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 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 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

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 The idea is to sample near the boundaries of the C- space obstacles 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

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 Motion Planning in 3D space for a rigid body. Medial Axis of the free space is like a Roadmap:

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