Since existing results about fixed-time stabilization are only applied to strict feedback systems, this paper investigates the nonsingular fixed-time stabilization of more general high-order nonlinear systems. Based on a novel concept named coordinate mapping of time domain, a control method is first proposed to transform the nonsingular fixed-time convergence problem into the finite-time convergence problem of a transformed time-varying system. By extending the existing, adding a power integrator technique into the considered time-varying system, a periodic controller is constructed to stabilize the original system in fixed time. The results of simulations verify the effectiveness of the proposed method.
The purpose of this research was to achieve visual simulation of circular weft-knitted transfer-jacquard fabric based on a computer-aided design platform. The corresponding mathematical models were established according to pattern presentations after analyzing the structural characteristics of this kind of stitch. To determine the spatial geometry of the loops, eight-point models were built, especially the introduced multi-course loop model. By comparing the influence of four usual lights on stereoscopic sense, directional light was selected to establish an illumination model. Based on these models and matrix operations, spatial positions of different loop types in the intermesh structure were confirmed by coordinate mapping. The simulation effects of three important parameters of yarn spline rendering were analyzed and discussed, so as to choose the most reasonable data. Integrated with a transfer-jacquard design program, the approach realized three-dimensional structural simulation of circular knitting transfer-jacquard fabric with a naturalistic visual impression which can shorten the proofing process and even inspire the design potential of developers.
Fisheye images with a far larger Field of View (FOV) have severe radial distortion, with the result that the associated image feature matching process cannot achieve the best performance if the traditional feature descriptors are used. To address this challenge, this paper reports a novel distorted Binary Robust Independent Elementary Feature (BRIEF) descriptor for fisheye images based on a spherical perspective model. Firstly, the 3D gray centroid of feature points is designed, and the position and direction of the feature points on the spherical image are described by a constructed feature point attitude matrix. Then, based on the attitude matrix of feature points, the coordinate mapping relationship between the BRIEF descriptor template and the fisheye image is established to realize the computation associated with the distorted BRIEF descriptor. Four experiments are provided to test and verify the invariance and matching performance of the proposed descriptor for a fisheye image. The experimental results show that the proposed descriptor works well for distortion invariance and can significantly improve the matching performance in fisheye images.
This chapter examines imperial initiatives in mapping space, registering people, and ordering knowledge. The author draws a distinction between the mapping practices of pre-modern or tributary empires and those of early modern and modern imperial formations. In the latter case, authority was increasingly derived from the production and accumulation of knowledge via scientific techniques that relied on abstraction and quantification, whether at home or abroad. The author shows that modern imperial practices based on measurement were not limited to the West, but were also employed in the Ottoman Empire, Qing China, and parts of Mughal India. The chapter’s focus is the emergence of coordinate mapping as a tool of imperial expansion and control from the Renaissance through the mid-twentieth century. Similar techniques of legibility and quantification were applied to registering people and ordering knowledge. James C. Scott’s work on legibility in modern state building is foundational to this chapter.
A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.
This paper proposes a method for obtaining driver’s fixation points and establishing a preview model based on actual vehicle tests. Firstly, eight drivers were recruited to carry out the actual vehicle test on the actual straight and curved roads. The curvature radii of test curved roads were selected to be 200, 800, and 1500 m. Subjects were required to drive at a speed of 50, 70 and 90 km/h, respectively. During the driving process, eye movement data of drivers were collected using a head-mounted eye tracker, and road front scene images and vehicle statuses were collected simultaneously. An image-world coordinate mapping model of the visual information of drivers was constructed by performing an image distortion correction and matching the images from the driving recorder. Then, fixation point data for drivers were accordingly obtained using the Identification-Deviation Threshold (I-DT) algorithm. In addition, the Jarque–Bera test was used to verify the normal distribution characteristics of these data and to fit the distribution parameters of the normal function. Furthermore, the preview points were extracted accordingly and projected into the world coordinate. At last, the preview data obtained under these conditions are fit to build general preview time probability density maps for different driving speeds and road curvatures. This study extracts the preview characteristics of drivers through actual vehicle tests, which provides a visual behavior reference for the humanized vehicle control of an intelligent vehicle.