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Mul$‐Robot
Systems

Probabilis$c
Modeling
III

        CSCI
7000‐006

    Monday,
October
19,
2009


         Nikolaus
Cor...
So
far


•  Probabilis$c
models
for
reac$ve
and

   delibera$ve
systems

•  Parameter
calibra$on
using


  –  Control
para...
Today

•  Modeling
of
delibera$ve
systems
with
large

   state
space

  –  Probabilis$c
models
for
sub‐systems

  –  Discr...
Review:
Probabilis$c
Modeling

•  Enumerate
all
possible
states
of
a
system

•  Calculate
all
state
transi$on
probabili$es...
Modeling
of
large
state
spaces

•  Iden$fy
key
sources
of
uncertainty
in
a
system

  –  Actua$on

  –  Sensing

  –  Commu...
Example:
coverage

•  Algorithm

   –  Build
a
minimal

      spanning‐tree
on‐line

   –  Move
from
blade
to

      blade...
Basic
Naviga$on
Behaviors





9/20/2007
             Nikolaus
Correll
   7

Quan$fying
Sensor
&
Actuator

                        Noise

6000
experiments
in
Webots,
10%
wheel‐slip





    Time
for
...
Discrete
Event
System
Simula$on

                                                            Webots‐Generated


          ...
DES
vs.
Webots:
Naviga$on

        uncertainty


                        50%
slip.

                        10%
slip

Discrete
Event
System
Simula$on

•  Simula$ng
the
algorithm
generates
sample

   trajectories
in
state
space

•  Previous
...
DES
vs.
Webots:
Communica$on


                         No
Comm.

                         Comm.





 10%
wheel
slip

Example:
Distributed
Robot
Garden

•  Mo$va$on:
Precision

   Agriculture

•  Robots
water
and
forage

   tomato
plants

•...
Sub‐tasks
/
Sources
of
uncertainty

•  Visual
recogni$on
of
ripe
and
green
tomatoes

•  Visual
servoing
with
monocular
vis...
Robo$c
Plaeorm

      Localiza(on
                               Vision

   Hagisonic
Stargazer
                    Logite...
Plant


 Humidity
Sensor

   Vegetronix





                                              Wireless
router

              ...
Filter‐based
object
recogni$on

•  Filter
image

   –  Sobel

   –  Hough
transform

   –  Color

   –  Spectral

      hi...
Inventory

•  Challenges

   –  Percep$on
                               1
   6

   –  Not
possible
from
single
perspec$ve...
Visual
Servoing/Grasping

•  Challenges

   –  Percep$on
(fruits
+
stem)
                           2


   –  Limited
DOF
...
Results:
Visual
Servoing/Grasping

•  Percep$on

  –  75%
correctly

     detected

•  Visual
Servo

  –  75%
correct
gras...
Task
Alloca$on

•  Challenges

   –  Unreliable
channel
(ad‐
      hoc
wifi)

   –  Uncertainty
in

      naviga$on
and
tas...
Naviga$on

•  Challenges

   –  Narrow
passages

   –  Deadlocks
(mul$‐robot)

   –  Communica$on

•  Localiza$on

   –  S...
Model
the
distributed
garden

•  Measure
average
$me
and
success
rate
of

  –  Naviga$on
from
A
to
B

  –  Watering

  –  ...
Possible
model


T1:
Harvest
                       T2:
Robot
          
x
*

       T3:
Robot

  request
                ...
Open
research
ques$ons

•  What
about
rare
events?

  –  How
oten
do
we
have
to
try
each
sub‐system?

  –  How
oten
do
we
...
Summary

•  Complex
delibera$ve
systems
can
be
modeled

   by
studying
sample
trajectories
through
state

   space

•  Ope...
October 19, Probabilistic Modeling III
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Transcript of "October 19, Probabilistic Modeling III"

  1. 1. Mul$‐Robot
Systems
 Probabilis$c
Modeling
III
 CSCI
7000‐006
 Monday,
October
19,
2009
 Nikolaus
Correll

  2. 2. So
far

 •  Probabilis$c
models
for
reac$ve
and
 delibera$ve
systems
 •  Parameter
calibra$on
using

 –  Control
parameters
 –  Geometric
proper$es
 •  System
iden$fica$on
for
reac$ve
swarms

  3. 3. Today
 •  Modeling
of
delibera$ve
systems
with
large
 state
space
 –  Probabilis$c
models
for
sub‐systems
 –  Discrete
Event
System
simula$on
 •  Examples
 –  Coverage
 –  Task
alloca$on

  4. 4. Review:
Probabilis$c
Modeling
 •  Enumerate
all
possible
states
of
a
system
 •  Calculate
all
state
transi$on
probabili$es
 •  Write
down
rate
equa$ons
for
the
probability
 of
the
system
to
be
a
in
a
certain
state
 •  Solve
equa$ons
analy$cally/numerically
 •  Problem:
What
about
systems
with
large
state
 spaces


  5. 5. Modeling
of
large
state
spaces
 •  Iden$fy
key
sources
of
uncertainty
in
a
system
 –  Actua$on
 –  Sensing
 –  Communica$on
 •  Measure/approximate
probability
density
 func$on
 •  Sample
from
these
distribu$ons
when
 simula$ng
the
algorithm
 S.
Ru$shauser,
N.
Correll,
and
A.
Mar$noli.
Collabora$ve
Coverage
using
a
 Swarm
of
Networked
Miniature
Robots.
Robo$cs
&
Autonomous
Systems,
 57(5):517‐525,
2009.

  6. 6. Example:
coverage
 •  Algorithm
 –  Build
a
minimal
 spanning‐tree
on‐line
 –  Move
from
blade
to
 blade
reac$vely
 –  Localiza$on
by
coun$ng
 blades
 –  Start‐over
when
lost
 •  Uncertainty
 –  Naviga$on

  7. 7. Basic
Naviga$on
Behaviors
 9/20/2007
 Nikolaus
Correll
 7

  8. 8. Quan$fying
Sensor
&
Actuator
 Noise
 6000
experiments
in
Webots,
10%
wheel‐slip
 Time
for
covering
one
blade
 Probability
of
no
naviga$on
error
 (geometric
distribu$on)

  9. 9. Discrete
Event
System
Simula$on
 Webots‐Generated

 Event
Time
Data
 Choose
robot
(closest
 next
event
$me),
add
 event
$me
for
robot
 Determine
next
node
n
to
visit
 Algorithm
 Naviga$on
 Failure
 Success?
 probabilites
 Yes
 No
 Move
Robot
 Move
Robot
 No
 to
n
 somewhere
else
 All
Blades
 inspected?
 Yes

  10. 10. DES
vs.
Webots:
Naviga$on
 uncertainty
 50%
slip.
 10%
slip

  11. 11. Discrete
Event
System
Simula$on
 •  Simula$ng
the
algorithm
generates
sample
 trajectories
in
state
space
 •  Previous
example:
limited
to
naviga$on
 uncertainty
 •  Simula$on
can
model
arbitrary
level
of
detail,
 including
communica$on

  12. 12. DES
vs.
Webots:
Communica$on
 No
Comm.
 Comm.
 10%
wheel
slip

  13. 13. Example:
Distributed
Robot
Garden
 •  Mo$va$on:
Precision
 Agriculture
 •  Robots
water
and
forage
 tomato
plants
 •  Pots
monitor
humidity
 level
and
coordinate
 robo$c
system
 •  Robots
inventory
each
 plant
and
store
it
into
its
 pot’s
database

  14. 14. Sub‐tasks
/
Sources
of
uncertainty
 •  Visual
recogni$on
of
ripe
and
green
tomatoes
 •  Visual
servoing
with
monocular
vision
 •  Manipula$on
with
4‐DOF
arm
 •  Coordina$on
/
task
alloca$on
of
 heterogeneous
system
over
wireless
network
 •  Mul$‐robot
naviga$on
in
$ght
environments

  15. 15. Robo$c
Plaeorm
 Localiza(on
 Vision
 Hagisonic
Stargazer
 Logitech
QuickCam
 Computa(on
 Dell
La$tude
D620
 Manipula(on
 Crustcrawler
4‐DOF
 Watering
System
 Hargrave
 Differen(al
Wheels
 iRobot
Create
 Ubuntu
Linux,
Willow
Garage
ROS,
USB

  16. 16. Plant
 Humidity
Sensor
 Vegetronix
 Wireless
router
 Temperature@lert
 Infra‐red
Beacon
 iRobot
Roomba
base
 OpenWRT
Linux,
Atheros
chipsets

  17. 17. Filter‐based
object
recogni$on
 •  Filter
image
 –  Sobel
 –  Hough
transform
 –  Color
 –  Spectral
 highlights
 –  Size
and
shape
 Sobel
 Hough
 Color
 Spectral
 •  Weighted
sum
of
 Highlights
 filters
highlights
 object
loca$on

  18. 18. Inventory
 •  Challenges
 –  Percep$on
 1
 6
 –  Not
possible
from
single
perspec$ve
 •  Algorithm
 2
 5
 -  Fetch
fruit
inventory
from
pot
(JSON)
 -  Object
recogni$on
from
6
non‐ 3
 4
 overlapping
perspec$ves
 -  Merge
observa$on
with
inventory
 •  Confidence
grows
with
every
 measurement
 •  Inventory
dura$on:
45s

  19. 19. Visual
Servoing/Grasping
 •  Challenges
 –  Percep$on
(fruits
+
stem)
 2
 –  Limited
DOF
/
workspace
 •  Algorithm
 -  Select
fruit
with
the
 strongest
confidence
 -  Servo
to
ini$al
posi$on
 -  Servo
to
fruit
using
image
 Jacobian
 -  Rely
on
radius
es$mate
for
 depth
 F.
Chaumele
and
S.
Hutchinson,
“Visual
servo
control
 part
i:
Basic
approaches,”
Robo$cs
&
Automa$on
 -  Close
gripper
/
retract
arm
 Magazine,
vol.
13,
no.
4,
pp.
82–90
 when
arrived

  20. 20. Results:
Visual
Servoing/Grasping
 •  Percep$on
 –  75%
correctly
 detected
 •  Visual
Servo
 –  75%
correct
grasps
 (10
trials)
 –  28.3s
+/‐
10s
per
 grasp

  21. 21. Task
Alloca$on
 •  Challenges
 –  Unreliable
channel
(ad‐ hoc
wifi)
 –  Uncertainty
in
 naviga$on
and
task
 execu$on
 •  Robots
reply
with
their
 distance
+
length
of
task
 queue
(approx.
$me)
 •  Plant
selects
“best”
 robot
 •  Alloca$on
repeated
 periodically

  22. 22. Naviga$on
 •  Challenges
 –  Narrow
passages
 –  Deadlocks
(mul$‐robot)
 –  Communica$on
 •  Localiza$on
 –  Sensor
fusion:
odometry
+
passive
 infrared
beacons
 –  Broadcast
posi$on
at
1Hz
 •  Mo$on
planning
 –  Grid‐map
of
the
environment:
sta$c
 obstacles
+
other
robots
 –  Wavefront
algorithm
(Latombe)
 –  Reac$ve
behavior
for
avoiding
 bumps
 –  Reac$ve
behavior
for
docking

  23. 23. Model
the
distributed
garden
 •  Measure
average
$me
and
success
rate
of
 –  Naviga$on
from
A
to
B
 –  Watering
 –  Communica$on
 –  Harves$ng
 •  Compare
 –  Different
task
alloca$on
schemes
 –  Distribu$on
of
sensing,
actua$on,
and
computa$on
 (ex:
humidity
sensing
on
the
plant
vs.
robot)

  24. 24. Possible
model
 T1:
Harvest
 T2:
Robot
 
x
*

 T3:
Robot
 request
 receives
task
 73s
+/‐
15s
 reaches
plant
 (p|Naviga$on
failure)x
 28.3s+/‐10s
 25%
 Assump$ons
 ‐ No
task
alloca$on
(single
robot)
 T4:
Robot
 ‐ Infinite
number
of
grasping
trial
 grasps
 Next
step
 ‐simulate
task
alloca$on
based
on
 communica$on
model
 ‐finite
number
of
fruits
per
plant

  25. 25. Open
research
ques$ons
 •  What
about
rare
events?
 –  How
oten
do
we
have
to
try
each
sub‐system?
 –  How
oten
do
we
need
to
simulate
the
en$re
 system?

  26. 26. Summary
 •  Complex
delibera$ve
systems
can
be
modeled
 by
studying
sample
trajectories
through
state
 space
 •  Open
problems
 –  Genera$ng
sufficient
number
of
samples
 –  Rare
events

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