73 research outputs found
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
Online, interactive user guidance for high-dimensional, constrained motion planning
We consider the problem of planning a collision-free path for a
high-dimensional robot. Specifically, we suggest a planning framework where a
motion-planning algorithm can obtain guidance from a user. In contrast to
existing approaches that try to speed up planning by incorporating experiences
or demonstrations ahead of planning, we suggest to seek user guidance only when
the planner identifies that it ceases to make significant progress towards the
goal. Guidance is provided in the form of an intermediate configuration
, which is used to bias the planner to go through . We
demonstrate our approach for the case where the planning algorithm is
Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our
approach allows to compute highly-constrained paths with little domain
knowledge. Without our approach, solving such problems requires
carefully-crafting domain-dependent heuristics
Efficient motion planning for problems lacking optimal substructure
We consider the motion-planning problem of planning a collision-free path of
a robot in the presence of risk zones. The robot is allowed to travel in these
zones but is penalized in a super-linear fashion for consecutive accumulative
time spent there. We suggest a natural cost function that balances path length
and risk-exposure time. Specifically, we consider the discrete setting where we
are given a graph, or a roadmap, and we wish to compute the minimal-cost path
under this cost function. Interestingly, paths defined using our cost function
do not have an optimal substructure. Namely, subpaths of an optimal path are
not necessarily optimal. Thus, the Bellman condition is not satisfied and
standard graph-search algorithms such as Dijkstra cannot be used. We present a
path-finding algorithm, which can be seen as a natural generalization of
Dijkstra's algorithm. Our algorithm runs in time, where~ and are the number of vertices and
edges of the graph, respectively, and is the number of intersections
between edges and the boundary of the risk zone. We present simulations on
robotic platforms demonstrating both the natural paths produced by our cost
function and the computational efficiency of our algorithm
On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages
We extend our study of Motion Planning via Manifold Samples (MMS), a general
algorithmic framework that combines geometric methods for the exact and
complete analysis of low-dimensional configuration spaces with sampling-based
approaches that are appropriate for higher dimensions. The framework explores
the configuration space by taking samples that are entire low-dimensional
manifolds of the configuration space capturing its connectivity much better
than isolated point samples. The contributions of this paper are as follows:
(i) We present a recursive application of MMS in a six-dimensional
configuration space, enabling the coordination of two polygonal robots
translating and rotating amidst polygonal obstacles. In the adduced experiments
for the more demanding test cases MMS clearly outperforms PRM, with over
20-fold speedup in a coordination-tight setting. (ii) A probabilistic
completeness proof for the most prevalent case, namely MMS with samples that
are affine subspaces. (iii) A closer examination of the test cases reveals that
MMS has, in comparison to standard sampling-based algorithms, a significant
advantage in scenarios containing high-dimensional narrow passages. This
provokes a novel characterization of narrow passages which attempts to capture
their dimensionality, an attribute that had been (to a large extent) unattended
in previous definitions.Comment: 20 page
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