This article studies a class of pursuit problems admitting both a simple geometric solution as well as a more general analytic treatment. The results are specialized to demonstrate solutions to certain elementary problems typically posed to high schoolers, although a full analytic treatment, requiring some more comfort with geometry and calculus, is typically avoided at that stage.

Drone technology has undoubtedly become an integral part of our everyday life these days. The business and industrial use of unmanned aerial vehicles (UAV) can provide advantageous solutions in many areas of life, and they are also optimal for emergency situations and for accessing hard-to-reach places. However, their application poses numerous technological and regulatory challenges to be overcome. One of the weak links in the operation of UAVs is the limited availability of energy. In order to address this issue authors developed a novel trajectory planning method for UAVs to optimize the energy necessity during flight. First, an “energy map” was created, which was the basis for trajectory planning, i.e., determining the energy consumption of the individual components. This was followed by configuring the 3D environment including partitioning of the work space (WS), in fact, defining the free spaces, occupied spaces (obstacles) and semi-occupied/free spaces. Then the corresponding graph-like path(s) were generated on the basis of the partitioned space, where a graph search-based heuristic trajectory planning was initiated, taking into account the most important wind conditions including velocity and direction. Finally, in order to test the theoretical results, some sample environments were created to test and analyse the proposed path generations. The method eventually proposed was able to determine the optimal path in terms of energy consumption.

This paper designs and fabricates a small-type permanent-magnet linear motor and driver for automation applications. It covers structural design, magnetic circuit analysis, control strategies, and hardware development. Magnetic circuit analysis software JMAG is used for flux density distribution, back electromotive force(back-EMF), and electromagnetic force analysis. To address end effects and cogging force, auxiliary core structures and control strategies are proposed. The motor has a three-phase, six-coil, seven-pole configuration, achieving a peak phase voltage of 3.621 V at 1.0 m/s with a total harmonic distortion(THD) of 0.49 % and the voltages of each phase are balancing a phase voltage error of -0.002 V. The average electromagnetic force is 5.46 N/A. The driver uses a three-phase inverter with voltage space vector pulse width modulation(VSVPWM), dq-axes current closed-loop control, electromagnetic force control, and S-curve motion trajectory control. Simulations with JMAG-RT models in MATLAB/Simulink verify the control strategies. A microcontroller (TMS320F280045) serves as the control core, and a magnetic encoder with a 488 nm resolution provides position feedback. Each phase winding has an equivalent resistance of approximately 3.0 Ω and an inductance of approximately 1.98 mH. The S-curve motion trajectory control achieves a maximum position error of approximately 5.0 μm and a speed ripple of approximately 0.03 m/s at steady speed. With cogging force improvement, the maximum electromagnetic force is 4.90 N, and the q-axis current compensates around 1.05 A based on mover position. S-curve motion trajectory control results in highly stable and responsive performance. Practical tests show that the designed small-type permanent-magnet linear motor and its driver provide efficient, stable, and high-precision solutions for automation applications.

With the rapid spread of built-in GPS handheld smart devices, the trajectory data from GPS sensors has grown explosively. Trajectory data has spatio-temporal characteristics and rich information. Using trajectory data processing techniques can mine the patterns of human activities and the moving patterns of vehicles in the intelligent transportation systems. A trajectory similarity measure is one of the most important issues in trajectory data mining (clustering, classification, frequent pattern mining, etc.). Unfortunately, the main similarity measure algorithms with the trajectory data have been found to be inaccurate, highly sensitive of sampling methods, and have low robustness for the noise data. To solve the above problems, three distances and their corresponding computation methods are proposed in this paper. The point-segment distance can decrease the sensitivity of the point sampling methods. The prediction distance optimizes the temporal distance with the features of trajectory data. The segment-segment distance introduces the trajectory shape factor into the similarity measurement to improve the accuracy. The three kinds of distance are integrated with the traditional dynamic time warping algorithm (DTW) algorithm to propose a new segment–based dynamic time warping algorithm (SDTW). The experimental results show that the SDTW algorithm can exhibit about 57%, 86%, and 31% better accuracy than the longest common subsequence algorithm (LCSS), and edit distance on real sequence algorithm (EDR) , and DTW, respectively, and that the sensitivity to the noise data is lower than that those algorithms.

Predicting human trajectories poses a significant challenge due to the complex interplay of pedestrian behavior, which is influenced by environmental layout and interpersonal dynamics. This complexity is further compounded by variations in scene density. To address this, we introduce a novel dataset from the Festival of Lights in Lyon 2022, characterized by a wide range of densities (0.2-2.2 ped/m2). Our analysis demonstrates that density-based classification of data can significantly enhance the accuracy of predictive algorithms. We propose an innovative two-stage processing approach, surpassing current state-of-the-art methods in performance. Additionally, we utilize a collision-based error metric to better account for collisions in trajectory predictions. Our findings indicate that the effectiveness of this error metric is density-dependent, offering prediction insights. This study not only advances our understanding of human trajectory prediction in dense environments but also presents a methodological framework for integrating density considerations into predictive modeling, thereby improving algorithmic performance and collision avoidance.

Background/Objectives: Concurrent opioid (OPI) and benzodiazepine (BZD) use may exacerbate falls/fractures risk compared to no use or use alone. Yet, patients may need concurrent OPI-BZD use for co-occurring conditions (e.g., pain and anxiety). Therefore, we examined the association between longitudinal OPI-BZD dosing patterns and subsequent injurious falls risk. Methods: We conducted a retrospective cohort study including non-cancer fee-for-service Medicare beneficiaries initiating OPI and/or BZD in 2016-2018. We identified OPI-BZD use patterns during the 3 months following OPI and/or BZD initiation (i.e., trajectory period) using group-based multi-trajectory models. We estimated time to first injurious fall within 3 months post-trajectory period using inverse-probability-of-treatment-weighted Cox proportional hazards models. Results: Among 622,588 beneficiaries (age≥65=84.6%, female=58.1%, White=82.7%; having injurious falls=0.45%), we identified 13 distinct OPI-BZD trajectories: Group(A):Very-low OPI-only (early discontinuation)(44.9% of the cohort); (B):Low OPI-only (rapid decline)(15.1%); (C):Very-low OPI-only (late discontinuation)(7.7%); (D):Low OPI-only (gradual decline)(4.0%); (E):Moderate OPI-only (rapid decline)(2.3%); (F):Very-low BZD-only (late discontinuation)(11.5%); (G):Low BZD-only (rapid decline)(4.5%); (H):Low BZD-only (stable) (3.1%); (I):Moderate BZD-only (gradual decline)(2.1%); (J):Very-low OPI (rapid decline)/Very-low BZD (late discontinuation)(2.9%); (K):Very-low OPI (rapid decline)/Very-low BZD (increasing)(0.9%); (L):Very-low OPI (stable)/Low BZD (stable)(0.6%); and (M):Low OPI (gradual decline)/Low BZD (gradual decline)(0.6%). Compared with Group(A), 6 trajectories had increased 3-month injurious fall risks: (C): HR, 95%CI=1.78, 1.58-2.01; (D): 2.24, 1.93-2.59; (E): 2.60, 2.18-3.09; (H): 2.02, 1.70-2.40; (L): 2.73, 1.98-3.76; and (M): 1.96, 1.32-2.91. Conclusions: Our findings suggest that 3-month injurious fall risk varied across OPI-BZD trajectories, highlighting the importance of considering both dose and duration when assessing fall risks of OPI-BZD use among older adults.

In this paper, we analyzed the live fish trajectory recorded from an experiment in an experimental vertical slot fishway. Combined with a numerical simulation, we demonstrated that randomness shown in fish trajectory might not merely be attributed to fish's random choices in its swimming, also could be an adaption consequence to the bulk unsteady turbulent flow structure. Simple superposing the fish trajectory on the time-averaged flow field obtained either by interpolating on discrete point measurements or numerical simulation is not an ideal method for fish movement description in fishway engineering. How to model the fish paths in transient flow and the necessity of simultaneous recording of the flow field and the fish locomotion are challenging topics. The suggested spectrum analysis of the flow field may provide a new general method to reproduce the fish trajectory in a complex turbulent flow.

The purpose of this study is to compare and analyze the kinematic characteristics of the upper limb segments during the archery shooting of Paralympic Wheelchair Class archers (ARW2 - second wheelchair class – paraplegia or comparable disability) and Paralympic Standing Class archers (ARST - standing archery class – loss of 25 points in the upper limbs or lower limbs), where archers are classified according to their disability grade among elite disabled archers. The participants of this study were selected as seven elite athletes with disabilities, 4 ARW2, and 3 ARST. The analysis variables were 1) the time required for each phase, 2) the angle of inclination of the body center, 3) the change of trajectory of body center, and 4) the change of movement locus of bow center by phase when performing six shots in total. The ARW2 group showed a longer time than the ARST group, and the angle of the body did not show a significant difference between the two groups. Although there was no significant difference in the mean score between the two groups, it was judged that kinematic performance according to each group was, in that there was a measurable variation in kinematic variables.

Recently, a large number of Transformer-based solutions have emerged for the trajectory prediction task, but there are shortcomings in the effectiveness of Transformers in trajectory prediction. Specifically, while position encoding preserves some of the ordering information, the self-attention mechanism at the core of the Transformer has its alignment invariance that leads to the loss of temporal information, which is crucial for trajectory prediction. For this reason, we design a simple and efficient strategy for temporal information extraction and prediction of trajectory sequences using the self-attention mechanism and linear layers. Experimental results show that the strategy we designed can effectively combine the advantages of the linear layer and self-attention mechanisms, compensating for the shortcomings of the Transformer. Additionally, we conducted an empirical study to explore the effectiveness of the linear layer and sparse self-attention mechanisms in trajectory prediction.

This article explores the intricate journey of neural progenitor cells from the ventricular zones of the embryonic brain, focusing on their pivotal role in the formation of rich club networks, which are integral to the brain's functional architecture. Initially, the ventricular zones, particularly the cerebral ventricular zone, serve as the primary sites for the proliferation and differentiation of neural progenitors, giving rise to various types of neurons and glial cells. We delve into the sequential migration patterns of these cells, emphasizing how early-migrating neurons, destined to form deeper cortical layers, establish extensive and robust connections, potentially evolving into rich club nodes. These nodes are characterized by their high-degree connectivity and serve as crucial hubs for integrating and disseminating information across disparate brain regions.The article further discusses the implications of this developmental pathway in the context of brain network efficiency, resilience, and cognitive function. We highlight how disruptions in early cell migration can lead to anomalies in rich club formation, drawing connections to various neurodevelopmental disorders such as autism, ADHD and schizophrenia. Additionally, the significance of rich club nodes in maintaining efficient information transfer and network resilience is elucidated, underscoring their role in supporting complex cognitive processes and overall brain dynamics.In summary, this article offers a comprehensive overview of the developmental trajectory from the ventricular zones to the establishment of rich club networks, providing insights into the fundamental processes that shape the brain's intricate connectivity and functional capabilities. Ric

This study investigated the accuracy and precision of a commercially available PNT solution that uses DGNSS-SBAS technology. Time and position data were sampled at a frequency of 20Hz during both short and long trajectory of a simulated controlled dry-land slalom, as well as during a real-world on-water slalom exercise. The primary objective was to assess the positional accuracy, availability, integrity, and service continuity of the PNT solution while evaluating its ability to differentiate between trajectories. Additionally, the simulated results were compared with an on-water real-world slalom test to validate the findings. The results of the controlled dry-land slalom test indicate that the PNT solution provided accurate measurements with an overall mean±SD Hrms of 0.20±0.02m. The integrity measures, HDOD and PDOP were found to be ideal to excellent, with values of 0.68±0.03, and 1.36±0.07, respectively. The PNT solution utilised an average of 20±1 satellites from the constellation, resulting in an accuracy of

Calculating a minimum-time trajectory requires the solving of a boundary value problem resulting from invocation of necessary conditions of optimality to set up a set of ordinary differential equations to solve the trajectory between the initial position and desired ending position with set constraints on the path between the two. This manuscript expresses the minimum time optimum trajectory between a satellite in a geosynchronous orbit and a target set on earth’s surface utilizing a non-rotating earth centric coordinate system. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Simulation precision (validated by the quaternion normalization condition) reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the ubiquitous 321 “aerospace” rotation sequence and a 99.84% increase over the so-called 313 “orbital” rotation sequence. Utilizing the proposed optimal trajectory candidate yields a total flight time of 2 hours, 34 minutes and 46 seconds, or an average velocity of 3.85 kilometers per second, while impacting the target with a velocity of 11.54 kilometers per second.

Human milk is recommended for feeding preterm infant. Yet the potential impact of specific breast-milk lipid components on the initial growth rate of very-preterm infants has received scant attention. The current pilot study aims to determine whether breast-milk lipidome had any impact on the early growth pattern of preterm infants fed their own mother’s milk. A prospective monocentric observational birth cohort was established, enrolling 147 preterm infants, who received their own mother’s breast-milk throughout hospital stay. Among that cohort, infants who experienced slow (n=15) or fast (n=11) growth were selected, based on the change in their weight Z-score between birth and hospital discharge (-1.54± 0.42 and -0.48± 0.19 Z-score, respectively). Liquid chromatography-high resolution-mass spectrometry was used to obtain lipidomic signatures in breast-milk. Multivariate analyses made it possible to identify breast-milk lipid species that allowed clear-cut discrimination between the 2 infants’ groups. Validation of the selected biomarkers was performed by means of various multidimensional statistical techniques, false-discovery rate and ROC curve computation. Breast-milk associated with fast growth contained more medium chain-saturated fatty acid and -sphingomyelin, dihomo-γ-linolenic acid (DGLA)-containing phosphethanolamine, and less oleic acid-containing triglyceride and DGLA-oxylipin. Their predictive ability of preterm early-growth rate was validated in presence of confounding clinical factors.

Goal-conditioned reinforcement learning (RL) holds promise for addressing intricate control challenges by enabling agents to learn and execute desired skills through separate decision modules. However, the irregular occurrence of required skills poses a significant challenge to effective learning. In this paper, we demonstrate the detrimental effects of this imbalanced skill(sub-goal) distribution and propose a novel training approach, Classified Experience Replay (CER), designed to mitigate this challenge. We demonstrate that adapting our method to conventional RL methods significantly enhances the performance of the RL agent. Considering the challenges inherent in tasks such as driving, characterized by biased occurrences of required sub-goals, our study demonstrates the improvement in trained outcomes facilitated by the proposed method. In addition, we introduce a specialized framework tailored for self-driving tasks on highways, integrating Model Predictive Control (MPC) into our RL trajectory optimization training paradigm. Our approach, utilizing CER with the suggested framework, yields remarkable advancements in trajectory optimization for RL agents operating in highway environments.

This research addresses the formidable challenge of achieving precise trajectory tracking for autonomous vehicle formations in uncertain environments. It introduces an adaptive control system tailored for autonomous vehicles, with a primary focus on ensuring prescribed performance in trajectory tracking within a leader-follower formation paradigm. The system incorporates a guidance law that allows the leader vehicle to dynamically adjust desired yaw angles and speeds for follower vehicles based on the established reference trajectory, enhancing tracking accuracy and responsiveness to environmental changes. To address practical external disturbances, the study utilizes Radial Basis Function Neural Networks (RBFNN) in conjunction with second-order filters for error approximation. This approach is further strengthened by a carefully formulated adaptive law. The innovative integration of a barrier Lyapunov function with the backstepping method significantly enhances the system’s adaptability and robustness, ensuring trajectory tracking performance meets predetermined standards. Simulation results illustrate the control system’s adept handling of various external disturbances, consistently maintaining trajectory tracking errors within predefined limits. This underscores the system’s potential to markedly enhance the operational reliability and efficiency of autonomous vehicle formations in unpredictable environmental conditions.

This paper presents a new adaptive and optimal algorithm for the trajectory tracking control of a quadrotor using iterative learning algorithm (ILA) and enumerative learning algorithm. Ordinarily the ILA, as an adaptive method, can perform well with PID control to improve the controller’s performance for a nonlinear system. Quadrotors are considered as non-linear and unstable systems which the use of an adaptive and optimal controller can increase its stability and decrease error level. In this method, a PID controller is proposed for the outer and inner control loops of a quadrotor and the ILA is used to adapt PID control gains. Subsequently, an enumerative learning algorithm is used to optimize the learning rates of the ILA. For this purpose, at first, the dynamic model of the quadrotor is acquired. After that, the structure of the inner and outer control loops is defined. In the end, the simulation results for the trajectory tracking control of a quadrotor are demonstrated. Through simulation, it is concluded that as time increases, the performance of the suggested control method in trajectory tracking control becomes better and better and error signals convergence to zero.

Vibration problems have become one of the most important factors affecting robot performance. To this end, a terminal residual vibration suppression method based on joint trajectory optimization is proposed to improve the accuracy and stability of robot motion. Firstly, based on the characteristics of the friction nonlinearity due to joint coupling and physical feasibility of dynamic parameters, a semidefinite programming method is used to identify dynamic parameters with actual physical meaning, thereby obtaining an accurate dynamic model. Then, based on the result of the residual vibration time domain analysis, a joint trajectory optimization model with the goal of minimizing joint tracking error is established. The Chebyshev collocation method is used to discretize the optimization model. The dynamic model is used as the optimization constraint, and barycentric interpolation is used to obtain the optimized joint motion trajectory. Finally, industrial robot experiments prove that the vibration suppression method proposed in this article can reduce the maximum acceleration amplitude of residual vibration by 62% and the vibration duration by 71%. Compared with the input shaping method, the method proposed in this paper can reduce the terminal residual vibration more effectively and ensure the consistency of running time and trajectory.

Aiming at the problem of UAV cluster configuration reconstruction, in order to obtain the cluster reconstruction method, the theory and simulation of cluster reconstruction control strategy is studied by simplifying the model，deducing the theoretical formula and analyzing the example. Taking 10 UAVs cluster as an example, the distribution of UAVs in different configurations was analyzed. According to the change of cluster configuration, the principle of formation reconstruction and the execution ability of configuration, the cluster capability was analyzed. The group behavior is modeled by group behavior rules, reconfiguration topology analysis and reconfiguration cost measurement. Based on the cluster parameters and configuration characteristics, simulation experiments were carried out to obtain the change curve of the reconstruction cost and time and the trajectory movement diagram of the UAV in different configurations.

Space exploration presents vast prospects for scientific, industrial, and economic progress. This paper introduces the MeSat mission as a pioneering approach to Mars exploration. MeSat aims to deepen our understanding of Martian conditions and resources by employing an optimized Earth-to-Mars trajectory, enabling a comprehensive study of the Martian atmosphere and surface. The mission comprises a Cargo Microsatellite hosting three 6U CubeSats and two 3U CubeSats, deployed into four separate Mars orbits forming a constellation. Each CubeSat carries distinct payloads: a THz radiometer for water detection, a high-resolution surface camera, a top-tier spectrometer, and a Fourier Transform Spectrometer (FTS) for wind speed readings. This paper focuses on two pivotal innovations: the development of a 183GHz radiometer payload for detecting water on Mars and a optimal mission design algorithm that analyzes a fuel-efficient low-thrust trajectory from Earth to Mars. Regarding the THz payload for water detection, a subharmonic Schottky diode-based mixer is meticulously designed to efficiently down-convert radio signals. The down-converted signals are carefully analyzed using a customized Do-It-Yourself (DIY) spectrum meter, which facilitated the capture and processing of acquired data. To provide the necessary Local Oscillator signals for the mixer, a Tripler employing three-anode Schottky diodes is developed. Additionally, the Tripler requires a signal generator for its entry frequency, which is addressed by developing a DIY signal generator. Together, these components, comprising the Schottky diode mixer, Tripler, and DIY circuits, collectively form the complete THz payload, demonstrating exceptional power efficiency with a total consumption of only 3.7W. The study employs a dual-step hybrid optimization algorithm (PSO-Homotopy) to analyze fuel-efficient low-thrust trajectories from Earth to Mars, incorporating the Ephemeris dynamics model to account for gravitational perturbations in the entire solar system. In practical mission design, crucial factors like hyperbolic excess velocity, diverse opportunities for Earth launch and Mars rendezvous, varied propulsion systems, and Time of Flight (TOF) play vital roles in trajectory optimization.

With the rise of the Internet of Things (IOT), mobile devices and Location-Based Social Network (LBSN), an abundant amount of trajectory data has made research on location prediction more popular. The check-in data shared through LBSN hides information related to life patterns, obtaining this information is helpful for location prediction. However, the trajectory data recorded by mobile devices is different from check-in data that has semantic information. In order to obtain the user’s semantic, relevant studies match the stay point to the nearest Point of Interest (POI), but location error may lead to wrong semantic matching. Therefore, we propose A Self-Attention for Next Location Prediction based on Semantic Mining to predict the next location. When calculating the semantic feature of a stay point, the first step is to search for the k nearest POI, then use the reciprocal of the distance from the stay point to the k nearest POI and the number of categories as weights. Finally, we use the probability to express semantic without losing other important semantic information. Furthermore, this research combined with sequential pattern mining can bring richer semantic features. In order to better perceive the trajectory, temporal features learn periodicity of time series by sine function. In terms of location features, we build a directed weighted graph and regard the frequency of users visiting locations as the weight, so the location features are rich in contextual information. We then adopt the Self-Attention model to capture long-term dependencies in long trajectory sequences. Experiments in Geolife show that the semantic matching of this study improved by 45.78% in TOP@1 compared with the closest distance search for POI. Compared with the baseline, the model proposed in this study improved by 2.5% in TOP@1.

Deploying UAVs as aerial base stations is an exceptional approach to reinforce terrestrial infrastructure owing to their remarkable flexibility and superior agility. However, it is essential to design their flight trajectory effectively to make the most of UAV-assisted wireless communications. This paper presents a novel method for improving wireless connectivity between UAVs and terrestrial users through effective path planning. This is achieved by developing a goal-directed trajectory planning method using active inference. First, we create a global dictionary using TSPWP instances executed on various training examples. This dictionary contains letters representing available hotspots, tokens representing local paths, and words depicting complete trajectories and hotspot order. By using this world model, the UAV can understand the TSPWP’s decision-making grammar and how to use the available letters to form tokens and words at various levels of abstraction and time scales. With this knowledge, the UAV can assess encountered situations and deduce optimal routes based on the belief encoded in the world model. Our proposed method outperforms traditional Q-learning by providing fast, stable, and reliable solutions with good generalization ability.

This study presents the substantiation, development, and analysis of a technique for planning the autonomous vehicle (AV) motion reference parameters. The trajectory plan, speed and acceleration distributions, including other AV's kinematic parameters, are determined using sequential optimization. The study objectives are based on an analysis of the fundamental problems of AV motion planning summarized in this area's latest publications. The proposed approach combines the basic principles of the finite element method (FEM) and nonlinear optimization with nonlinear constraints. First, the generalization on representing an investigated function by finite elements (FE) is briefly described. A one-dimension FE with two nodes and three degrees of freedom (DOF) in a node was chosen as the basic one, corresponding to the 5th-degree polynomial. Next, a method for determining the motion trajectory is presented. The following are considered: formation of a restricted space for the AV's allowable maneuvering, the geometry of motion trajectory and its relation with vehicle steerability parameters, cost functions and their influences on the desirable trajectory's nature, compliance of nonlinear restrictions of the node parameters with the motion area boundaries. At the second stage, a technique for optimizing AV speed and acceleration redistribution is presented. The model considers possible combinations of cost functions, conditions of limiting the kinematic parameters with the tire slip critical speed, maximum speed level, maximum longitudinal acceleration, and critical lateral acceleration. In the simulation section, several variants of trajectories were searched and compared. Several versions of distributing the longitudinal speed and acceleration curves are determined, and their comparative analysis is fulfilled. At the end of the paper, the advantages and drawbacks of the proposed technique are noted. The conclusion is made regarding the options for improving the method in further studies.

The dynamics of a low-energy charged particle in an axis-symmetric magnetic field is known to be a regular superposition of periodic–although possibly incommensurate–motions. The projection of the particle orbit along the two non-ignorable coordinates (x,y) may be expressed in terms of each other: y=y(x), yet–to our knowledge–such a functional relation has never been directly produced in literature, but only by way of a detour: first, equations of motion are solved, yielding x=x(t),y=y(t), and then one of the two relations is inverted, x(t)→t(x). In this paper we present a closed-form functional relation which allows to express coordinates of the particle’ orbit without the need to pass through the hourly law of motion.

Trajectory Optimization (TO) is the sequence of processes that are considered in order to produce the best path that mends the overall performance or reduces the consumption of the resources where the restriction system remains maintained. In this survey, an inclusive review of the latest advancements in modeling and optimization of trajectory generation in robotic applications will be discussed broadly. In recent times, numerous studies have employed optimal control techniques involving direct and indirect methods in order to convert the authentic Trajectory Optimization problem into a constrained parameter optimization problem. Moreover, a huge variety of optimization algorithms such as Genetic Algorithms (GA), Simulated Annealing (SA), Sequential Quadratic Programming (SQP), and Particle Swarm Optimization (PSO) are used aiming to find the optimal solutions for trajectory planning. It is observable that, minimizing the jerk, energy consumption, and execution time among the most widely used design objectives, on the other hand, the robot’s joints configurations and the motor torques are the most used design variables. This paper aims to review the fundamental techniques and their coincident robotic applications in the field of trajectory optimization aiming to afford some steering for related researchers.

Model predictive control (MPC) is a multi-objective control technique that can handle 2 system constraints. However, the performance of an MPC controller highly relies on a proper 3 prioritization weight for each objective, which highlights the need for a precise weight tuning 4 technique. In this paper, we propose an analytical tuning technique by matching the MPC 5 controller performance with the performance of a linear quadratic regulator (LQR) controller. The 6 proposedmethodology derives the transformation of LQRweightingmatrixwith a fixedweighting 7 factor using discrete algebraic Riccati equation (DARE) and designs MPC controller using the 8 idea of discrete time linear quadratic tracking problem (LQT) in the presence of constraints. 9 The proposed methodology ensures the optimal performance between unconstrained MPC and 10 LQR controller and provides a sub-optimal solution while the constraints are active during 11 transient operations. The resultingMPC behaves as the discrete time LQR by selecting appropriate 12 weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. 13 In this paper, the effectiveness of the proposed technique is investigated in the application of 14 a novel vehicle collision avoidance system which is designed in the form of linear inequality 15 constraints within MPC. The simulation results confirm the potency of the proposed MPC control 16 technique in performing a safe, feasible and collision free path while respecting the inputs, states 17 and collision avoidance constraints.

Keyhole neurosurgery implies reaching a target area inside the brain through an entry point specified by the neurosurgeon. In order to avoid complications, a risk assessment procedure must be done to establish the minimum risk trajectory from the entry point to the target area. The neurosurgeon establishes the risk values for the brain structure according to the type of intervention. The preset brain structure risk value is used to assess the risk value for each voxel of the brain. This paper proposes an improved risk assessment methodology based on the sum of N maximum risk values for each voxel. Then, risk assessment for a trajectory is done by adding the risk of all voxels that are part of the path. The safest trajectory is defined as the trajectory with the lower risk. Our proposed search trajectory methodology includes a Genetic Algorithm (GA) for finding the safest trajectories. The use of a GA drastically reduces the number of trajectories to analyze, speeding up the planning procedure. The achieved results were qualified by expert neurosurgeons as satisfactory. Our proposed method allows neurosurgeons to calibrate the surgical planning system by allowing them to establish the risk brain structure and the risk value for each structure.

This article addresses the trajectory tracking between two non-identical systems with chaotic properties. We employ the Rossler chaotic and RCL-shunted Josephson junctions model in similar phase space to study trajectory tracking. In order to achieve the goal tracking, we afford two stages to approximate the target tracking. The first stage utilizes the active control technique to transfer the output signal from the RCLs-J system into the quasi-Rossler system. Then next, the RCLs-J system employs the proposed the iterative learning control scheme and the control signal from the drive system to trace the trajectory of Rossler system. The numerical results demonstrate the proposed method and the tracking system is asymptotically stable.

Background and objective: The impairments and duration of PASC (Post-acute sequelae of COVID-19) symptoms in mental health have up to date not been comprehensively examined. Our objective is to provide longitudinal data on the mental health of Post-COVID patients and to identify risk and protective factors associated with a severe or prolonged course. Methods: Mental health of 265 Post-COVID patients of the outpatient Post-COVID centre of the University-Hospital Erlangen was assessed 17.1 (T0) and 22.5 months after infection (T1). An online survey with validated questionnaires for Post-COVID symptoms (Post-COVID-Syndrome-Score), depression (Patient-Health-Questionnaire 9), somatic symptoms (Patient-Health-Questionnaire 15), anxiety (Generalized-Anxiety-Disorder 7), fatigue (Fatigue-Severity-Scale) and Post-Exertional Malaise (PEM) (DePaul Post-Exertional-Malaise Screening) was conducted in the home environment. Results: 80% of patients experienced severe PASC at follow up. Clinically relevant symptoms of depression, persistent somatic symptoms, anxiety, and fatigue were reported by 55.8%, 72.5%, 18.9% and 89.4% respectively. Depressive, anxiety and somatic symptom severity decreased significantly over time; fatigue and PEM remained on an unchanged high level. Risk factor for higher depression scores was older age; prior psychiatric illness treated with psychotherapy was associated with more severe depressive, somatic, anxiety and PASC symptoms. PEM symptoms were significantly associated with longer duration between acute infection and initial presentation in the Post-COVID centre. Conclusion: Our findings align with previous research, claiming severe mental health symptoms in PASC syndrome, lasting for months after infection. In-depth assessment of risk and protective factors for mental health implications of PASC is needed for planning health services and disease prevention.

Pedestrian trajectories are crucial for self-driving cars to plan their paths effectively. The sensors implanted in these self-driving vehicles, despite being state-of-the-art ones, often face inaccuracies in the perception of surrounding environments due to technical challenges for adverse weather conditions, interference from other vehicles sensors and electronic devices, and signal reception failure, leading to incompleteness in trajectory data. But for real-time decision making for autonomous driving, the trajectory imputation is no less crucial. Previous attempts to address this issue such as statistical inference and machine learning approaches have shown promise. Yet, the landscape of deep learning is rapidly evolving with new and more robust models emerging. In this research, we have proposed an encoder-decoder architecture, Human Trajectory Imputation Model, coined as HTIM, to tackle these challenges. This architecture aims to fill in the missing parts of pedestrian trajectories. The model has been evaluated using the Intersection drone inD dataset, containing trajectory data at suitable altitudes preserving naturalistic pedestrian behavior with varied dataset sizes. To assess the effectiveness of our model, we have utilized L1, MSE, Quantile and ADE loss. Our experiments have demonstrated that HTIM outperforms the majority of the state-of-the-art methods in this field, thus indicating its superior performance in imputing pedestrian trajectories.

This study presents a novel kinematic tracking model, designed for a networked exoskeleton system that is asynchronously taught by a remote therapist. On the server side, the therapist’s rehabilitation exercises are quantitatively assessed using a monocular passive vision system. The resultant analytical metrics are then transmitted asynchronously over the network to patients equipped with exoskeletons. On the client side, the exoskeleton utilizes these analytical metrics as reference paths for exercises, complemented by electromyography (EMG) feedback. This work introduces a calibration approach aimed at estimating angular positions by utilizing EMG observations. The calibration model establishes real-time correlations between polynomial reference positions. This calibration mechanism is integrated into simulations of both upper and lower limb exoskeletons. We further explore redundant kinematics, incorporating an EMG observer for linear, time-variant rehabilitation tracking control. Our methodology is validated using vision-based metric data and experimental EMG measurements for various exercises, including shoulder flexion, elbow flexion, and rowing-like movements. This work also includes computer simulations for tracking the control of rehabilitation exercises, demonstrating the adaptability of the system in reliably, robustly, and effectively following desired trajectories.

The motion of Unmanned Surface Vehicles (USVs) is frequently disturbed by the ocean wind, wave and current. A poorly designed controller will lead to failures and even safety problems during actual navigation. In order to obtain satisfied control performance of the motion for the USVs, a Model Predictive Control (MPC) based on improved Nonlinear Disturbance Observer (NDO) is proposed. Firstly, the USV model is approximately linearized and MPC is designed for the multivariable system with constraints. In order to compensate the influence of disturbances, an improved NDO is designed, with which the calculation time for the MPC saved a lot. Finally, comparison experiments are conducted between the MPC with NDO and the MPC with improved NDO, and the results show that they have similar performance to the USVs. However, the proposed method has less parameter to be tuned and it is much more time-saving compared to the MPC with traditional NDO.

With the great development of intelligent transportation systems (ITS), travel time prediction has attracted the attentions of many researchers and a large number of prediction methods have been developed. However, as an unavoidable topic, the predictability of travel time series is the basic premise for travel time prediction has received less attention than the methodology. Based on the analysis of the complexity of travel time series, this paper defines travel time predictability to express the probability of correct travel time prediction and proposes an entropy-based method to measure the upper bound of travel time predictability. Multiscale entropy is employed to quantify the complexity of travel time series, and the relationships between entropy and the upper bound of travel time predictability are presented. Empirical studies are made with vehicle trajectory data in an express road section. The effectiveness of time scales, tolerance, and series length to entropy and travel time predictability are analysis, and some valuable suggestions about the accuracy of travel time predictability are discussed. Finally, the comparisons between travel time predictability and actual prediction results from two prediction models, ARIMA and BPNN, are conducted. Experimental results demonstrate the validity and reliability of the proposed travel time predictability.

The paper addresses the challenging issue of trajectory tracking for uncertain quadrotor UAVs, particularly under the constraints of input saturation and external disturbances. It introduces adaptive laws for managing uncertainties in mass and inertia moments without requiring prior knowledge, ensuring effective control even with varying system parameters. To counteract the effects of input saturation, the study incorporates an auxiliary system designed to compensate for these limitations. Additionally, a disturbance observer(DO) is utilized to manage and mitigate the impact of time-varying external disturbances. The proposed control strategy integrates a sliding mode adaptive control approach with an inner-outer loop structure, enhancing robustness and adaptability. Numerical simulations demonstrate the effectiveness of the designed control strategy.

Robot manipulators are robotic systems that are frequently used in automation systems and able to provide increased speed, precision and efficiency in the industrial applications. Due to their nonlinear and complex nature, it is crucial to optimize the robot manipulator systems in terms of trajectory control. In this study, positioning analysis based on artificial neural networks (ANN) were performed for robot manipulator systems used in the textile industry and the optimal ANN model for the high-accuracy positioning was improved. The inverse kinematic analysis of a 6 degree of freedom (DOF) industrial denim robot manipulator were carried out via 4 different learning algorithms of Delta-Bar-Delta (DBD), Online Back Propagation (OBP), Quick Back Propagation (QBP) and Random Back Propagation (RBP) for proposed neural network predictor. From the results obtained, it was observed that QBP based 3-10-6 type ANN structure produced the optimal results in terms of estimation and modelling of trajectory control. In addition, 3-5-6 type ANN structure was also improved and its Root Mean Square Error (RMSE) and statistical R2 performances were compared to that of 3-10-6 ANN structure. Consequently, it can be concluded that the proposed neural predictors can successfully be employed in real-time industrial applications for robot manipulator trajectory analysis.

Due to constraints in launch platform and cost, the maneuverability of gliding-guided projectiles is limited, necessitating a rational design of their trajectory schemes. To reduce the sensitivity of trajectory schemes to uncertainties while ensuring compatibility between flight schemes and guidance control systems, and fully exploiting the control capability of the projectile, a closed-loop robust trajectory planning method is proposed. Models of major uncertain factors and states deviation at the control-start point are established. Based on the NIPCE method, the stochastic dynamic model is transformed into a high-dimensional deterministic model with PCE coefficients as state variables, and the uncertainty propagation law is obtained. A PID algorithm is employed to design a tracking guidance law based on position error feedback, and open-loop and closed-loop robust trajectory planning models are established accordingly. The optimal control problem is solved by transforming it into a nonlinear programming problem using the direct shooting method. Simulation results indicate that the NIPCE method can significantly improve the computational efficiency of uncertainty propagation while ensuring accuracy. Open-loop robust planning can effectively mitigate the sensitivity of gliding trajectories to uncertainties but cannot completely eliminate terminal dispersion. Closed-loop robust planning effectively improves control effort consumption on the basis of open-loop planning.

Traffic congestion and frequent traffic accidents have become main problems affecting urban traffic. Effective location prediction of vehicle trajectory can help alleviate traffic congestion, reduce the occurrence of traffic accidents, and optimize the urban traffic system. Vehicle trajectory is closely related to the surrounding Points of Interest (POI). POI can be considered as the spatial feature and can be fused with trajectory points to improve prediction accuracy. A Local Dynamic Graph Spatiotemporal- Long Short-Term Memory (LDGST-LSTM) is proposed in this paper to extract and fuse the POI knowledge and realize next location prediction. POI semantic information is learned by constructing the traffic knowledge graph, and spatial and temporal features are extracted by combining Graph Attention Network (GAT) and temporal attention mechanism. Moreover, the weights of POI that influence location prediction are visualized to improve the interpretability of the proposed model. The effectiveness of LDGST-LSTM is verified on two datasets, including Chengdu taxi trajectory data in October 2018 and August 2014. The accuracy and robustness of the proposed model are significantly improved compared with the benchmark models.

A class of controlled plants, whose dynamics is governed by a vector system of ordinary differential equations with a partially known right-hand side, is considered. The state variables and their velocities are assumed to be measurable. The aim is to design a controller which minimizes a loss function under certain constraints which arguments is the current state of the controlled plant. The designed control action is admitted to be a function of the current sub-gradient only, which supposed to be measurable on-line. The control design is based on ASG (Average Sub-Gradient method) — version of Integral Sliding Mode (ISM) concept, aimed to minimize on average a given convex (not obligatory strongly convex) cost function of the current state under a set of given constraints. An optimization type algorithm is developed and analyzed using ideas of SDM technique. The main results consist in proving the reachability of the "desired regime" (nonstationary analogue of sliding surface) from the beginning of the process and obtaining an explicit upper bound for the averaged loss function decrement, that is, the averaged in time functional convergence is proven and the rate of such convergence is estimated.

This paper discusses the use of networks of Inertial Measurement Units (IMU) for the reconstruction of trajectories from sensor data. Logistics is a natural application domain, to verify the quality of the handling of goods. This is a mass application and the economics of logistics impose that IMUs to be used must be low cost and use basic computational devices. The approach in the paper converts a strategy from the literature, used in the multi-target following problem, to reaching a consensus in a network of IMUs. The paper presents results on how to achieve the consensus in trajectory reconstruction, along with covariance intersection data fusion of the information obtained by all nodes in the network.

For a decade, the studies of dynamic control for unmanned aerial vehicles took a large interest, where drones as a useful technology in different areas were always suffering from several issues like instability-high energy consumption of batteries - inaccuracy of tracking targets. Different approaches are proposed for dealing with the non-linearity issues which present the most important features of this system. This paper describes our focus on the most common control strategies, known as model predictive control MPC, by developing a model based on the sensors embedded in our Tello quadrotor used for indoor purposes. The original controller of Tello quadrotor is supposed to be a slave, where the designed model predictive controller is created in MATLAB and imported to another embedded system, considered as a master; the objective of this model is to track the reference trajectory, almost keeping the stability of the system and ensure the low energy consumption. In the first part, a profound description of the modelling process of a dynamic model for drones is presented, explaining the design of MPC controller with both linear and non-linear strategies built in MATLAB. In the final part, simulation and results are discussed regarding its behaviour and performance, highlighting the MPC model's important role on drones' energy consumption profile.

Reasonable trajectory planning is the precondition for the parafoil airdrop system to achieve autonomous accurate homing and safe landing. In order to successfully realize the self-homing of the parafoil airdrop system, a new trajectory optimization design scheme is proposed in this paper. The scheme is based on the parafoil's unique flight and control characteristics and adopts a segmented homing design. Compared with the current common trajectory design method, its core feature is to avoid the problem that the straight-line flight distance before landing is limited by the radius of the height-reducing area and ensure landing accuracy and safety. Firstly, the different starting states of the parafoil airdrop system and the landing requirements were comprehensively considered, and the homing trajectory is reasonably segmented. Based on the requirements of energy control, stable flight, and landing accuracy, the optimal objective function of the trajectory was established, and the trajectory parameters, calculation methods, and constraints were given. Secondly, the cuckoo search algorithm was applied to optimize the objective function to obtain the final home trajectory. Finally, the trajectory planning under different airdrop conditions was simulated and verified. The results showed that the planned trajectories could reach the target point accurately and meet the flight direction requirements, proving the proposed scheme's correctness and feasibility.

With the rapid development of smart phones, tablets and their operative systems, many positioning enabled sensors have been built into these devices. Users can now accurately fix their location according to the function of GPS receivers. For indoor environments, as in the case we are studying, WiFi based positioning is preferred to GPS due to the attenuation or obstruction of signals. This paper deals with the automatic classification of customers in a Sports Shop Center on the basis of their movements around the shop's premises. To achieve this goal, we start by collecting (x,y) coordinates from customers while they visit the store. Consequently, any costumer's path through the shop is formed by a list of coordinates, obtained with a frequency of one measurement per minute. Then, a guess about the full trajectory is constructed and a number of parameters about these trajectories is calculated before performing an Unsupervised Learning Clustering Process. As a result, we can identify several types of customers, and the dynamics of their behavior inside the shop. This information is of great value to the company, to be used both in the long term and also in short periods of time, monitoring the current state of the shop at any moment, identifying different types of situation appearing during restricted periods, or predicting customer flow conditions

This paper proposes a novel hybrid control strategy for quadrotor unmanned aerial vehicles (UAVs) based on bio-inspired neural dynamics. This strategy addresses the velocity jump issue prevalent in traditional backstepping control and the control signal chattering problem common in traditional sliding mode control. The control system comprises an outer-loop bio-inspired backstepping controller and an inner-loop bio-inspired sliding mode controller, ensuring smooth trajectory tracking even in the presence of external disturbances. The stability of the quadrotor UAV control system is rigorously analyzed using Lyapunov stability theory. Extensive comparative simulation experiments are conducted to assess the robustness and effectiveness of the control system. Results demonstrate superior trajectory tracking performance of the proposed control system compared to other control systems for quadrotor UAVs.

Jump rope is a widely-applied basic training in various sports, yet it is understudied biomechanically. This study investigates the impact of cycle-tempo-induced motor control changes in elite jump rope athletes, addressing the biomechanical gap of cyclic skill control. The hypothesis posited two accelerations per jump cycle—one in front of and one behind the body—and anticipated that increased cycle frequency would alter the distribution of acceleration time within a cycle. Using 3D motion analysis, kinematic parameters were obtained and analyzed. The results confirmed the presence of two distinct accelerations per cycle. As tempo increased, the percentage of rear acceleration time increased while front acceleration time decreased, along with peak velocities increasing significantly (p<0.01). Rope trajectory analysis indicated a consistent movement pattern across tempos, primarily in the sagittal plane. Variations in skill control showed shorter contact phases and reduced vertical range of motion for the center of gravity and feet at higher tempos (p<0.05), along with significant reductions in joint range of motion for the lower limbs (p<0.01). These findings enhance the understanding of motor control adaptations to different tempos and have practical implications for developing coaching programs aimed at optimizing performance, stability, and efficiency in jump rope training.

In the extensive monitoring of maritime traffic, maritime management frequently encounters incomplete automatic identification system (AIS) data, particularly in critical static fields like vessel types. This shortfall presents substantial challenges in safety management, necessitating robust methods for data completion. Distinct from road traffic, where road width imposes constraints, maritime vessels of identical classifications often choose significantly divergent routes, deviating by several nautical miles. Sole dependence on trajectory clustering is insufficient. Addressing this issue, we segments the maritime area into spatiotemporal grids, transforming vessel paths into sequences of grid encodings. Utilizing natural language processing techniques, we integrate the Word2vec word embedding approach with our novel biLSTM self-attention chunk-max pooling net (biSAMNet) model, enhancing the classification of vessel trajectories. This method is crucial for determining static details like vessel types. Employing the Taiwan Strait as a case study and benchmarking against CNN, RNN, and methods based on the attention mechanism, our findings underscore our model’s superiority. The biSAMNet achieves an impressive vessel classification F1 score of 0.94, using only 5-dimensional word embeddings, highlighting the effectiveness of Word2vec pre-trained embedding layers. This research introduces a novel paradigm for processing vessel trajectory data, greatly enhancing the accuracy of filling in incomplete vessel type details.

Reducing the construction time for large logistics buildings can result in reduced construction management costs and economic gains from early operation. A large logistic building with a heavy load and long spans was constructed as a precast concrete (PC) structure, which requires the use of a sizable crane to lift heavy PC members. A basic analytical approach is employed to resolve potential errors in the planning of PC member erection and to build a systematic erection plan. Calculation techniques for the trajectory distance, which use the crane location, are applied to select an erection plan that minimizes crane work. A crane trajectory distance calculation algorithm for sustainable PC member erection in large logistic buildings with heavy loads and long spans has been developed. The developed model aids in creating simulation and optimization models to ensure minimal usage of cranes in the future and determining cost, construction time, CO2 emissions, and energy use for each erection plan.

This paper studies the trajectory tracking control of an autonomous underwater vehicle (AUV) based on a stochastic uncertain nonlinear system. We investigate the time-varying gain adaptive control method looking for possible approaches to alleviate the heavy computational burden. Under nonlinear growth, conditions satisfy polynomial growth conditions. These two problems are resolved the fast response time and good path tracking, respectively. Novel adaptive algorithms are developed exploiting the dynamic properties of the AUV motion. By appropriately turning the original controller design problems into parameters choosing problems and then solving them in a functional time-varying observer technical theorem. In order to deal with the station error of system converges to arbitrarily small domains with stochastic uncertain disturbance. A coordinate transformation is proposed for all system states to meet boundedness. We show that the convergence of the AUV trajectory errors can be guaranteed by the proposed contraction constraints in the stability analysis, closed-loop stability is proved, and the system is asymptotically probabilistic in the global scope. They are taking advantage of the guaranteed stability. Extensive simulation studies on the AUV model demonstrate the effectiveness and robustness of the proposed approach. A real-time time-varying gain constructive control strategy is further developed for the Hardware-in-the-loop simulation; the controller design results are imported into the AUV actuator model to verify the effectiveness of the controller design.

Different toll collection types of vehicles and different distribution of tollbooths lead to the toll plaza diverging area becoming a typical vehicle weaving area with frequent crossing behaviors and conflicts on highways. This study aims to identify contributing factors to conflict risks of four vehicle-following patterns in a toll plaza diverging area by developing random parameters ordered logit models with heterogeneity in means and variances. The model can flexibly capture the unobserved heterogeneity of the contributing factors in different vehicle-following patterns. Real-world vehicle trajectory data obtained from the toll plaza diverging area in Nanjing, China, are used for model estimation. The results show that vehicle-following patterns with the same toll collection types have higher percentage of severe conflict risks. The average acceleration of the following vehicles, lane marking indicator, the initial lanes and lane-changes of vehicles are significantly associated with the collision risk levels. The standard deviation of surrogate safety measures of all vehicles in sub-segments are found differ significantly between vehicle-following patterns. Furthermore, a series of likelihood ratio tests are adopted to test the spatial dependence in sub-segments of the diverging area. The findings of this study could provide valuable information for safety improvement in toll plazas.

Although Cable driven rehabilitation devices (CDRD) have advantages over traditional link-driven devices, including lightweight, ease of reconfiguration, remote actuation, etc, the majority of existing lower-limb CDRD is limited to rehabilitation in the sagittal plane. In this work, we extend our previous sagittal plane model (2DOF) to accommodate hip motion in the frontal plane (abduction/adduction) toward studying the feasibility of tracking bi-planar motion (combined frontal and sagittal plane motion) via intra-planar cable routing. Two optimization problems have been formulated to estimate an optimal location of the hip cuffs, first to estimate the optimal cuff location at each time step to identify a single ‘averaged’ optimal cuff location and second to calculate a single optimal cuff location for the entire gait cycle. The optimization solutions identified for the 3DOF model revealed that optimization of the location of cuffs on the anterior and posterior side of the hip joint for 4 cable configuration is not sufficient to generate the desired bi-planar motion. For simultaneous tracking of the bi-planar motion, 2 additional cables have been added at hip joints and are routed in an intra-planar manner. The simulation result with the 3DOF model confirmed successful bi-planar trajectory tracking. The various number of cables and cable routings for tracking bi-planar motion will be studied in future work.

A quantitative description of the second law of thermodynamics in small scale systems and over short time scales comes from various fluctuation theorems. The applicability of the transient fluctuation theorem in particular to small scale systems perturbed from an initial equilibrium steady-state distribution has been demonstrated both theoretically and experimentally in several works over the past few decades. In addition, some experimental works in the past have also made successful attempts to demonstrate the applicability of the fluctuation theorem to small scale systems evolving from a certain nonequilibrium steady-state distribution over relatively long time scales. To this end, this paper seeks to demonstrate the transient fluctuation theorem for a Brownian particle confined within a power-law trapping potential by following the trajectory of the particle that itself is translating linearly along one dimension with constant acceleration in a viscous fluid. Considered herein is an idealized version of this model, in that it is assumed that the force of the trapping potential is only felt by the translating Brownian particle confined within the trap, and that this Brownian particle moves relative to the fluid molecules that are held stationary. The results presented herein show that the transient fluctuation theorem applies not only to equilibrium steady-state distributions but also to nonequilibrium steady-state distributions of an ideal colloidal system in an accelerated frame of reference in the asymptotic (long-time) limit.

Infrastructure monitoring, inspection, repair, and replacement in space is crucial for continued usage and safety, yet it is expensive, time-consuming, and technical very challenging. New robotics technologies and artificial intelligence algorithms are potentially novel approaches that may alleviate such demanding operations using existing or novel sensing technologies. Space structures must necessarily be very light weight due to high costs of placing robots in space. Several methods are proposed and compared to control highly flexible space robotics, where a key challenge is the presence of flexible resonant modes at frequencies so low as to reside inside typical feedback controller bandwidths. Such conditions imply the very action of sending control signals to the ultra-light weight robotics will cause structural resonance. Implementations of incrementally increasing order are offered, achieving over ninety percent performance improvement in trajectory tracking errors, while improvement using unshaped methods merely achieve twenty-four percent improvement in direct comparison (where the only modification is the proposed control methodology). Based on superior performance, single-sinusoidal trajectory shaping is recommended with a corollary benefit of preparing future research into applying deterministic artificial intelligence whose current instantiation relies on single-sinusoidal, autonomous trajectory generation.

The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as $$\displaystyle{x_{n+1}=\frac{x_{n}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-1}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-2}}{ax_n+bx_{n-1}+cx_{n-2}}}$$ and $$\displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-1}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-2}}}$$ is investigated computationally with theoretical discussions and examples. It is noted that all the parameters $a, b, c$ and the initial values $x_{-2}, x_{-1}$ and $x_0$ are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

Aiming at the problem of model error and tracking dependence in the process of intelligent vehicle motion planning, an intelligent vehicle model transfer trajectory planning method based on deep reinforcement learning is proposed, which obtain an effective control action sequence directly. Firstly, an abstract model of the real environment is extracted. On this basis, Deep Deterministic Policy Gradient (DDPG) and vehicle dynamic model are adopted to jointly train a reinforcement learning model, and to decide the optimal intelligent driving maneuver. Secondly, the actual scene is transferred to equivalent virtual abstract scene by transfer model, furthermore, the control action and trajectory sequences are calculated according to trained deep reinforcement learning model. Thirdly, the optimal trajectory sequence is selected according to evaluation function in the real environment. Finally, the results demonstrate that the proposed method can deal with the problem of intelligent vehicle trajectory planning for continuous input and continuous output. The model transfer method improves the model generalization performance. Compared with the traditional trajectory planning, the proposed method output continuous rotation angle control sequence, meanwhile, the lateral control error is also reduced.

For many disciplines of science, all conceivable collisional cross sections and reactions must be precisely known. Although the recent decades were a trial of large-scale research to give these data, many essential atomic and molecular cross section data still missing, and the reliability of the existing cross sections has to be validated. In this paper, we present electron stripping, electron capture, and system breakdown cross sections in carbon (C5+) ions and lithium (Li2+) ions collisions with atomic hydrogen based on the Monte Carlo models of classical and quasi-classical trajectories. According to our expectation, the QCTMC results show higher results in comparison to standard CTMC data, emphasizing the role of Heisenberg correction constraint, especially in the low energy regime. On the Other hand, at high energy, the Heisenberg correction term has less influence as a projectile momentum increase. We present the total cross sections of electron stripping, electron capture, and system breakdown in C5+ ions and Li2+ ions collisions with atomic hydrogen in the impact energy range from 10 keV to 160 keV, which is of interest in astrophysical plasmas, atmospheric sciences, plasma laboratories, and fusion research.

The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamics of the economic system, characterizing the interaction between the efficiency of new technologies and the efficiency of capital productivity. Modifications in the model are determined by the following points: the mathematical model takes into account the dependence of the rate of accumulation on capital productivity, there is an external harmonic influence - the influx of investments and new technological solutions, the economic system has heredity, including time-dependent, which leads to a delayed effect - the system’s response to impact. The property of heredity in the mathematical model is taken into account using fractional derivatives of constant and variable orders. Mathematical model S.V. Dubovsky and its modifications are studied numerically using the Adams-Bashforth-Moulton algorithm. Oscillograms and phase trajectories are constructed, and an interpretation of the simulation results is given.

This work focuses on addressing the dynamic positioning and trajectory tracking problem for a 4 degree-of-freedom (DOF) unmanned underwater vehicle (UUV) in the presence of nonlinear dynamics, parametric uncertainties, system constraints, and time-varying external disturbances. To tackle this problem, a disturbance observer-based control (DOBC) scheme is proposed. The scheme is structured around the model predictive control (MPC) method integrated with an extended active observer (EAOB). Compared to the conventional disturbance observer, the EAOB has the unique ability to handle both external disturbances and system/measurement noises simultaneously. The EAOB leverages a combination of sensor measurements and a system dynamic model to estimate disturbances in real-time, which allows continuous estimation and compensation of time-varying disturbances back to the controller. The proposed disturbance observer-based MPC (DOBMPC) is implemented by feeding the estimated disturbances back into the MPC’s prediction model, which forms a robust adaptive controller with a parameter-varying model. The proposed control strategy is validated through simulations in a Gazebo and Robot Operating System (ROS) environment. The results show that it can effectively reject unpredictable disturbances and improve the UUV’s control performance.

This work aims to develop an autonomous system for the unmanned aerial vehicle (UAV) to land on a moving platform such as the automobile or marine vessels, providing a promising solution for a long-endurance flight operation, a large mission coverage range, and a convenient recharging ground station. Different from most state-of-the-art UAV landing frameworks which rely on UAV’s onboard computers and sensors, the proposed system fully depends on the computation unit situated on the ground vehicle/marine vessel to serve as a landing guidance system. Such novel configuration can therefore lighten the burden of the UAV and computation power on the ground vehicle/marine vessel could be enhanced. In particular, we exploit a sensor fusion-based algorithm for the guidance system to perform UAV localization, whilst a control method based upon trajectory optimization is integrated. Indoor and outdoor experiments are conducted and the result shows that a precise autonomous landing on a 43 X 43 cm platform could be performed.

Mountain systems within the Mediterranean region, e.g. the Pyrenees, are very sensitive to climate change. In the present study, we quantified the magnitude of extreme precipitation events and the number of days with torrential precipitation (daily precipitation ≥ 100 mm) in all the rain gauges available in the Pyrenees for the 1981-2015 period, analyzing the contribution of the synoptic scale in this type of events. The easternmost (under the Mediterranean influence) and north-westernmost (under Atlantic influence) areas of the Pyrenees registered the highest number of torrential events. The heaviest events are expected in the eastern part, i.e. 400 mm day-1 for a return period of 200 years. Northerly advections over the Iberian Peninsula, which present a low zonal index, i.e. im-plying a stronger meridional component, give rise to torrential events over the western Pyrenees; and easterly advections favour extreme precipitation over the eastern Pyrenees. The air mass travels a long way, from the east coast of North America, bringing heavy rainfall to the western Pyrenees. In the case of the torrential events over the eastern Pyrenees, the air mass causing the events in these areas is very short and originates in the Mediterranean Basin. The NAO index has no influence upon the occurrence of torrential events in the Pyrenees, but these events are closely related to certain Mediterranean teleconnections such as the WeMO

Estimation and planning play a vital role in the construction of an autonomous navigation framework. However, these problems are often considered separately, while planning gives robot a free-collision path towards the desired goal, estimation algorithm presents the executed trajectory in the sense that it has to be closed to the ground truth path as much as possible. Recently, a unified probabilistic framework, which supports solving these problems simultaneously, dubbed STEAP has been proposed. Nevertheless, its current version is only designated for an omni wheels robot, which allows robot to move and turn in vertical direction. Differential drive robot, on the other hand, though limited to move along only one direction, has been used in various situations due to its flexibility and lower cost in hardware designing. Thus, in this extension, our aim is to control a differential drive robot via STEAP. Moreover, in a more complicated environment such as labyrinth or maze, the original STEAP sometimes fails to find a path. Indeed, this problem is mainly caused by the poor initialization and the non-linearity in optimizer constraints. In our implementation, instead of dealing with these constraints, we employ a global planner algorithm such as Dijkstra or RRT to treat STEAP as an effective local planner module that focus on following the global path. Consequently, the experimental results show that the extended STEAP not only able to navigate a differential drive robot but also in a more complicated and unstructured environment.

A large amount of data is produced every day by stakeholders of the Air Traffic Management (ATM) system, in particular airline operators, airports, and air navigation service provider (ANSP). Most data is kept private for many reasons, including commercial and security concerns. More than data, shared information is precious, as it leverages intelligent decision-making support tools designed to smooth daily operations. We present a framework to detect, identify and characterise anomalies in past aircraft trajectory data. It is based on an open source of ADS-B based aircraft trajectories, and extracted information can benefit a wide range of stakeholders: Air Traffic Control (ATC) training centres could play more realistic simulations; ANSP may improve capacity indicators; academics improve safety models and risk estimations; and commercial stakeholders, like airlines and airports, may use such information to improve short-term predictions and optimise their operations. The technique is based on autoencoding artificial neural networks applied on flows of trajectories, which provide a useful reading grid associating cluster analysis with quantified level of abnormality. In particular, we find that the highest anomaly scores correspond to poor weather conditions, whereas anomalies with a lower score relate to ATC tactical actions.

In modern warfare, the diversified tasks can sometimes be challenging to fulfill with a single projectile, necessitating the incorporation of cooperation constraints in trajectory planning. Limited by the stringent requirements of the launch platform and lower costs, the maneuverability and ability to adjust the flight time range of projectiles are weak. Therefore, the rationality of performance indicators and flight time coordination strategies is especially critical. To fully exploit the control capabilities of projectiles, a battlefield area segmentation method is proposed, differentiated performance indicators and a cooperative trajectory planning model that considers the entire range of projectiles are established. Considering the limitations of existing flight time coordination strategies in applications, targeted improvements have been made in different cooperation scenarios, and a bi-level adaptive cooperation strategy(BACS) with both optimality and flexibility is proposed. To rapidly determine feasible conditions, a simple and universal method for obtaining the capability ranges of cooperation is introduced. The multi-phase optimal control problems are transformed into nonlinear programming problems using the Radau pseudo-spectral method, and simulation results show that the proposed methods are capable of handling trajectory planning tasks in different cooperation scenarios. The improved strategies effectively enhance the planning success rate under relatively harsh conditions and BACS demonstrates good compatibility with the problems studied.

This paper proposes training improvement methods of artificial neural networks (ANN) trajectory predictors. First, a dynamic power system time-series trajectory is split into several different segments to simplify the original ANN training problem. Moreover, the time-derivative of the trajectory is included to obtain an augmented loss function. Compared to previous studies which mainly focused on increasing the prediction accuracy, the aim of these novel techniques is to reduce the computational burden where the ANN output performance is still acceptable. The effectiveness of the developed methods is validated based on the WSCC three-machine nine-bus and IEEE 39-bus system models. The mean absolute error (MAE) and trajectory prediction results are analyzed, in which the numbers of neurons, hidden layers, and training epochs are constrained during the ANN training process. Rotor-angle difference between generators and the system frequency are investigated as the dynamic trajectories of the power system models. It is revealed that when the ANN architecture and epochs are constrained, the MAE results can be reduced, and the ANN training results can better reflect the original trajectory using the improvement approaches.

The increasing popularity of unconventional wells has sparked a heightened interest in evaluating and predicting their production performance. With the use of extended reach well structures, these wells are able to generate and access larger reservoir volumes. Hence, it is crucial to understand how the well's lateral trajectory affects its transient production performance. The assessment of lateral trajectory undulating amplitude effect on the flow behavior is performed in the current study based on the experimental results obtained at the University of North Dakota, Undulated Two-Phase (UTP) Flow Loop, injecting air and water mixture through a variable undulating amplitude section followed by a vertical section. The experiments showed that the undulating amplitude increase induced lower translational velocity, frequency, and length, with a consistent slug acceleration through the system profile from the inlet to the vertical section and a decreasing frequency when the slugs travel through the vertical section. Measured data shows that an increase of the horizontal pressure losses and variability is expected with a higher undulation amplitude, translating the fact that larger instabilities are observed for higher amplitudes. The numerical simulation predicted lower translational velocity and frequency, higher slug’s lengths, and similar vertical pressure losses when compared to the experimental results.

This paper proposes a high-performance and low-cost in-flight collision avoidance system based on background subtraction for unmanned aerial vehicles (UAVs). The pipeline of proposed in-flight collision avoidance system is as follows: (i) dynamic background subtraction to remove the background and to detect moving objects, (ii) denoise using morphology and binarization methods, (iii) Euclidean clustering to cluster the moving object and to remove noise blobs, (iv) distinguish independent objects and track the movement using Kalman filter, and (v) collision avoidance using proposed decision-making techniques. This work focuses on the design and the demonstration of a vision-based fast moving object detection and tracking system with decision-making capabilities to perform evasive maneuvers to replace high vision system such as event camera. The development of high-performance, low-cost unmanned aerial vehicles paired with rapid progress in vision-based perception systems herald a new era of autonomous flight systems with mission-ready capabilities. One of the key features of an autonomous UAV is a robust mid-air collision avoidance strategy. The novelty of our method lies in the motion-compensating moving object detection framework, which accomplishes the task with background subtraction via 2-D transformation approximation. Clustering and tracking algorithms process detection data to track independent objects, and stereo-camera-based distance estimation is conducted to estimate the 3-D trajectory, which is then used during decision-making procedures. The examination of the system is conducted with a quadrotor UAV test vehicle, and appropriate algorithm parameters for various requirements are deduced.

With the proliferation of locating devices, more and more raw spatial trajectories are formed, and many works enrich these raw trajectories with semantics, and mine patterns from both raw and semantic trajectories, but access control of spatial trajectories is not considered yet. We present a multi-policy secure model for semantic spatial trajectories. In our model, Mandatory Access Control, Role Based Access Control and Discretionary Access control are all enforced, separately and combined, and we represent the model semi-formally in Ontology Web Language.

On 17 October 1947, Niels Bohr was made a knight of the Order of the Elephant by the King of Denmark in view of his outstanding achievements and contributions to science. Bohr designed his own coat of arms that featured a pattern of Yin and Yang (Tai Chi symbol) to symbolize the wave-particle complementarity. However, Bohr’s Yin-Yang diagram (YYD) was neither drawn based on the principles of quantum mechanics, nor did it originate from the traditional Taoist YYD. Scientists still have doubts about the legitimacy of using YYD as the icon of the wave-particle complementarity, because the YYD belonging to quantum mechanics itself is unknown so far. This article reports the YYDs existing in quantum mechanics and justifies the role of YYD in the wave-particle duality by showing that any system, whether classical or quantum, has an ideal YYD as long as it satisfies Bohr’s principle of complementarity (BPC). The deviation of a deformed YYD from the ideal YYD indicates the extent to which a real system satisfies BPC. This article constructs the quantum YYD by the complex quantum trajectory of a particle tunneling via a step barrier, which displays the continuous transition between the wave behavior and the particle behavior. It appears that the YYD designed by Bohr in his coat of arms resembles the YYD generated by tunneling motion, not only in appearance but also in the governing equation.

Recent advancements have revolutionized interplanetary spacecraft missions by combining low-thrust propulsion systems with planetary Gravity-Assist (GA) maneuvers. This study investigates/improved a novel dual-step efficient-robust homotopy algorithm, grounded in indirect optimal control principles, to analyze fuel-optimal bang-bang control problems. The methodology integrates efficient techniques, including the homotopic method, compatible normalization, and improved switching function detection, aimed at enhancing optimal convergence in solving low-thrust gravity-assist spacecraft missions. To illustrate practical application, an Earth-to-Jupiter interplanetary scenario utilizing Mars-GA is examined. Results demonstrate the algorithm's superior efficacy in achieving fuel efficiency, robust convergence, and remarkable accuracy compared to existing solutions.

The rate constants of elementary processes in the atom-diatom system O(³P)+H₂(v), including the processes of vibrational relaxation and dissociation, were studied using the quasi-classical trajectory method. All calculations were carried out along the ground potential energy surface (PES) ³A′′ that was approximated by a neural network. Approximation data were obtained using ab initio quantum chemistry methods at the extended multi-configuration quasi-degenerate second-order perturbation theory XMCQDPT2 in a basis set limit. The calculated cross sections of the reaction channels are in good agreement with the literature data. A complete set of state-to-state rate constants was obtained for the metathesis reaction, the dissociation and VT relaxation of the H₂ molecule upon collision with an O atom. According to this data Arrhenius approximations over a wide temperature range were obtained for the thermal rate constants of considered processes. Data obtained on the dissociation constants and VT relaxation of vibrationally excited H₂ molecules can be used in constructing kinetic models describing the oxidation of hydrogen at high temperatures or highly nonequilibrium conditions.

Delta parallel robot has been widely used in precision parts processing, handling, sorting, and precision assembly, with high efficiency and motion stability being its important performance indexes. Any small line segment corner in trajectory planning causes tangential discontinuous trajectory abrupt change, and the process vibration and shock caused by it seriously affect its high-speed and high-precision performance. In this paper, a trajectory planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and micro-element integration method are used to establish the complete kinematics and dynamics equations of the Delta parallel robot, and the inverse kinematics/dynamics model-solving program is written based on Matlab software. Secondly, the end-effector trajectory of the Delta parallel robot is planned in Cartesian space, and the data points and inverse control points of the end-effector trajectory are obtained by the normalization method. Finally, the data points and control points are mapped to the joint space through the inverse kinematics equation, and the fifth-order B-spline curve is adopted for quadratic trajectory planning, which realizes the high-order continuous smoothing of trajectory planning. The simulation and experiment results show that the trajectory smoothing performance of continuous high-order curvature change can be improved using the proposed method, the tracking error of the end-effector is reduced by 21.12%, and the peak torques change of three joints is reduced by 3.5%, 11.6% and 1.6%, respectively.

In the era of electrification and artificial intelligence, direct current motors are widely utilized with numerous innovative adaptive and learning methods. Traditional methods utilize model-based algebraic techniques with system identification, such as recursive least squares, extended least squares, and autoregressive moving averages. The new method known as deterministic artificial intelligence asserts physical-based process dynamics to achieve target trajectory tracking. There are two common autonomous trajectory generation algorithms: sinusoidal function and Pontryagin's based generation algorithm. This thesis aims to simulate model-following and deterministic artificial intelligence methods using sinusoidal and Pontryagin's methods and compare their performance difference when following challenging step function slew maneuver.

Aiming at the problem of low charging efficiency caused by the scattered sensor nodes in traditional wireless rechargeable sensor networks (WRSNs), a UAV-assisted WRSN Online Charging Strategy Based on Dynamic Queue and Improved K-means (UOCS) is proposed. The scheme assumes that the energy consumption of nodes is unpredictable, and only generates charging requests when the energy is lower than a threshold, and performs on-demand responses to nodes that issue charging requests. The scheme combines the characteristics of one-to-one charging of UAVs, the selection and allocation timing of waiting queues and the number of UAVs, and the improved K-means partitioning based on space-time coordination(SPKM), which simplifies the problem of coordinated charging of multiple UAVs and maximizes energy. Using the efficiency and charging success rate, the optimal charging trajectory can be found under the constraint that the node will not starve to death due to power shortage. Finally, a simulation comparison experiment is carried out with the existing UAV charging scheduling strategy. UOCS achieves the optimal node survival rate with low algorithm complexity.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1^st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

One challenging problem is the representation of three-dimensional datasets that vary with time. These datasets can be though as a cloud of points that gradually deforms. But point-wise variations lack of information about the overall deformation pattern, and more importantly, about the extreme deformation locations inside the cloud. The present article applies a technique in computational mechanics to derive the strain-rate state of a time-dependent and three-dimensional data distribution, by which one can characterize its main trends of shift. Indeed, the tensorial analysis methodology is able to determine the global deformation rates in the entire dataset. With the use of this technique, one can characterize the significant fluctuations in a reduced multivariate description of an urban system and identify the possible causes of those changes: calculating the strain-rate state of a PCA-based multivariate description of an urban system, we are able to describe the clustering and divergence patterns between the districts of the city and to characterize the temporal rate in which those variations happen.

To address the trajectory tracking issue for quadrotors working under the influence of external disturbances, a control scheme is designed for position and attitude trajectory tracking. Firstly, the quadrotor dynamic model is derived for control design. Secondly, adaptive integral backstepping control (AIBS) is employed in the position loop in which adaptive estimation is used to estimate the upper bounds of disturbances. Subsequently, a new adaptive backstepping fast nonsingular integral terminal sliding mode control (ABFNITSM) is proposed to follow desired Euler angles. The intro-duction of fast nonsingular terminal sliding mode and integral element is to realize fast convergence and accurate tracking. Dead zone technique is applied to minimize estimation errors. Besides, a saturation function is utilized to eliminate chattering phenomenon. Finally, simulation experiments are conducted under the Simulink environment. The proposed control is verified by comparing it with traditional integral terminal sliding mode control (ITSM) and integral backstepping control (IBS).

This work presents a new scheme for autonomous control and obstacle detection of a catamaran unmanned surface vessel. Based on the Newtonian mechanics, hydrodynamics, and maneuvering modelling group modelling principles in the attached coordinate system, a three-degree-of-freedom motion model of the catamaran unmanned surface vessel is constructed. The fuzzy inference method is used to overcome the drawback that the traditional PID control cannot tune the PID parameters online, and the trajectory controller is designed. Meanwhile, 3D LIDAR is used to achieve obstacle detection. The results of the trajectory tracking simulations and experiments verify the accuracy of the model design and the effectiveness of the autonomous control design.

Unmanned aerial vehicles (UAVs) represent a new model of social robots for home care of dependent persons. In this regard, this article introduces a study on people’s feeling of safety and comfort while watching the monitoring trajectory of a quadrotor dedicated to determining their condition. Three main parameters are evaluated: the relative monitoring altitude, the monitoring velocity and the shape of the monitoring path around the person (ellipsoidal or circular). For this purpose, a new trajectory generator based on a state machine, which is successfully implemented and simulated in MATLAB/Simulink®, is described. The study is carried out with 37 participants using a virtual reality (VR) platform based on two modules, UAV Simulator and VR Visualiser, both communicating through the MQTT protocol. The participants’ preferences have been a high relative monitoring altitude, a high monitoring velocity and a circular path. These choices are a starting point for the design of trustworthy socially assistive UAVs flying in real homes.

The DEP force is usually calculated from the object’s point of view using the interaction of the object’s induced dipole moment with the inducing field. Recently, we described the DEP behavior of high- and low-conductive 200-µm 2D spheres in a square 1x1mm chamber with a plane-versus-plane electrode configuration from the system’s point of view. Here we extend our previous considerations to the plane-versus-plane and pointed-versus-pointed electrode configurations. The trajectories of the sphere center and the corresponding DEP forces were calculated from the gradient of the system’s overall energy dissipation for given starting points. The dissipation’s dependence on the sphere’s position in the chamber is described by the numerical “conductance field”, which is the DC equivalent of the capacitive charge-work field. While the plane-versus-plane electrode configuration is field-gradient free without an object, the presence of the highly or low-conductive spheres generates structures in the conductance fields, which result in very similar DEP trajectories. For both electrode configurations, the model describes trajectories with multiple endpoints, watersheds, and saddle points, very high attractive and repulsive forces in front of pointed electrodes, and the effect of mirror charges. Because the model accounts for inhomogeneous polarization within the objects, the approach allows the modeling of the complicated interplay of attractive and repulsive forces near electrode surfaces and chamber edges. Non-reversible DEP forces or asymmetric magnitudes for the highly and low-conductive spheres in large areas of the chamber indicate the presence of higher-order moments, mirror charges, etc.

The planetary boundary layer height (PBLH) is one of the key factors in influencing the dispersion of the air pollutants in the troposphere and hence the air pollutant concentration on ground level. For this reason, accurate air pollutant concentration depends on the performance of PBLH prediction. Recently, ceilometer, a lidar instrument to measure cloud base height, has been used by atmospheric scientists and air pollution control authorities to determine the mixing level height (MLH) in improving forecasting and understanding the evolution of aerosol layers above ground at a site. In this study, ceilometer data at an urban (Lidcombe) and a rural (Merriwa) location in the New South Wales, Australia was used to validate the PBLH prediction from two air quality models (CCAM-CTM and WRF-CMAQ) as well as to understand the aerosol transport from sources to receptor point at Merriwa for the three case studies where high PM10 concentration was detected in each of the three days. The results show that the PBLH prediction by the two air quality models corresponds reasonably well with observed ceilometer data and the cause and source of high PM10 concentration at Merriwa can be found by using ceilometer MLH data to corroborate with back trajectory analysis of transport of aerosols to the receptor point at Merriwa. Of the three case studies, one had aerosol source from north and north west of Merriwa in remote NSW where windblown dust is the main source, and the other two had sources from south and south east of Merriwa where anthropogenic sources dominate,

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

Anomaly detection is an active area of research with numerous methods and applications. This survey reviews the state-of-the-art of data-driven anomaly detection techniques and their application to the the aviation domain. After a brief introduction to the main traditional data-driven methods for anomaly detection, we review the recent advances in the area of neural networks, deep learning and temporal-logic based learning. We cover especially unsupervised techniques applicable to time series data because of their relevance to the aviation domain, where the lack of labeled data is the most usual case, and the nature of flight trajectories and sensor data is sequential, or temporal. The advantages and disadvantages of each method are presented in terms of computational efficiency and detection efficacy. The second part of the survey explores the application of anomaly detection techniques to aviation and their contributions to the improvement of the safety and performance of flight operations and aviation systems. As far as we know, some of the presented methods have not yet found an application in the aviation domain. We review applications ranging from the identification of significant operational events in air traffic operations to the prediction of potential aviation system failures for predictive maintenance.

Louis de Broglie in the beginning 20th century voices his theory of a double solution, according to which a pilot wave accompanies a particle, simulated as a point singularity, along the most optimal path from its creation on a source up to the detection. The pilot wave is a real hidden wave, which is similar to the wave function resulting from the solution of the Schrödinger equation. This theory is in agreement with de Broglie’s postulate about the matter waves. In this article we are based on the Helmholtz decomposition theorem according to which any velocity may be represented as a sum of two velocities – irrotational and solenoidal ones. The first velocity stems from the gradient of the scalar field. The second occurs from a pseudo-vector field. We proclaim that the gradients of the scalar field define guiding paths of the pilot wave. While the pseudo-vector field defines a particle solenoidal filling. We give mathematical models of the irrotational and solenoidal flows simulating the position of a particle in a guiding wave. Modified Navier-Stokes equation in pair with the continuity equation resulting in the Schrödinger equation gives such solutions consisting of superposition of the irrotational and solenoidal flow. It is declared that the guiding wave forms from the irrotational flows. In turn, the solenoidal flows underlie forming particles that travel along optimal paths slave by the guiding wave. There are described mathematical solutions of the spherical particle washed by the superfluid representing the guiding wave along which it travels.

Single particle tracking is a powerful technique to investigate the motion of molecules or particles. Here we review methods for analyzing the reconstructed trajectories, step needed for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean square displacement (MSD), highlighting sometimes-neglected factors potentially affecting results accuracy. We then report methods that exploit distributions of parameters other than displacements, e.g. angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in MSD analysis. Hidden Markov Models are also used for this purpose, and these allow identifying different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field: trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on combined different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.

Robots in space are necessarily extremely light and lack structural stiffness resulting in natural frequencies of resonance so low as to reside inside the attitude controller’s bandwidth. A variety of input trajectories can be used to drive a controller’s attempt to ameliorate the control-structural interactions where feedback is provided by low-quality, noisy sensors. Traditionally, step functions are used as the ideal input trajectory. However, step functions are not ideal in many applications, as they are discontinuous. Alternative input trajectories are explored in this manuscript and applied to an example system that includes a flexible appendage attached to a rigid main body. The main body is controlled by a reaction wheel. The equations of motion of the flexible appendage, rigid body, and reaction wheel are derived. A feedback controller is developed to account for the rigid body modes. Additional filters are added to compensate for the system’s flexible modes. Sinusoidal trajectories are autonomously generated to feed the controller. Whiplash compensation is additionally implemented for comparison. The control method without random errors with the smallest error is the sinusoidal trajectory method, which showed a 97.39% improvement when compared to the baseline response when step trajectories were commanded, while the sinusoidal method was inferior to traditional step trajectories when sensor noise and random errors were present.

A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.

Synthetic Aperture RADAR (SAR) is a radar imaging technique in which the relative motion of the sensor is used to synthesize a very long antenna and obtain high spatial resolution. Standard SAR raw data processing techniques assume uniform motion of the satellite (or aerial vehicle) and a fixed antenna beam pointing sideway orthogonally to the motion path, assumed rectilinear. Despite SAR data processing is a well established imaging technology that has become fundamental in several fields and applications, in this paper a novel approach has been used to exploit coherent illumination, demonstrating the possibility of extracting a large part of the ancillary data information from the raw data itself, to be used in the focusing procedure. In this work an effort has been carried out to try to focus the raw SAR complex data matrix without the knowledge of anyof the parameters needed in standard focusing procedures as Range Doppler (RD) algorithm, ω - K algorithm and Chirp Scaling (CS) algorithm. All the literature references regarding the algorithms needed to obtain a precise image from raw data use such parameters that refer both to the SAR system acquisition geometry and its radiometric specific parameters. In [12], authors introduced a preliminary work dealing with this problem and able to obtain, in the presence of a strong point scatterer in the observed scene, good quality images, if compared to the standard processing techniques. In this work the proposed technique is described and performances parameters are extracted to compare the proposed approach to RD.