285 research outputs found
Optimal Time-Convex Hull under the Lp Metrics
We consider the problem of computing the time-convex hull of a point set
under the general metric in the presence of a straight-line highway in
the plane. The traveling speed along the highway is assumed to be faster than
that off the highway, and the shortest time-path between a distant pair may
involve traveling along the highway. The time-convex hull of a point
set is the smallest set containing both and \emph{all} shortest
time-paths between any two points in . In this paper we give an
algorithm that computes the time-convex hull under the metric in optimal
time for a given set of points and a real number with
Path Planning For Persistent Surveillance Applications Using Fixed-Wing Unmanned Aerial Vehicles
This thesis addresses coordinated path planning for fixed-wing Unmanned Aerial Vehicles
(UAVs) engaged in persistent surveillance missions. While uniquely suited to this mission,
fixed wing vehicles have maneuver constraints that can limit their performance in this role.
Current technology vehicles are capable of long duration flight with a minimal acoustic
footprint while carrying an array of cameras and sensors. Both military tactical and civilian
safety applications can benefit from this technology. We make three main contributions:
C1 A sequential path planner that generates a C2 flight plan to persistently acquire a
covering set of data over a user designated area of interest. The planner features the
following innovations:
• A path length abstraction that embeds kino-dynamic motion constraints to estimate feasible path length
• A Traveling Salesman-type planner to generate a covering set route based on the path length abstraction
• A smooth path generator that provides C2 routes that satisfy user specified curvature constraints
C2 A set of algorithms to coordinate multiple UAVs, including mission commencement
from arbitrary locations to the start of a coordinated mission and de-confliction of
paths to avoid collisions with other vehicles and fixed obstacles
iv
C3 A numerically robust toolbox of spline-based algorithms tailored for vehicle routing
validated through flight test experiments on multiple platforms. A variety of tests
and platforms are discussed.
The algorithms presented are based on a technical approach with approximately equal
emphasis on analysis, computation, dynamic simulation, and flight test experimentation.
Our planner (C1) directly takes into account vehicle maneuverability and agility constraints
that could otherwise render simple solutions infeasible. This is especially important when
surveillance objectives elevate the importance of optimized paths. Researchers have devel
oped a diverse range of solutions for persistent surveillance applications but few directly
address dynamic maneuver constraints.
The key feature of C1 is a two stage sequential solution that discretizes the problem so that
graph search techniques can be combined with parametric polynomial curve generation.
A method to abstract the kino-dynamics of the aerial platforms is then presented so that
a graph search solution can be adapted for this application. An A* Traveling Salesman
Problem (TSP) algorithm is developed to search the discretized space using the abstract
distance metric to acquire more data or avoid obstacles. Results of the graph search are
then transcribed into smooth paths based on vehicle maneuver constraints. A complete
solution for a single vehicle periodic tour of the area is developed using the results of the
graph search algorithm. To execute the mission, we present a simultaneous arrival algorithm
(C2) to coordinate execution by multiple vehicles to satisfy data refresh requirements and
to ensure there are no collisions at any of the path intersections.
We present a toolbox of spline-based algorithms (C3) to streamline the development of C2
continuous paths with numerical stability. These tools are applied to an aerial persistent
surveillance application to illustrate their utility. Comparisons with other parametric poly
nomial approaches are highlighted to underscore the benefits of the B-spline framework.
Performance limits with respect to feasibility constraints are documented
Large bichromatic point sets admit empty monochromatic 4-gons
We consider a variation of a problem stated by Erd˝os
and Szekeres in 1935 about the existence of a number
fES(k) such that any set S of at least fES(k) points in
general position in the plane has a subset of k points
that are the vertices of a convex k-gon. In our setting
the points of S are colored, and we say that a (not necessarily
convex) spanned polygon is monochromatic if
all its vertices have the same color. Moreover, a polygon
is called empty if it does not contain any points of
S in its interior. We show that any bichromatic set of
n ≥ 5044 points in R2 in general position determines
at least one empty, monochromatic quadrilateral (and
thus linearly many).Postprint (published version
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
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