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 C-obstacle surfaces
Basic Ideas
Algorithm
Given
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 C-obstacle 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 mid-point 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 end-point.
• 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?
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