## 1 Introduction  
With the deepening research on artificial intelligence, computer control, and robot technology, the application of robots has expanded from traditional manufacturing fields to medical operations, disability-assistance services, disaster search and rescue, scientific detection, aerospace, wearable equipment, and other fields. Compared with rigid robots, soft robots are mainly made of soft materials, and their movements depend on the deformation of soft robots themselves. Therefore, their high flexibility, good conformity, excellent adaptability, and better environmental compatibility have attracted wide attention from scholars [1; 2; 3]. The soft gripper is a branch of the field of soft robots with the design inspiration coming from naturally soft animals, such as jellyfish, octopus, starfish, and so on. The complex grasping and griping postures are realized through the control of force and displacement [4; 5]. Common pneumatically driven soft actuators are fiber reinforced soft actuators and multi-cavity pressurized fluid actuators [6; 7; 8]. The multi-cavity pressure drives the gripper to achieve different degrees of bending deformation of the soft gripper by adjusting the cavity pressure [9]. With light weight and high power, movements such as elongation, bending, and torsion can be achieved by simple controls. In view of these, the application prospect of the multi-cavity pneumatically actuated gripper has been widely concerned by scholars [10; 11; 12; 13; 14]. [PERSON] et al. [4] proposed an analytical model for dimensionally enhanced soft pneumatic actuators, which provides a direction for deterministic design of soft actuators. [PERSON] et al. [1] developed a six-finger soft gripper suitable for the biochemical field, which can capture living animals. [PERSON] et al. [15] designed a general soft gripper by using the principle of variable stiffness to make the fillersinside the soft gripper reversibly convert between the \"fluid-like\" state and the \"solid-like\" state. [PERSON] et al. [16] designed a closed-clamping soft gripper, which can clamp and release objects by inflating and deflating pneumatic artificial muscles. [PERSON] et al. [1] designed a soft gripper consisting of two layers of materials with different ductility that can produce spiral bending under pressure. [PERSON] et al. [17] developed a soft gripper based on a honeycomb pneumatic network. By changing the internal pressure of the airbag, the fingertip and long-distance grasping of the object are realized. Prof. [PERSON] et al. [18] developed a pneumatic four-finger soft gripper made of hyperelastic materials with variable effective-grasping length by using fibers to constrain pneumatic humanoid fingers and flexible pneumatic soft hands. The pneumatic soft gripper has multiple-grasping mechanisms, which can well grasp a variety of irregular objects and has good grasping effect and commercial prospects. [PERSON] et al. [19] used variable-length soft actuators and embedded flexible materials to establish a geometric steady-state model for simulating an octopus' claws and designed a continuous manipulator by embedding 12 wire ropes in silica gel to achieve bending, stretching, and grasping. [PERSON] et al. [20] at Seoul University used SMA as the driving element and made soft manipulators based on programmed intelligent soft composite (SSC), which can capture many irregular objects. [PERSON] et al. [21] proposed a nonlinear predictive control strategy SNN-ESGP, which is comprised of a novel model called echo state Gaussian process (ESGP) that is suitable for modeling nonlinear unknown systems as well as measuring their uncertainties, and a single neural network (SNN) serves as the controller of the system. [PERSON] et al. [22] proposes a new hybrid dynamic neural network (DNN) and proportional integral derivative (PID) controller for the position of the PAM. To enhance the proficiency of the controller, the problem under study is designed in the form of an optimization trend.