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!

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Two models for robots

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(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

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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

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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

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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

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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

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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

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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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