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 CompletenessWeaker Completeness

Complete planner Heuristic planner

Probabilistic completeness:

MotivationMotivation

• Geometric complexity• Space dimensionality

Example

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Example: Random points

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Random points in collision

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Connecting Collision-free Random points

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Probabilistic Roadmap Probabilistic Roadmap (PRM)(PRM)

free space

mmbb

mmgg

milestone

[Kavraki, Svetska, Latombe,Overmars, 95][Kavraki, Svetska, Latombe,Overmars, 95]

local path

The Principles of PRM The Principles of PRM PlanningPlanning

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.

With expansion

Without expansion

Results

IssuesIssues Why random sampling?

Smart sampling strategies Final path smoothing

Issues: ConnectivityBad 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