Dynamic Region-biased Rapidly-exploring Random Trees by Jory - - PowerPoint PPT Presentation

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Dynamic Region-biased Rapidly-exploring Random Trees by Jory - - PowerPoint PPT Presentation

Apr 21, 2023 444 likes •970 views

Dynamic Region-biased Rapidly-exploring Random Trees by Jory Denny, Read Sandstrom, Andrew Bregger, and Nancy M. Amato University of Richmond, Richmond VA, USA Texas A&M University, College Station, TX, USA Presenter: Jae Won Choi RRT

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SLIDE 1

Dynamic Region-biased Rapidly-exploring Random Trees

by Jory Denny, Read Sandstrom, Andrew Bregger, and Nancy M. Amato University of Richmond, Richmond VA, USA Texas A&M University, College Station, TX, USA Presenter: Jae Won Choi

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SLIDE 2

RRT Review

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SLIDE 3

RRT Review

  • RRT - Randomized Sampling
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SLIDE 4

RRT Review

  • RRT - Randomized Sampling
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SLIDE 5

RRT Review

  • RRT - Randomized Sampling
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SLIDE 6

RRT Review

  • RRT - Randomized Sampling
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SLIDE 7

RRT Review

  • RRT - Randomized Sampling
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SLIDE 8

RRT Review

  • RRT - Randomized Sampling
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SLIDE 9

RRT Review

  • RRT - Randomized Sampling
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SLIDE 10

RRT Review

  • RRT - Randomized Sampling
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SLIDE 11

RRT Review

  • RRT - Randomized Sampling
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SLIDE 12

RRT Review

  • RRT - Randomized Sampling

+ Simple way to construct an approximate model of problem space

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SLIDE 13

RRT Review

  • RRT - Randomized Sampling

+ Simple way to construct an approximate model of problem space

  • Weak with narrow and cluttered spaces
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SLIDE 14

Related Work 1

  • Dynamic Domain RRT

+ Reduces unnecessary samples from boundary regions + High probability of sampling narrow passage

  • Worst case same as Regular RRT

(a)Regular RRT sampling domain (b)Visible Voronoi region (c)Dynamic Domain

Dynamic-Domain RRTs: Efficient Exploration by Controlling the Sampling Domain by Yershova, Jaillet, Simeon, and La Valle.

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SLIDE 15

Related Work 2

  • Obstacle-based RRT (OBRRT) :
  • Growing tree based on obstacle hints
  • 1. Choose a node to grow from –
  • 2. Choose a growth method
  • 3. Generate target configuration
  • 4. Extend from source configuration

toward target configuration

G0: Basic Extension G1: Random position, Same orientation G2: Random obstacle vector, Random Orientation G3: Random Obstacle Vector, Same Orientation G4: Rotation followed by Extension G5: … G6: … … G9

An Obstacle-Based Rapidly-Exploring Random Tree by Samuel Rodriguez, Xinyu Tang, Jyh-Ming Lien and Nancy M. Amato

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SLIDE 16

Related Work 3

  • Retraction-based RRT

+ Improve performance of RRT in narrow passages by sampling near the boundary of C-obstacle

  • Slower than Regular RRT when there are no narrow passages

An Efficient Retration-based RRT Planner by Liangjun Zhang and Dinesh Manocha

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SLIDE 17

Related Work 4

  • RRT*
  • Tree locally rewires itself to

ensure optimization of a cost function + Effective in finding shortest path

  • In practice, it requires many

iterations to produce near

  • ptimal solutions

(a) 500, (b) 1500, (c) 2500, (d) 5000, (e) 10,000, (f) 15,000 iterations

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SLIDE 18

More Related Works

  • RRT-Blossom
  • Stable Sparse-RRT

…

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SLIDE 19

Dynamic Region RRT

Input: Environment e and a query (qs, qg) 1. G <- Compute Embedding Graph(e) [pre computation] 2. F <- Compute Flow Graph (G, qs, qg) 3. R <- Initialize Regions (F, qs) 4. While not done do 5. Region Biased RRT Growth (F, R)

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SLIDE 20

Dynamic Region RRT

Input: Environment e and a query (qs, qg) 1. G <- Compute Embedding Graph(e) [pre computation] 2. F <- Compute Flow Graph (G, qs, qg) 3. R <- Initialize Regions (F, qs) 4. While not done do 5. Region Biased RRT Growth (F, R)

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SLIDE 21

Dynamic Region RRT

Input: Environment e and a query (qs, qg) 1. G <- Compute Embedding Graph(e) [pre computation] 2. F <- Compute Flow Graph (G, qs, qg) 3. R <- Initialize Regions (F, qs) 4. While not done do 5. Region Biased RRT Growth (F, R)

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SLIDE 22

Dynamic Region RRT

Input: Environment e and a query (qs, qg) 1. G <- Compute Embedding Graph(e) [pre computation] 2. F <- Compute Flow Graph (G, qs, qg) 3. R <- Initialize Regions (F, qs) 4. While not done do 5. Region Biased RRT Growth (F, R)

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SLIDE 23

Dynamic Region RRT

Input: Environment e and a query (qs, qg) 1. G <- Compute Embedding Graph(e) [pre computation] 2. F <- Compute Flow Graph (G, qs, qg) 3. R <- Initialize Regions (F, qs) 4. While not done do 5. Region Biased RRT Growth (F, R)

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SLIDE 24
  • 1. Embedding Graph
  • Computing Embedding Graph
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SLIDE 25
  • 1. Embedding Graph
  • Computing Embedding Graph

Generalized Voronoi Graph

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SLIDE 26
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

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SLIDE 27
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

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SLIDE 28
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

Saddle Maximum Minimum F = z coordinate of a point

  • n manifold M
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SLIDE 29
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

Saddle Maximum Minimum 2 Minimums 2 Maximums Saddle Saddle Saddle Saddle F = z coordinate of a point

  • n manifold M

F = y coordinate of a point

  • n manifold M
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SLIDE 30
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

Saddle Maximum Minimum F = z coordinate of a point

  • n manifold M
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SLIDE 31
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

  • 3. Embed the Reeb graph back to

the Environment

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SLIDE 32
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

  • 3. Embed the Reeb graph back to

the Environment

Naïve Reeb Graph Algorithm: O(n2)

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SLIDE 33
  • 1. Embedding Graph
  • Computing Embedding Graph
  • 1. Compute Tetrahedralization of

the environment

  • 2. Construct a Reeb Graph from

the Tetrahedralization

  • 3. Embed the Reeb graph back to

the Environment

Naïve Reeb Graph Algorithm: O(n2) Fast Reeb Graph Algorithm: O(n log(n))

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SLIDE 34
  • 2. Flow Graph
  • Computing Flow Graph
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SLIDE 35
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
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SLIDE 36
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
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SLIDE 37
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
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SLIDE 38
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
  • 2. Backtrack from the nearest node to qg

to trim unrelated edges to a solution path (pruning)

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SLIDE 39
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
  • 2. Backtrack from the nearest node to qg

to trim unrelated edges to a solution path (pruning)

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SLIDE 40
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
  • 2. Backtrack from the nearest node to qg

to trim unrelated edges to a solution path (pruning)

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SLIDE 41
  • 2. Flow Graph
  • Computing Flow Graph
  • 1. Perform BFS from the nearest node qs
  • 2. Backtrack from the nearest node to qg

to trim unrelated edges to a solution path (pruning)

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SLIDE 42
  • 3. Region-biased RRT Growth
  • Four steps
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SLIDE 43
  • 3. Region-biased RRT Growth
  • Four steps
  • 1. Region-biased RRT extension

* Samples the region for a and then performs like any RRT method

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SLIDE 44
  • 3. Region-biased RRT Growth
  • Four steps
  • 1. Region-biased RRT extension

* Samples the region for a and then performs like any RRT method

  • 2. Advance regions along flow edges
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SLIDE 45
  • 3. Region-biased RRT Growth
  • Four steps
  • 1. Region-biased RRT extension

* Samples the region for a and then performs like any RRT method

  • 2. Advance regions along flow edges
  • 3. Delete useless regions(heuristic)
  • 4. Create new regions
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SLIDE 46
  • 3. Region-biased RRT Growth
  • Four steps
  • 1. Region-biased RRT extension

* Samples the region for a and then performs like any RRT method

  • 2. Advance regions along flow edges
  • 3. Delete useless regions(heuristic)
  • 4. Create new regions
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SLIDE 47

Evaluation

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SLIDE 48

Results on Holonomic

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SLIDE 49

Results on non-holonomic

+ Dynamic biased RRT works on non-holonomic problems

  • SyClop performs better

* SyClop has faster neighbor selection routine

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SLIDE 50

Results

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SLIDE 51

Q&A