On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.

A Topological Analysis of the Magnetic Breakout Model for an Eruptive Solar Flare

Maclean, R., Beveridge, C., Longcope, D.W., Brown, D.S. and Priest, E.R., 2005, A topological analysis of the magnetic breakout model for an eruptive solar flare, Proc. Roy. Soc., 461, 2099-2120. Sponsorship: PPARC/STFC

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.

The topological behaviour of 3D null points in the Sun's corona

Brown D. S. and Priest E. R. 2001, The topological behaviour of 3D null points in the Sun's corona, Astronomy and Astrophysics, 367, 339-346

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.

Using incomplete online metric maps for topological exploration with the Gap Navigation Tree

This paper presents a general, global approach to the problem of robot exploration, utilizing a topological data structure to guide an underlying Simultaneous Localization and Mapping (SLAM) process. A Gap Navigation Tree (GNT) is used to motivate global target selection and occluded regions of the environment (called “gaps”) are tracked probabilistically. The process of map construction and the motion of the vehicle alters both the shape and location of these regions. The use of online mapping is shown to reduce the difficulties in implementing the GNT.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

Topological design and modulation strategy for buck-boost three-level inverters

To date, designed topologies for DC-AC inversion with both voltage-buck and boost capabilities are mainly focused on two-level circuitries with extensions to three-level possibilities left nearly unexplored. Contributing to this area of research, this paper presents the design of a number of viable buck-boost three-level inverters that can also support bidirectional power conversion. The proposed front-end circuitry is developed from the Cuk-derived buck-boost two-level inverter, and by using the "alternative phase opposition disposition" (APOD) modulation scheme, the buck-boost three-level inverters can perform distinct five-level line voltage and three-level phase voltage switching by simply controlling the active switches located in the designed voltage boost section of the circuits. As a cost saving option, one active switch can further be removed from the voltage-boost section of the circuits by simply re-routing the gating commands of the remaining switches without influencing the ac output voltage amplitude. To verify the validity of the proposed inverters, Matlab/PLECS simulations were performed before a laboratory prototype was implemented for experimental testing.

Topological design and modulation strategy for buck-boost three-level inverters

To date, designed topologies for DC-AC inversion with both voltage buck and boost capabilities are mainly focused on two-level circuitries with extensions to three-level possibilities left nearly unexplored. Contributing to this area of research, this paper presents the design of a number of viable buck-boost three-level inverters that can also support bidirectional power conversion. The proposed front-end circuitry is developed from the Cuk-derived buck-boost two-level inverter, and by using the ldquoalternative phase opposition dispositionrdquo modulation scheme, the buck-boost three-level inverters can perform distinct five-level line voltage and three-level phase voltage switching by simply controlling the active switches located in the designed voltage boost section of the circuits. As a cost saving option, one active switch can further be removed from the voltage boost section of the circuits by simply rerouting the gating commands of the remaining switches without influencing the AC output voltage amplitude. To verify the validity of the proposed inverters, MATLAB/PLECS simulations were performed before a laboratory prototype was implemented for experimental testing.

An adaptive appearance-based map for long-term topological localization of mobile robots

"This work considers a mobile service robot which uses an appearance-based representation of its workplace as a map, where the current view and the map are used to estimate the current position in the environment. Due to the nature of real-world environments such as houses and offices, where the appearance keeps changing, the internal representation may become out of date after some time. To solve this problem the robot needs to be able to adapt its internal representation continually to the changes in the environment. This paper presents a method for creating an adaptive map for long-term appearance-based localization of a mobile robot using long-term and short-term memory concepts, with omni-directional vision as the external sensor."--publisher website