5,035 research outputs found
A survey on fractional order control techniques for unmanned aerial and ground vehicles
In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade
BeSpaceD: Towards a Tool Framework and Methodology for the Specification and Verification of Spatial Behavior of Distributed Software Component Systems
In this report, we present work towards a framework for modeling and checking
behavior of spatially distributed component systems. Design goals of our
framework are the ability to model spatial behavior in a component oriented,
simple and intuitive way, the possibility to automatically analyse and verify
systems and integration possibilities with other modeling and verification
tools. We present examples and the verification steps necessary to prove
properties such as range coverage or the absence of collisions between
components and technical details
alphaCertified: certifying solutions to polynomial systems
Smale's alpha-theory uses estimates related to the convergence of Newton's
method to give criteria implying that Newton iterations will converge
quadratically to solutions to a square polynomial system. The program
alphaCertified implements algorithms based on alpha-theory to certify solutions
to polynomial systems using both exact rational arithmetic and arbitrary
precision floating point arithmetic. It also implements an algorithm to certify
whether a given point corresponds to a real solution to a real polynomial
system, as well as algorithms to heuristically validate solutions to
overdetermined systems. Examples are presented to demonstrate the algorithms.Comment: 21 page
On the determination of cusp points of 3-R\underline{P}R parallel manipulators
This paper investigates the cuspidal configurations of 3-RPR parallel
manipulators that may appear on their singular surfaces in the joint space.
Cusp points play an important role in the kinematic behavior of parallel
manipulators since they make possible a non-singular change of assembly mode.
In previous works, the cusp points were calculated in sections of the joint
space by solving a 24th-degree polynomial without any proof that this
polynomial was the only one that gives all solutions. The purpose of this study
is to propose a rigorous methodology to determine the cusp points of
3-R\underline{P}R manipulators and to certify that all cusp points are found.
This methodology uses the notion of discriminant varieties and resorts to
Gr\"obner bases for the solutions of systems of equations
Enumerative Real Algebraic Geometry
Enumerative Geometry is concerned with the number of solutions to a
structured system of polynomial equations, when the structure comes from
geometry. Enumerative real algebraic geometry studies real solutions to such
systems, particularly a priori information on their number. Recent results in
this area have, often as not, uncovered new and unexpected phenomena, and it is
far from clear what to expect in general. Nevertheless, some themes are
emerging.
This comprehensive article describe the current state of knowledge,
indicating these themes, and suggests lines of future research. In particular,
it compares the state of knowledge in Enumerative Real Algebraic Geometry with
what is known about real solutions to systems of sparse polynomials.Comment: Revised, corrected version. 40 pages, 18 color .eps figures. Expanded
web-based version at http://www.math.umass.edu/~sottile/pages/ERAG/index.htm
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