast reaction time and potential for miniaturization [1]. Due to their unique reversible electrical and mechanical properties, piezoelectric actuators have been used as sensor and actuator components in various robotic devices. The applications of piezoelectric materials range from buzzers to diesel engines, fuel injectors, sonar, ultrasound, and nanopositioners in scanning microscopes [2, 3]. As actuators, piezoelectric materials are increasingly important in the latest positioning technologies thanks to their precise displacement [4] as well as several other advantages, such as quick response, large generative force, and high electromechanical coupling [5]. Piezoelectric actuators are categorized into stack actuators and bending actuators, characterized by the diversity of layers forming the actuator. The multilayers can either be double mounted or single-ended as a cantilever [6, 7]. A particular case of multilayer bending actuators is a piezoelectric bimorph actuator, which consists of two layers of piezoelectric material connected over their length surfaces [5]. The resultant bending motion becomes the working principle in micromechanical applications. Consequently, piezoelectric bimorphs have been involved in areas related to precise position control, among others [3; 5]. An essential characteristic of bending piezoelectric bimorphs is that the deflection of the bender's tip is dependent on an alternating driving voltage. Many studies have investigated the behavior of piezoelectric actuators. Other studies have investigated the nonlinear behavior of bending piezoelectric bimorphs structures under exposure to high electric fields, modeling asymmetrical bending piezoelectric bimorph structures and the static behavior of the expected bending moment, and providing analytical description of the bending piezoelectric bimorphs' free tip deflection by matrix calculus. The universal deformation state equations have been further extended to trimorph bending structures. The free tip deflection of piezoelectric multilayer beam bending actuators under the influence of an electric load was presented by [PERSON] and [PERSON] [8]. The dynamic behavior of a bimorph bending structure excited to bending vibrations by external harmonic forces, bending moments, pressure loads, and electrical driving voltages, including a flexible plate attached at the free bender's tip, was established as well, and a system of differential equations describing the dynamics of a bimorph was formulated. These establishments of piezoelectric responses have contributed to its application as a micro-manipulating system [9]. Piezoelectric actuators have been implemented in industrial, automotive, aviation, aerospace, medical, and consumer electronics applications. Their quiet drive settings make piezoelectric actuators an auto-focusing mechanism in microphone-equipped video cameras and mobile phones. In addition, as piezo actuators require no lubrication, they can be used in cryogenic and vacuum environments, among others. Using a stack actuator, extremely fine control is possible, with controlled voltages corresponding to slow expansion motions. As a result, a piezoelectric actuator can operate billions of times without wear or deterioration. The motion speed is exceptional, and is limited only by the object's inertia, movement, and the output capability of the electronic driver. When operating in an energized condition, a piezoelectric actuator consumes a small amount of electrical power and produces limited heat [10; 11; 12]. Grasping and moving small objects from one location to another depends on the shape and weight of the object and whether it is fragile or firm. The essential operation of the micro-gripper relies on the mechanism of the specific type of actuators employed, such as a thermo-piezoelectric actuator.