Cooperative Pursuit with Multi-Pursuer and One Faster Free-moving Evader

This paper addresses a multi-pursuer single-evader pursuit-evasion game where the free-moving evader moves faster than the pursuers. Most of the existing works impose constraints on the faster evader such as limited moving area and moving direction. When the faster evader is allowed to move freely without any constraint, the main issues are how to form an encirclement to trap the evader into the capture domain, how to balance between forming an encirclement and approaching the faster evader, and what conditions make the capture possible. In this paper, a distributed pursuit algorithm is proposed to enable pursuers to form an encirclement and approach the faster evader. An algorithm that balances between forming an encirclement and approaching the faster evader is proposed. Moreover, sufficient capture conditions are derived based on the initial spatial distribution and the speed ratios of the pursuers and the evader. Simulation and experimental results on ground robots validate the effectiveness and practicability of the proposed method

Graph Optimization Approach to Range-based Localization

In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization. Range and trajectory smoothness constraints are constructed in a position graph, then the robot trajectory over a sliding window is estimated by a graph based optimization algorithm. Moreover, convergence analysis of the algorithm is provided, and the effects of the number of iterations and window size in the optimization on the localization accuracy are analyzed. Extensive experiments on quadcopter under a variety of scenarios verify the effectiveness of the proposed algorithm and demonstrate a much higher localization accuracy than the existing range-based localization methods, especially in the altitude direction

The Tur\'an number of special linear forest and star-path forest

The Tur\'an number of a graph $F$, denoted $ex(n, F)$, is the maximum number of edges in an $F$-free graph on $n$ vertices. Let $P_{\ell}$, $S_{\ell}$ denote the path and star on $\ell$ vertices, respectively. A linear forest is a forest whose connected components are paths. In 2013, Lidick\'y et al. considered the Tur\'an number of linear forest and $k_1P_4 \bigcup k_2 S_3$ for sufficiently large $n$. Recently, Fang and Yuan determine the Tur\'an numbers of $P_{\ell} \bigcup kS_{\ell-1}$, $k_1P_{2\ell} \bigcup k_2 S_{2\ell-1}$, $2P_5 \bigcup kS_4$ for $n$ appropriately large and characterized the corresponding extremal graphs. In this paper, We determine $ex(n, P_9 \bigcup P_7)$ for all $n\geq 16$ and characterize all extremal graphs, which partially confirms a conjecture proposed by Yuan and Zhang [L.T. Yuan, X.D. Zhang, J. Graph. Theory 98(3) (2021) 499--524]. And we determine the Tur\'an numbers of $\bigcup\limits _{i=1}^{k_1} P_{\ell _i} \bigcup\limits _{j=1}^{k_2} S_{a _j}$ for $n$ appropriately large, where $a_j\leq 2k_2+2 \sum\limits_{i=1}^{k_1} \lfloor\frac{\ell_i}{2}\rfloor-2j$ for any $j\in [k_2]$, which generalizes the results of Fang and Yuan. The corresponding extremal graphs are also completely characterizedComment: arXiv admin note: substantial text overlap with arXiv:1711.07734 by other author

Integrated Relative-Measurement-Based Network Localization and Formation Maneuver Control (Extended Version)

This paper studies the problem of integrated distributed network localization and formation maneuver control. We develop an integrated relative-measurement-based scheme, which only uses relative positions, distances, bearings, angles, ratio-of-distances, or their combination to achieve distributed network localization and formation maneuver control in $\mathbb{R}^d (d \ge 2)$. By exploring the localizability and invariance of the target formation, the scale, rotation, and translation of the formation can be controlled simultaneously by only tuning the leaders' positions, i.e., the followers do not need to know parameters of the scale, rotation, and translation of the target formation. The proposed method can globally drive the formation errors to zero in finite time over multi-layer $d\!+\!1$-rooted graphs. A simulation example is given to illustrate the theoretical results.Comment: 12 pages; 7 figures, title corrected, DOI adde

Rayleigh wave tomography in North-China from ambient seismic noise

2008/2009The theory and methodology of ambient noise tomography has been studied and applied to North-China successfully. Continuous vertical-component seismograms, spanning the period from January 1, 2007 to February 28, 2008 recorded by 190 broadband stations and 10 very broadband stations, have been used. The cross correlation technique has been applied to ambient noise data recorded by North-China Seismic Array for each station pairs of the array. Rayleigh wave group velocity dispersion curves are measured at periods between 4 s and 40 s by multiple filter technique. We obtain 5630 high quality dispersion curves. Surface wave tomography is conducted to generate group velocity maps with a grid spacing of 0.25º×0.25º. These maps display higher resolution and extend to shorter periods than previous surface wave tomography maps. Then genetic algorithm is used to invert pure path dispersion curves. The 3-D shear wave velocity structure from 0 to 50 km depth is readily constructed. To the authors' knowledge, the resolution presented here is, so far, the highest one in China mainland. The original results of this thesis are: 1, The SNR of Green Function is proportional to the square root of observation time and can be enhanced by using the symmetric component. The inhomogeneous distribution of seismic noise gives rise to the asymmetry of Green Function. Using more than one year's data, one can get more symmetric and higher SNR Green Function. 2, The characteristics of ambient seismic noise are different for different period bands. In 4-10 s, a coherent phase with large amplitude near zero lag time is observed. In 10-20 s, the sources of ambient seismic noise have a very clear seasonal variability. The azimuthal distributions of noise share a great similarity with the map of average ocean wave height map obtained by TOPEX-Poseidon. In 20-50s range, Rayleigh wave Green Functions are almost symmetrical and show less seasonal variation in both signal strength and directivity, which indicates that the distribution of noise is - ii - almost homogeneous. In 4-20s range, the amplitudes of positive and negative components of Green Functions are obviously asymmetrical, but the arrival times are almost identical, indicating that the distribution of noise has much influence on the amplitude of Green Function, but less influence on arrival time. 3, Tomographic maps at short periods reveal an evident lateral heterogeneity in the curst of North-China, quite well in agreement with known geological and tectonic features. The North China Basin is imaged as a broad low velocity area, while the Taihangshan and Yanshan uplifts and Ordos block are imaged as high velocity zones, and the Quaternary intermountain basins show up as small low-velocity anomalies. 4, The 3-D S-wave crustal velocity model in North China shows a distinct low velocity belt with NW trend at 10 km of depth near Zhangjiakou-Bohai seismic zone. This low velocity belt and the southern margin of Yanshan high velocity anomaly draw the outline of Zhangjiakou-Bohai seismic zone and its northern border line. There is a well-defined low velocity zone in middle-to-lower crust (15-25 km) in the Beijing-Tianjin-Tangshan region, which may be caused by intrusion of hot mantle materials. 5, We analyzed the seismogenic structure near Tangshan，Luanxian and Ninghe earthquake region. We infer that these three earthquakes are mainly caused by vertical deformation of upper mantle and material exchange between crust and upper mantle. The magma intrudes the crust along faults near the boundary of crust and upper mantle, which leads to the low velocity anomaly in the uppermost mantle. The magma intrusion heats up the lower crustal material and drops its viscosity. Some minerals are dehydrated. The water moves up and is trapped in the middle crust. The existence of liquid affects the structure and composition of the fault zone, further changes the stress state, weakens the seismotectonic region and triggers the earthquakes.XXI Ciclo198

Regular graphs with a complete bipartite graph as a star complement

Let $G$ be a graph of order $n$ and $\mu$ be an adjacency eigenvalue of $G$ with multiplicity $k\geq 1$. A star complement $H$ for $\mu$ in $G$ is an induced subgraph of $G$ of order $n-k$ with no eigenvalue $\mu$, and the vertex subset $X=V(G-H)$ is called a star set for $\mu$ in $G$. The study of star complements and star sets provides a strong link between graph structure and linear algebra. In this paper, we study the regular graphs with $K_{t,s}\ (s\geq t\geq 2)$as a star complement for an eigenvalue$\mu$, especially, characterize the case of$t=3$completely, obtain some properties when$t=s$, and propose some problems for further study