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# Asymptotically near-optimal RRT for fast, high-quality, motion planning LBT-RRT roadmaps: Two trees are simultaneously maintained by ouralgorithm. A lower bound (T_lb) tree and an approximation tree.  The cost  for reaching a node using the (possibly non collision-free) edges of the T_lb will serve as a lower bound for the optimal cost. The secondtree, 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 $1+\varepsilon$ 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 scenario 6 DOF Alternating barriers scenario 12 DOF 2-robot Cubicles scenario

Success rate for algorithms on different scenarios.   Maze scenario Alternating barriers scenario Cubicles scenario

Path lengths for algorithms on different scenarios   Maze scenario Alternating barriers scenario Cubicles scenario

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