124 research outputs found
Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic
Rapidly-exploring random trees (RRTs) are popular in motion planning because
they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s)
extend RRTs to the problem of finding the optimal solution, but in doing so
asymptotically find the optimal path from the initial state to every state in
the planning domain. This behaviour is not only inefficient but also
inconsistent with their single-query nature.
For problems seeking to minimize path length, the subset of states that can
improve a solution can be described by a prolate hyperspheroid. We show that
unless this subset is sampled directly, the probability of improving a solution
becomes arbitrarily small in large worlds or high state dimensions. In this
paper, we present an exact method to focus the search by directly sampling this
subset.
The advantages of the presented sampling technique are demonstrated with a
new algorithm, Informed RRT*. This method retains the same probabilistic
guarantees on completeness and optimality as RRT* while improving the
convergence rate and final solution quality. We present the algorithm as a
simple modification to RRT* that could be further extended by more advanced
path-planning algorithms. We show experimentally that it outperforms RRT* in
rate of convergence, final solution cost, and ability to find difficult
passages while demonstrating less dependence on the state dimension and range
of the planning problem.Comment: 8 pages, 11 figures. Videos available at
https://www.youtube.com/watch?v=d7dX5MvDYTc and
https://www.youtube.com/watch?v=nsl-5MZfwu
Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs
In this paper, we present Batch Informed Trees (BIT*), a planning algorithm
based on unifying graph- and sampling-based planning techniques. By recognizing
that a set of samples describes an implicit random geometric graph (RGG), we
are able to combine the efficient ordered nature of graph-based techniques,
such as A*, with the anytime scalability of sampling-based algorithms, such as
Rapidly-exploring Random Trees (RRT).
BIT* uses a heuristic to efficiently search a series of increasingly dense
implicit RGGs while reusing previous information. It can be viewed as an
extension of incremental graph-search techniques, such as Lifelong Planning A*
(LPA*), to continuous problem domains as well as a generalization of existing
sampling-based optimal planners. It is shown that it is probabilistically
complete and asymptotically optimal.
We demonstrate the utility of BIT* on simulated random worlds in
and and manipulation problems on CMU's HERB, a
14-DOF two-armed robot. On these problems, BIT* finds better solutions faster
than RRT, RRT*, Informed RRT*, and Fast Marching Trees (FMT*) with faster
anytime convergence towards the optimum, especially in high dimensions.Comment: 8 Pages. 6 Figures. Video available at
http://www.youtube.com/watch?v=TQIoCC48gp
RMPD - A Recursive Mid-Point Displacement Algorithm for Path Planning
Motivated by what is required for real-time path planning, the paper starts
out by presenting sRMPD, a new recursive "local" planner founded on the key
notion that, unless made necessary by an obstacle, there must be no deviation
from the shortest path between any two points, which would normally be a
straight line path in the configuration space. Subsequently, we increase the
power of sRMPD by using it as a "connect" subroutine call in a higher-level
sampling-based algorithm mRMPD that is inspired by multi-RRT. As a consequence,
mRMPD spawns a larger number of space exploring trees in regions of the
configuration space that are characterized by a higher density of obstacles.
The overall effect is a hybrid tree growing strategy with a trade-off between
random exploration as made possible by multi-RRT based logic and immediate
exploitation of opportunities to connect two states as made possible by sRMPD.
The mRMPD planner can be biased with regard to this trade-off for solving
different kinds of planning problems efficiently. Based on the test cases we
have run, our experiments show that mRMPD can reduce planning time by up to 80%
compared to basic RRT
Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search
Path planning in robotics often requires finding high-quality solutions to
continuously valued and/or high-dimensional problems. These problems are
challenging and most planning algorithms instead solve simplified
approximations. Popular approximations include graphs and random samples, as
respectively used by informed graph-based searches and anytime sampling-based
planners. Informed graph-based searches, such as A*, traditionally use
heuristics to search a priori graphs in order of potential solution quality.
This makes their search efficient but leaves their performance dependent on the
chosen approximation. If its resolution is too low then they may not find a
(suitable) solution but if it is too high then they may take a prohibitively
long time to do so. Anytime sampling-based planners, such as RRT*,
traditionally use random sampling to approximate the problem domain
incrementally. This allows them to increase resolution until a suitable
solution is found but makes their search dependent on the order of
approximation. Arbitrary sequences of random samples approximate the problem
domain in every direction simultaneously and but may be prohibitively
inefficient at containing a solution. This paper unifies and extends these two
approaches to develop Batch Informed Trees (BIT*), an informed, anytime
sampling-based planner. BIT* solves continuous path planning problems
efficiently by using sampling and heuristics to alternately approximate and
search the problem domain. Its search is ordered by potential solution quality,
as in A*, and its approximation improves indefinitely with additional
computational time, as in RRT*. It is shown analytically to be almost-surely
asymptotically optimal and experimentally to outperform existing sampling-based
planners, especially on high-dimensional planning problems.Comment: International Journal of Robotics Research (IJRR). 32 Pages. 16
Figure
On the performance of sampling-based optimal motion planners
Sampling based algorithms provide efficient methods of solving robot motion planning problem. The advantage of these approaches is the ease of their implementation and their computational efficiency. These algorithms are probabilistically complete i.e. they will find a solution if one exists, given a suitable run time. The drawback of sampling based planners is that there is no guarantee of the quality of their solutions. In fact, it was proven that their probability of reaching an optimal solution approaches zero. A breakthrough in sampling planning was the proposal of optimal based sampling planners. Current optimal planners are characterized with asymptotic optimality i.e. they reach an optimal solutions as time approaches infinity. Motivated by the slow convergence of optimal planners, post-processing and heuristic approach have been suggested. Due to the nature of the sampling based planners, their implementation requires tuning and selection of a large number of parameters that are often overlooked. This paper presents the performance study of an optimal planner under different parameters and heuristics. We also propose a modification in the algorithm to improve the convergence rate towards an optimal solution
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