Sampling Strategies for Probabilistic Roadmaps Random Sampling for capturing the connectivity of the...
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Sampling Strategies for Probabilistic Roadmaps Random Sampling for capturing the connectivity of the C-space:
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Transcript of Sampling Strategies for Probabilistic Roadmaps Random Sampling for capturing the connectivity of the...
Sampling Strategies for Probabilistic Roadmaps
Random Sampling for capturing theconnectivity of the C-space:
Sampling Strategies for Probabilistic Roadmaps
Random Sampling for capturing theconnectivity of the C-space:
Sampling Strategies for Probabilistic Roadmaps
Random Sampling for capturing theconnectivity of the C-space:
Sampling Strategies for Probabilistic Roadmaps
Random Sampling for capturing theconnectivity of the C-space:
Sampling Strategies for Probabilistic Roadmaps
Random Sampling for capturing theconnectivity 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 roadmapsfor 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 C-space 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
