Asymptotically near-optimal RRT for fast, high-quality, motion planning
This work addresses the trade-off between speed and solution quality in motion planning for robotics, offering an incremental improvement over existing algorithms like RRT and RRT*.
The paper introduces LBT-RRT, a sampling-based motion planning algorithm that achieves asymptotically near-optimal solutions within a factor of 1+epsilon of optimal, enabling a trade-off between the speed of RRT and the optimality of RRT*/RRG, with demonstrated performance in 3 to 12 degrees of freedom scenarios showing high-quality paths and minimal runtime overhead compared to RRT.
We present Lower Bound Tree-RRT (LBT-RRT), a 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 RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. 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 graph, which we call the lower-bound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. 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 RRG and RRT*) with little running-time overhead when compared to RRT.