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