# A Hybrid Soft Actuator Inspired by Grass-Spike: Design Approach, Dynamic Model, and Applications
## 1 Introduction  
Soft robotics is a novel approach to the design of entire robotic systems or partial mechanisms by imitating the structural characteristics or functional mechanisms of various living creatures. [PERSON] et al. observed that a gecko can stay on a vertical, dry, flat, slippery surface and found that the adhesive force between the gecko's toes and the surface is proportional to the shearing force. Based on this, they invented Stickybot [1]. Inspired by the underwater movement and grasping technique of octopuses, [PERSON] et al. invented the OCTOPUS robot [2]. [PERSON] et al. demonstrated a biological vine-like manipulator actuated by air pressure through a thin pipe, which was originally inspired by the growth mechanism of fungi or grapevines [3]. [PERSON] et al. invented Hygrobot, which imitates the behavior of a seed in the presence of humidity [4]. All these approaches have shown that soft robotics can provide us with new perspectives to address challenging issues in the field of robotic system design. An important issue for traditional electro-magnetic actuators is that their mass and volume are typically proportional to the generated torque; accordingly, the safety issues should be considered,for example in a workplace where human workers and robots coexist. To ensure safety, the boundary of the robot's workspace needs to be known, which in turn makes it difficult to adapt the workplace to a new arrangement or to deploy the requisite facilities when a production process changes [5]. To solve this issue, one way is to employ a machine learning algorithm to predict the human workers' movement and prevent a collision with the robotic systems [6]; another way is to design a robotic system whose mass is reduced, resulting in a small moment of inertia, which eventually helps to prevent exceeding the safety limits [7]. In soft robotics, robotic systems are made of soft materials, e.g., silicone or textile, which guarantee enough flexibility and dexterity to mimic the behavior of a living organism [7; 8; 9; 10]. The tetrapod robot developed by Harvard University is able to adapt its walking pattern with respect to the environmental situation such as the shape of the terrain, various obstacles, etc. [11]. The GoQBot from Tufts University was inspired by caterpillars' ballistic rolling mechanism by which it can replicate a fast self-propelled rotary locomotion [12]. [PERSON] et al. at Bristol University showed a reconfigurable crawling robot that uses dielectric elastomer actuators to convert the change in the electro-magnetic field into a propulsion force to move forward [10]. One common feature of the aforementioned soft robots is using air pressure as a source of actuation; accordingly, the robots are tethered to an air supply tube, which might impose a limitation on the robot's workspace. Vibration-driven locomotion might have the potential to make soft robots free from being tethered by a power line, as well as from being actuated by air pressure. [PERSON] et al. proposed a miniature vibration-driven planar locomotion robot for which the velocity could be controlled by two solenoids [13]. Bristle-bots have also been popular in the field of small robotic system design (either soft or rigid) due to vibration-driven characteristic and compactness. [PERSON] et al. presented a bristle-bot that was made of a polymer material for the body and two paper legs and its modeling [14]. Studies from various perspectives have been reported; for instance, the group behavior of multiple bristle-bots [15], the design of a millimeter-scale bristle robot (body length less than 10 mm) [16], and so on. Since soft robots have \"soft\" bodies, the modeling approaches for rigid body mechanisms cannot be applied directly, and the modeling process of soft robots is known to be difficult by its nature. [PERSON], [PERSON], and [PERSON] introduced an approach to address this problematic issue for their elephant trunk-like manipulator [17]. They first regarded the elephant trunk-like manipulator as a continuum of multiple segments.