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Human locomotion was investigated in a goal-oriented task where subjects had to walk to and through a doorway starting from a fixed position and orientation in space. The door was located at different positions and orientations in space, resulting in a total of 40 targets. While no specific constraint was provided to subjects in terms of the path they were to follow or the expected walking speeds, all of them generated very similar trajectories in terms of both path geometry and velocity profiles. These results are reminiscent of the stereotyped properties of the hand trajectories observed in arm reaching movements in studies over the last 20 years. This observation supports the hypothesis that common constraining mechanisms govern the generation of segmental and whole-body trajectories. In contrast, we observed that the subjects placed their feet at different spatial positions across repetitions, making unlikely the hypothesis that goal-oriented locomotion is planned as a succession of steps. Rather, our results suggest that common planning and/or control strategies underlie the formation of the whole locomotor trajectory during a spatially oriented task. [ABSTRACT FROM AUTHOR]

Despite the theoretically infinite number of possible trajectories a human may take to reach a distant doorway, we observed that locomotor trajectories corresponding to this task were actually stereotyped, both at the geometric and the kinematic levels. In this paper, we propose a computational model for the formation of human locomotor trajectories. Our model is adapted from smoothness maximization models that have been studied in the context of hand trajectory generation. The trajectories predicted by our model are very similar to the experimentally recorded ones. We discuss the theoretical implications of this result in the context of movement planning and control in humans. In particular, this result supports the hypothesis that common principles, such as smoothness maximization, may govern the generation of very different types of movements (in this case, hand movements and whole-body movements). [ABSTRACT FROM AUTHOR]

A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated. [ABSTRACT FROM AUTHOR]

This paper proposes a method for gait trajectory generation using an artificial vector field for stable walking for a biped robot. The tip of the robot while walking can often deviate from the desired trajectory as a result of the disturbances forced by unexpected outside factors. In our approach, though no prepared trajectory is specified a priori, the tip follows the artificial vectors designed in the workspace. Moreover, the prediction simulation is performed online. The simulator judges the stability under comparison with the present state and the prediction results, and then the gait parameters are adaptively improved in feedforward for the stable walk. The numerical and physical experimental results show the validity of the proposed method in a continuous walk. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 159(4): 54– 61, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10. 1002/eej. 20547 [ABSTRACT FROM AUTHOR]

Background: Longitudinal pediatric neuroimaging studies have demonstrated increasing volumes of white matter and regionally-specific inverted U shaped developmental trajectories of gray matter volumes during childhood and adolescence. Studies of monozygotic and dyzygotic twins during this developmental period allow exploration of genetic and non-genetic influences on these developmental trajectories. Method: Magnetic resonance imaging brain scans were acquired on a pediatric sample of 90 monozygotic twin pairs, 38 same-sex dyzygotic twin pairs, and 158 unrelated typically developing singletons. Structural equation modeling was used to estimate the additive genetic, common environment, and unique environment effects, as well as age by heritability interactions, on measures of brain volumes from these images. Results: Consistent with previous adult studies, additive genetic effects accounted for a substantial portion of variability in nearly all brain regions with the notable exception of the cerebellum. Significant age by heritability interactions were observed with gray matter volumes showing a reduction in heritability with increasing age, while white matter volume heritability increased with greater age. Conclusion: Understanding the relative contributions of genetic and nongenetic factors on developmental brain trajectories may have implications for better understanding brain-based disorders and typical cognitive development. [ABSTRACT FROM AUTHOR]

A mobile robot must move without unacceptable rapid motion. To address this issue, we propose a preview controller using the time-based spline approach. With this approach, it is also important to plan an adequate trajectory. Here an approach to trajectory planning which has the trajectory determination strategy via a virtual manipulator is proposed. Numerical and experimental results are shown to confirm the proposed algorithm. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(4): 65–71, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10349 [ABSTRACT FROM AUTHOR]

1. In this paper a new formulation of the self-thinning law for plant populations is presented, based on dynamical principles. The basis of the new approach is explicitly to separate the equation of state (total = mean × number) from the change in state (δtotal = mean × δnumber + number × δmean). 2. Using the dynamical approach, an analytical expression for the self-thinning exponent is derived which shows that the self-thinning exponent follows a trajectory, but whenever the total is constant the self-thinning exponent must, by definition, = -1. Conversely, whenever the total varies the self-thinning exponent must, by definition, differ from -1. The underlying general principles of self-thinning trajectories are deduced. 3. The new dynamic interpretations are general because they are independent of the details about how the changes in the number and mean occurred. 4. The theory is demonstrated using a typical self-thinning experiment. [ABSTRACT FROM AUTHOR]

Focuses on the flight performance of birds. Reduction in the angle of the flight trajectory in moulting birds; Technique used to elevate flight costs in parent birds feeding young; Comparison between velocity and pre-moult conditions.

Recent interest in continuity of care has meant that the illness trajectory experienced by intensive care unit (ICU) patients has received more attention. Using continuous quality improvement as a framework, this paper describes information obtained during a 3-year period relating to ICU patients' long-term experiences after being discharged from hospital. This information identified that most participants had been discharged home but that many experienced problems with mobility, disability and fatigue. Changes in employment status and the need for financial assistance were noted. As a result of the information provided by this activity, clinical practice has changed and a number of formal research studies have been undertaken. [ABSTRACT FROM AUTHOR]

Studies the social trajectories and the evolution of social behavior. Components of the social decisions; Emphasis on the mathematical modeling of the evolution and maintenance of the social system; Types of evolutionary shifts in a trajectory.

In the vicinity of the critical point of chaos as the accumulation point of period doubling bifurcations, the characteristic index is closely related to the bifurcation structure. Chaos is a typical nonlinear system, and hence its trajectory cannot be accurately reconstructed. However, qualitative evaluation is possible for the index that characterizes the vicinity of the critical point by a linear approximation model. In this paper, the lagged regression threshold model is used to quantitatively understand the characteristics of chaos, such as the Lyapunov index and the characteristic index. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(5): 1–9, 1999 [ABSTRACT FROM AUTHOR]

In conventional global optimization techniques, such as the trajectory method, the usual procedure is to start the trajectory from an initial point and try an optimization. In contrast, this paper proposes a model in which the trajectories are started in parallel from multiple initial points, and global optimization is achieved by providing interactions among the trajectories. It is shown by calculating the Lyapunov index that the trajectory becomes chaotic in a conservative system unless annealing is applied. It is shown by performance evaluation for numerical examples that the globally optimal solution is always obtained by increasing the number of trajectories in the proposed model. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(3): 40–48, 1999 [ABSTRACT FROM AUTHOR]

A boundary element procedure is developed concerning the prediction of the quasistatic crack growth in uniformly heated bimaterials. This procedure assumes the existence of an initial small crack in one of the two phases, and further cracking progress from this point due to thermal loading. The resulting mixed boundary value problem is solved by applying an incremental boundary-only method in conjunction with the multidomain technique. Fracture characterizing parameters are evaluated utilizing special crack tip singular elements and appropriate formulas. The crack path is predicted using the strain energy release rate criterion, and the mesh is updated at the end of each increment. The presented results are in good agreement with previously reported experimental results and those obtained by the finite element method. Various numerical studies were conducted and interpreted concerning crack-path dependence on individual material property mismatch. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article investigates the effect of spatial disintegration in moving images at high object velocities: when the visual system interprets the same object in consecutive fields as different entities. For a 50-Hz display this effect is found to roughly occur in the velocity range of 20-45 degrees/s, and to depend marginally on the resolution level of the objects involved. A more important influence is that of the trajectory length of the object: the maximum velocity at which no disintegration occurs is found to depend on it in a linear fashion. A simple model is presented that describes the visual appearance of the disintegration effect as well as explains the data quantitatively. [ABSTRACT FROM AUTHOR]

New insights into the grain-bed impact process arising from both numerical and physical experiments involving single grain impacts lead to a more complete conceptual model of the aeolian saltation process that in turn allows a simple model of aeolian impact ripples to be developed. The saltating population may be idealized as consisting of (1) long trajectory, high impact-energy, constant impact-angle 'successive saltations', and (2) short trajectory, low impact-energy 'reptations'. If is argued that the spatial variations in mass flux due to the reptating population lead to the growth and translation of impact ripples. Using the sediment continuity equation, an expression for the spatial variation in the ejection rate of reptating grains from a sinusoidally perturbed bed, and a probability distribution for the reptation lengths, a simple stability analysis demonstrates that the fiat bed is unstable to small amplitude perturbations. A fastest-growing wavelength emerges that is roughly six times the mean reptation length, and is only weakly dependent upon the detailed shape of the probability distribution of reptation lengths. The results match well with the observed initial wavelengths in wind tunnel experiments. [ABSTRACT FROM AUTHOR]

Following a previous report [1], this paper describes the geometrical optics theory applied to waveguides. The ray theory so be used as a foundation is based on the Maupertuis principle. It has been pointed out that the theory is not the one based on Hamilton's principle. Both theories are different in concept. However, the difference in the ray trajectory appears only in anisotropic media. In this paper, the anisotropic medium is assumed to be uniform along the waveguide axis whereas it is inhomogeneous in the cross section. Hence, the conventional isotropic waveguldes are included in the present theory. The objective of the paper is to construct geometrically the field of the eigenmode propagating in such a waveguide. Since the construction method for the phase of the field has already been reported, the field amplitude is derived mainly from geometrical considerations. Since some examples coincide with the known results obtained from the field theory, it is presumed that the geometrical interpretation of amplitude holds, in general. New geometrical formulas that cannot be derived from the solutions of the wave equation are obtained. [ABSTRACT FROM AUTHOR]

We show that for an aberrated wavefront the ray trajectories and the caustic are, respectively, the general solution and the particular solution of a Clairaut's nonlinear differential equation. As an example, we obtain the analytical expressions for the caustic and the ray trajectories of spherical aberration and coma. [ABSTRACT FROM AUTHOR]

Flatness‐based trajectory planning for the distributed‐parameter system consisting of a rigid body carried by multiple heavy ropes is discussed. The suspension points (controlled ends) of the ropes are assumed to be freely movable. The other ends of the ropes are parametrized by a flat output of the nonlinear boundary system at the load that describes the motion of the rigid body. This parametrization is then used to express the solution of the linearized partial differential equations for the heavy ropes under small angle approximations around a vertical equilibrium configuration by the means of operational calculus. It is shown that the system trajectories of the ropes depend on distributed delays and advances of the flat output trajectory at the load‐side boundary system. Evaluating the derived parametrization of the heavy ropes at the controllable ends yields the desired open‐loop controller by using a planned trajectory for the flat output. This control can be used to realize a desired transition of the load position and orientation in finite time. The introduced method is illustrated for the example of a linear infinite‐dimensional model of two heavy ropes carrying a rigid rod. [ABSTRACT FROM AUTHOR]

This contribution focuses on the optimal trajectory planning for a Segway model (inverted pendulum on two independently actuated wheels). Basis for this planning is the dynamical model for this under‐actuated, non‐holonomic multibody system. For the stabilization as well as the trajectory control, a partial input/output linearization is performed, where the orientation of the robot w.r.t. the horizontal plane and the inclination angle of the pendulum are used as output. The remaining non‐linear part is linearized about the upright equilibrium position and stabilized with an LQR controller. The trajectory optimization is based on the partially linearized system, where the output (orientation and inclination) is parameterized by B‐Splines. The system is required to move through predefined points in the horizontal plane. For the optimization the control points of the B‐Splines serve as optimization variables and the overall energy of the robot serves as cost functional. Maximum motor velocities, motor torques and the ground reaction forces are the constraints. The latter are crucial when planning trajectories where the robot must pass (swing) under vertical obstacles while not losing ground contact. These maneuvers are characterized by high horizontal accelerations in order to lower the head of the robot and bring it back to upright equilibrium. [ABSTRACT FROM AUTHOR]

Mobile data collection is one of research highlights for sparse threedimensional underwater sensor networks. Therein, optimal or nearoptimal cruise trajectory planning of mobile sink is very crucial. A 3D Dubins curves based continuous path programming algorithm (GA-3DTSP in short) for underwater mobile sink with non-holonomic constraints such as well-known autonomous underwater vehicle is proposed. The objective of GA-3DTSP algorithm is to trace sparsely deployed sensor nodes by mobile sink so as to achieve near-optimal energy conservation efficiency. First, an extended 3D Dubins curve is proposed and the length calculation formulae for 3D Dubins curve are investigated. Furthermore, genetic algorithm is used to tackle this difficult NP-complete problem of planning shortest paths in a heuristic manner. Finally, simulation results verify that the proposed GA- 3DTSP method can conserve cruise energy of mobile sink effectively. [ABSTRACT FROM AUTHOR]

Abstract: Trajectory clustering, which aims at discovering groups of similar trajectories, has long been considered as a corner stone task for revealing movement patterns as well as facilitating higher level applications such as location prediction and activity recognition. Although a plethora of trajectory clustering techniques have been proposed, they often rely on spatio‐temporal similarity measures that are not space and time invariant. As a result, they cannot detect trajectory clusters where the within‐cluster similarity occurs in different regions and time periods. In this paper, we revisit the trajectory clustering problem by learning quality low‐dimensional representations of the trajectories. We first use a sliding window to extract a set of moving behaviour features that capture space‐ and time‐invariant characteristics of the trajectories. With the feature extraction module, we transform each trajectory into a feature sequence to describe object movements and further employ a sequence‐to‐sequence auto‐encoder to learn fixed‐length deep representations. The learnt representations robustly encode the movement characteristics of the objects and thus lead to space‐ and time‐invariant clusters. We evaluate the proposed method on both synthetic and real data and observe significant performance improvements over existing methods. [ABSTRACT FROM AUTHOR]

Enhancing the performance of passive target tracking and trajectory estimation of marine traffic ships is focused using a monocular camera mounted on an unmanned surface vessel. To accurately estimate the trajectory of a target traffic ship, the relative bearing and range information between the observing ship and the target ship is required. Monocular vision provides bearing information with reasonable accuracy but with no explicit range information. The relative range information can be extracted from the bearing changes induced by the relative ship motion in the framework of bearings-only tracking (BOT). BOT can be effective in crossing situations with large bearing angle changes. However, it often fails in head-on or overtaking situations due to small bearing angle changes and the resulting low observability of the tracking filter. To deal with the lack of observability, the vertical pixel distance between the horizon and the target ship in the image is used, which improves the overall target tracking performance. The feasibility and performance of the proposed tracking approach were validated through field experiments at sea. [ABSTRACT FROM AUTHOR]

In the framework of the behavioural approach, a new definition of the passive circuit component is proposed. It is based on the concept of a forwards concatenation set of an admissible trajectory. The so far elusive notion of the non-dynamic circuit component is also clarified. As an example of application, the passivity and available energy of the N-dimensional resistive, the Thévenin source, is thoroughly investigated. [ABSTRACT FROM AUTHOR]