Entropy of deterministic trajectory via trajectories ensemble

We present a formulation of the single-trajectory entropy using the trajectories ensemble. The single-trajectory entropy is affected by its surrounding trajectories via the distribution function. The single-trajectory entropies are studied in two typical potentials, i.e., harmonic potential and double-well potential, and in viscous environment by interacting trajectory method. The results of the trajectory methods are in agreement well with the numerical methods(Monte Carlo simulation and difference equation). The single-trajectory entropies increasing(decreasing) could be caused by absorption(emission) heat from(to) the thermal environment. Also, some interesting trajectories, which correspond to the rare evens in the processes, are demonstrated.

Identifying Anomaly Aircraft Trajectories in Terminal Areas Based on Deep Autoencoder and Its Application in Trajectory Clustering

Anomalous trajectory detection and traffic flow classification for complicated airspace are of vital importance to safety and efficiency analysis.Some researchers employed density-based unsupervised machine learning method to exploit these trajectories related to air traffic control(ATC)actions.However,the quality of position data and the tiny density difference between traffic flows in the terminal area make it particularly challenging.To alleviate these two challenges,this paper proposes a novel framework which combines robust deep auto-encoder(RDAE)model and density peak(DP)clustering algorithm.Specifically,the RDAE model is utilized to reconstruct denoising trajectory and identify anomaly trajectories in the terminal area by two different regularizations.Then,the nonlinear components captured by the encoder of RDAE are input in the DP algorithm to classify the global traffic flows.An experiment on a terminal airspace at Guangzhou Baiyun Airport(ZGGG)with anomaly label shows that the proposed combination can automatically capture non-conventional spatiotemporal traffic patterns in the aircraft movement.The superiority of RDAE and combination are also demonstrated by visualizing and quantitatively evaluating the experimental results.

Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

喂子坪秦岭杂岩麻粒岩相变沉积岩的变质作用p-T演化及其构造意义

秦岭杂岩位于秦岭造山带北秦岭构造带,是研究秦岭造山带早古生代构造演化的重要岩石构造单元。喂子坪地区发育有典型的秦岭杂岩,其中的混合岩是由变沉积岩经历了强烈的深熔作用形成的。本研究对其进行了岩相学、变质相平衡模拟和LA-ICP-MS锆石U-Pb年代学研究,以深入揭示它们的变质温压演化特征,进而阐明它们指示的构造意义。混合岩的中色体由含石榴子石角闪黑云斜长片麻岩和含石榴子石黑云角闪斜长片麻岩组成。含石榴子石角闪黑云斜长片麻岩只记录了峰期变质矿物组合,为镁铁闪石+石榴子石+斜长石+石英+黑云母+钛铁矿+熔体,而含石榴子石黑云角闪斜长片麻岩记录了3个变质演化阶段,分别是早期进变质阶段(M1):黑云母+斜长石+石英;峰期变质阶段(M2):镁铁闪石+石榴子石+斜长石+石英+黑云母+钛铁矿+熔体;退变质阶段(M3):普通角闪石+斜长石+黑云母+石英+熔体。全岩成分视剖面图模拟计算显示含石榴子石角闪黑云斜长片麻岩和含石榴子石黑云角闪斜长片麻岩压力峰期的变质温压条件分别为790~810℃/990~1040 MPa和840~862℃/1000~1190 MPa。含石榴子石黑云角闪斜长片麻岩3组局部矿物组合域成分视剖面图模拟计算得到压力峰期后变质阶段的温压条件为735~814℃/400~810 MPa、721~794℃/430~700 MPa、740~810℃/470~780 MPa。因此,本研究揭示了喂子坪地区秦岭杂岩片麻岩记录了近等温降压的p-T轨迹。LA-ICP-MS锆石U-Pb定年得到含石榴子石角闪黑云斜长片麻岩和2个浅色体样品中的变质锆石206Pb/238U加权平均年龄分别为383.2±7.0 Ma、400±3.6 Ma和406.7±7.8 Ma。结合已发表的数据,喂子坪地区变沉积岩麻粒岩相峰期变质作用和强烈的混合岩化作用的时代约为410~390 Ma,而约380 Ma的年龄可能代表退变质冷却到固相线的时代。片麻岩近等温降压的变质演化轨迹指示喂子坪地区秦岭杂岩的变沉积岩在下地壳经历了麻粒岩相变质作用和随后的快速抬升,与碰撞造山引起的地壳增厚和随后的地壳伸展有关。

Joint Optimization of Resource Allocation and Trajectory Based on User Trajectory for UAV-Assisted Backscatter Communication System

The Backscatter communication has gained widespread attention from academia and industry in recent years. In this paper, A method of resource allocation and trajectory optimization is proposed for UAV-assisted backscatter communication based on user trajectory. This paper will establish an optimization problem of jointly optimizing the UAV trajectories, UAV transmission power and BD scheduling based on the large-scale channel state signals estimated in advance of the known user trajectories, taking into account the constraints of BD data and working energy consumption, to maximize the energy efficiency of the system. The problem is a non-convex optimization problem in fractional form, and there is nonlinear coupling between optimization variables.An iterative algorithm is proposed based on Dinkelbach algorithm, block coordinate descent method and continuous convex optimization technology. First, the objective function is converted into a non-fractional programming problem based on Dinkelbach method,and then the block coordinate descent method is used to decompose the original complex problem into three independent sub-problems. Finally, the successive convex approximation method is used to solve the trajectory optimization sub-problem. The simulation results show that the proposed scheme and algorithm have obvious energy efficiency gains compared with the comparison scheme.

Trajectory planning for multi-robot coordinated towing system based on stability

Given the unconstrained characteristics of the multi-robot coordinated towing system,the rope can only provide a unidirectional constraint force to the suspended object,which leads to the weak ability of the system to resist external disturbances and makes it difficult to control the trajectory of the suspended object.Based on the kinematics and statics of the multi-robot coordinated towing system with fixed base,the dynamic model of the system is established by using the Newton-Euler equations and the Udwadia-Kalaba equations.To plan the trajectories with high stability and strong control,trajectory planning is performed by combining the dynamics and stability of the towing system.Based on the dynamic stability of the motion trajectory of the suspended object,the stability of the suspended object is effectively improved through online real-time planning and offline manual adjustment.The effectiveness of the proposed method is verified by comparing the motion stability of the suspended object before and after planning.The results provide a foundation for the motion planning and coordinated control of the towing system.

Optimization of LSTM Ship Trajectory Prediction Based on Hybrid Genetic Algorithm

Accurate prediction of the movement trajectory of sea surface targets holds significant importance in achieving an advantageous position in the sea battle field.This prediction plays a crucial role in ensuring security defense and confrontation,and is essential for effective deployment of military strategy.Accurately predicting the trajectory of sea surface targets using AIS(Automatic Identification System)information is crucial for security defense and confrontation,and holds significant importance for military strategy deployment.In response to the problem of insufficient accuracy in ship trajectory prediction,this study proposes a hybrid genetic algorithm to optimize the Long Short-Term Memory(LSTM)algorithm.The HGA-LSTM algorithm is proposed for ship trajectory prediction.It can converge faster and obtain better parameter solutions,thereby improving the effectiveness of ship trajectory prediction.Compared to traditional LSTM and GA-LSTM algorithms,experimental results demonstrate that this algorithm outperforms them in both single-step and multi-step prediction.

General Optimal Trajectory Planning:Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning(GOTP)framework for autonomous vehicles(AVs)that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently.Firstly,we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline.Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve.Considering the road constraints and vehicle dynamics,limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system.Furthermore,in selecting the optimal trajectory,we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’behavior and summarizing their manipulation characteristics of“seeking benefits and avoiding losses.”Finally,by integrating the idea of receding-horizon optimization,the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility,optimality,and adaptability.Extensive simulations and experiments are performed,and the results demonstrate the framework’s feasibility and effectiveness,which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants.Moreover,we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’manipulation.

Research on Anthropomorphic Obstacle Avoidance Trajectory Planning for Adaptive Driving Scenarios Based on Inverse Reinforcement Learning Theory

The forward design of trajectory planning strategies requires preset trajectory optimization functions,resulting in poor adaptability of the strategy and an inability to accurately generate obstacle avoidance trajectories that conform to real driver behavior habits.In addition,owing to the strong time-varying dynamic characteristics of obstacle avoidance scenarios,it is necessary to design numerous trajectory optimization functions and adjust the corresponding parameters.Therefore,an anthropomorphic obstacle-avoidance trajectory planning strategy for adaptive driving scenarios is proposed.First,numerous expert-demonstrated trajectories are extracted from the HighD natural driving dataset.Subsequently,a trajectory expectation feature-matching algorithm is proposed that uses maximum entropy inverse reinforcement learning theory to learn the extracted expert-demonstrated trajectories and achieve automatic acquisition of the optimization function of the expert-demonstrated trajectory.Furthermore,a mapping model is constructed by combining the key driving scenario information that affects vehicle obstacle avoidance with the weight of the optimization function,and an anthropomorphic obstacle avoidance trajectory planning strategy for adaptive driving scenarios is proposed.Finally,the proposed strategy is verified based on real driving scenarios.The results show that the strategy can adjust the weight distribution of the trajectory optimization function in real time according to the“emergency degree”of obstacle avoidance and the state of the vehicle.Moreover,this strategy can generate anthropomorphic trajectories that are similar to expert-demonstrated trajectories,effectively improving the adaptability and acceptability of trajectories in driving scenarios.

Research on aiming methods for small sample size shooting tests of two-dimensional trajectory correction fuse

The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.

A deep multimodal fusion and multitasking trajectory prediction model for typhoon trajectory prediction to reduce flight scheduling cancellation

Natural events have had a significant impact on overall flight activity,and the aviation industry plays a vital role in helping society cope with the impact of these events.As one of the most impactful weather typhoon seasons appears and continues,airlines operating in threatened areas and passengers having travel plans during this time period will pay close attention to the development of tropical storms.This paper proposes a deep multimodal fusion and multitasking trajectory prediction model that can improve the reliability of typhoon trajectory prediction and reduce the quantity of flight scheduling cancellation.The deep multimodal fusion module is formed by deep fusion of the feature output by multiple submodal fusion modules,and the multitask generation module uses longitude and latitude as two related tasks for simultaneous prediction.With more dependable data accuracy,problems can be analysed rapidly and more efficiently,enabling better decision-making with a proactive versus reactive posture.When multiple modalities coexist,features can be extracted from them simultaneously to supplement each other’s information.An actual case study,the typhoon Lichma that swept China in 2019,has demonstrated that the algorithm can effectively reduce the number of unnecessary flight cancellations compared to existing flight scheduling and assist the new generation of flight scheduling systems under extreme weather.

Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

Triceps skinfold thickness trajectories and the risk of all-cause mortality:A prospective cohort study

BACKGROUND The measurement of triceps skinfold(TSF)thickness serves as a noninvasive metric for evaluating subcutaneous fat distribution.Despite its clinical utility,the TSF thickness trajectories and their correlation with overall mortality have not been thoroughly investigated.AIM To explore TSF thickness trajectories of Chinese adults and to examine their associations with all-cause mortality.METHODS This study encompassed a cohort of 14747 adults sourced from the China Health and Nutrition Survey.Latent class trajectory modeling was employed to identify distinct trajectories of TSF thickness.Subjects were classified into subgroups reflective of their respective TSF thickness trajectory.We utilized multivariate Cox regression analyses and mediation examinations to explore the link between TSF thickness trajectory and overall mortality,including contributory factors.RESULTS Upon adjustment for multiple confounding factors,we discerned that males in the‘Class 2:Thin-stable’and‘Class 3:Thin-moderate’TSF thickness trajectories exhibited a markedly reduced risk of mortality from all causes in comparison to the‘Class 1:Extremely thin’subgroup.In the mediation analyses,the Geriatric Nutritional Risk Index was found to be a partial intermediary in the relationship between TSF thickness trajectories and mortality.For females,a lower TSF thickness pattern was significantly predictive of elevated all-cause mortality risk exclusively within the non-elderly cohort.CONCLUSION In males and non-elderly females,lower TSF thickness trajectories are significantly predictive of heightened mortality risk,independent of single-point TSF thickness,body mass index,and waist circumference.

Adaptive Robust Control with Leakage-Type Control Law for Trajectory Tracking of Exoskeleton Robots

This paper investigates the trajectory following problem of exoskeleton robots with numerous constraints. However, as a typical nonlinear system with variability and parameter uncertainty, it is difficult to accurately achieve the trajectory tracking control for exoskeletons. In this paper, we present a robust control of trajectory tracking control based on servo constraints. Firstly, we consider the uncertainties (e.g., modelling errors, initial condition deviations, structural vibrations, and other unknown external disturbances) in the exoskeleton system, which are time-varying and bounded. Secondly, we establish the dynamic model and formulate a close-loop connection between the dynamic model and the real world. Then, the trajectory tracking issue is regarded as a servo constraint problem, and an adaptive robust control with leakage-type adaptive law is proposed with the guaranteed Lyapunov stability. Finally, we conduct numerical simulations to verify the performance of the proposed controller.

Trajectory compensation for multi-robot coordinated lifting system considering elastic catenary of the rope

The multi-robot coordinated lifting system is an unconstrained system with a rigid and flexible coupling.The deformation of the flexible rope causes errors in the movement trajectory of the lifting system.Based on the kinematic and dynamic analysis of the lifting system,the elastic catenary mod-el considering the elasticity and mass of the flexible rope is established,and the effect of the deform-ation of the flexible rope on the position and posture of the suspended object is analyzed.According to the deformation of flexible rope,a real-time trajectory compensation method is proposed based on the compensation principle of position and posture.Under the lifting task of the low-speed move-ment,this is compared with that of the system which neglects the deformation of the flexible rope.The trajectoy of the lifting system considering the deformation of flexible rope.The results show that the mass and elasticity of the flexible rope can not be neglected.Meanwhile,the proposed trajectory compensation method can improve the movement accuracy of the lifting system,which verifies the ef-fectiveness of this compensation method.The research results provide the basis for trajectory plan-ning and coordinated control of the lifting system。

Trajectory Tracking for MmWave Communication Systems via Cooperative Passive Sensing

A cooperative passive sensing framework for millimeter wave(mmWave)communication systems is proposed and demonstrated in a scenario with one mobile signal blocker.Specifically,in the uplink communication with at least two transmitters,a cooperative detection method is proposed for the receiver to track the blocker’s trajectory,localize the transmitters and detect the potential link blockage jointly.To facilitate detection,the receiver collects the signal of each transmitter along a line-of-sight(LoS)path and a non-line-of-sight(NLoS)path separately via two narrow-beam phased arrays.The NLoS path involves scattering at the mobile blocker,allowing its identification through the Doppler frequency.By comparing the received signals of both paths,the Doppler frequency and angle-of-arrival(AoA)of the NLoS path can be estimated.To resolve the blocker’s trajectory and the transmitters’locations,the receiver should continuously track the mobile blocker to accumulate sufficient numbers of the Doppler frequency and AoA versus time observations.Finally,a gradient-descent-based algorithm is proposed for joint detection.With the reconstructed trajectory,the potential link blockage can be predicted.It is demonstrated that the system can achieve decimeterlevel localization and trajectory estimation,and predict the blockage time with an error of less than 0.1 s.

Trajectory Design and Flight Result of Gravity-1 Launch Vehicle

Gravity-1(YL-1) launch vehicle completed its maiden flight from the Yellow Sea near Haiyang City, Shandong Province, on January 11, 2024, this mission successfully launched three Yunyao satellites into their 500 km orbit. The YL-1 has a performance of 4.2 tons for 500 km sun-synchronous orbit and 6.5 tons for low Earth orbit. The success of YL-1 has further enriched China's launch vehicle spectrum, and will facilitate the launch of medium and large satellites and satellite constellations. In this paper, the flight ballistic solution of YL-1 is introduced. The flight trajectory consists of seven flight segments. The trajectory design comprehensively considered the characteristics and safety requirements of the vehicle to achieve effective utilization of the performance. Through comparative analysis of the flight trajectory and the predicted trajectory, the result confirmed that the flight trajectory was consistent with the design results, the design methodology was correct, and the flight test met the expected requirements. Subsequently, the vehicle will be employed for commercial application launch services.

A Back-stepping Based Trajectory Tracking Controller for a Non-chained Nonholonomic Spherical Robot

Spherical robot has good static and dynamic stability, which provides it with strong viability in hostile environment, but the lack of effective control methods has hindered its application and development. This article deals with the dynamic trajectory tracking problem of the spherical robot BHQ-2 designed for unmanned environment exploration. The dynamic model of the spherical robot is established with a simplified Boltzmann-Hamel equation, based on which a trajectory tracking controller is designed by using the back-stepping method. The convergence of the controller is proved with the Lyapunov stability theory. Numerical simulations show that with the controller the robot can globally and asymptotically track desired trajectories, both linear and circular.

Evaluation and simulation analysis of China's copper security evolution trajectory

Copper metal is one important raw material of national economy, and its security is tightly linked with industrialization process. A comprehensive security evaluation index system, including three first class indicators, nine second class indicators and fourteen third class indicators, was constructed based on the pressure-state-response （PSR） model. And efficacy coeff^cient method was adopted in dimensionless treatment and entropy method was used to obtain the weight. Then, the data of China＇s copper from 1992 to 2011 were studied and collected. By processing these data, a comprehensive safety index of China＇s copper was got. The results showed that the comprehensive safety index of China＇s copper rose from its low point. The safety pressure state of China＇s copper was improved. The safety state of China＇s copper continued to be tight. The response state continued to rise. The overall situation of China＇s copper safety was improving, but still not optimistic.

河南洛宁太华变质杂岩区早元古代变质作用P-T-t轨迹及其大地构造意义

太华变质杂岩广泛出露于华北克拉通南缘,总体呈SW-NE向展布。在河南洛宁地区,太华变质杂岩以TTG片麻岩、斜长角闪片麻岩和变泥质片麻岩为主。斜长角闪片麻岩中可识别出三个阶段的变质矿物组合:进变质阶段矿物组合(M1)为石榴子石变斑晶内部的包裹体矿物组合(Amp1+Pl1+Qtz),变质高峰期矿物组合(M2)为石榴子石变斑晶边部和基质矿物组合(Grt2+Amp2+Pl2+Qtz),退变质阶段矿物组合(M3)为"白眼圈"状后成合晶组合(Amp3+Pl3+Qtz)。运用矿物温度计与压力计估算三个阶段的P-T条件分别为:进变质阶段约600～680℃/7.0～7.6kbar,变质高峰期为680～790℃/9.5～10.7kbar,退变质阶段为580～720℃/6.5～7.6kbar。变泥质片麻岩中保留了进变质阶段(M1)包裹体矿物组合(Bt1+Pl1+Qtz)和峰期变质阶段(M2)矿物组合(Grt2+Bt2+Pl2+Qtz)两个阶段。其中未发现后期退变质反应结构,石榴子石中也未发现成分环带。P-T条件估算结果分别为:M1阶段620～710℃/4.9～5.6kbar,M2阶段710～760℃/7.3～8.3kbar。洛宁地区太华变质杂岩记录了顺时针的近等温降压型的P-T轨迹,可能经历了与华北中部造山带其它杂岩类似的变质演化过程,推测其形成于华北克拉通东部陆块和西部陆块沿中部造山带的拼合过程中。SIMS与ICP-MS锆石U-Pb定年表明,斜长角闪片麻岩记录了1938～1967Ma的变质事件,比华北中部造山带其它变质杂岩区所广泛记录的～1850Ma变质事件早了约100Ma,暗示中部造山带的拼合可能是一个长期的、复杂的过程。