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Intro to Robotics - Spr 2009 - Final Project Presentation - Robix Robot - DrawBot

Intro to Robotics - Spr 2009 - Final Project Presentation - Robix Robot - DrawBot

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    Drawbot Final Presentation Drawbot Final Presentation Presentation Transcript

    • Introduction to Robotics ENGR-5301-55 Lamar University Spring, 2009 Ram Balasubramanian & Gary Decaney April 30, 2009
      • What is a Robot?
      • What is Robotics?
      • Robix Robot
      • What is Draw-Bot?
      • Project Calculations
        • Phase I – Kinematic Analysis
        • Phase II – Dynamic Analysis & The Jacobian
        • Phase III – Differential Motion/Velocity Analysis
        • Phase IV – Trajectory Planning
      • Draw-Bot construction
      • Draw-Bot programming
      • Questions
      • Demo
      • A robot is:
        • A virtual or mechanical or artificial agent
        • Usually an Electro-Mechanical system which, by its appearance or movements, conveys a sense of intent or agency of its own
        • The word “robot” can refer to both physical robots and virtual software agents, but latter are usually referred to as “bots”
      http://en.wikipedia.org/wiki/Robot
      • Robotics - the Science and Technology of robots
        • Their design
        • Their manufacture
        • Their application
      • Robotics has connections to electronics, mechanics and software
      • The word “Robotics” was first used in Isaac Asimov’s short story Runaround (1942). Asimov proposed the “Laws of Robotics”:
        • Law Zero - A robot may not injure humanity, or, through inaction, allow humanity to come to harm
        • Law One – A robot may not injure a human being, or, through inaction, allow a human being to come to harm, unless this would violate a higher order law.
        • Law Two – A robot must obey orders given it by human beings, except where such orders would conflict with a higher order law.
        • Law Three - A robot must protect its own existence as long as such protection does not conflict with a higher order law.
      http://www.robotmatrix.org/whatisrobot.htm
      • Robix Rascal Classroom Robot Set
      • Low Cost ($550US)
      • On the Market for 15 years
      • Complete with Controller Card and Software
      • Repeatable, reusable, reprogrammable
      http://www.robix.com/default.html
      • Demonstrates repeatability
      • Uses 3 servos to draw pattern on paper
      • Sample pattern uses star shape
      • Project pattern uses hour-glass shape
      • Phase I – Kinematic Analysis
      • Phase II – Dynamic Analysis & The Jacobian
      • Phase III – Differential Motion/Velocity Analysis
      • Phase IV – Trajectory Planning
      • Students were to use the Denavit-Hartenberg model representation to form the Equations of Motion
      • Total Transformation Matrix:
      • R T H = R T 1 1 T 2 2 T 3 = A 1 A 2 A 3
      • Each A Matrix represents the transformation between each joint, from one frame of reference to the next.
      • Equations of Motion:
      • n z =C 3 S 2 θ 1 = tan -1 (o y /o x ) and θ 1 = θ 1 +180˚
      • o z =C 2 θ 2 = tan -1 (p z /[p x C 1 +p y S 1 -a 1 ])
      • a z =S 2 S 3
      • Using concepts taught in class, students were to perform a dynamic analysis of n-degree of freedom system (in this case, 3-DOF)
      • Students were to generate the Jacobian and differential operators
        • Jacobian – representation of the geometry of the elements of a mechanism in time
        • Differential Operator – product of differential translations and rotations, minus the unit matrix
      • Jacobian:
      • Differential Operator:
      • Students were to develop the dynamic equations of motion for their setup
      • Also, determine how much torque is required in each joint to complete an action with a certain speed or in a certain time
      • Extremely long calculations
      • General format:
      • Equations for all three joints:
      • For the Final Phase, students were to determine the needed motions of their setup and to perform Trajectory Planning for their robot
      • For simplicity’s sake, Third Order Polynomial Trajectory Planning was utilized
      • Third order polynomial:
      • θ ( t ) = c 0 + c 1 t + c 2 t 2 + c 3 t 3
      • Boundary conditions:
      • Less than 1 hour to construct
      • Base w/ diagonal link, 3 servos, 5 links, pen, rubber band, clamps
      • 1 st Attempt, program from Project Book
        • Star-shaped pattern (supposedly)
        • Did not work, parameters for each servo different for our setup
      • 2 nd Attempt, program shape corners using “teach method”
        • Hour-glass shape pattern
        • Did not work, went from corner to corner in correct sequence, but in severely curved lines.
      • 3 rd Attempt, program interval points along shape pattern
        • Repeat hour-glass shape pattern
        • Not perfect, but does resemble pattern, and is repeatable
          • Individual segments are still curvy
          • Additional interval points needed to straighten out
          • Trajectory planning complex concept for simple pattern
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