## 1 Introduction
Micro-grippers have been developed using two parallel lead zirconate titanate (PZT) layers with a fixed range of displacement [13; 14]. Other micromanipulation mechanisms have been designed to enable the tip of the micro-gripper to move in parallel. Static characteristics, control of the micro-manipulator, and variation of deflection with the frequency have all been reported. This work aims to extend the investigation of parallel micro-gripping in terms of the effect of the sandwiched supporting layer on the deflection of the piezoelectric bimorph actuator. This fact allows us to understand to what extent the rigidity of the bimorph varies due to the brass layer between both piezo-ceramic layers. The second aim involves the implementation of a parallel micro-gripper by utilizing the piezoelectric bimorph itself to grasp soft objects instead of attaching an additional flexible cantilever. It has been well reported that piezoelectric actuators have been used to drive the micro-manipulation of micro-objects. A piezoelectric actuator can be used to provide movement to the flexible amplification mechanism of the micro-gripper. While this may deliver a large force, its size is significant and it has a complex structure. This study aims to achieve the grasping action directly from the piezoelectric bimorph in order to minimize the weight and complexity of the micro-gripper [15]. In addition, we aim to establish the supporting brass layer's essential role in providing the micro-gripper's basic behavior and increasing its life cycle. Usually, the integration of piezoelectric-based grippers into a robotic arm to construct micromanipulators requires the implementation of efficient electrical instrumentation. This electronic configuration should be able to handle the high voltages required by the actuators while providing precise power transfer to motorized actuators which can mobilize the gripper towards the position where the object to be manipulated is placed [16; 17; 18]. The instrumentation development must be completed with effective control actions able to drive the robotic manipulator. The application of such a controller may solve the reference trajectory tracking problem. At the same time, the motion satisfies the state restrictions related to the joint limits and the limited piezoelectric range of motion. The compatibility of these two problems is commonly a control design challenge, because while the tracking error must be stabilized while satisfying the restrictions. This fact restricts the application of the traditional barrier Lyapunov function, for example, as well as other equivalent techniques that can handle the state restrictions. Recently, several control design variants have attempted to aggregate both problems using safe operating conditions or the application of positive functions in the design. Based on this problem, there is a clear motivation to design new controllers that can drive the motion of the robotic manipulator and the actuators associated with the gripping device. This study aims to provide a new option by designing a novel control that can integrate both problems using a modified class of barrier Lyapunov function which uses state-dependent parameters that depend on the distance between the current state and the sets of restrictions. The main contributions of this study are: (a) A novel state constraint adaptive controller that solves position tracking for a robotic manipulator holding a gripper based on parallel bimorph piezoelectric actuators; and (b) the formal manner of constructing the state-dependent gain, taking into account both the effect of tracking error and the presence of state restrictions in the manipulator.