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Intro to Robotics

by: Terrence Terry II

Intro to Robotics ME 4140

Terrence Terry II
GPA 3.83

Stephen Canfield

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Stephen Canfield
Class Notes
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This 4 page Class Notes was uploaded by Terrence Terry II on Wednesday October 21, 2015. The Class Notes belongs to ME 4140 at Tennessee Tech University taught by Stephen Canfield in Fall. Since its upload, it has received 65 views. For similar materials see /class/225731/me-4140-tennessee-tech-university in Mechanical Engineering at Tennessee Tech University.

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Date Created: 10/21/15
Review Linear Algebra scalars nonbold italics t q vectors bold nonitalics x y Matrices bold non italics R T Dot product The length or norm of a vector x is given as Cross product Questions Prove two vectors are parallel prove two vectors are perpendicular Matrix Addition Subtraction Matrix Multiplication Rule on matrix size in multiplication Matrix Division Transpose Rank Robotics Review Sheet Position Kinematics Most common representation based on a DampH convention 09 ch04 39306 a109 1 39 09 ca cQ ca 6139 T1 1 1 1 1 1 1 1 I 0 wt 0061 d 0 0 0 1 with DampH parameters assigned according to the Spong et al convention frame i on joint i1 DampH link Parameter Table 06 a d 1 angle bn 20 and distance from 20 to distance from X0 angle bn X0 21 measured 21 measured along to X1 measured and X1 about X1 X1 along 20 measured about 20 2 angle bn 21 and distance from 21 to distance from X1 angle bn X1 22 measured 22 measured along to X2 measured and X2 about X2 X2 along 21 measured about 21 Forward Kinematics given qi i1n solve Tquoto Inverse kinematics given Tquot solve q1 i1n Other formulations given via screw systems quaternions and Lie Algebra plucker coordintates Velocity Kinematics gtlto z 1 aJ H Jomt I Is revolute 1 J 171 Z J Zlil 0 Partitioning singularities Joint i is prismatic Acceleration Kinematics 56 J Jq Robot Dynamics Dq Cq 1 1 gq 7 with DqWWMVJWMJmqTRxqLRxqTJmq 11 ck cx e qqx 11 1 Balk 351k 8d cxjk 7 2 361 3 3 Robot Control Single Joint Control Second order model ignores dynamic effects of motor inductance Singlejoint control ignores the dynamic effects ofthe otherjoints the Cqqq terms Js2 BktkkIm tGR Controller PD PID controllers are stable can provide desired behavior in setpoint tracking problem For a general timevarying tracjectory feedforward control is implemented as shown Fs 1Gs Define the feedforward function as the inverse ofthe plant controller cancels the plant dynamics The result is stable control 0 tracking error in absence ofdisturbances Statespace control approach Define the controller as Kq


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