Sampling Strategies for PRMs
modified from slides of
T.V.N. Sri Ram
Basic PRM algorithm
Issue
• Narrow passages
OBPRMs
•A randomized roadmap method for path and
manipulation planning (Amato,Wu ICRA’96)
•OBPRM: An obstacle-based PRM for 3D workspaces
(Amato,Bayazit, Dale, Jones and Vallejo)
Roadmap candidate points chosen on Cobstacle surfaces
Basic Ideas
Given
Algorithm
Finding points on C-objects
1. Determine a point o (the
origin) inside s
2. Select m rays with
origin o and directions
uniformly distributed in
C-space
3. For each ray identified
above, use binary
search to determine a
point on s
Issues
• Selection of o in Cobstacle is crucial
– To obtain uniform
distribution of samples
on the surface, would
like to place origin
somewhere near the
center of C-object.
– Still skewed objects
would present a
problem
Issues (contd)
• Paths touch C-obstacle
Main Advantage
• Useful in manipulation planning where the
robot has to move along contact surfaces
• Useful when C-space is very cluttered.
Results
Bridge Test
The Bridge Test for Sampling Narrow
Passages with Probabilistic Roadmap
Planners (Hsu, Jiang, Reif, Sun
ICRA’03)
Main Idea
• Accept mid-point as a new node in roadmap
graph if two end-points are in collision and midpoint is free
• Constrain the length of the bridge: Favourable to
build these in narrow passages
Algorithm
Contribution over previous
Obstacle–Based Methods
• Avoids sampling “uninteresting” obstacle
boundaries.
• Local Approach: Does not need to
“capture” the C-obstacle in any sense
• Complementary to the Uniform Sampling
Approach
Issues
• Deciding the probability density (πB )around a
point P, which has been chosen as first endpoint.
• Combining Bridge Builder and Uniform Sampling
– π =(1-w). πB +w.πv
– πB : probability density induced by the Bridge Builder
– πv : probability density induced by uniform sampling
Results
Nmil
Nclear Ncon
Medial-Axis Based PRM
MAPRM: A Probabilistic Roadmap Planner
with Sampling on the Medial Axis of the Free
Space (Wilmarth, Amato, Stiller ICRA’99)
Definitions
Main Ideas
• Beneficial to have samples on the medial axis;
however, computation of medial axis itself is
costly.
• Retraction : takes nodes from free and obstacle
space onto the medial axis w/o explicit
computation of the medial axis.
• This method increases the number of nodes
found in a narrow corridor
– independent of the volume of corridor
– Depends on obstacles bounding it
Approach for Free-Space
• Find xo (nearest boundary point) for each
point x in Free Space.
• Search along the ray xox and find
arbitrarily close points xa and xb s.t. xo is
the nearest point on the boundary for xa
but not xb.
• Called canonical retraction map
Extended Retraction Map
• Doing only for Free-Space => Only more clearance.
Doesn’t increase samples in Narrow Passages
• Retract points that fall in Cobstacle also.
• Retract points in the direction of the nearest boundary
point
Results for 2D case
• LEFT: Helpful: obstacle-space that retracts to narrow
passage is large
• RIGHT: Not Helpful: Obstacle-space seeping into medial
axis in narrow corridor is very low
MAPRM for 3D rigid bodies
Example 2
Example 3
Main Results
• Demonstrates an approach to use medial
axis based ideas with random sampling
• Advantages:
– Useful in cluttered environments. Where a
great volume of obstacle space is adjacent to
narrow spaces
– Above Environment: Bisection technique for
evaluating point on medial axis???
Limitations
• Additional primitive: “Nearest Contact
Configuration”. For larger (complex)
problems, this time may become
significant….
• Extension to higher dimensions difficult.
Which direction to search for nearest
contact?