Embedded Systems Motors - Laboratory for Perceptual Robotics

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30 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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Laboratory for Perceptual Robotics


Department of Computer Science

Embedded Systems

Control

2

Laboratory for Perceptual Robotics


Department of Computer Science

Basic Tools of Control Theory



Open
-

and Closed
-
Loop Control



Laplace Transform (just briefly)



The Canonical Spring
-
Mass
-
Damper



Equilibrium Setpoint Control



Qualitative Second
-
Order Response



Closed
-
Loop Transfer Function



Time
-

and Frequency
-
Domain Response

3

Laboratory for Perceptual Robotics


Department of Computer Science

Motor Circuits



α
-
motor neurons initiate overt motion
---
they’re fast



on average, each will innervate
approximately 200 individual muscle
fibers.



relatively slow γ
-
motor neuron
regulates muscle tone by setting the
reference length of the spindle receptor.



Golgi tendon organ measures the
tension in the tendon and inhibits the α
-
motor neuron if it exceeds safe levels


4

Laboratory for Perceptual Robotics


Department of Computer Science

Negative Feedback



If the measured spindle length is
greater than the reference, the α
-
motor
neuron cause a contraction of the
muscle tissue



if the measured spindle length is less
than the reference, the α
-
motor neuron
is inhibited, allowing the muscle to
extend



...the α
-
motor neuron changes its output
so as to cancel some of its input...


Negative Feedback

5

Laboratory for Perceptual Robotics


Department of Computer Science

Negative Feedback





first submitted for a patent in 1928 by Harold S. Black



Black’s patent application was met with great
skepticism, reportedly associated with a perpetual motion
machine



subsequently, it was the basis for Watt
’s

governor



spawned the field of cybernetics



now heralded as a fundamental principle of stability in
compensated dynamical systems

6

Laboratory for Perceptual Robotics


Department of Computer Science

The Muscle Stretch Reflex




7

Laboratory for Perceptual Robotics


Department of Computer Science

Open
-
Loop Control




an initiating stimulus causes a response without further stimulation


SR reflexes
-

e.g. withdrawl reflex

8

Laboratory for Perceptual Robotics


Department of Computer Science

Closed
-
Loop Control




a (time
-
varying) setpoint is achieved by constantly measuring
and correcting in order to actively reject disturbances




autopilot




Norbert Weiner
-

cybernetics (helmsman),
homeostasis, endocrine system living things as
feedback regulators

9

Laboratory for Perceptual Robotics


Department of Computer Science

Laplace Transform


assume: x(t) ~ Ce
st




L
( d/dt (x(t)) ) = s
L
( x(t) )




L
( d
2
/dt
2

(x(t)) ) = s
2

L
( x(t) )

...a linear differential equation with constant coefficients and
a finite number of terms is Laplace
-
transformable...they
transform into polynomials in s…

10

Laboratory for Perceptual Robotics


Department of Computer Science

Laplace Transform


assume: x(t) ~ Ce
st




L
( d/dt (x(t)) ) = s
L
( x(t) )




L
( d
2
/dt
2

(x(t)) ) = s
2

L
( x(t) )

an N
th

order differential equation


a
n
D
n

+ a
n−1
D
n−1
+ …+ a
0

= 0


into an N
th

order polynomial

a
n
s
n

+ a
n−1
s
n−1
+ …+ a
0

= 0

11

Laboratory for Perceptual Robotics


Department of Computer Science

Example: and RC Circuit

12

Laboratory for Perceptual Robotics


Department of Computer Science

Example: and RC Circuit

“transfer” function

s

13

Laboratory for Perceptual Robotics


Department of Computer Science

Spring
-
Mass
-
Damper

14

Laboratory for Perceptual Robotics


Department of Computer Science

Spring
-
Mass
-
Damper

15

Laboratory for Perceptual Robotics


Department of Computer Science

Wall Following