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

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

Coordinated Robot Navigation via Hierarchical Clustering

We introduce the use of hierarchical clustering for relaxed, deterministic coordination and control of multiple robots. Traditionally an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of $n$ perfectly sensed and actuated Euclidean spheres in a $d$-dimensional ambient space (for arbitrary $n$ and $d$). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller which is quadratic in $n$ and algebraic in $d$ and prove that its execution brings all but a measure zero set of initial configurations to the desired goal with the guarantee of no collisions along the way.Comment: 29 pages, 13 figures, 8 tables, extended version of a paper in preparation for submission to a journa

Fast and adaptive fractal tree-based path planning for programmable bevel tip steerable needles

© 2016 IEEE. Steerable needles are a promising technology for minimally invasive surgery, as they can provide access to difficult to reach locations while avoiding delicate anatomical regions. However, due to the unpredictable tissue deformation associated with needle insertion and the complexity of many surgical scenarios, a real-time path planning algorithm with high update frequency would be advantageous. Real-time path planning for nonholonomic systems is commonly used in a broad variety of fields, ranging from aerospace to submarine navigation. In this letter, we propose to take advantage of the architecture of graphics processing units (GPUs) to apply fractal theory and thus parallelize real-time path planning computation. This novel approach, termed adaptive fractal trees (AFT), allows for the creation of a database of paths covering the entire domain, which are dense, invariant, procedurally produced, adaptable in size, and present a recursive structure. The generated cache of paths can in turn be analyzed in parallel to determine the most suitable path in a fraction of a second. The ability to cope with nonholonomic constraints, as well as constraints in the space of states of any complexity or number, is intrinsic to the AFT approach, rendering it highly versatile. Three-dimensional (3-D) simulations applied to needle steering in neurosurgery show that our approach can successfully compute paths in real-time, enabling complex brain navigation