3,663 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
An Efficient Algorithm for Computing High-Quality Paths amid Polygonal Obstacles
We study a path-planning problem amid a set of obstacles in
, in which we wish to compute a short path between two points
while also maintaining a high clearance from ; the clearance of a
point is its distance from a nearest obstacle in . Specifically,
the problem asks for a path minimizing the reciprocal of the clearance
integrated over the length of the path. We present the first polynomial-time
approximation scheme for this problem. Let be the total number of obstacle
vertices and let . Our algorithm computes in time
a path of total cost
at most times the cost of the optimal path.Comment: A preliminary version of this work appear in the Proceedings of the
27th Annual ACM-SIAM Symposium on Discrete Algorithm
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
The Ariadne's Clew Algorithm
We present a new approach to path planning, called the "Ariadne's clew
algorithm". It is designed to find paths in high-dimensional continuous spaces
and applies to robots with many degrees of freedom in static, as well as
dynamic environments - ones where obstacles may move. The Ariadne's clew
algorithm comprises two sub-algorithms, called Search and Explore, applied in
an interleaved manner. Explore builds a representation of the accessible space
while Search looks for the target. Both are posed as optimization problems. We
describe a real implementation of the algorithm to plan paths for a six degrees
of freedom arm in a dynamic environment where another six degrees of freedom
arm is used as a moving obstacle. Experimental results show that a path is
found in about one second without any pre-processing
06421 Abstracts Collection -- Robot Navigation
From 15.10.06 to 20.10.06, the Dagstuhl Seminar 06421 ``Robot Navigation\u27\u27generate automatically was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
CAT-RRT: Motion Planning that Admits Contact One Link at a Time
Current motion planning approaches rely on binary collision checking to
evaluate the validity of a state and thereby dictate where the robot is allowed
to move. This approach leaves little room for robots to engage in contact with
an object, as is often necessary when operating in densely cluttered spaces. In
this work, we propose an alternative method that considers contact states as
high-cost states that the robot should avoid but can traverse if necessary to
complete a task. More specifically, we introduce Contact Admissible
Transition-based Rapidly exploring Random Trees (CAT-RRT), a planner that uses
a novel per-link cost heuristic to find a path by traversing high-cost obstacle
regions. Through extensive testing, we find that state-of-the-art optimization
planners tend to over-explore low-cost states, which leads to slow and
inefficient convergence to contact regions. Conversely, CAT-RRT searches both
low and high-cost regions simultaneously with an adaptive thresholding
mechanism carried out at each robot link. This leads to paths with a balance
between efficiency, path length, and contact cost
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