Compliant mobile robotics is a developing bioinspired concept of propulsion for locomotion. This paper studies the modeling and analysis of a compliant tail-propelled fish-like robot. This biomimetic design uses a fluid-filled network of channels embedded into the soft body to actuate the compliant tail and generate thrust. This study analyzes the nonlinear dynamics of Fish Tail Fluidic Actuator (FTFA). The fluidic expansion under pressure creates a bending moment in the tail. It is demonstrated that the tail response follows the theoretical formulation extracted from the accurate modeling. In this modeling, tail is assumed as a continuous Euler–Bernoulli beam considering large deflection and nonlinear strain. Then, the implementation of Hamilton's principle and the method of calculation lead to the motion equations. The assumed mode method is used to achieve the mathematical model in the multi-mode system that is more similar to the soft continuous system. We investigate the tendencies of the tail amplitude, swimming speed, and Strouhal number when the input driving frequency changes. The simulation results disclose that high swimming efficiency can be obtained at the multi-order resonances; meanwhile, the compliant fish robot is pushed at the corresponding frequency illustrating nonlinear behavior.
a The carangiform fish robot consists of a compliant body with an embedded actuator . b The biomimetic robotic fish with dielectric elastomer propulsion mechanism . c Robot fish with a wire-driven active body and compliant Tail . d FILOSE fish-like robot built from a rigid head, a compliant body, and a rigid caudal fin . e Cyclic hydraulic actuation of a soft body through an actuator producing undulating motions. The design has been extended to deform under a hydraulic and closed-circuit drive system that uses water as a transmission fluid to actuate the soft body 
This work is carried out by Behzad Janizadeh Haji1 and Mahdi Bamdad1
1 School of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood 3619995161, Iran
and published on JBE Volume 19, Issue 3, May 2022, Page 629–642 https://doi.org/10.1007/s42235-022-00166-4