# A Hybrid Soft Actuator Inspired by Grass-Spike: Design Approach, Dynamic Model, and Applications
## 1 Introduction
Then, they applied the Euler-Lagrange equation as a tool to derive a dynamic model. Consequently, the dynamic model of the elephant trunk-like manipulator could be obtained, which was similar to a typical rigid body model structure [17; 18]. [PERSON] developed a bristle-bot, described the kinetic energy and potential energy explicitly, and presented the movement of his robotic system including anisotropic friction based on the principle of virtual work. He also proposed an approach in which the Euler-Lagrange equation served as a primary tool to obtain the equation of motion [19; 20]. Therefore, by following the above-mentioned approaches, we can obtain the dynamic model of soft robotic systems. In this paper, we propose a hybrid soft actuator inspired by a grass-spike. If we place the grass-spike on a taut wire and apply vibration to the rope, the elasticity of the spikes is converted into a propulsion force; consequently, it moves. The moving direction depends on the leaning angle of the spikes. To mimic the movement characteristic of the grass-spike at a functional level, the proposed hybrid soft actuator consists of a rigid core part, as well as a soft spike part wrapped around the rigid core. The rigid core part is a cylinder-shaped body, and it has a small motor with a counterweight to generate vibration inside the body. The soft spike part has aligned silicone spikes on a flat silicone substrate. The term \"hybrid soft\" comes from this structural feature, designed to have a rigid core + soft spikes, and the proposed actuator will be referred to as a \"hybrid soft actuator (HSA)\" throughout the paper. If we attach a wire to the end of the HSA and place it in the tubular passage, then it can drag/manipulate a mass attached to the other end of the wire. Being modularized with a wire and a tubular passage, the HSA is able to work as a linear actuator. This modularized HSA will be referred to as a hybrid soft actuator module (HSAM). In addition to our design approach, we also introduce two dynamic models: an HSA model and an interactive control model between the HSAM and a mass, respectively. By following the approaches introduced in [18; 19], we first derive the HSA model. We also introduce a system identification process to estimate unknown frictional parameters based on empirical data. The interactive control model can be derived by analyzing the HSAM and the mass as a bilateral control system. Again, the system identification process is followed to estimate the damping effect. The simulation results are presented for both models; in particular, the outcomes from the HSAM simulation will be used to determine the number of HSAMs to generate a desired amount of force. Lastly, two potential applications--an elbow manipulator and a robotic hand grasper--are presented to demonstrate the feasibility of the HSA and HSAM to be utilized for soft robotics applications. The rest of paper is organized as follows: Our HSA design approach is presented in Section 2. The derivation of the dynamic model of the HSA and the interactive control model of the HSAM is introduced in Section 3. Section 4 discusses the experiments to validate the derived model and estimate the unknown friction and damping parameters by the system identification. The simulation results for the HSA and the HSAM are depicted in Section 5. Section 6 gives the conclusion of this paper.