Transcript Sampling Strategies for Probabilistic Roadmaps

Sampling Strategies for
Probabilistic Roadmaps
Random Sampling for capturing the
connectivity of the C-space:
Sampling Strategies for
Probabilistic Roadmaps
Random Sampling for capturing the
connectivity of the C-space:
Sampling Strategies for
Probabilistic Roadmaps
Random Sampling for capturing the
connectivity of the C-space:
Sampling Strategies for
Probabilistic Roadmaps
Random Sampling for capturing the
connectivity of the C-space:
Sampling Strategies for
Probabilistic Roadmaps
Random Sampling for capturing the
connectivity of the C-space:
How efficient is the sampling strategy?
Are the narrow passages well captured in the
roadmap?
Are the narrow passages well captured in the
roadmap?
Are you keeping redundant free samples in the
roadmap?
3 Papers that address these issues:
Visibility-based Probabilistic roadmaps
for Motion planning
- Simeon, Laumond and Nissoux (2000)
The Gaussian Sampling Strategy for PRM’s
- Boor, Mark and Stappen (1999)
Motion Planning for a Rigid Body Using
Random Networks on the Medial Axis
of the Free Space
- Wilmart, Amato and Stiller (1999)
3 Papers that address these issues:
Visibility-based Probabilistic roadmaps
for Motion planning
- Simeon, Laumond and Nissoux (2000)
The Gaussian Sampling Strategy for PRM’s
- Boor, Mark and Stappen (1999)
Motion Planning for a Rigid Body Using
Random Networks on the Medial Axis
of the Free Space
- Wilmart, Amato and Stiller (1999)
3 Papers that address these issues:
Visibility-based Probabilistic roadmaps
for Motion planning
- Simeon, Laumond and Nissoux (2000)
The Gaussian Sampling Strategy for PRM’s
- Boor, Mark and Stappen (1999)
Motion Planning for a Rigid Body Using
Random Networks on the Medial Axis
of the Free Space
- Wilmart, Amato and Stiller (1999)
3 Papers that address these issues:
Visibility-based Probabilistic roadmaps
for Motion planning
- Simeon, Laumond and Nissoux (2000)
The Gaussian Sampling Strategy for PRM’s
- Boor, Mark and Stappen (1999)
Motion Planning for a Rigid Body Using
Random Networks on the Medial Axis
of the Free Space
- Wilmart, Amato and Stiller (1999)
Visibility-based probabilistic
roadmaps for motion planning
By Simeon, Laumond and Nissoux in 2000
Classical PRM versus Visibility roadmap
Computes a very compact roadmap.
Visibility domain of a free configuration q:
q
The C-space fully captured by ‘guard’ nodes.
The C-space fully captured by ‘guard’ nodes.
The C-space fully captured by ‘guard’ nodes.
The C-space being captured by ‘guards’ and
‘connection’ nodes.
The C-space being captured by ‘guards’ and
‘connection’ nodes.
The C-space fully captured by ‘guards’ and
‘connection’ nodes.
We do not need any other additional node in the
roadmap
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Results
6-dof puzzle example
Remarks
Maintains a very compact roadmap to handle.
Remarks
Maintains a very compact roadmap to handle.
But:

There is a tradeoff with high cost of processing each new
milestone.
Remarks
Maintains a very compact roadmap to handle.
But:


There is a tradeoff with high cost of processing each new
milestone.
How many iterations needed to capture the full connectivity?
Remarks
Maintains a very compact roadmap to handle.
But:



There is a tradeoff with high cost of processing each new
milestone.
How many iterations needed to capture the full connectivity?
The problem of capturing the narrow passage effectively is
still the same as in the basic PRM.
The Gaussian Sampling Strategy for
PRM’s
By Boor, Overmars and Stappen in 1999.
The idea is to sample near the boundaries of the Cspace obstacles with higher probability.
How to sample near boundaries with higher
probability?
How to sample near boundaries with higher
probability?
Using the notion of blurring using a Gaussian, used in
image processing.
How to simulate this effect using PRM’s?
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Algorithm
Remarks
Advantage:

May lead to discovery of narrow passages or
openings to narrow passages.
Remarks
Advantage:

May lead to discovery of narrow passages or
openings to narrow passages.
Disadvantages:

The Algorithm dose not distinguish between open
space boundaries and narrow passage boundaries.
Remarks
Advantage:

May lead to discovery of narrow passages or
openings to narrow passages.
Disadvantages:


The Algorithm dose not distinguish between open
space boundaries and narrow passage boundaries.
If the volume of narrow passage is low then it
would be captured with low probabilities.
Remarks
Advantage:

May lead to discovery of narrow passages or
openings to narrow passages.
Disadvantages:



The Algorithm dose not distinguish between open
space boundaries and narrow passage boundaries.
If the volume of narrow passage is low then it
would be captured with low probabilities.
In ‘n’ dimensions it is still like sampling in ‘n-1’
dimensions.
Sampling on the Medial Axis of the
Free Space
By Wilmarth, Amato and Stiller in 1999.
Motion Planning in 3D space for a rigid body.
Medial Axis of the free space is like a Roadmap:
MAPRM
MAPRM
MAPRM
MAPRM
MAPRM
MAPRM
MAPRM
MAPRM
Results
Remarks
Not so efficient for any irregular shaped objects.
Remarks
Not so efficient for any irregular shaped objects.
Works only for 6-DOF rigid objects. Not for any n-DOF/
articulated robots.
Remarks
Not so efficient for any irregular shaped objects.
Works only for 6-DOF rigid objects. Not for any n-DOF/
articulated robots.
For simple general cases it would take more time than basic
PRM’s.
Conclusion
We saw 3 unique sampling strategies:
Visibility based
 Milestone management
Gaussian Sampling
 Capturing the c-obstacle boundaries
Medial axis sampling of free space
- works in 3D space and for rigid bodies