Presentation for the course :

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Presentation for the course :

Advanced Robotics

Behdad Soleimani

9 March 2009



Overview



Definitions



Algorithm



Analysis



Experiments



Pros and Cons



Experimental Comparison : Narrow Passages



Adaptive and Relaxed VPRM

2

3

Basic PRM

Visibility
-
based PRM

4



Local Method (admissibility)




Roadmap (adjacency)





Visibility Domain (reachability)





Free
-
space Coverage (
ε
-
goodness)




Visibility Roadmap (undirected set of guards
and connection nodes)

5

Essence: cover the
CS
free

with guards, and
connect them using connection nodes



Size of visibility roadmaps : bounded





Termination Criterion, Probabilistic Coverage








Side
-
effects : due to random generation





Visibility & Connectivity

6

7

Robot Arm
(6DOF)


Local Method :
Linear


Roadmap’s size :


26


CPU time :

(for solving the
first problem)

370 sec

8

Robot Arm
(6DOF)


Local Method :
Linear


Roadmap’s size :


26


CPU time :

(for solving the
first problem)

370 sec

9

Rolling Bridge
(4DOF)


Local Method :
Manhattan


Roadmap’s size :


25


CPU time :

(for solving the
first problem)

2 sec

10

Rolling Bridge
(4DOF)


Local Method :
Manhattan


Roadmap’s size :


25


CPU time :

(for solving the
first problem)

2 sec



Small Size




Termination condition




Two main steps of the PRM
-
based algorithms :



Sampling the
CS
free

and generating new nodes (
more expensive!
)



Testing and connecting the node to the existing roadmap (
far less expensive!
)


Visib
-
PRM :
O
(n) , Basic
-
PRM :
O
(n
2
)
n: no. of random collision
-
free configurations




Two main shortcomings: “unlucky” sampling, narrow passages


11

Note

:

Visibility
-
based

PRM

is

NOT

a

method

for

solving

Narrow

Passage

Problem,

although

it

tends

to

perform

better

in

those

situations

than

the

Basic

PRM
.

12

13

Workspace dimensions :

200 * 200 * 150


Width of rectangular passage :

50


Moving object :

5 blocks

length 50 , cross
-
section 10





Values averaged over 10 runs



Same set of configurations for
both algorithm


14

RELAXED (
x
) : Relaxed Acceptance Test of VPRM

15

Modified Visibility
-
based PRM


T. Siméon, J.
-
P. Laumond., and C.
Nissoux
, “Visibility based probabilistic
roadmaps for motion planning.”
Advanced Robotics Journal
, 14(6), 2000.



J.
-
P. Laumond, T. Siméon , “Notes on visibility roadmaps and path
planning”
4
th

Workshop on Algorithmic Foundations of Robotics (WAFR),
Hannover, USA
(2000)
.




T
-
M Bu, Z
-
J Li, and Z Sun, “Adaptive and Relaxed Visibility
-
based PRM”,
In proc. of IEEE International Conference on Robotics and Biomimetics
(ROBIO)
, pp 174
-
179, 2005

16

During this presentation,
approximately 500
children died… two
-
thirds of them were preventable.