Topological objects in the O(3) nonlinear sigma model

We study the topological defects in the nonlinear O(3) sigma model in terms of the decomposition of U(1) gauge potential. Time-dependent baby skyrmions are discussed in the (2 + 1)-dimensional spacetime with the CP1 field. Furthermore, we show that there are three kinds of topological defects-vortex lines, point defects and knot exist in the (3 + 1)-dimensional model, and their topological charges, locations and motions are determined by the phi-mapping topological current theory.

Solitons with isospin

We study the symmetries of the soliton spectrum of a pair of T-dual integrable models, invariant under global SL(2)(q) circle times U(1) transformations. They represent an integrable perturbation of the reduced Gepner parafermions, based on certain gauged SL(3)-WZW model. Their (semiclassical) topological soliton solutions, carrying isospin and belonging to the root of unity representations of q-deformed SU(2)(q)-algebra are obtained. We derive the semiclassical particle spectrum of these models, which is further used to prove their T-duality properties. (c) 2005 Elsevier B.V All rights reserved.

Noether and topological currents equivalence and soliton/particle correspondence in affine sl(2)((1)) Toda theory coupled to matter

A submodel of the so-called conformal affine Toda model coupled to the matter field (CATM) is defined such that its real Lagrangian has a positive-definite kinetic term for the Toda field and a usual kinetic term for the (Dirac) spinor field. After spontaneously broken the conformal symmetry by means of BRST analysis, we end up with an effective theory, the off-critical affine Toda model coupled to the matter (ATM). It is shown that the ATM model inherits the remarkable properties of the general CATM model such as the soliton solutions, the particle/soliton correspondence and the equivalence between the Noether and topological currents. The classical solitonic spectrum of the ATM model is also discussed. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Topological solitons in the CPN model

We investigate the solitons in the CPN supercript stop model in terms of the decomposition of gauge potential. Based on the phi-mapping topological current theory, the charge and position of solitons is determined by the properties of the typical component. Furthermore, the motion and the bifurcation of multi-soliton is discussed. And the knotted solitons in high dimension is explored also.

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using phi-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a 6 function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of phi-mapping. In our solution, the flux of this soliton is naturally quantized.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Electrically charged topological solitons

Two new families of T-dual integrable models of dyonic type are constructed. They represent specific A(n)((1)) singular non-abelian affine Toda models having U(1) global symmetry. Their I-soliton spectrum contains both neutral and U(I)-charged topological solitons sharing the main properties of 4-dimensional Yang-Mills-Higgs monopoles and dyons. The semiclassical quantization of these solutions as well as the exact counterterms and the coupling constant renormalization are studied. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields

We consider an integrable conformally invariant two-dimensional model associated to the affine Kac-Moody algebra sl3(ℂ). It possesses four scalar fields and six Dirac spinors. The theory does not possesses a local Lagrangian since the spinor equations of motion present interaction terms which are bilinear in the spinors. There exists a submodel presenting an equivalence between a U(1) vector current and a topological current, which leads to a confinement of the spinors inside the solitons. We calculate the one-soliton and two-soliton solutions using a procedure which is a hybrid of the dressing and Hirota methods. The soliton masses and time delays due to the soliton interactions are also calculated. We give a computer program to calculate the soliton solutions. © 2002 Published by Elsevier Science B.V.

Soliton spectrum of integrable models with local symmetries

The soliton spectrum (massive and massless) of a family of integrable models with local U(1) and U(1) ⊗U(1) symmetries is studied. These models represent relevant integrable deformations of SL(2,ℝ) ⊗U(1) n-1-WZW and SL(2,ℝ) ⊗ SL(2,ℝ) ⊗U(1) n-2-WZW models. Their massless solitons appear as specific topological solutions of the U(1)(or U(1) ⊗ U(1)-) CFTs. The nonconformal analog of the GKO-coset formula is derived and used in the construction of the composite massive solitons of the ungauged integrable models. © SISSA/ISAS 2002.

Topological SLAM Using Fast Vision Techniques

In this paper we propose a method for vision only topological simultaneous localisation and mapping (SLAM). Our approach does not use motion or odometric information but a sequence of colour histograms from visited places. In particular, we address the perceptual aliasing problem which occurs using external observations only in topological navigation. We propose a Bayesian inference method to incrementally build a topological map by inferring spatial relations from the sequence of observations while simultaneously estimating the robot's location. The algorithm aims to build a small map which is consistent with local adjacency information extracted from the sequence measurements. Local adjacency information is incorporated to disambiguate places which otherwise would appear to be the same. Experiments in an indoor environment show that the proposed technique is capable of dealing with perceptual aliasing using visual observations only and successfully performs topological SLAM.

Topological SLAM using neighbourhood information of places

Perceptual aliasing makes topological navigation a difficult task. In this paper we present a general approach for topological SLAM~(simultaneous localisation and mapping) which does not require motion or odometry information but only a sequence of noisy measurements from visited places. We propose a particle filtering technique for topological SLAM which relies on a method for disambiguating places which appear indistinguishable using neighbourhood information extracted from the sequence of observations. The algorithm aims to induce a small topological map which is consistent with the observations and simultaneously estimate the location of the robot. The proposed approach is evaluated using a data set of sonar measurements from an indoor environment which contains several similar places. It is demonstrated that our approach is capable of dealing with severe ambiguities and, and that it infers a small map in terms of vertices which is consistent with the sequence of observations.

A multi-hypothesis topological SLAM approach for loop closing on edge-ordered graphs

We present a method for topological SLAM that specifically targets loop closing for edge-ordered graphs. Instead of using a heuristic approach to accept or reject loop closing, we propose a probabilistically grounded multi-hypothesis technique that relies on the incremental construction of a map/state hypothesis tree. Loop closing is introduced automatically within the tree expansion, and likely hypotheses are chosen based on their posterior probability after a sequence of sensor measurements. Careful pruning of the hypothesis tree keeps the growing number of hypotheses under control and a recursive formulation reduces storage and computational costs. Experiments are used to validate the approach.

Vision-based topological mapping and localisation

Competent navigation in an environment is a major requirement for an autonomous mobile robot to accomplish its mission. Nowadays, many successful systems for navigating a mobile robot use an internal map which represents the environment in a detailed geometric manner. However, building, maintaining and using such environment maps for navigation is difficult because of perceptual aliasing and measurement noise. Moreover, geometric maps require the processing of huge amounts of data which is computationally expensive. This thesis addresses the problem of vision-based topological mapping and localisation for mobile robot navigation. Topological maps are concise and graphical representations of environments that are scalable and amenable to symbolic manipulation. Thus, they are well-suited for basic robot navigation applications, and also provide a representational basis for the procedural and semantic information needed for higher-level robotic tasks. In order to make vision-based topological navigation suitable for inexpensive mobile robots for the mass market we propose to characterise key places of the environment based on their visual appearance through colour histograms. The approach for representing places using visual appearance is based on the fact that colour histograms change slowly as the field of vision sweeps the scene when a robot moves through an environment. Hence, a place represents a region of the environment rather than a single position. We demonstrate in experiments using an indoor data set, that a topological map in which places are characterised using visual appearance augmented with metric clues provides sufficient information to perform continuous metric localisation which is robust to the kidnapped robot problem. Many topological mapping methods build a topological map by clustering visual observations to places. However, due to perceptual aliasing observations from different places may be mapped to the same place representative in the topological map. A main contribution of this thesis is a novel approach for dealing with the perceptual aliasing problem in topological mapping. We propose to incorporate neighbourhood relations for disambiguating places which otherwise are indistinguishable. We present a constraint based stochastic local search method which integrates the approach for place disambiguation in order to induce a topological map. Experiments show that the proposed method is capable of mapping environments with a high degree of perceptual aliasing, and that a small map is found quickly. Moreover, the method of using neighbourhood information for place disambiguation is integrated into a framework for topological off-line simultaneous localisation and mapping which does not require an initial categorisation of visual observations. Experiments on an indoor data set demonstrate the suitability of our method to reliably localise the robot while building a topological map.

Topological map induction using neighbourhood information of places

In topological mapping, perceptual aliasing can cause different places to appear indistinguishable to the robot. In case of severely corrupted or non-available odometry information, topological mapping is difficult as the robot is challenged with the loop-closing problem; that is to determine whether it has visited a particular place before. In this article we propose to use neighbourhood information to disambiguate otherwise indistinguishable places. Using neighbourhood information for place disambiguation is an approach that neither depends on a specific choice of sensors nor requires geometric information such as odometry. Local neighbourhood information is extracted from a sequence of observations of visited places. In experiments using either sonar or visual observations from an indoor environment the benefits of using neighbourhood clues for the disambiguation of otherwise identical vertices are demonstrated. Over 90% of the maps we obtain are isomorphic with the ground truth. The choice of the robot’s sensors does not impact the results of the experiments much.