Space-time Trajectories Research Articles

Longitudinal and Lateral Trajectory Planning for the Typical Duty Cycle of Autonomous Load Haul Dump

With the development of intelligent mining, autonomous driving will be the basic function of intelligent Load Haul Dump (LHD). Trajectory planning is the key part of autonomous driving. Due to the articulated structure, the motion state variables of the front and rear bodies are strongly nonlinear, leading to complex nonlinear collision avoidance constraints. In addition, the articulated angle and angular velocity of the LHD have physically constraints. At the same time, the terminal attitude constraint should be considered since LHD is a mining equipment. All these factors bring great difficulties to LHD trajectory planning and none of the existing methods can deal with these factors directly. In order to solve these problems, according to the most common working scenario, a novel trajectory planning method is proposed for autonomous LHD based on numerical optimization, leading to a safe and feasible time-space trajectory for efficient production. The novelty of this work is the introduction of a longitudinal and lateral trajectory planning for the typical duty cycle of LHD. More importantly, by the ingenious concept for modeling, there are two salient features of the proposed method. Firstly, no angles are used as the decision variable, and secondly, the collision constraints of the rear car are not directly considered. Through this way, the number of nonlinear constraints and the complexity of the model can keep in a reasonable level, which makes the model easy to solve. At the same time, by giving the collision-free condition and limiting the heading angular velocity, the generated trajectory is collision-free and satisfies the physical constraints of articulated angle. Case studies confirm the effectiveness of the proposed method. Adopting the proposed method to generate a spatiotemporal trajectory is beneficial to ensure safety and improve production efficiency.

Robust Human Activity Recognition Using Multimodal Feature-Level Fusion

Automated recognition of human activities or actions has great significance as it incorporates wide-ranging applications, including surveillance, robotics, and personal health monitoring. Over the past few years, many computer vision-based methods have been developed for recognizing human actions from RGB and depth camera videos. These methods include space-time trajectory, motion encoding, key poses extraction, space-time occupancy patterns, depth motion maps, and skeleton joints. However, these camera-based approaches are affected by background clutter and illumination changes and applicable to a limited field of view only. Wearable inertial sensors provide a viable solution to these challenges but are subject to several limitations such as location and orientation sensitivity. Due to the complementary trait of the data obtained from the camera and inertial sensors, the utilization of multiple sensing modalities for accurate recognition of human actions is gradually increasing. This paper presents a viable multimodal feature-level fusion approach for robust human action recognition, which utilizes data from multiple sensors, including RGB camera, depth sensor, and wearable inertial sensors. We extracted the computationally efficient features from the data obtained from RGB-D video camera and inertial body sensors. These features include densely extracted histogram of oriented gradient (HOG) features from RGB/depth videos and statistical signal attributes from wearable sensors data. The proposed human action recognition (HAR) framework is tested on a publicly available multimodal human action dataset UTD-MHAD consisting of 27 different human actions. K-nearest neighbor and support vector machine classifiers are used for training and testing the proposed fusion model for HAR. The experimental results indicate that the proposed scheme achieves better recognition results as compared to the state of the art. The feature-level fusion of RGB and inertial sensors provides the overall best performance for the proposed system, with an accuracy rate of 97.6%.

Microwave Imaging of Non-Rigid Moving Target Using 2D Sparse MIMO Array

This paper develops a microwave/mmw (millimeter-wave) imaging method for moving objects of non-rigid body which can be used in the heavy traffic scenarios. This method is proposed with a 2D sparse MIMO (multiple-input multiple-output) array composed of two orthogonal linear arrays. In comparison to the RX antennas, a smaller number of TX antennas is used to decrease the data acquisition time of this system when using TDM (time division multiplexing) signal transmitting technique. The 2D sparse MIMO array is deployed with wide-band signals transmitted to reconstruct the backscattering coefficient in 3D space using synthetic aperture imaging technique. Then a series of synthesized 3D snapshot images are generated during the motion of the target. The non-rigid human body target is decomposed into 25 joints tracked by an optical device which is Kinect in this paper. After the decomposition, the movement of each joint can be described as a space-time trajectory tracked by Kinect, providing a preliminary indication of the 3D position of each joint. With the indication, we divide every microwave/mmw image into 25 sub-images corresponding to the joints’ position to form an image sequence of each joint. Subsequently, a segmental joint estimation method is proposed to estimate the accurate motion parameters of each joint from the image sequence. The decorrelation of the images in large angle observation can be significantly reduced by the segmental estimation which leads global optimized motion parameters. Consequently, the estimated parameters are taken into the effective movement compensation of each component. Meanwhile, the image refocusing method is presented to generate the well-focused image of each component. Finally, all the images of components are fused into one image of the whole target to reconstruct the 3D high-resolution image. Imaging simulations and measuring data experiments show that this method is efficient.

Dynamical criticality in open systems: Nonperturbative physics, microscopic origin, and direct observation

Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on both the macroscopic large deviation properties and the microscopic origin of such spontaneous symmetry breaking in the open weakly asymmetric exclusion process. By studying the joint fluctuations of the current and a collective order parameter, we uncover the full dynamical phase diagram for arbitrary boundary driving, which is reminiscent of a $\mathbb{Z}_2$ symmetry-breaking transition. The associated joint large deviation function becomes non-convex below the critical point, where a Maxwell-like violation of the additivity principle is observed. At the microscopic level, the dynamical phase transition is linked to an emerging degeneracy of the ground state of the microscopic generator, from which the optimal trajectories in the symmetry-broken phase follow. In addition, we observe this new symmetry-breaking phenomenon in extensive rare-event simulations, confirming our macroscopic and microscopic results.

A Combinatorial Dynamic Network Trajectory Reservation Algorithm for Connected Autonomous Vehicles

We present a combinatorial assignment algorithm for reserving space-time trajectories from origins to destinations given an ordered list of vehicles. Space-time trajectories include guaranteed arrival times at every node in the path, including at the destination. Traffic flows are modeled using the cell transmission model, a Godunov approximation to the kinematic wave model. Space-time trajectories are constructed to follow the cell transmission model constraints and first-in-first-out behavior. Reservation-based intersection control for connected autonomous vehicles, which determines intersection access and delays for individual vehicles, is used to ensure that reserved trajectories are followed. The algorithm is suitable for city networks. Results show that vehicles with higher priority tend to have much lower travel times. In addition, the trajectory reservation system reduced overall congestion in the network compared with dynamic user equilibrium assignments.

Error Measures for Trajectories Estimations with Geo-tagged Mobility Sample Data.

Although geo-tagged mobility data (e.g., cell phone data and social media data) can be potentially used to estimate individual space-time travel trajectories, they often have low sample rates that only tell travelers' whereabouts at the sparse sample times while leaving the remaining activities to be estimated with interpolation. This study proposes a set of time geography-based measures to quantify the accuracy of the trajectory estimation in a robust manner. A series of measures including activity bandwidth and normalized activity bandwidth are proposed to quantify the possible absolute and relative error ranges between the estimated and the ground truth trajectories that cannot be observed. These measures can be used to evaluate the suitability of the estimated individual trajectories from sparsely sampled geo-tagged mobility data for travel mobility analysis. We suggest cutoff values of these measures to separate useful data with low estimation errors and noisy data with high estimation errors. We conduct theoretical analysis to show that these error measures decrease with sample rates and people's activity ranges. We also propose a lookup table-based interpolation method to expedite the computational time. The proposed measures have been applied to 2013 geo-tagged tweet data in New York City and 2014 cell-phone data in Shenzhen, China. The results illustrate that the proposed measures can provide estimation error ranges for exceptionally large datasets in much shorter times than the benchmark method without using lookup tables. These results also reveal managerial results into the quality of these data for human mobility studies, including their distribution patterns.

Daily commuting in the Bratislava metropolitan area: case study with mobile positioning data

Suburban development in the metropolitan area of Bratislava (Slovakia) led to an unprecedented redistribution of population. As the majority of suburbanized families are car-dependent, the influx of new residents is a major source of growing traffic problems. However, due to the unwillingness of suburban in-migrants to change their registration (approximately 100,000 unregistered residents), the commuting based on the census data is insufficient to capture the real pattern of daily mobility in the hinterland of Bratislava. Yet, mobile positioning data represent a powerful source of information with high spatial accuracy and endless options for use. The objective of this study is to analyze mobility patterns of commuting in the Bratislava metropolitan area using mobile positioning data. The experiment was carried out in September 2017 over a fourteen-day period with a sample of 191,404 mobile phone users. The key task was to find a suitable methodological approach to extract useful information of human mobility patterns. We used the concept of anchor points, which represent main nodes of human activity and space–time trajectories. Extracting the localization of “work” and “sleep” we modeled the origin-destination matrix of daily commuting with a spatial accuracy not available until now.

Assessing travel time reliability implications due to roadworks on private vehicles and public transport services in urban road networks

Abstract Roadworks are perhaps the most controversial topic in transport professional field. On one hand, they are a necessity to assure the current and future functionality of the traffic network, while on the other, they are seen as a major disturbance by road users with concerns for excessive travel time delays. The impact of roadworks is usually analysed at a local level however the network-wide effects are crucial to ensure reliable travel times. Moreover the analysis usually focusses on private cars and the reliability impact on public transport services are too important to ignore. This paper investigates the impact of roadworks undertaken on a given road link over wider parts of the network and assesses travel time reliability for both cars and buses. This research involves setting up of a conventional network assignment model to arrive at the route choice of drivers as a result of the roadworks and then integrates the outcomes with a microsimulation model to generate space-time trajectories to arrive at travel times of individual vehicles. We adopted a reliability measure from the literature to compute travel time reliability of a given type of vehicle by unique origin-destination (O-D) pair combinations and also more generally to provide a wider picture at an aggregated network level. The method was tested on a real life network in England, and travel time reliability results were analysed both at the network scale and significant O-D pair level for private cars and bus routes.

Aging in a Relativistic Biological Space-Time.

Here we present a theoretical and mathematical perspective on the process of aging. We extend the concepts of physical space and time to an abstract, mathematically-defined space, which we associate with a concept of “biological space-time” in which biological dynamics may be represented. We hypothesize that biological dynamics, represented as trajectories in biological space-time, may be used to model and study different rates of biological aging. As a consequence of this hypothesis, we show how dilation or contraction of time analogous to relativistic corrections of physical time resulting from accelerated or decelerated biological dynamics may be used to study precipitous or protracted aging. We show specific examples of how these principles may be used to model different rates of aging, with an emphasis on cancer in aging. We discuss how this theory may be tested or falsified, as well as novel concepts and implications of this theory that may improve our interpretation of biological aging.

Data-Driven Method to Estimate the Maximum Likelihood Space–Time Trajectory in an Urban Rail Transit System

The Urban Rail Transit (URT) passenger travel space–time trajectory reflects a passenger’s path-choice and the components of URT network passenger flow. This paper proposes a model to estimate a passenger’s maximum-likelihood space–time trajectory using Automatic Fare Collection (AFC) transaction data, which contain the passenger’s entry and exit information. First, a method is presented to construct a space–time trajectory within a tap in/out constraint. Then, a maximum likelihood space–time trajectory estimation model is developed to achieve two goals: (1) to minimize the variance in a passenger’s walk time, including the access walk time, egress walk time and transfer walk time when a transfer is included; and (2) to minimize the variance between a passenger’s actual walk time and the expected value obtained by manual survey observation. Considering the computational efficiency and the characteristics of the model, we decompose the passenger’s travel links and convert the maximum likelihood space–time trajectory estimation problem into a single-quadratic programming problem. Real-world AFC transaction data and train timetable data from the Beijing URT network are used to test the proposed model and algorithm. The estimation results are consistent with the clearing results obtained from the authorities, and this finding verifies the feasibility of our approach.

A multi-aircraft conflict detection and resolution method for 4-dimensional trajectory-based operation

Conflict Detection and Resolution (CD&R) is the key to ensure aviation safety based on Trajectory Prediction (TP). Uncertainties that affect aircraft motions cause difficulty in an accurate prediction of the trajectory, especially in the context of four-dimensional (4D) Trajectory-Based Operation (4DTBO), which brings the uncertainty of pilot intent. This study draws on the idea of time geography, and turns the research focus of CD&R from TP to an analysis of the aircraft reachable space constrained by 4D waypoint constraints. The concepts of space–time reachability of aircraft and space–time potential conflict space are proposed. A novel pre-CD&R scheme for multiple aircraft is established. A key advantage of the scheme is that the uncertainty of pilot intent is accounted for via a Space-Time Prism (STP) for aircraft. Conflict detection is performed by verifying whether the STPs of aircraft intersect or not, and conflict resolution is performed by planning a conflict-free space–time trajectory avoiding intersection. Numerical examples are presented to validate the efficiency of the proposed scheme.

Synchronization of relativistic particles in the hyperbolic Kuramoto model.

We formulate a noncompact version of the Kuramoto model by replacing the invariance group SO(2) of the plane rotations by the noncompact group SO(1, 1). The N equations of the system are expressed in terms of hyperbolic angles αi and are similar to those of the Kuramoto model, except that the trigonometric functions are replaced by hyperbolic functions. Trajectories are generally unbounded, nevertheless synchronization occurs for any positive couplings κi, arbitrary positive multiplicative parameters λi and arbitrary exponents ωi. There are no critical values for the coupling constants. We measure the onset of synchronization by means of several order and disorder parameters. We show numerically and by means of exact solutions for N = 2 that solutions can develop singularities if the coupling constants are negative, or if the initial values are not suitably restricted. We describe a physical interpretation of the system as a cluster of interacting relativistic particles in 1 + 1 dimensions, subject to linear repulsive forces with space-time trajectories parametrized by the rapidity αi. The trajectories synchronize provided that the particle separations remain predominantly time-like, and the synchronized cluster can be viewed as a bound state of N relativistic particle constituents. We extend the defining equations of the system to higher dimensions by means of vector equations which are covariant with respect to SO(p, q).

Memory effect for impulsive gravitational waves

Impulsive gravitational plane waves, which have a δ-function singularity on a hypersurface, can be obtained by squeezing smooth plane gravitational waves with a Gaussian profile. They exhibit (as do their smooth counterparts) the velocity memory effect: after the wave has passed, particles initially at rest move apart with non-vanishing constant transverse velocity. A new effect is that, unlike the smooth case, (i) the velocities of particles originally at rest jump, (ii) the spacetime trajectories become discontinuous along the (lightlike) propagation direction of the wave.

Dissipative variational analysis for bounded dark solitons of electromagnetically induced transparency

Electromagnetically-controlled precision is one of novel topics in the electromagnetics. To realize the precision controlling of the electromagnetically complicated phenomenon, the systematic characteristics of medium environment needs considering. Based on the cancellation of interference caused by quantum coherence in the systematic environment of material, the electromagnetically-induced transparency (EIT) can be achieved. For this nonlinear phenomenon, due to the advancement of quantum spot and well, the controlling of the bounded sate of quantum in various dimensions of semiconductor can be operated. So the solid system presents a clear superiority of controlling EIT. High power electromagnetic field excites the dynamic characteristics in solid material, which is the result of systematic reaction between field and material. Under the excitation of electromagnetic pulse, because of quantum coherence, the dual-well semiconductor has the ability to induce the dark state of solitons. In the study of the complicated system of multiple physical fields, two aspects need investigating further. Firstly, in the induction process of electromagnetic filed and solid material, the features of high dispersion and nonlinear reaction appear increasingly. Thus, due to the environmental restriction on dispersion and nonlinear reaction, electromagnetic dissipation is a crucial point, which needs considering in the electromagnetically-controlled precision of the EIT. Secondly, compared with the formation of soliton, the coupling reaction of solitons under co-sate is much complicated. The relation among these factors is necessary to be investigated in the formulation of soliton excitation. Therefore, a dual-well semiconductor is employed as solid environment to analyze the dynamic characteristics of dark solitons in the EIT. In order to achieve the controlling of precision and regulating of the effect, the environmental features of solid materials ought to be systematically considered. Accordingly, the variational method is utilized, through which the bounded action of dissipation and nonlinear coherence is effectively studied for the dark solitons under co-sate, and under the condition of exciting dark soliton in the system of EIT. Using the density matrix and electric polarization, the spectrum of dynamic transmission deviation of EIT is calculated in the solid environment. With the assistance of relevant action principle, the bounded relation of dark solitons under co-state is practically investigated in the dissipative environment of solid system. In addition, the space-time trajectory is analyzed in the applicable region of characteristic equations of dark solution. The deduced result indicates that the systematical balance between dissipative weakening and coherent coupling supports the valuable approach to controlling the space-time evolution of dark solitons in precision. The results also show that the special effect has the potential applications in electromagnetically-controlled precision in the quantum information, ray sensor, controllable environment, etc.

Seismic attractor can assist in finding of geothermal area?

The seismic active zone is a distributed system consisting of various subareas. To understand a state of the system during a given period of time so called ‘the linear gradient frame’ technique was developed to search the stable characteristics for subareas. The search is based on analysis of geographic components, least-squares inversion and statistical estimators of seismic data. The stable subarea includes hypocenters of earthquakes, the space-time trajectories of which are restricted by a certain domain (seismic attractor). Fractal structures obtained in south of Iceland are in an agreement with geological history. The results are promising for the geothermal exploration.

On the role of control windows in continuum dynamics

The general role of control windows is investigated by an assessment of the fundamentals of continuum dynamics in the spacetime context. The momentum rate of change of a continuous body is evaluated with reference to a control window travelling in the spacetime trajectory manifold. The resulting formula involves the rate of change of the momentum in the control window and the rate of outflow of the momentum across the control window boundary. An effective tool for investigating challenging dynamical problems is thus available, and some interesting examples, taken from early and recent contributions, are illustrated. Among these, motions of chains falling under the action of gravity, object of several investigations in the past two centuries, are revisited. Around the middle of the nineteenth century, the problem was inserted as a daring task in the Mathematical Tripos at Cambridge. The choice of a special control window, named the skeleton, in motion with the solid case, provides the proper methodology for the formulation of solid–fluid interaction problems, with applications to turbines, jets, rockets and sprinklers. As a further significant application of travelling control windows, a variational formulation of conservation of mass is developed and shown to yield the notion of mass flow vector field, with applications in problems of fluid flow through a porous solid.

High-frequency Quasi-periodic Light Variations from Arc-shaped Gas Clouds Falling onto a Black Hole

Abstract We investigate the dynamical and radiative properties of arc-shaped gas clouds falling onto a stellar-mass black hole based on the three-dimensional general relativistic radiation-magnetohydrodynamics (3D-GRRMHD) simulation data. Assuming that the gas clouds radiate mainly due to the free–free emission and/or optically thick, inverse Compton scattering, we calculate how the emissivity distributions develop with time. We find that (1) gas clouds, each of which has a ring-like or arc shape, are intermittently formed, and that (2) they slowly fall onto the black hole, keeping nearly the Keplerian orbital velocity. These features support the dynamical properties of the gas clouds assumed in the spin measurement method proposed by Moriyama & Mineshige, but the radius of the inner edge of the accretion disk is larger than that of the marginally stable orbit (ISCO). Next, we examine how each gas cloud is observed by a distant observer by calculating the photon trajectories in the black hole spacetime. The luminosity of the accretion flow exhibits significant time variations on different timescales, reflecting the time evolution of the gas density distributions. The relatively slow variations on the time durations of 0.08–0.10 s is due to the formation and fall of gas clouds, while quasi-periodic flux peaks with short time intervals (0.01 s) are due to the quasi-periodic enhancement of light from the non-axisymmetric arc-shaped clouds through the beaming effect. This may account for the high-frequency quasi-periodic oscillations (HF QPOs) observed in black hole binaries. The observational implications and future issues are briefly discussed.

A unified follow-the-leader model for vehicle, bicycle and pedestrian traffic

In this research we performed new bicycle and pedestrian experiments to supplement data extracted from existing follow-the-leader experiments in vehicles, bicycles and pedestrians, and studied their spacetime trajectories and flow-density (or spacing-velocity) phase diagrams. The strong similarities in the spacetime trajectories and the bi-variate phase plots as well as the relative consistence of the estimated proportionality parameter across all three types of traffic, suggest that a unified behavioral mechanism is at play in human-driven traffic. It is suggested that this mechanism is essentially a safety-driven behavior that vehicles, bicycles or pedestrians adopt a safe speed for a given spacing between them. This behavior is well described by a well-known model in vehicular traffic and it is shown in this paper that a scaled version of this model applies to all three types of traffic. A unified relaxation-driven social force traffic model is then proposed to incorporate this behavior mechanism. Simulations with the same setup as the real-life experiments were carried out for vehicle, bicycle, and pedestrian traffic using the unified traffic model and the simulated spacetime trajectories and fundamental diagrams show remarkable consistence with the experimental results.

Detecting and visualizing cohesive activity-travel patterns: A network analysis approach

This article presents a network analytical framework to detect individual-based activity-travel patterns (ATPs) in space and time. Compared to many existing classification methods (e.g., hot-spot detection, sequential alignment method), the network method substantiates the social meanings underlying the interconnectedness and similarities of people's activity trajectories and better integrates spatial interaction (colocation or distance-decay) and temporal connections (concurrence or sequence) of daily lives in the measure of similarity. This approach enables us to detect variant community structures, with individuals in the same community interacting relatively more than individuals belonging to different communities, by decomposing the complex trajectories into different meaningful events (e.g., activities, trips, tours, and subsequences). We also demonstrate the practicality and scientific merit of the network analysis approach in a case study of household travel behavior in Charlotte, North Carolina. Results derived from disaggregated survey data establish the effectiveness and flexibility of the network methods to detect cohesive communities of individuals and ATPs by different narratives of everyday-life events. This study also suggests that the network analysis approach has great potential to classify large datasets of other space-time trajectories and to discover policy-sensitive activity, trip, and tour patterns that help us develop policy and planning alternatives for sustainable communities and mobility.

Russian regional evolutions: comparative gross regional product dynamics of the subjects of the Russian Federation, 1995–2013

ABSTRACTAnalysis of the comparative space–time trajectories of 79 subjects of the Russian Federation in 1995–2013 indicates an overall increase in inequality, and enables the classification of areas into two unequal groups. The first includes 80% of Russian regions with below-average gross regional product per capita (GRPPC). These regions have moved closer together, with most growing slower than average. Their development indicates a strong degree of path dependence. The second is a small group of high GRPPC regions that are very diverse and whose development was characterized by considerable instability. Identification and interpretation of these trends plays an important role in the design of effective policies for regional social–economic development.