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Glue Lecture 2 Slides
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Smriti Chopra ECE Ph.D. Candidate Georgia Tech
Control of Mobile Robots: Glue Lectures
Instructor:
Glue Lecture 2: Robot Models
Pay attention, this lecture will help you all with Quiz 2!
2
Two models for robots
3
(a)
(b)
x =R
2(vr + vl) cos
y =R
2(vr + vl) sin
=R
L(vr vl)
x = v cos
y = v sin
= !
In Action
4
From one robot model to another
5
A
B
t = 10s
High level task !
x = v cos
y = v sin
= !
From one robot model to another
6
A
B
t = 10s
High level task !
Control design -
v, !
x = v cos
y = v sin
= !
From one robot model to another
7
A
B
t = 10s
High level task !
Control design -
Commands sent to the robots -
v, !
vr, vl
vr =2v + !L
2R
vl =2v !L2R
x = v cos
y = v sin
= !
x =R
2(vr + vl) cos
y =R
2(vr + vl) sin
=R
L(vr vl)
An intuitive example
8
For inputs , find the corresponding angular wheel velocities
v = 0, ! = constant
vr =2v + !L
2R
vl =2v !L2R
vr =CL
2R
vl = CL2R
vr, vl
Back to our musical bot
9
A
B
t = 10s
Finding (and consequently ) simple?
v, ! vr, vl No Feedback !!!
Important state information (where is the bot currently)
x = v cos
y = v sin
= !
Wheel encoders
10
x0 = x+Dc cosy0 = y +Dc sin
0 = +Dr Dl
L
Dc =Dr +Dl
2
Total N ticks per revolution
Dl = 2RticklN
Dr = 2RtickrN
dt
For your general curiosity
11
x0 = x+Dc cosy0 = y +Dc sin
0 = +Dr Dl
L
x =R
2(vr + vl)cos
y =R
2(vr + vl)sin
=R
L(vr vl)
Dr = Rvrdt
Dl = Rvldt
x(t+ dt) = x(t) + xdt
An Odometry example
12
If my robot starts at the origin (pos and orientation is 0), where is it located after 0.1s, given that 10 ticks were recorded for the right wheel and 6 ticks for the left wheel. Wheel radius is 2m, total ticks is 100, distance between wheels is 4m.
Dl = 2RticklN
Dr = 2RtickrN
Dc =Dr +Dl
2
x0 = x+Dc cosy0 = y +Dc sin
0 = +Dr Dl
L
x0 = 1.0053my0 = 0m0 = 0.1257 rad
Check the forums, and good luck with Quiz 2!
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