## 1 Introduction
The fuzzy logic [23] can deal with nonlinear and uncertain systems, so it can be used to estimate the optimal impedance parameters in real time. However, its effectiveness depends on the rule base, which is built on the initial sample dataset. This paper proposes a combination of iterative learning control (ILC), fuzzy logic, and impedance control. The ILC based on the gradient descent algorithm [24; 25] is used to determine the impedance parameters in unknown environments. However, the ILC process takes time for the impedance parameter to converge to the desired optimal value. Therefore, it is not conducive to perform in real time. Instead, it is performed with various sample objects to synthesize a sample dataset of optimal impedance parameters. This dataset is then used to design the rule base of the fuzzy impedance controller, which will run in real time to estimate the optimal parameters of impedance control under each given condition. Another important requirement of grippers is to keep an unknown object from sliding down after gripping and picking it up. In [26], the authors develop a microlaser Doppler velocimeter as a sensor to detect whether a grasped object is slipping or not. In [27; 28], a biomimetic tactile sensor is used to detect and classify slip events. These methods require complicated installation at the contact between the gripper's finger and the object. In this paper, a six-axis force/torque sensor (FTS) mounted on the gripper will be used to design the gripping force estimator, which will calculate the appropriate gripping force in real time to keep the unknown object from sliding down instead of trying to detect slippage. The FTS is simple to mount and avoids direct contact with the object. It also proves effective when it is possible to quickly and accurately estimate the optimal gripping force when picking objects up. The main contribution of this paper is the proposal of an optimal fuzzy impedance controller, which can operate in real time to safely grasp and hold fragile and unknown objects of varying stiffness and shapes. The optimal fuzzy impedance controller is the combining schema of the impedance control, fuzzy logic control, and ILC. Many studies mention the combination of impedance control and fuzzy logic but do not specify the process of building the sample data for designing the rule base, which plays a very important role in determining the effectiveness of the fuzzy controller. In this study,the ILC process is employed to optimize the sample dataset for designing the rule base to enhance the effectiveness of the fuzzy impedance controller. Besides, the design of the gripping force estimator based on an FTS is a simple but effective application proposal in keeping an unknown object from sliding down when picking it up. Compared with other methods, such as PID control, the proposed method has advantages in that the control parameters are automatically estimated in real time and the force control has higher accuracy and stability. Its effectiveness has been verified by conducting the simulation, experiment, and comparison. The following content of the paper is organized as follows: Section 2 describes the control schema and system description. Section 3 presents the impedance iterative learning control. Section 4 describes the fuzzy impedance controller. Section 5 presents the simulations, experiments, and comparisons. Section 6 discusses the results. Section 7 is the conclusion.