Probabilistic Roadmap Hadi Moradi

Overview What is PRM? What are previous approaches? What’s the algorithm? Examples

What is it? A planning method which computes collision-free paths for robots of virtually any type moving among stationary obstacles

Problems before PRMs Hard to plan for many dof robots Computation complexity for high-dimensional configuration spaces would grow exponentially Potential fields run into local minima Complete, general purpose algorithms are at best exponential and have not been implemented

Weaker Completeness Complete planner  Heuristic planner  Probabilistic completeness:

Motivation Geometric complexity Space dimensionality

Example a a x x PR manipulator Cylinder 360 270 180 90 0.25 0.5 0.75 x 0.25 0.5 0.75 1.0 PR manipulator Cylinder

Example: Random points 360 270 180 a 90 a x x 0.25 0.5 0.75 1.0 PR manipulator Cylinder

Random points in collision 360 270 180 a 90 a x x 0.25 0.5 0.75 1.0 PR manipulator Cylinder

Connecting Collision-free Random points 360 270 180 a 90 a x x 0.25 0.5 0.75 1.0 PR manipulator Cylinder

Probabilistic Roadmap (PRM) local path free space milestone mb mg [Kavraki, Svetska, Latombe,Overmars, 95]

The Principles of PRM Planning Checking sampled configurations and connections between samples for collision can be done efficiently. A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space.

The Learning Phase Construct a probabilistic roadmap

The Query Phase Find a path from the start and goal configurations to two nodes of the roadmap

The Query Phase Need to find a path between an arbitrary start and goal configuration, using the roadmap constructed in the learning phase.

What if we fail? Maybe the roadmap was not adequate. Could spend more time in the Learning Phase Could do another Learning Phase and reuse R constructed in the first Learning Phase.

Example – Results This is a fixed-based articulated robot with 7 revolute degrees of freedom. Each configuration is tested with a set of 30 goals with different learning times.

Results With expansion Without expansion

Issues Why random sampling? Smart sampling strategies Final path smoothing

Issues: Connectivity Bad Good

Disadvantages Spends a lot of time planning paths that will never get used Heavily reliant on fast collision checking An attempt to solve these is made with Lazy PRMs Tries to minimize collision checks Tries to reuse information gathered by queries

References Kavraki, Svestka, Latombe, Overmars, IEEE Transactions on Robotics and Automation, Vol. 12, No. 4, Aug. 1996