Abhra Roy Chowdhury

Bio-harmonized Dynamic Model of a Biology Inspired Carangiform Robotic Fish Underwater Vehicle

Abstract This paper presents a novel dynamic model of a bio-inspired robotic fish underwater vehicle by unifying conventional rigid body dynamics and bio-fluid-dynamics of a carangiform fish swimming given by Lighthills (LH) slender body theory It proposes an inclusive mathematical design for better control and energy efficient path travel for the robotic fish. The system is modeled as an 2-link robot manipulator (caudal tail) with a mobile base (head). Lighthill caudal-tail reactive forces and moments are shown to contribute towards thrust generation and yaw balance. These LH reactive forces are shown to generate the inertial added mass during the robotic fish locomotion. This forward thrust drives the robotic fish head represented by a unified non-linear equation of motion in earth fixed frame. Using the proposed dynamic model an open-loop (manual) operating region for the identified kinematic parameter tail beat frequency (TBF) is established. Obtained Kinematic results also resemble with real fish kinematic results. The objective is to mimic the propulsion technique of the carangiform swimming style and to show the fish behavior navigating efficiently over large distances at impressive speeds and its exceptional character in fluid environment.

Kinematics study and implementation of a biomimetic robotic-fish underwater vehicle based on Lighthill slender body model

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.

Finding answers to biological control methods using modulated patterns: An application to bio-inspired robotic fish

This paper presents a bio-inspired robotic fish undulatory swimming behaviour modeling and control using modulated pattern generators (MPG). Carangiform fish locomotion pattern is closely mimicked using a LH body wave (with its parameters: Tail-beat frequency (TBF) and Caudal amplitude (CA)) modulated by rhythmic central pattern generator (CPG) signal. A Matsuoka based non-linear oscillator CPG structure is used to generate desired rhythmic pattern preserving control properties like system stability (limit cycle behaviour) and synchronization. A two level locomotion control architecture based on vertebrate fish biology is proposed. Higher level controller generates desired trajectory as encoded patterns MPGs. Synchronization of the desired trajectories at each joint with the robotic fish dynamics generates desired fishlike locomotion behavior. Lower level control scheme uses an inverse dynamics model based policy for tracking this locomotion pattern (joint positions). It is shown that MPGs can represent the shape (amplitude) and phase (frequency) patterns of high-dimensional periodic inputs using simple kinematic parameters. Proposed inverse dynamics model based tracking control strategy is found to perform in a stable operating margin..

Design, modeling and open-loop control of a BCF mode bio-mimetic robotic fish

This paper deals with the design of a bio-inspired fish like underwater vehicle. As the applications of underwater robots grow, finding efficient propulsion techniques is of the utmost importance. The current research has focused on the use of biomimetic propulsion, which simulates the undulation of fish tail, i.e. the sinusoidal oscillation. The objective is to mimic the propulsion technique of the BCF mode carangiform swimming style to swim efficiently over large distances at impressive speeds. Beginning from the CAD construction in Solidworks, 3D motion simulations in Matlab VRML and open-loop experimental and simulation results are provided to illustrate the effectiveness of the proposed methodology.

Inverse dynamics control of a bio-inspired robotic-fish underwater vehicle propulsion based on Lighthill slender body theory

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.

Kinematic parameter based behaviour modelling and control of a bio-inspired robotic fish

Fish swimming demonstrates impressive speeds and exceptional characteristics in the fluid environment. The objective of this paper is to mimic undulatory swimming behaviour and its control in a body caudal fin (BCF) carangiform fish in a robotic counterpart. Based on fish biology a 2-level behavior based control scheme is proposed. High level control is modeled by robotic fish swimming behavior. It uses a Lighthill (LH) body wave to generate desired joint trajectory patterns. LH wave has intrinsic kinematic parameters Tail-beat frequency (TBF) and Caudal amplitude (CA) which can be modulated to change this trajectory. Parameter information is retrieved from a biological fish memory inspired brain map. This map stores operating region information on TBF and CA parameters. Based on a environment based error feedback signal robotic fish map selects the right parameter/s value showing adaptive behaviour. A finite state machine methodology has been used to model this brain-kinematic-map control. Low level control is implemented using computed torque method (CTM) with dynamic PD compensation, to track encoded patterns (trajectory) for fish-tail undulation. Three types of parameter adaptation for the two chosen parameters have been shown to successfully emulate fish swimming behavior. Joint-position tracking results are found to be satisfactory. Error magnitudes are smaller and its convergence is fast.

Finding an operating region for a bio-inspired robotic fish underwater vehicle in the Lighthill framework

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.

Bio-harmonized control experiments of a carangiform robotic fish underwater vehicle

This paper presents experimental implementation and comparison of three different control schemes of a bio-inspired robotic fish underwater vehicle. The dynamics model is obtained by unifying conventional rigid body dynamics and bio-fluid dynamics of a carangiform fish swimming given by Lighthill’s(LH) slender body theory. It proposes an inclusive mathematical design for better control and energy efficient path travel for the robotic fish. The system is modeled as an two-link robot manipulator (caudal tail) with a mobile base (head). This forward thrust drives the robotic fish head represented by a combined non-linear equation of motion in earth fixed frame. We develop and compare the dynamic motion closed loop control strategy of the bio-harmonized robotic fish based on three different non-linear control schemes using CTM (Computed Torque Method), FF (Feed-Forward) controllers both with dynamic PD compensation and finally a proposed combination of CTM with FF. 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 FF path is employed by FF scheme through the desired trajectories. FF model-based strategy results in an improved tracking and shorter route to travel between two points. Overall results indicate that performances of the proposed control schemes based on the inverse dynamic model are comparable and useful for robotic fish motion tracking in fluid environment. Graphical Abstract

Genetic algorithm based intelligent station-keeping for spherical underwater robot

In this paper, a spherical underwater robot is proposed that uses six degree of freedom thrust allocator to determine the magnitude and the direction of thrust required for each water-jetted bilge pump thruster to create force and moment equilibrium. However, in order to ensure safe operation of the underwater robot it is equipped with redundant thruster configuration and therefore is over-actuated. Therefore, the choice of a particular solution for thrust allocation is found using an optimization process. In this work, the thrust allocation problem is formulated as an optimization problem, with an objective to minimize the total power consumption of the spherical underwater robot. A set of all physically realizable surge, sway and heave force for the ith thruster is called as its Attainable Thrust Region (ATR). Since the thrust force produced by each thruster is restricted to its ATR, the power consumption of underwater robot is determined by establishing a relationship between the power consumption and the thrust of an individual bilge pump. The formulated optimal thrust allocation problem is solved using Mincon (Sequential Quadratic Programming) and GA (Genetic Algorithm) optimization algorithm. The percentage savings in total power consumption for thruster system using the GA as compared to Mincon method is 33.82 %.

Brain-Map Based Carangiform Swimming Behaviour Modeling and Control in a Robotic Fish Underwater Vehicle

Fish swimming demonstrates impressive speeds and exceptional characteristics in the fluid environment. The objective of this paper is to mimic undulatory swimming behaviour and its control of a body caudal fin (BCF) carangiform fish in a robotic counterpart. Based on fish biology kinematics study, a 2-level behavior based distributed control scheme is proposed. The high-level control is modeled by robotic fish swimming behavior. It uses a Lighthill (LH) body wave to generate desired joint trajectory patterns. Generated LH body wave is influenced by intrinsic kinematic parameters Tail-beat frequency (TBF) and Caudal amplitude (CA) which can be modulated to change the trajectory pattern. Parameter information is retrieved from a fish memory (cerebellum) inspired brain map. This map stores operating region information on TBF and CA parameters obtained from yellow fin tuna kinematics study. Based on an environment based error feedback signal, robotic fish map selects the right parameters value showing adaptive behaviour. A finite state machine methodology has been used to model this brain-kinematic-map control. The low-level control is implemented using inverse dynamics based computed torque method (CTM) with dynamic PD compensation. It tracks high-level generated and encoded patterns (trajectory) for fish-tail undulation. Three types of parameter adaptation for the two chosen parameters have been shown to successfully emulate robotic fish swimming behavior. Based on the proposed control strategy joint-position and velocity tracking results are discussed. They are found to be satisfactory with error magnitudes within permissible bounds.