RRT-Connect: An Efficient Approach to Single-Query Path Planning - - PowerPoint PPT Presentation

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RRT-Connect: An Efficient Approach to Single-Query Path Planning - - PowerPoint PPT Presentation

Apr 04, 2024 45 likes •306 views

RRT-Connect: An Efficient Approach to Single-Query Path Planning James J. Kuffner, Jr. Steven M. LaValle ICRA 2000 Presented by Manel Baradad 6.882 Embodied Intelligence Spring 2020 Problem Single-query path planning, from start to goal. In

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RRT-Connect: An Efficient Approach to Single-Query Path Planning

James J. Kuffner, Jr. Steven M. LaValle ICRA 2000 Presented by Manel Baradad

6.882 Embodied Intelligence Spring 2020

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Problem

Single-query path planning, from start to goal. In “high-dimensional” configuration spaces

Find path from A to B Move an object: from State A to State B

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Two Ingredients

  • Rapidly-exploring random trees (RRT):
  • 2 x RRT: One from start and one from goal

Greedy Heuristic to connect them RRT Exploration

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Rapidly-exploring random trees (RRT’s)

K = 0

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Rapidly-exploring random trees (RRT’s)

K = T

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Rapidly-exploring random trees (RRT’s)

q sampled uniformly at random

  • ver all space

K = T

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Rapidly-exploring random trees (RRT’s)

Closest to q in the actual graph K = T

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Rapidly-exploring random trees (RRT’s)

qnew :closest to q within Ɛ from qnear If no qnew, repeat random q K = T

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Rapidly-exploring random trees (RRT’s)

Repeat for K = T + 1

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Rapidly-exploring random trees (RRT’s)

Simple uniform sampling of q favors exploration P(node being qnear) ~ size of the Voronoi region ~ unexplored region

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Rapidly-exploring random trees (RRT’s)

Simple uniform sampling of q favors exploration P(node being qnear) ~ size of the Voronoi region ~ unexplored region

High P of being qnear Low P of being qnear

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2 x RRT

How to dig a tunnel from A to B? Just start caving from each side Worse case you have two tunnels! Just build two RRT’s from start and goal. Have some attracting heuristic so that they meet.

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RRT-Connect

K = 0

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RRT-Connect

K = T

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RRT-Connect

K = T q at random uniformly

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RRT-Connect

K = T

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RRT-Connect

K = T

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RRT-Connect

K = T Connect B: Previous qnew acts as q for B

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RRT-Connect

K = T Connect B: Previous qnew acts as q for B

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RRT-Connect

K = T

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RRT-Connect

K = T + 1 Repeat, swapping behavior between A and B

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Examples

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Improvement: RRT*

Idea: store and use a cost per node (distance to A/B). 1) Expand minimum costs: ~When adding nodes, add the ones of minimum cost.

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Improvement: RRT*

Idea: store and use a cost per node (distance to A/B). 2) Update costs: ~When a new node is added, look in its neighborhood to see if the tree can be rewired to reduce costs

qnew qA qnew qA

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RRT-connect A* (Shakey paper)

Randomized Non-randomized Greedy heuristic Admissible heuristic Suboptimal Optimal Faster for “typical“ problems Slower but optimal

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Open question

Would it be useful to have N RTTs expanded from N states instead of just 2 (start and goal)? What these states would correspond to? How much could it be parallelized?

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