Path Topology Research Articles

Topology, Oxidation States, and Charge Transport in Ionic Conductors

AbstractRecent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge‐invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday's picture of ionic transport—whereby each atom carries a well‐defined integer charge—with a rigorous quantum description of the electronic charge‐density distribution, which hardly suggests its partition into well defined atomic contributions. In this paper, these progresses are reviewed; in particular, it is shown how, by relaxing some general topological conditions, charge may be transported in ionic conductors without any net ionic displacements. After reporting numerical experiments which corroborate these findings, a new connection between the topological picture and the well‐known Marcus–Hush theory of electron transfer is introduced in terms of the topology of adiabatic paths drawn by atomic trajectories. As a significant byproduct, the results reviewed here permit to classify different regimes of ionic transport according to the topological properties of the electronic structure of the conducting material. Finally, a few recent applications to energy materials and planetary sciences are reported.

UAV-Supported Route Planning for UGVs in Semi-Deterministic Agricultural Environments

Automated agricultural operations must be planned and organized to reduce risk and failure potential while optimizing productivity and efficiency. However, the diversity of natural outdoor environments and the varied data types and volumes required to represent an agricultural setting comprise critical challenges for the deployment of fully automated agricultural operations. In this regard, this study develops an integrated system for enabling an unmanned aerial vehicle (UAV) supported route planning system for unmanned ground vehicles (UGVs) in the semi-structured environment of orchards. The research focus is on the underpinning planning system components (i.e., world representation or map generation or perception and path planning). In particular, the system comprises a digital platform that receives as input a geotagged depiction of an orchard, which is obtained by a UAV. The pre-processed data define the agri-field’s tracks that are transformed into a grid-based map capturing accessible areas. The grid map is then used to generate a topological path planning solution. Subsequently, the solution is translated into a sequence of coordinates that define the calculated optimal path for the UGV to traverse. The applicability of the developed system was validated in routing scenarios in a walnuts’ orchard using a UGV. The contribution of the proposed system entails noise reduction techniques for the accurate representation of a semi-deterministic agricultural environment for enabling accuracy in the route planning of utilized automated machinery.

Concurrent optimization of topological configuration and continuous fiber path for composite structures — A unified level set approach

This study proposes a novel topology optimization approach for design of continuous steering fiber path for composite structures using a level set method. The radial basis function (RBF) is employed to construct the level set function (LSF). Fiber orientations are parameterized by LSF and fiber paths can be determined instinctively for the inherent advantages of the level set approach. Besides, the fast-marching method is employed to extrapolate the primary fiber paths to the secondary fiber paths, which can avoid the manufacturing drawbacks such as gaps and overlaps to a large extent. A detection and filtering technique is proposed here to alleviate the orientation disorder at the intersection of the diffusion surfaces. Two design schemes are developed to optimize both structural topology and fiber path. In a sequential procedure, topology optimization is conducted first with isotropic materials; and then fiber paths are optimized on the basis of fixed topological boundary. In a simultaneous optimization procedure, structural boundaries and fiber paths are optimized alternately through two inner loops. In this study, three numerical examples are presented to demonstrate the effectiveness of the proposed methods, and the results show that optimization of fiber path is beneficial to improvement of structural performance. In general, the simultaneous optimization scheme exhibits better optimal outcome in comparison with the sequential optimization scheme.

Learning Minimum-Time Flight in Cluttered Environments

We tackle the problem of minimum-time flight for a quadrotor through a sequence of waypoints in the presence of obstacles while exploiting the full quadrotor dynamics. Early works relied on simplified dynamics or polynomial trajectory representations that did not exploit the full actuator potential of the quadrotor, and, thus, resulted in suboptimal solutions. Recent works can plan minimum-time trajectories; yet, the trajectories are executed with control methods that do not account for obstacles. Thus, a successful execution of such trajectories is prone to errors due to model mismatch and in-flight disturbances. To this end, we leverage deep reinforcement learning and classical topological path planning to train robust neural-network controllers for minimum-time quadrotor flight in cluttered environments. The resulting neural network controller demonstrates substantially better performance of up to 19% over state-of-the-art methods. More importantly, the learned policy solves the planning and control problem simultaneously online to account for disturbances, thus achieving much higher robustness. As such, the presented method achieves 100% success rate of flying minimum-time policies without collision, while traditional planning and control approaches achieve only 40%. The proposed method is validated in both simulation and the real world, with quadrotor speeds of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$42 \,\mathrm{k}\mathrm{m}\mathrm{h}^{-1}$</tex-math></inline-formula> and accelerations of 3.6 g.

Simultaneous topology and fiber path optimization of composite structures with MAC constraints

The pursuit of stiffer lightweight structures has led to the development of new concepts such as the Variable Stiffness Composite Laminates (VSCL), which further enhance the design potential of these highly tailored materials. As the number of design variables rise, more robust topology optimization formulations are necessary to achieve optimal solutions. In this work, a design optimization framework is developed by assigning material and fiber orientation on discrete patches of the VSCL structures. A gradient-based optimization method is used in the framework by applying the Discrete Material Optimization (DMO) formulation. The main goal is to design structures to meet dynamic performance objectives, with particular emphasis on the synthesis of modes with a target design. Accordingly, the objective function depends on the eigenvalues (natural frequencies), while one set of constraints depends on the eigenvectors (mode shapes). The Modal Assurance Criterion (MAC) is simultaneously used to perform mode tracking between the different design iterations and to evaluate the correlation between the synthetized modes and the pre-defined objective shapes. In this study, the calculation of the weight derivatives is also revised for the DMO formulation to show the contribution of the missing terms in the final optimal results. The optimization framework is examined for some potential applications related to dynamic decoupling and dynamic synthesis. It is shown that the design approach tailors the dynamic response of the composite structure and it can effectively be used to design resonators based on a reference model.

Minimum-Time Quadrotor Waypoint Flight in Cluttered Environments

We tackle the problem of planning a minimum-time trajectory for a quadrotor over a sequence of specified waypoints in the presence of obstacles while exploiting the full quadrotor dynamics. This problem is crucial for autonomous search and rescue and drone racing scenarios but was, so far, unaddressed by the robotics community <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in its entirety</i> due to the challenges of minimizing time in the presence of the non-convex constraints posed by collision avoidance. Early works relied on simplified dynamics or polynomial trajectory representations that did not exploit the full actuator potential of a quadrotor and, thus, did not aim at minimizing time. We address this challenging problem by using a hierarchical, sampling-based method with an incrementally more complex quadrotor model. Our method first finds paths in different topologies to guide subsequent trajectory search for a kinodynamic point-mass model. Then, it uses an asymptotically-optimal, kinodynamic sampling-based method based on a full quadrotor model on top of the point-mass solution to find a feasible trajectory with a time-optimal objective. The proposed method is shown to outperform all related baselines in cluttered environments and is further validated in real-world flights at over 60 km/h in one of the world’s largest motion capture systems. We release the code open source.

Structural topology optimization and path planning for composites manufactured by fiber placement technologies

Fiber reinforced polymers (FRP) suit superbly for lightweight applications. Enormous lightweight potential is launched in combination with fiber placement technologies and topology optimization – both providing high design flexibility and high material efficiency. But FRP show specific material characteristics, such as mechanical anisotropy. Fiber placement processes are also limited to certain designs. Both aspects must be taken into account during topology optimization. Furthermore, a strategy is required to transfer the topology optimization results into fiber placement paths. This paper presents a corresponding workflow that combines existing as well as newly developed methods: The anisotropic material properties are factored by the topology optimization algorithm, which simultaneously optimizes the parts shape and local fiber orientation. Puck’s failure criteria for FRP is evaluated throughout topology optimization for reducing weight while maintaining the parts ability to withstand the specified loads. A dilate sensitivity filter restricts the minimum feature width of the final structure to account for fiber bundle widths, and avoids non-manufacturable undercuts transverse to the placement plane. Finally, a methodology consisting of clustering and a streamline algorithm is utilized to generate manufacturing tolerant fiber placement paths.

Valley-protected topological interface state of the elastic wave: From discrete model to multistable mechanical metamaterials

Topological metamaterials provide a new strategy to guide wave energy and exhibit unprecedented robustness. In this study, a novel design strategy is proposed to realize programmable topological metamaterials with local resonant eigenstates. Firstly, in the discrete spring-mass model, two resonant masses and two base masses are introduced into the hexagonal lattice, and a local resonant eigenstate-induced Dirac cone can be formed at the high symmetry point of the Brillouin zone. By introducing the spring stiffness difference, a topological bandgap is opened near the Dirac degeneracy frequency. Thereafter, the nontrivial nature of the bandgap is verified by the theoretical evaluation of the Berry curvature and Chern number. Secondly, the symmetry-breaking configuration is extended to a continuum plate-resonator model. The numerical results demonstrate that the interface state wave propagates along the interface path at a frequency located at the edge-bulk band. Finally, by using the asymmetric effective stiffness of the bistable structure between tension and compression, a programmable topological interface path is realized. The proposed reconfigurable design based on asymmetry significantly expands the design space of metamaterials.

Object-Based Reliable Visual Navigation for Mobile Robot.

Visual navigation is of vital importance for autonomous mobile robots. Most existing practical perception-aware based visual navigation methods generally require prior-constructed precise metric maps, and learning-based methods rely on large training to improve their generality. To improve the reliability of visual navigation, in this paper, we propose a novel object-level topological visual navigation method. Firstly, a lightweight object-level topological semantic map is constructed to release the dependence on the precise metric map, where the semantic associations between objects are stored via graph memory and topological organization is performed. Then, we propose an object-based heuristic graph search method to select the global topological path with the optimal and shortest characteristics. Furthermore, to reduce the global cumulative error, a global path segmentation strategy is proposed to divide the global topological path on the basis of active visual perception and object guidance. Finally, to achieve adaptive smooth trajectory generation, a Bernstein polynomial-based smooth trajectory refinement method is proposed by transforming trajectory generation into a nonlinear planning problem, achieving smooth multi-segment continuous navigation. Experimental results demonstrate the feasibility and efficiency of our method on both simulation and real-world scenarios. The proposed method also obtains better navigation success rate (SR) and success weighted by inverse path length (SPL) than the state-of-the-art methods.

Functional limit theorems for Volterra processes and applications to homogenization* *Johann Gehringer is supported by an EPSRC studentship, Xue-Mei Li by the EPRSC grants EP/V026100/1 and EP/S023925/1, and Julian Sieber by the EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation (EP/S023925/1).

We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process in the rough path topology. As an application, we establish weak convergence as ɛ → 0 of the solution of the random ordinary differential equation (ODE) and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the Lévy area correction of the limiting rough driver. Furthermore, we prove that the stochastic flows of the random ODE converge to those of the Kunita type Itô SDE dx t = G(x t , dt), where G(x, t) is a semi-martingale with spatial parameters.

Quantitative Investigation of Halogen and Hydrogen Bonding in 2‐Chloro, 4‐X‐Benzoic Acids

AbstractThe crystal structure, Hirshfeldsurface analysis, topological analysis of the electron density and total interaction energies of four compounds, 2‐Chloro, 4‐X‐Benzoic Acids (where X=I, Br, Cl and F) have been analysed. The packing similarity was evaluated in all compounds using theXPacanalysis. The qualitative information about intermolecular interactions is derived from the crystal structure and Hirshfeld surface analyses whereas quantitative information are determined by the QTAIM analysis as well as total interaction energies fromCrystalExplorer. The topological properties are estimated for all compounds in both crystal geometry and gas phase usingTOPONDandAIMALL, respectively. The carboxylic acid O−H⋅⋅⋅O HB dimers, C−H⋅⋅⋅O HBs and Cπ⋅⋅⋅Cπaromatic stacking interactions are found to be common interactions in all compounds. The topological properties and bond paths demonstrate them as non‐covalent stabilizing interactions in the crystalline state. The hierarchy of interactions concerning their strength is observed in the following order such that O−H⋅⋅⋅O HB dimers&gt;Cπ⋅⋅⋅Cπaromatic stacking interactions&gt;C−H⋅⋅⋅O HBs&gt;Type II X⋅⋅⋅Cl interactions and C−H⋅⋅⋅Cl HBs&gt;Type I homo‐halogen X⋅⋅⋅X interactions in all compounds. Additionally, the strength of Type I homo‐halogen X⋅⋅⋅X interactions vary in the order: I⋅⋅⋅I&gt;Br⋅⋅⋅Br&gt;Cl⋅⋅⋅Cl&gt;F⋅⋅⋅F. The hierarchy of interactions is further supported by molecular electrostatic potential surfaces associated with both positive and negative potential regions.

Design of efficient location‐based multipath self‐adaptive balancer router using particle swarm optimization in wireless sensor network

SummaryThe power sensor terminals control in wireless sensor network (WSN) communicate within a small number of its radio range. As a branch operating based on the cluster routing protocol, it has proven to be effective in network topology management, energy reduction, and path connection link quality of the path. Location‐based clusters are categorized into member nodes and group/cluster heads (CHs). The CH election process increases the overhead of the network. The processing and energy limitations of the nodes are considered for the CH election process. The allocation of system resources is the major issue in the area of networks. In this work, the proposed multipath self‐adaptive balancer routing‐based particle swarm optimization (MLBAR‐PSO) achieves load balancing by means of the link quality of the route and the calculated average latency and reliability of the path. In this way, different trust values are set in each category. The forwarding node value is the value of each node based on the weight value, which is calculated based on the energy ratio of the node and the distance between the hiding node and the target node. Particle swarm optimization (PSO) selects the head cluster from a specific location within the cluster to enable other nodes to interact with the CH without spending energy. Also, the algorithm is used to find the optimal path for the base station and significantly increases the energy to reduce the distance and delay over the lifetime of the network.

Study on the Construction and Development Path of Gymnasiums considering Ecological Environment Restrictions.

Under the restriction of ecological and environmental factors, our requirements have improved for the development path of gymnasium construction. According to the previous way to carry out the development path of gymnasium construction will make our construction work encounter a lot of unnecessary troubles, so we can improve the success rate of the development path of gymnasium construction under the constraints of the ecological environment by carrying out relevant evasive operations according to the constraints of ecological environment. The topological path and path algorithm used to improve the efficiency of stadium construction and development path under the constraints of ecological environment, TEG algorithm, Q-TEG model, Q-TEG algorithm, Dtra algorithm, TraD algorithm, ResR algorithm, and Q-TED algorithm used in resource reservation plus time slot plus hosting bring the following advantages: (1) we use topological path and path algorithm to explore topological representation methods suitable for development path. The overview provides a theoretical basis for guidance, for forwarding technology scheduling mechanisms and multi-path forwarding mechanisms to provide higher flexibility. (2) We use the TEG algorithm of resource reservation plus time slot plus trusteeship, Q-TEG model, and Q-TEG algorithm under multi-model model can deal with the capacity and link of queue in each stadium construction development path well. It is more convenient to set the packet loss threshold for the propagation experiment tested in the simulation. Better help gymnasium construction and development path transmission is successful. (3) The use of the Dtra algorithm, TraD algorithm, ResR algorithm, and Q-TED algorithm in our stadium construction development path of a good deal of the transmission link structure between each node, so that the transmission efficiency between nodes becomes higher, making our stadium construction development path operation more efficient and convenient.

Formation of the quasi-planar B56 boron cluster: topological path from B12 and disk aromaticity.

Formation and stability of the B56 boron cluster were investigated using a topological approach and the disk aromaticity model. An extensive global energy minimum search for the B56 system which was carried out by means of the Mexican Enhanced Genetic Algorithm (MEGA) in conjunction with density functional theory computations, confirms a quasi-planar structure as its energetically most stable isomer. Such a structural motif is derived by applying a topological leapfrog operation to a B12 form. Its high thermodynamic stability can be explained by the disk aromaticity model in which the delocalization of its π orbitals can be assigned to the levels of a particle in a circular box with the [(1σ)2 (1π)4 (1δ)4 (1φ)4 (2σ)2 (1γ)4 (2π)4 (2δ)4 (1η)4 (2φ)4 (1θ)2] electronic configuration. This π delocalization is confirmed by other delocalization indices. While the B56 has a similar electron delocalization to that of the quasi-planar B50, they have opposite magnetic ring current properties because of the symmetry selection rules of their HOMO-LUMO electronic transitions. The π delocalization in the boron clusters is larger at long distances as compared to carbon clusters at similar sizes, but such a trend is reversed at shorter distances.

Freezing Unicast Paths in Sensor Swarms

Drone swarms have great potential to convey sensor information. However, a swarm may have a very high degree of topology dynamics. This impedes the sensor data distribution from the sensor node to consumers which are external to the swarm. A high sensor data rate requires reliable and efficient forwarding between the sensor and the consumer. This often makes unicast the preferred data forwarding method. But routing protocols struggle to achieve stable paths in high-mobile topologies. This makes unicast forwarding without suffering substantial packet loss very difficult. In this paper, we investigate how the swarm nodes can help to provide a stable path for the duration of a sensor data transfer. Stability is achieved by freezing the positions of the swarm nodes for the duration of the unicast flow. We investigate three different mechanisms to trigger this freeze, where two are based on the Ad-hoc On-demand Distance Vector (AODV) routing protocol. The results are very promising, with throughput for one flow remaining stable at almost 100% with 20 m/s swarm mobility, compared to the baseline results of 82% throughput. The results also indicate that even swarms without reactive routing may benefit from the freeze method to provide stable unicast paths as required.

PlaceRAN: optimal placement of virtualized network functions in Beyond 5G radio access networks

The fifth-generation mobile evolution introduces Next-Generation Radio Access Networks (NG-RAN), splitting the RAN protocol stack into the eight disaggregated options combined into three network units, i.e., Central, Distributed, and Radio. The disaggregated units reach full interoperability on Open RAN. Further advances allow the RAN software to be virtualized (vNG-RAN) on top of general-purpose hardware, enabling the management of disaggregated units and protocols as radio functions. The placement of these functions is challenging since the best decision must be based on multiple constraints, e.g., the RAN protocol stack split, routing paths in network topologies with restricted bandwidth and latency, asymmetric computational resources, etc. The literature does not deal with general placement problems with high functional split options and protocol stack analysis. This article proposes the first exact model for positioning radio functions for vNG-RAN planning, named PlaceRAN, as a Binary Integer Linear Programming (BILP) problem. The objective is to minimize the computing resources and maximize the aggregation of radio functions. The evaluation considered two realistic network topologies, and the results reveal that PlaceRAN achieves an optimized high-performance aggregation level. It is flexible for RAN deployment overcoming the network restrictions, and up to date with the most advanced vNG-RAN design and development.

RAPTOR: Robust and Perception-Aware Trajectory Replanning for Quadrotor Fast Flight

Recent advances in trajectory replanning have enabled quadrotor to navigate autonomously in unknown environments. However, high-speed navigation still remains a significant challenge. Given very limited time, existing methods have no strong guarantee on the feasibility or quality of the solutions. Moreover, most methods do not consider environment perception, which is the key bottleneck to fast flight. In this article, we present RAPTOR, a robust and perception-aware replanning framework to support fast and safe flight, which addresses these issues systematically. A path-guided optimization approach that incorporates multiple topological paths is devised, to ensure finding feasible and high-quality trajectories in very limited time. We also introduce two perception-aware planning approaches to actively observe and avoid unknown obstacles. A risk-aware trajectory refinement ensures that unknown obstacles which may endanger the quadrotor can be observed earlier and avoid in time. The motion of yaw angle is planned to actively explore the surrounding space that is relevant for safe navigation. The proposed methods are tested extensively through benchmark comparisons and challenging indoor and outdoor aggressive flights. We release our implementation as an open-source package <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> for the community.

Growing Neural Gas Based Topological Environmental Map Building and Path Planning in Unknown Environment

Growing Neural Gas Based Topological Environmental Map Building and Path Planning in Unknown Environment

The Ponzano–Regge cylinder and propagator for 3d quantum gravity

We investigate the propagator of 3d quantum gravity, formulated as a discrete topological path integral. We define it as the Ponzano–Regge amplitude of the solid cylinder swept by a 2d disk evolving in time. Quantum states for a 2d disk live in the tensor products of N spins, where N is the number of holonomy insertions connecting to the disk boundary. We formulate the cylindric amplitude in terms of a transfer matrix and identify its eigen-modes in terms of spin recoupling. We show that the propagator distinguishes subspaces with different total recoupled spin. This may select the vanishing overall spin sector at late time depending on the chosen cylinder boundary data, leading to an emergent symmetry scenario in the continuum limit. We discuss applications to quantum circuits and the possibility of experimental simulations of this 3d quantum gravity propagator.

Extracting 3D Indoor Maps with Any Shape Accurately Using Building Information Modeling Data

Indoor maps lay the foundation for most indoor location-based services (LBS). Building Information Modeling (BIM) data contains multiple dimensional computer-aided design information. Some studies have utilized BIM data to automatically extract 3D indoor maps. A complete 3D indoor map consists of both floor-level maps and cross-floor paths. Currently, the floor-level indoor maps are mainly either grid-based maps or topological maps, and the cross-floor path generation schemes are not adaptive to building elements with irregular 3D shapes. To address these issues, this study proposes a novel scheme to extract an accurate 3D indoor map with any shape using BIM data. Firstly, this study extracts grid-based maps from BIM data and generates the topological maps directly through the grid-based maps using image thinning. A novel hybrid indoor map, termed Grid-Topological map, is then formed by the grid-based maps and topological maps jointly. Secondly, this study obtains the cross-floor paths from cross-floor building elements by a four-step process, namely X-Z projection, boundary extraction, X-Z topological path generation, and path-BIM intersection. Finally, experiments on eight typical types of cross-floor building elements and three multi-floor real-world buildings were conducted to prove the effectiveness of the proposed scheme, the average accuracy rates of the evaluated paths are higher than 88%. This study will advance the 3D indoor maps generation and inspire the application of indoor maps in indoor LBS, indoor robots, and 3D geographic information systems.