Rapidly Expanding Random Trees

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Rapidly Expanding Random Trees

• David Johnson

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RRTs

• Promoted by Steve Lavalle and James Kuffner
• Alternative to other randomized approaches
• Probabilistic roadmap planner

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Why another?

• Need to extend to
• Non-holonomic (car)
• Differential constraints (velocity, etc)
• Actuator constraints
• PRM depends on connecting points
• May require a generalized nonlinear controller
• slow
• Solved over thousands of connections

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RRT Components

• X Configuration Space or more general
• X C-space Velocity Acceleration .

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RRT Components
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Basic RRT algorithm
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Basic Extend
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Example in holonomic empty space
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Why Rapidly Exploring?

• What is the probability that a vertex will be
  extended?
• Proportional to the area of its Voronoi region
• If just choose a vertex at random and extend,
  then it would act like random walk instead
• Biased towards start vertex

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Refinement vs. Expansion
refinement
expansion
Where will the random sample fall? How to control
the behavior of RRT?
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Determining the Boundary
Expansion dominates
Balanced refinement and expansion
The tradeoff depends on the size of the bounding
box
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Extension to Non-holonomic

• The new_state computation handles all the
  complicated part
• Given a state x and inputs u
• Integrate numerically to get new position
• What input u do we use?
• All
• One
• Heuristic

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Problem

• Non-biased RRT explores in all directions
• Not aimed at the goal
• Use a small percentage of targets to be the goal
  or its neighborhood

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How Far to Extend?

• Use distance measures from collision detection
• Big steps when far away

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Bi-directional

• Grow from start and goal
• Extend a tree
• Try to connect nearest vertex of other tree to
  new vertex
• Swap roles
• Connecting trees can be difficult
• Controls problem

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Examples

• http//msl.cs.uiuc.edu/rrt/gallery.html