Spatially-distributed coverage optimization and control with limited-range interactions

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.Comment: 31 pages, some figures left out because of size limits. Complete preprint version available at http://motion.csl.uiuc.ed

Control System Algorithms for Groups of UAVs

The paper deals with the research of control system algorithms for the groups of unmanned aerial vehicles. When UAVs are on mission, it’s suitable to control them using less amount of pilots, and control them as a swarm. Using the ad-hoc communication between the agents, and remote control of one master relatively to the group of slave-type vehicles, this type of system is quite usable for the list of actually necessary tasks. This work describes 4 novel control system algorithms for a group of UAVs

Simulation of public key cryptographic algorithms for groups using Mathematica

RESUMEN: En primer lugar, tratamos el conocido como criptosistema RSA [9], primer criptosistema de los llamados de clave pública y que tiene como base los conocidos grupos RSA, que son grupos de la forma Z(n), para n un número entero positivo y n(n) el número de unidades de Zn. A continuación abordamos el criptosistema de ElGamal [1], construido originalmente sobre el grupo multiplicativo Zn p para p un número primo. Seguidamente, en los capítulos 4, 5 y 6 llevamos a cabo implementaciones del mismo criptosistema de ElGamal, pero sobre otros grupos, tales como un cuerpo nito cualquiera, que es una extensión natural del caso de Z p , el caso no conmutativo de las matrices circulantes y, para analizar, el grupo de puntos de una curva elíptica, grupo este ampliamente usado en la actualidad debido a sus reducidas necesidades de ancho de banda, es decir, de información enviada a través de la red o el medio inalámbrico. En todos y cada uno de los casos tratados en esta memoria se ha hecho una implementación de los métodos matemáticos necesarios para un uso real de los criptosistemas, usando para ello el software Mathematica ABSTRACT: First, we treat the RSA cryptosystem [9], the frst cryptosystem of public key calls and which is based on the known RSA groups, which are groups of the form Z (n), for n a positive integer and (n) the number of units of Zn. Then, we study the ElGamal cryptosystem [1], originally built on the multiplicative group Z p for p a prime number. Next, in Chapters 4, 5 and 6 we carry out implementations of the same ElGamal cryptosystem, but on other groups, such as any unite body, which is a natural extension of the case of Zp , the non-commutative case of the circulating matrices and, nally, the group of points on an elliptic curve, this group is widely used today due to its low bandwidth needs, that is, information sent through the network or wireless medium . In each and every one of the cases treated in this report, an implementation of the mathematical methods necessary for a real use of cryptosystems has been made, using Mathematica software for thi

Blockchain Solutions for Multi-Agent Robotic Systems: Related Work and Open Questions

The possibilities of decentralization and immutability make blockchain probably one of the most breakthrough and promising technological innovations in recent years. This paper presents an overview, analysis, and classification of possible blockchain solutions for practical tasks facing multi-agent robotic systems. The paper discusses blockchain-based applications that demonstrate how distributed ledger can be used to extend the existing number of research platforms and libraries for multi-agent robotic systems.Comment: 5 pages, FRUCT-2019 conference pape

Algorithms for group isomorphism via group extensions and cohomology

The isomorphism problem for finite groups of order n (GpI) has long been known to be solvable in $n^{\log n+O(1)}$ time, but only recently were polynomial-time algorithms designed for several interesting group classes. Inspired by recent progress, we revisit the strategy for GpI via the extension theory of groups. The extension theory describes how a normal subgroup N is related to G/N via G, and this naturally leads to a divide-and-conquer strategy that splits GpI into two subproblems: one regarding group actions on other groups, and one regarding group cohomology. When the normal subgroup N is abelian, this strategy is well-known. Our first contribution is to extend this strategy to handle the case when N is not necessarily abelian. This allows us to provide a unified explanation of all recent polynomial-time algorithms for special group classes. Guided by this strategy, to make further progress on GpI, we consider central-radical groups, proposed in Babai et al. (SODA 2011): the class of groups such that G mod its center has no abelian normal subgroups. This class is a natural extension of the group class considered by Babai et al. (ICALP 2012), namely those groups with no abelian normal subgroups. Following the above strategy, we solve GpI in $n^{O(\log \log n)}$ time for central-radical groups, and in polynomial time for several prominent subclasses of central-radical groups. We also solve GpI in $n^{O(\log\log n)}$ time for groups whose solvable normal subgroups are elementary abelian but not necessarily central. As far as we are aware, this is the first time there have been worst-case guarantees on a $n^{o(\log n)}$-time algorithm that tackles both aspects of GpI---actions and cohomology---simultaneously.Comment: 54 pages + 14-page appendix. Significantly improved presentation, with some new result

A new problem in string searching

We describe a substring search problem that arises in group presentation simplification processes. We suggest a two-level searching model: skip and match levels. We give two timestamp algorithms which skip searching parts of the text where there are no matches at all and prove their correctness. At the match level, we consider Harrison signature, Karp-Rabin fingerprint, Bloom filter and automata based matching algorithms and present experimental performance figures.Comment: To appear in Proceedings Fifth Annual International Symposium on Algorithms and Computation (ISAAC'94), Lecture Notes in Computer Scienc

CONTROL ALGORITHMS FOR GROUPS OF KINEMATIC UNICYCLE AND SKID-STEERING MOBILE ROBOTS WITH RESTRICTED INPUTS

Abstract. The paper presents analytical and practical studies concerning the control problems of a group of Wheeled Mobile Robots (WMRs) subject to physical constraints. Firstly, controllers for achieving trajectory tracking for kinematic unicycle-like and skidsteering mobile robots with restricted control inputs are established. Next, the underlying tracking controllers are applied for group control under the condition of actuator constraints. In particular we are developing control strategies for establishing rigid and convoy-like formations for vehicles with bounded inputs. The group control approach is based on the concepts of virtual robot and virtual formation. The proposed controllers employ smooth bounded functions that can easily be realized. The performance of the resulting controllers are demonstrated by means of numerical and simulation results

Multidimensional Cooley–Tukey Algorithms Revisited

AbstractThe representation theory of Abelian groups is used to obtain an algebraic divide-and-conquer algorithm for computing the finite Fourier transform. The algorithm computes the Fourier transform of a finite Abelian group in terms of the Fourier transforms of an arbitrary subgroup and its quotient. From this algebraic algorithm a procedure is derived for obtaining concrete factorizations of the Fourier transform matrix in terms of smaller Fourier transform matrices, diagonal multiplications, and permutations. For cyclic groups this gives as special cases the Cooley–Tukey and Good–Thomas algorithms. For groups with several generators, the procedure gives a variety of multidimensional Cooley–Tukey type algorithms. This method of designing multidimensional fast Fourier transform algorithms gives different data flow patterns from the standard “row–column” approaches. We present some experimental evidence that suggests that in hierarchical memory environments these data flows are more efficient