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In this project… <ul><li>Building an electro-mechanical fish that mimics a real fish motion( prototype development under progress ) </li></ul><ul><li>Kinematics and Dynamics analysis </li></ul><ul><li>Overview Of Solidworks and 3 D Simulation </li></ul><ul><li>Simulation Results ( open loop and closed loop control ) </li></ul>a a Z 0 X 0 Y 0 Z 3 X 2 Y 1 X 1 Y 2 d 2 Z 1 X 3 Z 2
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Fish Classification <ul><li>Anguilliform: Propulsion by a muscle wave in the body like the Eel. </li></ul><ul><li>Carangiform: Oscillating a tail fin and a tail peduncle like the Tuna </li></ul><ul><li>Ostraciform: Oscillating only a tail fin without moving the body like the Boxfish. </li></ul> Figure 8 Swim ming Forms (2)
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How do fish swim? <ul><li>Fi sh swim by their skeletons and muscles work together to allow them to swim . </li></ul><ul><li>With pushing water away behind them, through by various methods. </li></ul><ul><li>C.M. Breder (1966) classified into the following three general categories based on length of a tail fin and strength of its oscillation : </li></ul><ul><li>(a) Anguilliform, (b) Carangiform, (c) Ostraciiform </li></ul>
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Hydrodynamics: Effects of shape on drag <ul><li>Laminar flow and turbulence </li></ul>Disk Sphere teardrop
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Carangiform/Thunniform swimming <ul><li>One of the most impressive aquatic swimmer. </li></ul>Thunniform a) = torpedo-shaped b) allows minimal drag while swimming c) best shape for a pelagic cruise d) 43.4 mph leaping
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MATHEMATICAL MODELING <ul><li>Effectors and Actuators </li></ul><ul><li>An effector is any device that affects the environment . </li></ul><ul><li>A robot's effector is under the control of the robot. </li></ul><ul><li>Effectors: </li></ul><ul><ul><li>Caudal fins, </li></ul></ul><ul><ul><li>Pectoral fins, </li></ul></ul><ul><ul><li>Dorsal fins, </li></ul></ul><ul><ul><li>Pelvic and Anal fins. </li></ul></ul><ul><li>The role of the controller is to get the effectors to produce the desired effect on the environment , </li></ul><ul><ul><li>this is based on the robot's task. </li></ul></ul>
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Effectors and Actuators <ul><li>An actuator is the actual mechanism that enables the effector to execute an action. </li></ul><ul><li>Actuators typically include : </li></ul><ul><ul><li>electric motors, </li></ul></ul><ul><ul><li>hydrauli c cylinders, </li></ul></ul><ul><ul><li>pneumatic cylinders, </li></ul></ul><ul><ul><li>etc. </li></ul></ul><ul><li>The terms effector and actuator are often used interchangeably to mean "whatever makes the robot take an action." </li></ul><ul><li>This is not really proper use : </li></ul><ul><ul><li>Actuators and effectors are not the same thing . </li></ul></ul><ul><ul><li>And we'll try to be more precise . </li></ul></ul>
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Robot::Body <ul><li>Typically defined as a graph of links and joints : </li></ul>A link is a part, a shape with physical properties. A joint is a constraint on the spatial relations of two or more links .
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Types of Joints Respectively, a ball joint , which allows rotation around x, y, and z, a hinge joint , which allows rotation around z, and a slider joint , which allows translation along x. These are just a few examples…
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Degrees of freedom <ul><li>Most simple actuators control a single degree of freedom , </li></ul><ul><ul><ul><li>i.e., a single motion (e.g., up-down, left-right, in-out, etc.). </li></ul></ul></ul><ul><ul><li>A motor shaft controls one rotational degree of freedom , for example. </li></ul></ul><ul><ul><li>A sliding part on a crane controls one translational degree of freedom . </li></ul></ul><ul><li>How many degrees of freedom (DOF) a robot has is very important in determining how it can affect its world, </li></ul><ul><ul><li>and therefore how well, if at all, it can accomplish its task. </li></ul></ul><ul><li>We say many times that sensors must be matched to the robot's task. </li></ul><ul><li>Similarly, effectors must be well matched to the robot's task also. </li></ul>When we design a robot our first task is decide the number of DOF and the geometry.
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DOF <ul><li>In general, a free body in space has 6 DOF: </li></ul><ul><ul><li>three for translatio n (x,y,z), </li></ul></ul><ul><ul><li>three for orientation/rotation (roll, pitch, and yaw). </li></ul></ul><ul><li>We need to know, for a given effector (and actuator/s): </li></ul><ul><ul><li>how many DOF are available to the robot , </li></ul></ul><ul><ul><li>how many total DOF any given robot has. </li></ul></ul><ul><li>If there is an actuator for every DOF , then all of the DOF are controllable. </li></ul><ul><li>Usually not all DOF are controllable , which makes robot control harder. </li></ul>
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Definition of a HOLONOMIC robot <ul><li>When the number of controllable DOF is equal to the total number of DOF on a robot, the robot is called holonomic. </li></ul><ul><li>If the number of controllable DOF is smaller than total DOF , the robot is non-holonomic. </li></ul><ul><li>If the number of controllable DOF is larger than the total DOF , the robot is redundant. (like a human hand) </li></ul>Holonomic <= > Controllable DOF = total DOF Non-Holonomic <= > Controllable DOF < total DOF Redundant <= > Controllable DOF > total D OF
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Kinematics <ul><li>Kinematics is the study of motion without regard for the forces that cause it. </li></ul><ul><li>It refers to all time-based and geometrical properties of motion. </li></ul><ul><li>It ignores concepts such as torque, force, mass, energy, and inertia . </li></ul><ul><li>In order to control a ROBOT, we have to know its kinematics: </li></ul><ul><ul><li>1. what is attached to what, </li></ul></ul><ul><ul><li>2. how many joints there are, </li></ul></ul><ul><ul><li>3. how many DOF for each joint, </li></ul></ul><ul><ul><li>etc. </li></ul></ul>
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<ul><li>1) Draw sketch </li></ul><ul><li>2) Number links. Base= 0 , Last link = n </li></ul><ul><li>3) Identify and number robot joints </li></ul><ul><li>4) Draw axis Z i for joint i </li></ul><ul><li>5) Determine joint length a i- 1 </li></ul><ul><li>between Z i- 1 and Z i </li></ul><ul><li>6) Draw axis X i- 1 </li></ul><ul><li>7) Determine joint twist i - 1 </li></ul><ul><li>measured around X i- 1 </li></ul><ul><li>8) Determine the joint offset d i </li></ul><ul><li>9) Determine joint angle i around Z i </li></ul><ul><li>10&11) Write link transformation and </li></ul><ul><li>“ concatenate” </li></ul>Direct Kinematics Algorithm
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Denavit-Hartenberg Convention <ul><li>Given the starting configuration of the mechanism and joint angles, we can compute the new configuration. </li></ul><ul><li>For a mechanism robot, this would mean calculating the position and orientation of the end effector given all the joint variables. </li></ul><ul><li>Denavit-Hartenberg Convention </li></ul><ul><li>Link and Joint Parameters </li></ul><ul><li>Joint angle θ i : the angle of rotation from the X i-1 axis to the X i axis about the Z i-1 axis. It is the joint variable if joint i is rotary. </li></ul><ul><li>Joint distance di : the distance from the origin of the (i-1) coordinate system to the intersection of the Z i-1 axis and the X i axis along the Z i-1 axis. It is the joint variable if joint i is prismatic. </li></ul><ul><li>Link length ai : the distance from the intersection of the Z i-1 axis and the X i axis to the origin of the ith coordinate system along the X i axis. </li></ul><ul><li>Link twist angle α i : the angle of rotation from the Z i-1 axis to the Z i axis about the X i axis. </li></ul>
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Denavit-Hartenberg Parameters <ul><li>Identified link parameters for the </li></ul><ul><li>Robotic Fish model . </li></ul>Transformation Matrix: = Where and were the corresponding rotational and translational matrices respectively.
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Dynamic Model of n-link: Dynamic model robot can be calculated by the below mentioned equation: D(q) = a n x n inertial acceleration - related symmetric matrix whose elements are: ) = an n x 1 nonlinear Coriolis and centrifugal force vector whose elements are =
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Dynamic Model of n-link: <ul><li>Where, </li></ul>and G(q) = an n x 1 gravity loading force vector whose elements are Where
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Dynamic Model of 2-link <ul><li>Based on the Lagrange –Euler methodology, Dynamics model for two links is shown below. For calculating the Dynamics of the whole model is done through MATLAB. </li></ul>Employing velocity coefficients matrix for revolute joints, we can write: The standard matrix for revolute joint is represented as
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Dynamic Model of 2-link Assuming all the product of inertias is zero, we find:
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Dynamic Model of 2-link <ul><li>Utilizing inertia and derivative of transformation matrices we can calculate the inertial-type symmetric matrix D(q) </li></ul>=
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Dynamic Model of 2-link We can calculate the value for ,
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Dynamic Model of 2-link Next we need to derive the gravity related terms,
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Dynamic Model of 2-link <ul><li>Finally Lagrange-Euler equation of motion for two link manipulator are found and shown below: </li></ul>
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Robot::Controller <ul><li>Controllers direct a robot how to move. </li></ul><ul><li>There are two controller paradigms </li></ul><ul><ul><li>Open-loop controllers execute robot movement without feedback. </li></ul></ul><ul><ul><li>Closed-loop controllers execute robot movement and judge progress with sensors. They can thus compensate for errors. </li></ul></ul>
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Simulation Results <ul><li>Open Loop - Step Response </li></ul><ul><li>Torque applied to first joint Torque applied to second joint </li></ul>
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Simulation Results <ul><li>Input (torque) as Sine function </li></ul><ul><li>Torque applied to first joint Torque applied to first joint </li></ul>
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Simulation Results Open Loop Model Simmechanics Model VRML MODEL
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How can robot fish be used? <ul><li>There are many recent researches about biomimetic fish robot area such as Robo Tuna, ESSEX ROBOTIC FISH, STINGRAY. </li></ul><ul><li>These studies can suggest a new and high efficient propulsion device for the ship or underwater vehicle. </li></ul>
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<ul><li>For example, Maurizio Porfiri, assistant professor at Polytechnic Institute of New York University, has designed a robotic fish that leads real fish to safe water. </li></ul><ul><li>Currently, the robotic fish can lead fish away from power plant turbines. </li></ul>Figure 2 3: Robotic Fish that protects fish from danger
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Conclusion <ul><li>L earn t the different motion types and the needed mechanisms for the prototype development. </li></ul><ul><li>T o implement these mechanisms, controller development is required. </li></ul><ul><li>T ried to inspire by biological fishes ’ motion </li></ul>
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References <ul><li>How a Fish Can Swim? Retrieved in December 16, from How Does a Fish Swim? | eHow.com http://www.ehow.com/how-does_4690184_a-fish-swim.html#ixzz18NF80duo </li></ul><ul><li> </li></ul><ul><li>Principles of the Swimming Fish Robot , Retrieved in December 17, from </li></ul><ul><li>http://www.nmri.go.jp/eng/khirata/fish/general/principle/index_e.html </li></ul><ul><li> </li></ul><ul><li>Propulsion Technology, Retrieved in December 17, from http://www.tailboats.com/propulsion_technology.html </li></ul><ul><li>Robo Tuna II , Retrieved In 17 December, from http://web.mit.edu/towtank/www/Tuna/Tuna2/tuna2.html </li></ul><ul><li>Robotic fish that protect fish from danger, Retrieved in 19 December, from </li></ul><ul><ul><li> http://www.goodcleantech.com/2010/06/nyu_scientist_develops_robotic.php </li></ul></ul><ul><li>Why do Fish Have Scales? Retrieved in December 14, from http://www.letusfindout.com/why- do-fish-have-scales/ </li></ul><ul><li>Why do Fish go belly up when they die? , Retrieved in December 18, from http://www.answerbag.com/q_view/153382#ixzz18NZ1QtVw </li></ul>
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