3,324 research outputs found
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
Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning
We present a sampling-based framework for multi-robot motion planning which
combines an implicit representation of a roadmap with a novel approach for
pathfinding in geometrically embedded graphs tailored for our setting. Our
pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated
RRT algorithm for the discrete case of a graph, and it enables a rapid
exploration of the high-dimensional configuration space by carefully walking
through an implicit representation of a tensor product of roadmaps for the
individual robots. We demonstrate our approach experimentally on scenarios of
up to 60 degrees of freedom where our algorithm is faster by a factor of at
least ten when compared to existing algorithms that we are aware of.Comment: Kiril Solovey and Oren Salzman contributed equally to this pape
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
PRM-RL: Long-range Robotic Navigation Tasks by Combining Reinforcement Learning and Sampling-based Planning
We present PRM-RL, a hierarchical method for long-range navigation task
completion that combines sampling based path planning with reinforcement
learning (RL). The RL agents learn short-range, point-to-point navigation
policies that capture robot dynamics and task constraints without knowledge of
the large-scale topology. Next, the sampling-based planners provide roadmaps
which connect robot configurations that can be successfully navigated by the RL
agent. The same RL agents are used to control the robot under the direction of
the planning, enabling long-range navigation. We use the Probabilistic Roadmaps
(PRMs) for the sampling-based planner. The RL agents are constructed using
feature-based and deep neural net policies in continuous state and action
spaces. We evaluate PRM-RL, both in simulation and on-robot, on two navigation
tasks with non-trivial robot dynamics: end-to-end differential drive indoor
navigation in office environments, and aerial cargo delivery in urban
environments with load displacement constraints. Our results show improvement
in task completion over both RL agents on their own and traditional
sampling-based planners. In the indoor navigation task, PRM-RL successfully
completes up to 215 m long trajectories under noisy sensor conditions, and the
aerial cargo delivery completes flights over 1000 m without violating the task
constraints in an environment 63 million times larger than used in training.Comment: 9 pages, 7 figure
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