6,913 research outputs found
A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles
Self-driving vehicles are a maturing technology with the potential to reshape
mobility by enhancing the safety, accessibility, efficiency, and convenience of
automotive transportation. Safety-critical tasks that must be executed by a
self-driving vehicle include planning of motions through a dynamic environment
shared with other vehicles and pedestrians, and their robust executions via
feedback control. The objective of this paper is to survey the current state of
the art on planning and control algorithms with particular regard to the urban
setting. A selection of proposed techniques is reviewed along with a discussion
of their effectiveness. The surveyed approaches differ in the vehicle mobility
model used, in assumptions on the structure of the environment, and in
computational requirements. The side-by-side comparison presented in this
survey helps to gain insight into the strengths and limitations of the reviewed
approaches and assists with system level design choices
Unconstrained and Curvature-Constrained Shortest-Path Distances and their Approximation
We study shortest paths and their distances on a subset of a Euclidean space,
and their approximation by their equivalents in a neighborhood graph defined on
a sample from that subset. In particular, we recover and extend the results of
Bernstein et al. (2000). We do the same with curvature-constrained shortest
paths and their distances, establishing what we believe are the first
approximation bounds for them
Visual Monitoring for Multiple Points of Interest on a 2.5D Terrain using a UAV with Limited Field-of-View Constraint
Varying terrain conditions and limited field-of-view restricts the visibility
of aerial robots while performing visual monitoring operations. In this paper,
we study the multi-point monitoring problem on a 2.5D terrain using an unmanned
aerial vehicle (UAV) with limited camera field-of-view. This problem is NP-Hard
and hence we develop a two phase strategy to compute an approximate tour for
the UAV. In the first phase, visibility regions on the flight plane are
determined for each point of interest. In the second phase, a tour for the UAV
to visit each visibility region is computed by casting the problem as an
instance of the Traveling Salesman Problem with Neighbourhoods (TSPN). We
design a constant-factor approximation algorithm for the TSPN instance.
Further, we reduce the TSPN instance to an instance of the Generalized
Traveling Salesman Problem (GTSP) and devise an ILP formulation to solve it. We
present a comparative evaluation of solutions computed using a branch-and-cut
implementation and an off-the-shelf GTSP tool -- GLNS, while varying the points
of interest density, sampling resolution and camera field-of-view. We also show
results from preliminary field experiments
Reachability by Paths of Bounded Curvature in a Convex Polygon
Let be a point robot moving in the plane, whose path is constrained to
forward motions with curvature at most one, and let be a convex polygon
with vertices. Given a starting configuration (a location and a direction
of travel) for inside , we characterize the region of all points of
that can be reached by , and show that it has complexity . We give an
time algorithm to compute this region. We show that a point is
reachable only if it can be reached by a path of type CCSCS, where C denotes a
unit circle arc and S denotes a line segment
The traveling salesman problem for lines and rays in the plane
In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of
regions (neighborhoods) and we seek a shortest tour that visits each
region. In the path variant, we seek a shortest path that visits each region.
We present several linear-time approximation algorithms with improved ratios
for these problems for two cases of neighborhoods that are (infinite) lines,
and respectively, (half-infinite) rays. Along the way we derive a tight bound
on the minimum perimeter of a rectangle enclosing an open curve of length .Comment: 10 pages, 5 figure
On Optimal Polyline Simplification using the Hausdorff and Fr\'echet Distance
We revisit the classical polygonal line simplification problem and study it
using the Hausdorff distance and Fr\'echet distance. Interestingly, no previous
authors studied line simplification under these measures in its pure form,
namely: for a given > 0, choose a minimum size subsequence of the
vertices of the input such that the Hausdorff or Fr\'echet distance between the
input and output polylines is at most . We analyze how the
well-known Douglas-Peucker and Imai-Iri simplification algorithms perform
compared to the optimum possible, also in the situation where the algorithms
are given a considerably larger error threshold than .
Furthermore, we show that computing an optimal simplification using the
undirected Hausdorff distance is NP-hard. The same holds when using the
directed Hausdorff distance from the input to the output polyline, whereas the
reverse can be computed in polynomial time. Finally, to compute the optimal
simplification from a polygonal line consisting of vertices under the
Fr\'echet distance, we give an time algorithm that requires
space, where is the output complexity of the simplification.Comment: Full version of the SoCG2018 pape
SU(2) graph invariants, Regge actions and polytopes
We revisit the the large spin asymptotics of 15j symbols in terms of cosines
of the 4d Euclidean Regge action, as derived by Barrett and collaborators using
a saddle point approximation. We bring it closer to the perspective of
area-angle Regge calculus and twisted geometries, and compute explicitly the
Hessian and phase offsets. We then extend it to more general SU(2) graph
invariants, showing that saddle points still exist and have a similar
structure. For graphs dual to 4d polytopes we find again two distinct saddle
points leading to a cosine asymptotic formula, however a conformal
shape-mismatch is allowed by these configurations, and the asymptotic action is
thus a generalisation of the Regge action. The allowed mismatch correspond to
angle-matched twisted geometries, 3d polyhedral tessellations with adjacent
faces matching areas and 2d angles, but not their diagonals. We study these
geometries, identify the relevant subsets corresponding to 3d Regge data and
flat polytope data, and discuss the corresponding Regge actions emerging in the
asymptotics. Finally, we also provide the first numerical confirmation of the
large spin asymptotics of the 15j symbol. We show that the agreement is
accurate to the per cent level already at spins of order 10, and the
next-to-leading order oscillates with the same frequency and same global phase.Comment: v2: Section added on the implications of our results for spin foam
models of quantum gravity, few amendments, references updated. 36 pages, many
figures and many footnotes v3: Comparison with more recent work added at the
end of the conclusion
On Triangluar Separation of Bichromatic Point Sets in Polygonal Environment
Let be a simple polygonal environment with vertices in the
plane. Assume that a set of blue points and a set of red points
are distributed in . We study the problem of computing triangles
that separate the sets and , and fall in . We call these
triangles \emph{inscribed triangular separators}. We propose an
output-sensitive algorithm to solve this problem in time, where is the size of convex hull of ,
and is the number of inscribed triangular separators. We also
study the case where there does not exist any inscribed triangular separators.
This may happen due to the tight distribution of red points around convex hull
of while no red points are inside this hull. In this case we focus to
compute a triangle that separates most of the blue points from the red points.
We refer to these triangles as \emph{maximum triangular separators}. Assuming
, we design a constant-factor approximation algorithm to compute such a
separator in time. "Eligible for best student paper
SLAM-Assisted Coverage Path Planning for Indoor LiDAR Mapping Systems
Applications involving autonomous navigation and planning of mobile agents
can benefit greatly by employing online Simultaneous Localization and Mapping
(SLAM) techniques, however, their proper implementation still warrants an
efficient amalgamation with any offline path planning method that may be used
for the particular application. In this paper, such a case of amalgamation is
considered for a LiDAR-based indoor mapping system which presents itself as a
2D coverage path planning problem implemented along with online SLAM. This
paper shows how classic offline Coverage Path Planning (CPP) can be altered for
use with online SLAM by proposing two modifications: (i) performing convex
decomposition of the polygonal coverage area to allow for an arbitrary choice
of an initial point while still tracing the shortest coverage path and (ii)
using a new approach to stitch together the different cells within the
polygonal area to form a continuous coverage path. Furthermore, an alteration
to the SLAM operation to suit the coverage path planning strategy is also made
that evaluates navigation errors in terms of an area coverage cost function.
The implementation results show how the combination of the two modified offline
and online planning strategies allow for an improvement in the total area
coverage by the mapping system - the modification thus presents an approach for
modifying offline and online navigation strategies for robust operation
Minimum Opaque Covers for Polygonal Regions
The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is
the problem of finding, for a set S in Euclidean space, the minimum-length set
F which intersects every straight line passing through S. In spite of its
simplicity, the problem remains remarkably intractable. The aim of this paper
is to establish a framework and fundamental results for minimum opaque covers
where S is a polygonal region in two-dimensional space. We begin by giving some
general results about opaque covers, and describe the close connection that the
OCP has with the Point Goalie Problem. We then consider properties of graphical
solutions to the OCP when S is a convex polygonal region in the plane
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