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Considering attitude-only measurements, physical limitations of actuator and state-independent observer time, a distributed velocity-free attitude coordination control problem for multiple formation spacecraft with torque saturation is studied in this work. Initially, aiming at speeding up the convergence rate and realizing the maximum value of the convergence time without requiring prior knowledge of the initial system state values, a fixed-time observer is constructed to estimate the desired time-varying states in fixed time. Then, a filter system is developed for the spacecraft with attitude-only measurements. With the application of the fixed-time observers and the filter systems, a distributed velocity-free attitude coordination controller with torque constraint is designed to grantee that the leader with desired state trajectory can be tracked coordinately by the formation spacecraft. Finally, the performance of the proposed controller is demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

The hyper-chaotic strange attractor of systems of four Chua's circuits that are mutually coupled by three strong and three weak couplings is studied, both experimentally and via simulation. A new metric to compare strange attractors is presented. It is found that the strength of the couplings between circuits have a complex and determining influence on the probability for the presence of a trajectory within their attractors. This influence is strictly local, i.e. the probability of the presence of the trajectories is determined by the coupling strength to the directly adjacent circuits and independent of the coupling strengths among other circuits. Fluctuations in the properties of Chua's circuits due to random fluctuations during the production of its components have a significant influence on the probability of presence of the attractor's trajectories that could be qualitatively, but not quantitatively, modeled by our simulation. The consequences of these results for the possibility to construct 'physical unclonable functions' as networks of Chua's circuits with a hyper-chaotic dynamics are discussed. [ABSTRACT FROM AUTHOR]

Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes two control strategies for the motion synchronization of the master-slave manipulators based on their ender trajectories. First, the basic equations used by the two control methods for motion synchronization are presented. Such procedures are proved to be stable for negative definite gain matrices, according to the Lyapunov theory. Then, the controlled items of the slave manipulator are determined for the ender trajectory synchronization by the coordinate transformations between the joint variables and the ender trajectory in the form of pseudo-Jacobian matrix. Finally, the two control methods for synchronization are validated by the numerical simulation for a master-slave system consisting of two planar three-degree-of-freedom (3-DOF) manipulators. [ABSTRACT FROM AUTHOR]

A novel method is proposed to achieve robust and real-time ball tracking in broadcast soccer videos. In sports video, the soccer ball is small, often occluded, and with high motion speed. Thus, it is difficult to detect the sole ball in a single frame. To solve this problem, rather than locate the ball in one of several frames through detection or tracking, we find the ball through optimizing its motion trajectory in successive frames. The proposed method includes three level processes: object level, intra-trajectory level, and inter-trajectory level processing. In object level, multiple objects instead of a single ball are detected and all of them are taken as ball candidates through shape and color features identification. Then at intra-trajectory level, each ball candidate is tracked by a Kalman filter and verified by detection in successive frames, which results in lots of initial short trajectories in a video shot. These trajectories are thereafter scored and filtered according to their length and spatial-temporal relationship in a time-line model. With these trajectories, we construct a distance graph, in which a node represents a trajectory, and an edge means distance between two trajectories. We then get the optimal path using the Dijkstra algorithm in the graph at the inter-trajectory level. The optimal path is composed by a sequence of initial trajectories which make the whole route smooth and long in duration. To get a complete and reasonable path, we finally apply cubic spline interpolation to bridge the gap between adjacent trajectories (the duration corresponding to when the ball is occluded). We select three representative real FIFA2006 soccer video clips (containing a total of 16,500 frames) and manually elaborately labeling each frame in it, and take it as ground-truth to evaluate the algorithm. The average F-score is 80.59%. The algorithm was used in our soccer analysis system and tested on a wide range of real soccer videos, and all the results are satisfied. The algorithm is effective and its whole speed far exceeds real-time, 35.6 fps on mpeg2 data on the Intel Conroe platform. [ABSTRACT FROM AUTHOR]

An interesting phenomenon in billiards was found. If the midpoints of every segment of a straight line in trajectory of a billiard were taken, they will form an interesting diagram which we call midpoint diagram. After research on several kinds of billiards, it was discovered that midpoint diagram which is made up of several discrete points corresponds to the periodic behavior of the billiard, and the midpoint diagram made up of lines corresponds to quasi-periodic behavior, while the midpoint diagram made up of large numbers of dispersion points corresponds to chaotic behavior. The midpoint diagram can be used to describe the dynamical behavior of billiards. [ABSTRACT FROM AUTHOR]

In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ∊ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ∊ to analyze experimental data by means of RPs. [ABSTRACT FROM AUTHOR]

Coded structured light is an active approach that obtains the shape of object. In our previous work, we proposed a new binary projection mechanism for inspecting semiconductor products. The mechanism consists of only a single light source in combination with a binary grating for projecting binary pattern. By shifting the binary grating in space and in every shifting taking a separate image of the illuminated surface, each position on the illuminated surface is attached with a unique binary string for correspondence. In the mechanism the inspection speed is governed by the number of needed images which also equals to the number of shiftings of the grating. To reduce image number, we propose that two neighbor bits are combined together to produce unique codeword, which is referred to as bit-pairing mechanism. This paper addresses how the spatial shifting of bit-pairing mechanism can be designed optimally for minimizing this number for faster inspection speed. An optimal solution to shifting strategy optimization is proposed that is applicable to any given binary patterns. Theoretical analysis and real image experiments are presented to illustrate the workability of the solutions. [ABSTRACT FROM AUTHOR]

This paper is an attempt to give new results, by a computer-assisted study, on some global bifurcations that change the structure of the domain of feasible trajectories (bounded discrete trajectories having an ecological sense) which can be obtained by the union of all rank preimages of axes. Three two-dimensional recurrence equations (or maps) are analyzed. The two first maps are degenerated invertible maps (i.e. the inverses of them are well defined except a set of zero lebergue measure) for which the basins of attractor are obtained by the backward iteration of a stable manifold of a saddle fixed point belonging to the basin boundary, and the interior domains of feasible trajectories are given by the intersection between the basin of attractor and the first quadrant. The other is a noninvertible map which is investigated by the use of critical curves, a powerful tool for the analysis of global properties of two-dimensional maps. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a continuous extension of the Ott, Grehogi and Yorke control method [Ott et al., 1990]. This extension allows the control of chaotic behavior in higher-order dynamical systems. To begin with, studying the so-called Poincaré Sections (PS) enables determining fixed points and the effect of small changes in the control Parameter on the system trajectory. Introduction of a stabilizer parameter in the control law keeps the dynamical properties and maintains them on a cyclic trajectory. The effectiveness of the proposed method is tested by numerical examples on the two typical Chen and Chua chaotic systems. [ABSTRACT FROM AUTHOR]

In this paper, the complex dynamical behaviors of the chaotic trajectories of Chen's system are analyzed in detail, with its precise bound derived for the first time. In particular, it is rigorously proved that all nontrivial trajectories of the system always travel alternatively through two specific Poincaré projections for infinitely many times. The results provide an insightful understanding of the complex topological structure of Chen's chaotic attractor. [ABSTRACT FROM AUTHOR]

In this paper we proposed an unsupervised neural architecture, called Temporal Parametrized Self Organizing Map (TEPSOM), capable of learning and reproducing complex robot trajectories and interpolating new states between the learned ones. The TEPSOM combines the Self-Organizing NARX (SONARX) network, responsible for coding the temporal associations of the robotic trajectory, with the Parametrized Self-Organizing (PSOM) network, responsible for an efficient interpolation mechanism acting on the SONARX neurons. The TEPSOM network is used to model the inverse kinematics of the PUMA 560 robot during the execution of trajectories with repeated states. Simulation results show that the TEPSOM is more accurate than the SONARX in the reproduction of the learned trajectories. [ABSTRACT FROM AUTHOR]

To generate strange nonchaotic attractor in quasiperiodically driven systems, there must be an unstable region in its phase-space. In this paper, a theoretical analysis shows that the quasiperiodic force acts as noise to lead the trajectory running into different expanding orbits when the trajectory repeatedly runs into the unstable region. Thus the resulting attractor is strange. The local-phase Lyapunov exponent is introduced for the study of low-frequency quasiperiodically driven systems. It is shown that the local-phase Lyapunov exponents can be approximated by the exponents of autonomous systems. The statistical properties of SNA system driven by low-frequency quasiperiodic force can then be approached by a set of autonomous systems. [ABSTRACT FROM AUTHOR]

In this paper we show that unbounded chaotic trajectories are easily observed in the iteration of maps which are not defined everywhere, due to the presence of a denominator which vanishes in a zero-measure set. Through simple examples, obtained by the iteration of one-dimensional and two-dimensional maps with denominator, the basic mechanisms which are at the basis of the existence of unbounded chaotic trajectories are explained. Moreover, new kinds of contact bifurcations, which mark the transition from bounded to unbounded sets of attraction, are studied both through the examples and by general theoretical methods. Some of the maps studied in this paper have been obtained by a method based on the Schröder functional equation, which allows one to write closed analytical expressions of the unbounded chaotic trajectories, in terms of elementary functions. [ABSTRACT FROM AUTHOR]

Existing neural network models are capable of tracking linear trajectories of moving visual objects. This paper describes an additional neural mechanism, disfacilitation, that enhances the ability of a visual system to track curved trajectories. The added mechanism combines information about an object's trajectory with information about changes in the object's trajectory, to improve the estimates for the object's next probable location. Computational simulations are presented that show how the neural mechanism can learn to track the speed of objects and how the network operates to predict the trajectories of accelerating and decelerating objects. [ABSTRACT FROM AUTHOR]