Sir J. Lighthill mathematical slender body swimming model formulates the biological fish propulsion mechanism (undulation) in fluid environment. The present research has focused on the relevance of Lighthill (LH) based biomimetic robotic propulsion. The objective of this paper is to mimic the propulsion mechanism of the BCF mode carangiform swimming style to show the fish behavior navigating efficiently over large distances at impressive speeds and its exceptional characteristics. The robotic fish model (kinematics and dynamics) is integrated with the Lighthill (LH) mathematical model framework. Comparative studies are undertaken between a LH model based and a non-LH based model. A comprehensive propulsion mechanism study of the different parameters namely the tail-beat frequency (TBF), the propulsive wavelength, and the caudal amplitude are studied under this framework. Yaw angle study for the underwater robotic fish vehicle is also carried out as it describes the course of the robotic fish vehicle. Inverse kinematics based approach is incorporated for trajectory generation of the robotic fish vehicle motion. Analysis of these critical parameters affecting the kinematics study of the vehicle vis a vis the real fish kinematic study [8] is carried out for a given trajectory. TBF is found to be the effective controlling parameter for the forward speed of the vehicle over a wide operating conditions. Performances and comparative results of propulsive wavelength and amplitude variations are also shown and discussed.

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This paper has focused on the formulation of the biological fish propulsion mechanism given by Sir J. Lighthill mathematical slender body theory for a bio-inspired robotic fish. A 2-joint, 3-link multibody vehicle model biologically inspired by a body caudal fin (BCF) carangiform fish propulsion is designed. The objective is to investigate and show that a machine mimicking real fish behavior can navigate efficiently over a given distance with a good balance of speed and maneuverability. The robotic fish model (kinematics and dynamics) is integrated with the Lighthill (LH) mathematical model framework. Different mathematical propulsive waveforms are combined with an inverse kinematics-based approach for generating fish body motion. Comparative studies are undertaken among a non-LH model, a LH model, and the proposed propulsive wave models based on a distance-based performance index. Proposed LH cubic and NURB quadratic functions are found to be 16.32% and 17.94% efficient than a non-LH function, respectively. With the help of the simulation results, closed-loop experiments are done and an operating region is established for critical kinematic parameters tail-beat frequency and propulsive wavelength. The simulation and experimental plots are compared and found to be similar to the kinematic behavior study of the biological yellowfin tuna.

A 2-joint, 3-link multibody vehicle model biologically inspired by a Body Caudal Fin (BCF) carangiform fish propulsion mechanism in fluid environment is presented in this paper. Under the Lighthill (LH) mathematical slender body theory different mathematical propulsive waveforms are developed to generate robotic fish locomotion. LH Cubic function is found to be 16.32 % efficient than a non-LH function. We develop the dynamic motion control strategy of the robotic fish based on two different control schemes, the CTM (Computed-Torque Method) and the FF (Feed-Forward) controller both with dynamic PD compensation. An inverse dynamic control method based on non-linear state function model including hydrodynamics is proposed to improve tracking performance. CTM control generates a feedback loop for linearization and decoupling robot dynamic model with a shorter response time while a dynamic PD compensation in the feed-forward path is employed by FF scheme through the desired trajectories. This model based strategy results in an improved tracking. Overall results indicate that control designs based on the inverse dynamic model are useful for robotic fish motion tracking.

Sir J. Lighthill mathematical slender body swimming model formulates the biological fish propulsion mechanism (undulation) in fluid environment. The present research has focused on the relevance of Lighthill (LH) based biomimetic robotic propulsion. A 2-joint, 3-link multibody vehicle model biologically inspired by a Body Caudal Fin (BCF) carangiform fish propulsion mechanism is designed. Different mathematical propulsive waveforms are proposed in LH frame-work to generate posterior body undulation. These functions are combined with inverse kinematics to generate various bio-inspired trajectories for the robotic fish vehicle motion. The robotic fish model (kinematics and dynamics) is integrated with the Lighthill (LH) mathematical model framework. Comparative studies are undertaken among a LH model and the proposed propulsive wave models. LH Cubic and NURB quadratic functions are found to be 16.32 % and 17.94 % efficient than a non-LH function respectively. Based on the simulation results of critical kinematic parameters TBF and Propulsive wavelength, an operating region is established to facilitate the open-loop (manual) control experiments.