# Probabilistic Roadmaps for Path Planning in High-Dimensional ...

Probabilistic Roadmap Hadi Moradi Overview What is PRM? What are previous approaches?

Whats 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 highdimensional 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 360 270 180 90

x PR manipulator 0 0.25 x

0.5 Cylinder 0.75 1.0 Example: Random points 360

270 180 90 x PR manipulator

0 0.25 x 0.5 Cylinder

0.75 1.0 Random points in collision 360 270 180

90 x PR manipulator 0

0.25 x 0.5 Cylinder 0.75 1.0

Connecting Collision-free Random points 360 270 180 90

x PR manipulator 0 0.25 x

0.5 Cylinder 0.75 1.0 Probabilistic Roadmap

(PRM) local path free space milestone mg mb

[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 Create random configurations Update Neighboring Nodes Edges End of Construction Step

Expansion Step End of Expansion Step The Query Phase Need to find a path between an arbitrary start and goal configuration, using the roadmap

constructed in the learning phase. Select start and goal Start Goal Connect Start and Goal to Roadmap Start

Goal Find the Path from Start to Goal Start Goal 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

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