Trajectories In Space Research Articles

Piecewise Time Polynomials-Based Control Methods for Obstacle Avoidance and Precision Positioning of Tower Crane Systems with Varying Cable Lengths

During the hoisting and lowering operations of a tower crane, dynamic variations in cable lengths significantly influence the oscillation frequency and amplitude of the load. These variations complicate the oscillation characteristics, heightening the challenge of balancing obstacle avoidance with precise positioning. To tackle this issue, we propose a trajectory planning and tracking control method that integrates hoisting control to reduce the impact of varying cable lengths on load swinging and achieve accurate positioning during obstacle navigation. A novel definition of swing angle is introduced to model the crane’s rigid and swinging components separately, enhancing model accuracy while simplifying complexity. A piecewise polynomial constructs the load trajectory in a low-dimensional flat space, which is then mapped to a high-dimensional generalized state space through a homeomorphic transformation, ensuring trajectory smoothness and traceability. A fractional-order sliding mode controller is employed to facilitate rapid and precise tracking of the actuated degrees of freedom, suppressing load oscillation while maintaining positioning accuracy. Experimental validation on a tower crane platform shows that the proposed strategy enables smooth obstacle avoidance and precise target point reaching, even with varying cable lengths.

Multi-objective optimal trajectory planning for manipulators based on CMOSPBO

Feasible, smooth, and time-jerk optimal trajectory is essential for manipulators utilized in manufacturing process. A novel technique to generate trajectories in the joint space for robotic manipulators based on quintic B-spline and constrained multi-objective student psychology based optimization (CMOSPBO) is proposed in this paper. In order to obtain the optimal trajectories, two objective functions including the total travelling time and the integral of the squared jerk along the whole trajectories are considered. The whole trajectories are interpolated by quintic B-spline and then optimized by CMOSPBO, while taking into account kinematic constraints of velocity, acceleration, and jerk. CMOSPBO mainly includes improved student psychology based optimization, archive management, and an adaptive ε-constraint handling method. Lévy flights and differential mutation are adopted to enhance the global exploration capacity of the improved SPBO. The ε value is varied with iterations and feasible solutions to prevent the premature convergence of CMOSPBO. Solution density estimation corresponding to the solution distribution in decision space and objective space is proposed to increase the diversity of solutions. The experimental results show that CMOSPBO outperforms than SQP, and NSGA-II in terms of the motion efficiency and jerk. The comparison results demonstrate the effectiveness of the proposed method to generate time-jerk optimal and jerk-continuous trajectories for manipulators.

The concept map as a tool for analyzing museum objects

AbstractThis paper discusses using the concept map to study museum objects. The tool's original purpose, which was created in the 1970s by Joseph Novak, was to graphically represent the construction of knowledge of scientific topics by learners, particularly children. Concept maps start from the premise that new knowledge is always built on previous knowledge and allow the representation, organization, and relationship between concepts, which are seen as the primary elements of knowledge. Novak recognized that its potential is insufficiently explored and encouraged its application in different disciplines and fields that deal with concepts and their relationships. This incentive led the Museum of Astronomy and Related Sciences (Rio de Janeiro, Brazil) to adopt the concept map on an experimental basis to analyze objects in its collection. At first, the tool sought to emphasize the conceptual potential of museum objects and shed more light on their trajectory in time and space and the numerous possible connections with events, institutions, concepts, people, and other objects. In the initial experimental phase, the maps were included in papers presented at academic events and discussed with professionals dedicated to science and technology collections and other specialists in Museology and Information Science. In the second stage, maps began to be produced in greater numbers and on demand, focusing on objects selected for a temporary exhibition. Based on the assumption that museum objects are both unique and representative of a class of objects that share the same name and function, the maps constructed were based on Ingetraut Dahlberg's Theory of Concept, which distinguishes between general and individual objects and concepts.

SISGAN: A Generative Adversarial Network Pedestrian Trajectory Prediction Model Combining Interaction Information and Scene Information

Accurate pedestrian trajectory prediction is crucial in many fields. This requires the full use and learning of pedestrians’ social interactions, movements, and environmental information. In view of the current research on pedestrian trajectory prediction, wherein most of the pedestrian interaction information is explored from the level of overall interaction, this paper proposes the SISGAN model, which designs a social interaction module from the perspective of the target pedestrian, and takes four kinds of interaction information as the influencing factors of pedestrian interaction, so as to describe the influence mechanism of pedestrian–pedestrian interaction. In addition, in terms of environmental information, the index density of pedestrian historical trajectory in space is taken into account in the extraction of environmental information, which increases the potential correlation between environmental information and pedestrians. Finally, we integrate social interaction information and environmental information and make the final trajectory prediction based on GAN. Experiments on ETH and UCY datasets demonstrate the effectiveness of the SISGAN model proposed in this paper.

Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

Accurate reconstruction of multi-source data information plays an essential role in remote intelligent operation, and prognostic and health maintenance (RIO-PHM) of industrial systems. However, traditional signal reconstruction methods such as compressed sensing fail to capture the spatio-temporal characteristics and coupling nature of the multi-source or multi-channel data. To alleviate this bottleneck, in this paper, a new wavelet-based spatiotemporal sparse quaternion dictionary learning (WSTS-QDL) algorithm is formulated for the reconstruction of multi-channel vibration data for the first time. Specifically, the wavelet-based spatiotemporal sparse low-rank matrix (SLRM) algorithm is elaborated and the sparse coefficient matrix of the multi-channel signals can be estimated using the split Bregman iteration (SBI) technique. Then, quaternion-based dictionary learning is introduced for multi-channel data reconstruction according to the updated sparse coefficient matrix during quaternion dictionary learning. Eventually, two equipmental scenarios including run-to-failure data of rolling bearing in bearing test bench and vibration signal of the failured bearing in corn thresher, are utilized for verification. The experimental results demonstrate that the highest recovery accuracy performance with scoring function and the lowest errors are achieved by the proposed method in contrast with the state-of-the-art benchmarks such as orthogonal matching pursuit (OMP) method and spatiotemporal sparse Bayesian learning (SSBL), and the waveform of phase space trajectory and points cloud distribution of the Poincare section in the original signal are similar/same to that obtained by the proposed method.

Turbulence from an Observer Perspective

Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.

Temporal geometric mapping defines morphoelastic growth model of Type B aortic dissection evolution

The human aorta undergoes complex morphologic changes that mirror the evolution of disease. Finite element analysis (FEA) enables the prediction of aortic pathologic states, but the absence of a biomechanical understanding hinders the applicability of this computational tool. We incorporate geometric information from computed tomography angiography (CTA) imaging scans into FEA to predict a trajectory of future geometries for four aortic disease patients. Through defining a geometric correspondence between two patient scans separated in time, a patient-specific FEA model can recreate the deformation of the aorta between the two time points, showing that pathologic growth drives morphologic heterogeneity. FEA-derived trajectories in a shape-size geometric feature space, which plots the variance of the shape index versus the inverse square root of aortic surface area (δS vs. AT−1), quantitatively demonstrate an increase in δS. This represents a deviation from physiologic shape changes and parallels the true geometric progression of aortic disease patients.

Robot Manipulator Minimum Jerk Trajectory Planning Based on the Improved Dung Beetle Optimizer Algorithm

Trajectory planning of robotic manipulators in complex environments involves generating smooth and collision-free paths, and key aspects to consider include dynamic environment perception, path planning, trajectory smoothing and optimization, and obstacle avoidance. This paper discusses different algorithms and finally proposes a fusion of the improved Dung Beetle Optimizer (IDBO) algorithm using chaotic mapping, sinusoidal random mutation, and nonlinear convergence strategies with the bidirectional Rapidly exploring Random Tree (RRT) algorithm to achieve manipulator trajectory planning and minimum jerk optimization trajectory. In the experiment, the IDBO algorithm was compared with other heuristic algorithms. The path obtained was shortened by 9.18% on average, and the calculation time was shortened by 33.81% on average. Then, the paper explored Cartesian coordinate space trajectory planning and joint space trajectory planning when the robot was working in 3D space, and verified the superiority of the latter. In controlling the movement of the robot, by combining the minimum angle jerk planning and the bidirectional RRT obstacle avoidance algorithm to drive the joint angle parameters obtained by the spatial trajectory planning, the trajectory of the robot manipulator can be smoother, more efficient, and avoid obstacles in complex 3D space. This research helps improve the performance, safety, and technical support of robots, and is of great research significance.

Phase space analysis of interacting and non-interacting models in f(Q, C) gravity

Abstract Using a dynamical system method, we have studied a Friedmann-Robertson-Walker (FRW) cosmological model within the context of $f(Q,C)$ gravity, where $Q$ is the non-metricity scalar and $C$ represents the boundary term, considering both interacting and non-interacting models. A set of autonomous equations is derived, and solutions are calculated accordingly. We assessed the critical points obtained from these equations, identified their characteristic values, and explored the physical interpretation of the phase space for this system. Two types of $f(Q,C)$ are assumed to be $(i)$ $f(Q,C)=Q+\alpha Q+\beta C logC$ and $(ii)$ $f(Q,C)=Q+\alpha Q+\frac{\beta}{C}$, where $\alpha$ and $\beta$ are the parameters. In Model I, we obtain two stable critical points, while in Model II, we identified three stable critical points for both interacting and non-interacting models. We look into how the phase space trajectories behave at every critical points. We calculate the values of the physical parameters for both systems at each critical point, indicating the Universe's accelerated expansion.

Creative space and scientific trajectory of academician V.N. Chernigovsky – first academic secretary of the department of physiology of the USSR Academy of Sciences

The article analyzes the prerequisites and conditions for choosing Academician V.N. Chernigovsky, academician-secretary of the Department of Physiology of the USSR Academy of Sciences, created in 1963. For this purpose, the scientific potential and creative success, career growth and individual qualities of Academician V.N. Chernigovsky within the framework of the methodological approach of “protected space” were considered. He was characterized by a high level of achievement motivation, he had high efficiency, and was characterized by thoroughness and accuracy in carrying out scientific work. V.N. Chernigovsky successfully developed a new direction in the field of visceral physiology and made a significant contribution to the idea of interoception. He worked hard, achieved results step by step, which added up, enhancing their combined effect and creating the basis for his recognition and career advancement. V.N. Chernigovsky had significant administrative experience in leading two leading physiological institutes. Creative space of academician V.N. Chernigovsky, his scientific trajectory and personal characteristics brought him to the forefront as a candidate for the position of Academician-Secretary of the new Department of Physiology of the USSR Academy of Sciences. Election of Academician V.N. Chernigovsky’s appointment to the position of academic secretary was not an accident, a game of chance or luck. This was the result of his intensive scientific and organizational work, which were predetermined by his personal qualities.

Restoring Adiabatic State Transfer in Time-Modulated Non-Hermitian Systems.

Non-Hermitian systems have attracted much interest in recent decades, driven partly by the existence of exotic spectral singularities, known as exceptional points (EPs), where the dimensionality of the system evolution operator is reduced. Among various intriguing applications, the discovery of EPs has suggested the potential for implementing a symmetric mode switch, when encircling them in a system parameter space. However, subsequent theoretical and experimental works have revealed that dynamical encirclement of EPs invariably results in asymmetric mode conversion; namely, the mode switching depends only on the winding direction but not on the initial state. This chirality arises from the failure of adiabaticity due to the complex spectrum of non-Hermitian systems. Although the chirality revealed has undoubtedly made a significant impact in the field, a realization of the originally sought symmetric adiabatic passage in non-Hermitian systems with EPs has since been elusive. In this work, we bridge this gap and theoretically demonstrate that adiabaticity, and therefore a symmetric state transfer, is achievable when dynamically winding around an EP. This becomes feasible by specifically choosing a trajectory in the system parameter space along which the corresponding evolution operator attains a real spectrum. Our findings, thus, offer a promise for advancing various wave manipulation protocols in both quantum and classical domains.

A reinforcement learning based sliding mode control for passive upper-limb exoskeleton

Rehabilitation devices such as actuated exoskeletons can provide mobility assistance for patients suffering from paralysis or muscle weakness. In order to improve the well-being of patients, the control design of exoskeletons is of paramount importance and highest priority. In this paper, we present a sliding reinforcement learning (RL) method control for an upper-limb exoskeleton, enabling it to learn following a desired trajectory in the Cartesian space. The deep deterministic policy gradient (DDPG) using an actor-critic architecture is employed to continuously adjust the non-singular terminal sliding mode control (NSTSMC) control inputs, based on previous experiences. The designed actor network learns the policy and the critic evaluates the quality of the actions chosen by the actor. The robustness of the proposed approach is studied when the system is subjected to random disturbances. The simulation results demonstrate that the proposed approach based on the RL method effectively fulfills exoskeleton tracking tasks. Moreover, a comparative analysis with the standard NSTSMC, computed torque (CT), and RL-based CT shows the superiority of the proposed approach in terms of position tracking error. These findings are further confirmed by various performance evaluation metrics.

Uniform attractors for the Bingham model

In this paper, on the base of the theory of attractors for non-invariant trajectory spaces, the limiting behavior of solutions to a periodic in spatial variables problem for the Bingham model is investigated. For the considered problem, necessary exponential estimates are established, the trajectory space is determined, and the existence of a minimal uniform trajectory and uniform global attractors is proved.

Non-minimal elliptic threefolds at infinite distance. Part I. Log Calabi-Yau resolutions

We study infinite-distance limits in the complex structure moduli space of elliptic Calabi-Yau threefolds. In F-theory compactifications to six dimensions, such limits include infinite-distance trajectories in the non-perturbative open string moduli space. The limits are described as degenerations of elliptic threefolds whose central elements exhibit non-minimal elliptic fibers, in the Kodaira sense, over curves on the base. We show how these non-crepant singularities can be removed by a systematic sequence of blow-ups of the base, leading to a union of log Calabi-Yau spaces glued together along their boundaries. We identify criteria for the blow-ups to give rise to open chains or more complicated trees of components and analyse the blow-up geometry. While our results are general and applicable to all non-minimal degenerations of Calabi-Yau threefolds in codimension one, we exemplify them in particular for elliptic threefolds over Hirzebruch surface base spaces. We also explain how to extract the gauge algebra for F-theory probing such reducible asymptotic geometries. This analysis is the basis for a detailed F-theory interpretation of the associated infinite-distance limits that will be provided in a companion paper [1].

Analysis of Polynomial Interpolation Characteristics Based on 6DOF Manipulator Trajectory Planning

Aiming at the problems of choosing and using polynomials of different times and mixed polynomials in the process of manipulator trajectory planning, such as difficulty, wide range of light and low accuracy, in this paper, the application of different polynomials in manipulator trajectory planning is systematically analyzed by using MATLAB Robot Toolbox simulation platform and Polynomial interpolation algorithm. Using a 6-dof robotic arm Puma560 as a simulation object, the effects of three-, five-, and seven-Polynomial interpolation on joint position and pose in joint space trajectory planning were analyzed, a preliminary understanding of the application of different polynomials, and secondly, the more complex application of the fifth and seventh degree polynomials in Descartes space for the trajectory planning of the manipulator, the influence of trajectory planning with different degree polynomials on the position and pose of manipulator joint is clarified. The results show that the higher the number of polynomials, the smoother the transition of the joint at the critical path points, but the greater the maximum angular velocity and angular acceleration of the joint, the Polynomial interpolation of joint space and Descartes space trajectory planning are 14% and 23% lower than the average of absolute maximum angular velocity and absolute maximum angular acceleration of the Polynomial interpolation, respectively. Based on the analysis of the research results, this paper presents the applicable conditions and applications of Polynomial interpolation method in trajectory planning, and further summarizes the application conditions and methods of mixed polynomials.

Intrinsic sense of touch for intuitive physical human-robot interaction.

The sense of touch is a property that allows humans to interact delicately with their physical environment. This article reports on a technological advancement in intuitive human-robot interaction that enables an intrinsic robotic sense of touch without the use of artificial skin or tactile instrumentation. On the basis of high-resolution joint-force-torque sensing in a redundant arrangement, we were able to let the robot sensitively feel the surrounding environment and accurately localize touch trajectories in space and time that were applied on its surface by a human. Through an intertwined combination of manifold learning techniques and artificial neural networks, the robot identified and interpreted those touch trajectories as machine-readable letters, symbols, or numbers. This opens up unexplored opportunities in terms of intuitive and flexible interaction between human and robot. Furthermore, we showed that our concept of so-called virtual buttons can be used to straightforwardly implement a tactile communication link, including switches and slider bars, which are complementary to speech, hardware buttons, and control panels. These interaction elements could be freely placed, moved, and configured in arbitrary locations on the robot structure. The intrinsic sense of touch we proposed in this work can serve as the basis for an advanced category of physical human-robot interaction that has not been possible yet, enabling a shift from conventional modalities toward adaptability, flexibility, and intuitive handling.

Optimization of Joint Space Trajectories for Assistive Lower Limb Exoskeleton Robots: Real-Time and Flexible Gait Patterns

This research focuses on designing a real-time, flexible gait planner for lower limb exoskeleton robots to assist patients with lower limb disabilities. Given the dynamic nature of gait parameters, which vary according to ground conditions and user intent, the challenge lies in developing a gait planner capable of adapting to these changes in real-time. To avoid planning complications in the cartesian space and to comply with the speed constraints of joint motors, this paper proposes planning in joint space. Furthermore, the approach also considers the maximum speed capabilities of the joint motors, aiming to generate an executable gait pattern and simultaneously enhance the robot’s walking speed by determining the minimum time required for implementation. The introduced gait planner optimizes joint trajectories for minimal angular acceleration. To provide flexibility, generalized boundary conditions suitable for different scenarios are defined. The effectiveness of the proposed planner is validated through comprehensive performance analysis, simulations, and successful implementation trials on the Exoped® robot in various scenarios.

The intelligibility of mobile trajectories: walking in public space

This paper deals with practices of personal mobility in public space, such as walking, passing-by and queuing, and their intelligible, recognizable and intersubjectively coordinated character. People co-exist in public places without having to explain their conduct in so-many-words; they smoothly navigate by coordinating their bodies and mobile trajectories without collisions; they queue without any instructions and differentiate between who joins the queue and who projects to butt in the queue. This article addresses the intelligibility of walking trajectories in public space, how they are bodily achieved and visibly interpreted. It reflects on mobility by relying on the notion of public in two different but complementary perspectives: a) by reference to mobility in the context of public places such as parks, squares, and streets; b) by reference to the public intelligibility and recognizability of mobile actions in social interaction. The convergence between these two notions of public enables us to investigate how mobile social actions are formed (made recognizable) and how they are ascribed (actually recognized) by co-present unacquainted persons in public space. The analysis draws on video recordings of mobile trajectories in streets, pathways, and squares.

A topological Hund nodal line antiferromagnet

The interplay of topology, magnetism, and correlations gives rise to intriguing phases of matter. In this study, through state-of-the-art angle-resolved photoemission spectroscopy, density functional theory, and dynamical mean-field theory calculations, we visualize a fourfold degenerate Dirac nodal line at the boundary of the bulk Brillouin zone in the antiferromagnet YMn2Ge2. We further demonstrate that this gapless, antiferromagnetic Dirac nodal line is enforced by the combination of magnetism, space-time inversion symmetry, and nonsymmorphic lattice symmetry. The corresponding drumhead surface states traverse the whole surface Brillouin zone. YMn2Ge2 thus serves as a platform to exhibit the interplay of multiple degenerate nodal physics and antiferromagnetism. Interestingly, the magnetic nodal line displays a d-orbital dependent renormalization along its trajectory in momentum space, thereby manifesting Hund’s coupling. Our findings offer insights into the effect of electronic correlations on magnetic Dirac nodal lines, leading to an antiferromagnetic Hund nodal line.

Illumination and Shadows in Head Rotation: Experiments with Denoising Diffusion Models

Accurately modeling the effects of illumination and shadows during head rotation is critical in computer vision for enhancing image realism and reducing artifacts. This study delves into the latent space of denoising diffusion models to identify compelling trajectories that can express continuous head rotation under varying lighting conditions. A key contribution of our work is the generation of additional labels from the CelebA dataset, categorizing images into three groups based on prevalent illumination direction: left, center, and right. These labels play a crucial role in our approach, enabling more precise manipulations and improved handling of lighting variations. Leveraging a recent embedding technique for Denoising Diffusion Implicit Models (DDIM), our method achieves noteworthy manipulations, encompassing a wide rotation angle of ±30°. while preserving individual distinct characteristics even under challenging illumination conditions. Our methodology involves computing trajectories that approximate clouds of latent representations of dataset samples with different yaw rotations through linear regression. Specific trajectories are obtained by analyzing subsets of data that share significant attributes with the source image, including light direction. Notably, our approach does not require any specific training of the generative model for the task of rotation; we merely compute and follow specific trajectories in the latent space of a pre-trained face generation model. This article showcases the potential of our approach and its current limitations through a qualitative discussion of notable examples. This study contributes to the ongoing advancements in representation learning and the semantic investigation of the latent space of generative models.