Introduction to RoboticsENGR-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:RTH = RT1

1T22T3 = A1A2A3

Each A Matrix represents the transformation between each joint, from one frame of reference to the next.

Equations of Motion:nz=C3S2 θ1 = tan-1(oy/ox) and θ1= θ1+180˚oz=C2 θ2 = tan-1(pz/[pxC1+pyS1-a1])az=S2S3

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) = c0 + c1t + c2t2 + c3t3

Boundary conditions:

Less than 1 hour to construct Base w/ diagonal link, 3 servos, 5 links,

pen, rubber band, clamps

1st Attempt, program from Project Book Star-shaped pattern (supposedly) Did not work, parameters for each servo different for our

setup 2nd 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. 3rd 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