elec 341 design project -2019

ELEC 341 DESIGN PROJECT SPECIFICATION==============================Author: Leo Stocco---------------------

Robot arms come in two varieties.• serial • parallel

A serial arm is a series of motors and links, followed by an end-effector. It has high dexterity, or in other words, can reach large spaces.

A parallel robot has its motors in the base and moves its end-effector using a linkage. It has less dexterity, but is lighter and faster since the motors are stationary.

The 4-bar linkage, is basically a parallelogram. It has two motors [q0,q1] , 2 degrees-of-freedom (DOF), an end-effector with planar motion [x,y].

A property of this arm, which is prized by engineering students, is that its geometry is simple to calculate.

The pinion is connected to the motor shaft, and the bull gear is connected to the upper arm of each robot base joint.

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ELEC 341 Design Project - 2019

System Components

Desired Trajectory• Ideal robot path and time vector• Pre-programmed into computerController• Computes path error• Scales by controller gains• Applies voltage to amplifierAmplifier• Converts control voltage into motor currentRobot• Moves as a result of motor torqueSensors• Measures joint positions• Converts into machine readable format (electrical signal)Actual Trafectory• As similar as possible to desired trajectory• Never exactly equal

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Each joint uses the Power Amplifier circuit to drive a Maxon motor with an optical encoder.

The op-amp and all electrical components are assumed to be ideal.A data-sheet is provided with all relevant motor specifications.

The encoder count provides a joint angle with a non-ideal resolution.

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Sys2019.slx• Simulink control system model file• YOU modify the forward & inverse kinematics blocksMech2019.isx• SimulationX mechanical system model file• Modify for R&D purposes onlyCONSTANTS.m• Used everywhere• Parameter valuesDEFAULT.m• Default system model (unity gain)Model.m• YOUR system model and …• YOUR controller gains• Over-writes default valuesTRAJECTORY.m• Task-space trajectory & time vectorEXC19_30W.m• Motor parameters from data sheet

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All electrical components (controllers, circuits, sensors, motor windings) are simulated using Matlab/Simulink.

A Simulink model is provided (Version R2017a)• Only modify green blocks• Directly enter Matlab code to compute Kinematics

• Don’t forget to account for gear ratio

• Controller blocks all set to variables assigned by m-files• Default values of 1 assigned in Default.m• Values over-written in Model.m

• The model shown above is what it would look like if the robot were modeled in the Mech Dyn blocks (Part I of project)

• Note that an Xfer function block is used for an integrator. A dedicated integrator block could also be used but an Xfer function block allows you to easily switch between unity gain and integration and to apply a gain to convert radians into degrees, for R&D

• The model you have has this replaced by a TCP/IP block that communicates with SimulationX and which returns both position and speed

• Pay special attention to physical units. Radians can not be interchanged with degrees

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You must design a PID controller to move the robot task-space coordinate [x,y], along a pre-defined trajectory.

Your goal is to minimize the maximum error (Mini-Max) of the robot along the entire trajectory.

Note that, to check my kinematics functions, I did the following in Matlab.• I started with the trajectory & computed the inverse kinematics to get the joint values• I used the joint values to plot the robot (blue)• I superimposed the trajectory (red) over top of the plotted robot

That is where these plots came from. Since the robot follows the trajectory, I trust that my functions are correct.

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All mechanical components (gears, robot arms & joints) are simulated using SimulationX.

A SimulationX model is provided (Version 4.0)• Gears, joints, links & end-effector• Full non-linear mechanical dynamics• Mass / density• Friction• Stiffness• Backlash• Gravity

The model is created parametrically• Like Simulink• No CAD required

SimulationX computes all linear & non-linear dynamics• Friction• Gravity• Backlash• Flexibility• Inertia

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SPECIFICATIONS

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HELP & FAQ

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GRADING

PART I• Model the linearized system and • Perform a theoretical optimization of the PID controller of each joint.• Report

• Slide deck with notes (Ariel - 10pt font)• Exactly like this document• 10 pages MAX (+ Appendices – like m-files)• PDF format - Notes Pages / Press Quality

PART II• Correct system models will be provided – check your work from PART I• Develop direct and inverse kinematics functions• Tune your PID controllers to minimize the position error of a realistic (linear +

non-linear) robot moving its end-point along a pre-defined motion path in task-space.

• Path error is automatically recorded by Simulink model• Report

• Same as for Part I

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elec 341 design project -2019

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