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Asymptotically near-optimal RRT for fast, high-quality, motion planning

Abstrac

Asymptotically near-optimal RRT for fast, high-quality, motion planning
LBT-RRT roadmaps: Two trees are simultaneously maintained by our algorithm. A lower bound (\(T_{\text{lb}}\)) tree and an approximation tree. The cost for reaching a node using the (possibly non collision-free) edges of the \(T_{\text{lb}}\) will serve as a lower bound for the optimal cost. The second tree, T_apx maintains collision-free nodes that approximate the optimal cost.

We present Lower Bound Tree-RRT (LBT-RRT), a novel, single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of \(1+\epsilon\) of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like the RRT* algorithm. When the approximation factor is unbounded, LBT-RRT behaves like the RRT algorithm. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary tree, which we call the lower-bound tree. The combination of the two trees, which is faster to maintain than the tree maintained by RRT*, efficiently guarantee asymptotic near-optimality.

We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRT*)  with little runtime overhead when compared to RRT.

Experimental results*

Benchmark scenarios. The start and goal configuration are depicted in green and red, respectively

3 DOF Maze scenario3 DOF Maze scenario
3 DOF Maze scenario

6 DOF Alternating barriers scenario
6 DOF Alternating barriers scenario

12 DOF 2-robot Cubicles scenario
12 DOF 2-robot Cubicles scenario

Success rate for algorithms on different scenarios

Maze scenario
Maze scenario

Alternating barriers scenario
Alternating barriers scenario

Cubicles scenario
Cubicles scenario

Path lengths for algorithms on different scenarios

Maze scenario
Maze scenario

Alternating barriers scenario
Alternating barriers scenario

 Cubicles scenario
Cubicles scenario

* Implemented using OMPL, the cubicles and the maze scenarios are provided with the OMPLdistribution.

Links

  • Oren Salzman and Dan Halperin
    Asymptotically near-optimal RRT for fast, high-quality, motion planning
    IEEE Transactions on Robotics, Volume 32, Issue 3, pages 473–483, 2014 [link][bibtex]
    arXiv:1308.0189v4 (full version) [link][bibtex]

Contacts

Oren Salzman
Dan Halperin
@article{sh-anorf-13,
  author = {Oren Salzman and an Halperin},
  journal = {{IEEE} Transactions on Robotics}, 
  title = {Asymptotically Near-Optimal RRT for Fast, High-Quality Motion Planning}, 
  year = {2016},
  volume = {32},
  number = {3},
  pages = {473--483},
  doi = {10.1109/TRO.2016.2539377}
}
@article{sh-anorf-13,
  author       = {Oren Salzman and an Halperin},
  title        = {Asymptotically near-optimal {RRT} for fast, high-quality, motion planning},
  journal      = {CoRR},
  volume       = {abs/1308.0189},
  year         = {2013},
  url          = {http://arxiv.org/abs/1308.0189},
  eprinttype   = {arXiv},
  eprint       = {1308.0189},
  timestamp    = {Mon, 13 Aug 2018 16:46:54 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/SalzmanH13.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}

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