828 research outputs found
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
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
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
On Recursive Random Prolate Hyperspheroids
This technical note analyzes the properties of a random sequence of prolate
hyperspheroids with common foci. Each prolate hyperspheroid in the sequence is
defined by a sample drawn randomly from the previous volume such that the
sample lies on the new surface (Fig. 1). Section 1 defines the prolate
hyperspheroid coordinate system and the resulting differential volume, Section
2 calculates the expected value of the new transverse diameter given a uniform
distribution over the existing prolate hyperspheroid, and Section 3 calculates
the convergence rate of this sequence. For clarity, the differential volume and
some of the identities used in the integration are verified in Appendix A
through a calculation of the volume of a general prolate hyperspheroid.Comment: 11 pages, 2 figure
Scalar Field Dark Matter: non-spherical collapse and late time behavior
We show the evolution of non-spherically symmetric balls of a
self-gravitating scalar field in the Newtonian regime or equivalently an ideal
self-gravitating condensed Bose gas. In order to do so, we use a finite
differencing approximation of the Shcr\"odinger-Poisson (SP) system of
equations with axial symmetry in cylindrical coordinates. Our results indicate:
1) that spherically symmetric ground state equilibrium configurations are
stable against non-spherical perturbations and 2) that such configurations of
the SP system are late-time attractors for non-spherically symmetric initial
profiles of the scalar field, which is a generalization of such behavior for
spherically symmetric initial profiles. Our system and the boundary conditions
used, work as a model of scalar field dark matter collapse after the turnaround
point. In such case, we have found that the scalar field overdensities tolerate
non-spherical contributions to the profile of the initial fluctuation.Comment: 8 revtex pages, 10 eps figures. Accepted for publication in PR
Hidden Degeneracy in the Brick Wall Model of Black Holes
Quantum field theory in the near-horizon region of a black hole predicts the
existence of an infinite number of degenerate modes. Such a degeneracy is
regulated in the brick wall model by the introduction of a short distance
cutoff. In this Letter we show that states of the brick wall model with non
zero energy admit a further degeneracy for any given finite value of the
cutoff. The black hole entropy is calculated within the brick wall model taking
this degeneracy into account. Modes with complex frequencies however do not
exhibit such a degeneracy.Comment: 8 pages, Latex fil
The Provable Virtue of Laziness in Motion Planning
The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms
that only evaluate edges along shortest paths between the source and target.
These algorithms were designed to minimize the number of edge evaluations in
settings where edge evaluation dominates the running time of the algorithm; but
how close to optimal are LazySP algorithms in terms of this objective? Our main
result is an analytical upper bound, in a probabilistic model, on the number of
edge evaluations required by LazySP algorithms; a matching lower bound shows
that these algorithms are asymptotically optimal in the worst case
Comparison of intramedullary nailing versus proximal locking plating in the management of closed extra-articular proximal tibial fracture
Background: To compare the outcomes of closed reduction and expert tibial nailing (ETN) versus minimally invasive proximal tibial plating in treating proximal extraarticular tibial fractures.Methods: This study included 30 cases of extraarticular proximal tibial shaft fractures. They were admitted to our department between March 2014 and June 2016 and treated respectively by closed reduction and ETN (group A, n=15) or minimally invasive proximal tibial plating (group B, n=15). To compare the therapeutic effects between two groups, the intraoperative condition, post-operative function, related complications and malalignment were investigated.Results: All the patients were successfully followed up till radiological union. The average union time for group A was 14.2 months and for group B was 16.7 months. 3 patients in group A developed delayed union and was treated with dynamization and ultimately lead to union whereas 1 patient developed non-union in group B. There were 3 cases of superficial infection in group B cured by antibiotics and repeated dressing change. Moreover, group A showed better result in terms of intraoperative blood loss, operation time, postoperative weight bearing time and fracture union time. Functional scores as calculated by the knee rating scale of the hospital for special surgery, 12 (80%) had excellent results in group A compared to 10 (66.66%) in group B which was not statistically significant.Conclusions: Compared with plate and screw fixation, ETN fixation has the advantages of fewer complications, shorter operation time, being less invasive, earlier postoperative rehabilitation and weight bearing, quicker fracture union and better functional recovery, thus being an effective way to treat extra articular proximal tibial fractures
Similarities in seroprevalence of Toxoplasma gondii, Trichinella spp., Trichuris suis and Ascaris suum in swine in the conventional and antibiotic free swine production systems
Helmith parasite infections in swine represent a significant, but understudied health concern for both the swine industry and consumers. While many parasitic infections cause subclinical infections, infected swine pose a public health risk from consumption of contaminated meat products
Bulk Kalb-Ramond field in Randall Sundrum scenario
We have considered the most general gauge invariant five-dimensional action
of a second rank antisymmetric Kalb-Ramond tensor gauge theory, including a
topological term of the form in a
Randall-Sundrum scenario. Such a tensor field (whose rank-3 field
strength tensor is ), which appears in the massless sector of a
heterotic string theory, is assumed to coexist with the gravity in the bulk.
The third rank field strength corresponding to the Kalb-Ramond field has a
well-known geometric interpretation as the spacetime torsion. The only
non-trivial classical solutions corresponding to the effective four-dimensional
action are found to be self-dual or anti-selfdual Kalb-Ramond fields. This
ensures that the four-dimensional effective action on the brane is
parity-conserving. The massive modes for both cases, lying in the TeV range,
are related to the fundamental parameters of the theory. These modes can be
within the kinematic reach of forthcoming TeV scale experiments. However, the
couplings of the massless as well as massive Kalb-Ramond modes with matter on
the visible brane are found to be suppressed vis-a-vis that of the graviton by
the warp factor, whence the conclusion is that both the massless and the
massive torsion modes appear much weaker than curvature to an observer on the
visible brane.Comment: 15 Pages,2 figures,Late
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