Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.

Integrable Hamiltonian systems defined on the Lie groups SO(3) and SU(2): an application to the attitude control of a spacecraft

This paper considers left-invariant control systems defined on the Lie groups SU(2) and SO(3). Such systems have a number of applications in both classical and quantum control problems. The purpose of this paper is two-fold. Firstly, the optimal control problem for a system varying on these Lie Groups, with cost that is quadratic in control is lifted to their Hamiltonian vector fields through the Maximum principle of optimal control and explicitly solved. Secondly, the control systems are integrated down to the level of the group to give the solutions for the optimal paths corresponding to the optimal controls. In addition it is shown here that integrating these equations on the Lie algebra su(2) gives simpler solutions than when these are integrated on the Lie algebra so(3).

Oriented vehicles travelling in spherical space

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3. For such problem, the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems defined on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are defined explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.

3D path planning with novel multiple 2D layered approach for complex human-robot interaction

Navigating cluttered indoor environments is a difficult problem in indoor service robotics. The Acroboter concept, a novel approach to indoor locomotion, represents unique opportunity to avoid obstacles in indoor environments by navigating the ceiling plane. This mode of locomotion requires the ability to accurately detect obstacles, and plan 3D trajectories through the environment. This paper presents the development of a resilient object tracking system, as well as a novel approach to generating 3D paths suitable for such robot configurations. Distributed human-machine interfacing allowing simulation previewing of actions is also considered in the developed system architecture.

Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

The locally twisted cubes

This paper introduces a new variant of the popular n-dimensional hypercube network Q(n), known as the n-dimensional locally twisted cube LTQ(n), which has the same number of nodes and the same number of connections per node as Q(n). Furthermore. LTQ(n) is similar to Q(n) in the sense that the nodes can be one-to-one labeled with 0-1 binary sequences of length n. so that the labels of any two adjacent nodes differ in at most two successive bits. One advantage of LTQ(n) is that the diameter is only about half of the diameter of Q(n) We develop a simple routing algorithm for LTQ(n), which creates a shortest path from the source to the destination in O(n) time. We find that LTQ(n) consists of two disjoint copies of Q(n) by adding a matching between their nodes. On this basis. we show that LTQ(n) has a connectivity of n.

Actors and objects: A socio-technical networks approach for construction management research

We explore the contribution of socio-technical networks approaches to construction management research. These approaches are distinctive for their analysis of actors and objects as mutually constituted within socio-technical networks. They raise questions about the ways in which the content, meaning and use of technology is negotiated in practice, how particular technical configurations are elaborated in response to specific problems and why certain paths or solutions are adopted rather than others. We illustrate this general approach with three case studies: a historical study of the development of reinforced concrete in France, the UK and the US, the recent introduction of 3D-CAD software into four firms and an analysis of the uptake of environmental assessment technologies in the UK since 1990. In each we draw out the ways in which various technologies shaped and were shaped by different socio-technical networks. We conclude with a reflection on the contributions of socio-technical network analysis for more general issues including the study of innovation and analyses of context and power.

Correlation between regioselectivity and site charge in propene polymerisation catalysed by metallocene

The reactions of propene with [Zr(cyclopentadienyl)(2)Me](+) have been investigated using density functional theory in order to study the correlation between regioselectivity and site charge in propene polymerisation. The reaction paths of the 1,2 and 2,1 additions of the methyl group to propene have been established. The geometries and energies of the reactants, transition states and products have been obtained using both PBEPBE/LANL2DZ and B3LYP/LANL2DZ methodologies. The results with both density functionals show that the activation energy for 1,2-insertion is lower than that for 2,1-insertion (Fig. 5) and this is consistent with the experiment results. Also for both density functionals, the difference of the thermal dynamic driving forces between the 2,1 product named 2-21 and the 1,2 product named 2-12 is significantly lower than the difference between the energy barriers. It is noted that in the reactants, the Mulliken partial charge on the central carbon atom C2 is positive and it can be concluded that 1,2-insertion is favoured because it can proceed via a cationic reaction.

Effect of wheat dwarfing genes on nitrogen-use efficiency

Near isogenic lines (NILs) varying for alleles for reduced height (Rht) and photoperiod insensitivity (Ppd-D1a) in a cvar Mercia background (rht (tall), Rht-B1b, Rht-D1b, Rht-B1c, Rht8c+Ppd-D1a, Rht-D1c, Rht12) were compared at a field site in Berkshire, UK, but within different systems (‘organic’, O, in 2005/06, 2006/07 and 2007/08 growing seasons v. ‘conventional’, C, in 2005/06, 2006/07, 2007/08 and 2008/09). In 2007 and 2008, further NILs (rht (tall), Rht-B1b, Rht-D1b, Rht-B1c, Rht-B1b+Rht-D1b, Rht-D1b+Rht-B1c) in both Maris Huntsman and Maris Widgeon backgrounds were added. The contrasting systems allowed NILs to be tested in diverse rotational and agronomic, but commercially relevant, contexts, particularly with regard to the assumed temporal distribution of nitrogen availability, and competition from weeds. For grain, nitrogen-use efficiency (NUE; grain dry matter (DM) yield/available N; where available N=fertilizer N+soil mineral N), recovery of N in the grain (grain N yield/available N), N utilization efficiency to produce grain (NUtEg; grain DM yield/above-ground crop N yield), N harvest index (grain N yield/above-ground crop N yield) and dry matter harvest index (DMHI; grain DM yield/above-ground crop DM yield) all peaked at final crop heights of 800–950 mm. Maximum NUE occurred at greater crop heights in the organic system than in the conventional system, such that even adding just a semi-dwarfing allele (Rht-D1b) to the shortest background, Mercia, reduced NUE in the organic system. The mechanism of dwarfing (gibberellin sensitive or insensitive) made little difference to the relationship between NUE and its components with crop height. For above-ground biomass: dwarfing alleles had a greater effect on DM accumulation compared with N accumulation such that all dwarfing alleles could reduce nitrogen utilization efficiency (NUtE; crop DM yield/crop N yield). This was particularly evident at anthesis in the conventional system when there was no significant penalty for severe dwarfism for N accumulation, despite a 3-tonne (t)/ha reduction in biomass compared to the tallest lines. Differences between genotypes for recovery of N in the grain were thus mostly a function of net N uptake after anthesis rather than of remobilized N. This effect was compounded as dwarfing, except when coupled with Ppd-D1a, was associated with delayed anthesis. In the organic experiments there was greater reliance on N accumulated before anthesis, and genotype effects on NUE were confounded with effects on N accumulated by weeds, which was negatively associated with crop height. Optimum height for maximizing wheat NUE and its components, as manipulated by Rht alleles, thus depend on growing system, and crop utilization (i.e. biomass or grain production).

Application of a hybrid tracking algorithm to motion analysis

An algorithm for tracking multiple feature positions in a dynamic image sequence is presented. This is achieved using a combination of two trajectory-based methods, with the resulting hybrid algorithm exhibiting the advantages of both. An optimizing exchange algorithm is described which enables short feature paths to be tracked without prior knowledge of the motion being studied. The resulting partial trajectories are then used to initialize a fast predictor algorithm which is capable of rapidly tracking multiple feature paths. As this predictor algorithm becomes tuned to the feature positions being tracked, it is shown how the location of occluded or poorly detected features can be predicted. The results of applying this tracking algorithm to data obtained from real-world scenes are then presented.

Configurational preferences of two 1,2-diamine adducts of bis(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)cobalt(II)

The preparation, the IR and ligand field spectra and the structures of the mixed-ligand addition compounds [(N,N-dimethyl-1,2-diaminoethane)bis(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)cobalt(II)], [Co(thtf)2me2en], and [(N,N,N′,N′-tetramethyl-1,2-diaminoethane)bis(1-(2-thienyl)-4,4,4-trifluoro-1,3-butanedionato)cobalt(II)], [Co(thtf)2me4en], are reported. The structures were determined by single crystal X-ray diffraction analysis (monoclinic, space group P21/c, Z=4 with a=10.708(6), b=19.531(6), c=13.352(6) Å, β=111.64(10)°, R1=0.0642 and wR2=0.1719 for [Co(thtf)2(me2en)] and a=12.033(6), b=15.565(6), c=15.339(6) Å, β=92.57(6)°, R1=0.0612 and wR2=0.1504 for [Co(thtf)2me4en]). The structures are distorted octahedral and the shortest cobalt–cobalt separation distances are 5.388(2) Å in [Co(thtf)2me2en] and 8.675(3) Å in [Co(thtf)2me4en]. In both compounds the diamine molecules attain the gauche conformation. The U(Z,Z) conformation of the β-dione leads to a semi-chair conformation of the β-dionato chelate rings. The relative orientation of the groups attached to the β-dionato moiety depends on the extent of stereoelectronic effects the N-substitution of the diamine entails. In [Co(thtf)2me2en] the intraligand distance separating the trifluoromethyl carbon atoms is 5.281(18) Å while in [Co(thtf)2me2en] it increases to 8.338(9) Å. The cobalt–cobalt separation distance, the orientation of the chelate rings and the extent of N-substitution seem to affect hydrogen bonding. While in [Co(thtf)2me2en] inter- and intraligand hydrogen bonding is implicated, it is totally absent in [Co(thtf)2me4en].

Cloud statistics and cloud radiative effect for a low-mountain site

In 2007, the Atmospheric Radiation Measurement (ARM) Mobile Facility (AMF) was operated for a nine-month period in the Murg Valley, Black Forest, Germany, in support of the Convective and Orographically-induced Precipitation Study (COPS). The synergy of AMF and COPS partner instrumentation was exploited to derive a set of high-quality thermodynamic and cloud property profiles with 30 s resolution. In total, clouds were present 72% of the time, with multi-layer mixed phase (28.4%) and single-layer water clouds (11.3%) occurring most frequently. A comparison with the Cloudnet sites Chilbolton and Lindenberg for the same time period revealed that the Murg Valley exhibits lower liquid water paths (LWPs; median = 37.5 g m−2) compared to the two sites located in flat terrain. In order to evaluate the derived thermodynamic and cloud property profiles, a radiative closure study was performed with independent surface radiation measurements. In clear sky, average differences between calculated and observed surface fluxes are less than 2% and 4% for the short wave and long wave part, respectively. In cloudy situations, differences between simulated and observed fluxes, particularly in the short wave part, are much larger, but most of these can be related to broken cloud situations. The daytime cloud radiative effect (CRE), i.e. the difference of cloudy and clear-sky net fluxes, has been analysed for the whole nine-month period. For overcast, single-layer water clouds, sensitivity studies revealed that the CRE uncertainty is likewise determined by uncertainties in liquid water content and effective radius. For low LWP clouds, CRE uncertainty is dominated by LWP uncertainty; therefore refined retrievals, such as using infrared and/or higher microwave frequencies, are needed.

Connectivity measures for internet topologies on the level of autonomous systems

Classical measures of network connectivity are the number of disjoint paths between a pair of nodes and the size of a minimum cut. For standard graphs, these measures can be computed efficiently using network flow techniques. However, in the Internet on the level of autonomous systems (ASs), referred to as AS-level Internet, routing policies impose restrictions on the paths that traffic can take in the network. These restrictions can be captured by the valley-free path model, which assumes a special directed graph model in which edge types represent relationships between ASs. We consider the adaptation of the classical connectivity measures to the valley-free path model, where it is -hard to compute them. Our first main contribution consists of presenting algorithms for the computation of disjoint paths, and minimum cuts, in the valley-free path model. These algorithms are useful for ASs that want to evaluate different options for selecting upstream providers to improve the robustness of their connection to the Internet. Our second main contribution is an experimental evaluation of our algorithms on four types of directed graph models of the AS-level Internet produced by different inference algorithms. Most importantly, the evaluation shows that our algorithms are able to compute optimal solutions to instances of realistic size of the connectivity problems in the valley-free path model in reasonable time. Furthermore, our experimental results provide information about the characteristics of the directed graph models of the AS-level Internet produced by different inference algorithms. It turns out that (i) we can quantify the difference between the undirected AS-level topology and the directed graph models with respect to fundamental connectivity measures, and (ii) the different inference algorithms yield topologies that are similar with respect to connectivity and are different with respect to the types of paths that exist between pairs of ASs.

Performance analysis of data transmissions in MPLS and non-MPLS networks

Basic Network transactions specifies that datagram from source to destination is routed through numerous routers and paths depending on the available free and uncongested paths which results in the transmission route being too long, thus incurring greater delay, jitter, congestion and reduced throughput. One of the major problems of packet switched networks is the cell delay variation or jitter. This cell delay variation is due to the queuing delay depending on the applied loading conditions. The effect of delay, jitter accumulation due to the number of nodes along transmission routes and dropped packets adds further complexity to multimedia traffic because there is no guarantee that each traffic stream will be delivered according to its own jitter constraints therefore there is the need to analyze the effects of jitter. IP routers enable a single path for the transmission of all packets. On the other hand, Multi-Protocol Label Switching (MPLS) allows separation of packet forwarding and routing characteristics to enable packets to use the appropriate routes and also optimize and control the behavior of transmission paths. Thus correcting some of the shortfalls associated with IP routing. Therefore MPLS has been utilized in the analysis for effective transmission through the various networks. This paper analyzes the effect of delay, congestion, interference, jitter and packet loss in the transmission of signals from source to destination. In effect the impact of link failures, repair paths in the various physical topologies namely bus, star, mesh and hybrid topologies are all analyzed based on standard network conditions.