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Nonlinear Modeling and Analysis of a Novel Robot Fish with Compliant Fluidic Actuator as a Tail

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Abstract

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.

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Abbreviations

\(u_{x} ,u_{y} ,u_{z}\) :

Displacement of the beam

\(\in_{xx}\) :

x-Direction normal strain

ρ:

Density of the beam

\(\omega\) :

Frequency of inlet pressure

w :

Transverse displacement of the centerline

\(\dot{u}_{x} ,\dot{u}_{y} ,\dot{u}_{z}\) :

Velocities component of the beam

V :

Mean velocity of the steady flow

\(A\) :

Cross-sectional of the beam

\(l\) :

Total length of the channel

\(r_{{\text{c}}}\) :

Radius of channel

\(l_{{\text{c}}}\) :

Length of a single channel segment

t :

Time

\(P\) :

Fluid pressure

\(B\) :

Volumetric force

\(\phi_{i}\) :

Mode shape of beam

\(\eta_{i}\) :

Generalized coordinate for beam transverse Displacement

\(T\) :

Total kinetic energy

\(L_{{\text{f}}}\) :

Hydrodynamic force

\(m\) :

Effective mass per unit length at the length x.

z :

Height from natural plan of compliant tail

\(D\) :

Drag force

\(a_{0}\) :

Big diameter of cross section of tail at x = 0

\(T_{{\text{b}}}\) :

Kinetic energy of the beam

\(T_{{{\text{fluid}}}}\) :

Kinetic energy of the fluid inside the channel

\(\rho_{{\text{f}}}\) :

Fluid density

L :

Tail length

\(v\) :

Absolute velocity of the fluid

\(v_{{\text{b}}}\) :

Velocity of the beam

\(v_{{{\text{pr}}}}\) :

Relative velocity vector of the fluid

E :

Young's modulus of compliant tail

\(m_{{\text{f}}}\) :

Mass per unit length of the fluid

\(p_{{\text{a}}}\) :

Amplitude of inlet pressure

\(\phi\) :

Channel density function

\(\phi^{*}\) :

Normalized channel density

\(p_{{{\text{in}}}}\) :

Inlet pressure

\(\mu_{{\text{f}}}\) :

Fluid viscosity

\(\psi_{m}\) :

Mode shape for fluid pressure

\(B_{m}\) :

Generalized coordinate for fluid pressure

\(U_{{\text{s}}}\) :

Strain energy of system

\(U\) :

Swimming speed

\(M_{{\text{f}}}\) :

Mass of fish robot

\(T_{{\text{f}}}\) :

Mean thrust

\(C_{{\text{D}}}\) :

Drag force coefficient

\(b_{0}\) :

Small diameter of cross section of tail at x = 0

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Authors and Affiliations

  1. School of Mechanical and Mechatronics Engineering, Shahrood University of Technology, Shahrood, 3619995161, Iran

    Behzad Janizadeh Haji & Mahdi Bamdad

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  1. Behzad Janizadeh Haji
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Correspondence to Mahdi Bamdad.

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Haji, B.J., Bamdad, M. Nonlinear Modeling and Analysis of a Novel Robot Fish with Compliant Fluidic Actuator as a Tail. J Bionic Eng 19, 629–642 (2022). https://doi.org/10.1007/s42235-022-00166-4

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  • DOI: https://doi.org/10.1007/s42235-022-00166-4

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