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.

A Ventral Diverterless High Offset S-shaped Inlet at Transonic Speeds

An investigation on the ventral diverterless high offset S-shaped inlet is carried out at Mach numbers from 0.600 to 1.534, angles of attack from -4° to 9.4°, and yaw angles from 0° to 8°. Results indicate： （1） a large region of low total pressure exists at the lower part of the inlet exit caused by the counter-rotating vortices in the S-shaped duct; （2） the performances of the inlet at Mach number 1.000 reach almost the highest, so the propulsion system could work efficiently in terms of aerodynamics; （3） the total pressure recovery increases slowly at first and then remains unvaried as the Mach number rises from 0.6 to 1.0, however, it does in an opposite manner in the conventional diverter-equipped S-shaped inlet; （4） the performances of the inlet are generally insensitive to angles of attack from -4° to 9.4° and yaw angles from 0° to 8° at Mach number 0.850, and angles of attack from -2° to 6° and yaw angles from 0° to 5° at Mach number 1.534.

Numerical Investigation of Electrohydrodynamic (EHD) Flow Control in an S-Shaped Duct

An electrohydrodynamic （EHD） method, which is based on glow discharge plasma, is presented for flow control in an S-shaped duct. The research subject is an expanding channel with a constant width and a rectangular cross section. An equivalent divergence angle and basic function are introduced to build the three-dimensional model. Subsequently, the plasma physical models are simplified as the effects of electrical body force and work （done by the force） on the fluid near the wall. With the aid of FLUENT software, the source terms of momentum and energy are added to the Navier-Stokes equation. Finally, the original performance of three models （A, B and C） is studied, in which model A demonstrates better performance. Then EHD control based on model A is discussed. The results show that the EHD method is an effective way of reducing flow loss and improving uniformity at the duct exit. The innovation in this study is the assessment of the EHD control effect on the flow in an S-shaped duct. Both the parametric modeling of the S-shaped duct and the simplified models of plasma provide valuable information for future research on aircraft inlet ducts.

Incorporating S-shaped testing-effort functions into NHPP software reliability model with imperfect debugging

Testing-effort（TE） and imperfect debugging（ID） in the reliability modeling process may further improve the fitting and prediction results of software reliability growth models（SRGMs）. For describing the S-shaped varying trend of TE increasing rate more accurately, first, two S-shaped testing-effort functions（TEFs）, i.e.,delayed S-shaped TEF（DS-TEF） and inflected S-shaped TEF（IS-TEF）, are proposed. Then these two TEFs are incorporated into various types（exponential-type, delayed S-shaped and inflected S-shaped） of non-homogeneous Poisson process（NHPP）SRGMs with two forms of ID respectively for obtaining a series of new NHPP SRGMs which consider S-shaped TEFs as well as ID. Finally these new SRGMs and several comparison NHPP SRGMs are applied into four real failure data-sets respectively for investigating the fitting and prediction power of these new SRGMs.The experimental results show that：（i） the proposed IS-TEF is more suitable and flexible for describing the consumption of TE than the previous TEFs;（ii） incorporating TEFs into the inflected S-shaped NHPP SRGM may be more effective and appropriate compared with the exponential-type and the delayed S-shaped NHPP SRGMs;（iii） the inflected S-shaped NHPP SRGM considering both IS-TEF and ID yields the most accurate fitting and prediction results than the other comparison NHPP SRGMs.

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.

Modeling behaviors of a coal pillar rib using the progressive S-shaped yield criterion

Spalling of pillar ribs has been a major hazard in the mining industry for decades.In the absence of rib support guidelines,accidents have continued to occur in recent years.Developing effective support guidelines requires a complete understanding of complex pillar damage mechanisms.Continuum models represent a convenient tool for analyzing this problem,but the behavior of such models is dependent of the choice of the constitutive model.In this study,a recently proposed constitutive model was used to simulate the rib fracturing process in a longwall chain pillar at West Cliff mine.After calibration,the model was able to capture the rib displacement profiles for multiple locations of the longwall face and the stress evolution 4 m into the pillar.The rib bolts in the model were found to be yielding over 60% of their length under the headgate loading condition.The model also predicted a steady damage accumulation in the rib for certain face locations,which is consistent with the description of the rib at the site.Damage was localized along the upper part of the pillar and underscored the role that the dirt band played in controlling rib deterioration at the site.The ability of the numerical model to replicate field measurements provides confidence in the capabilities of the new constitutive model.Finally,the need of using multi-point calibration is highlighted by comparing the results of the calibrated model to an alternative model calibrated to a smaller amount of data.

Analysis and Simulation of S-shaped Waveguide in Silicon-on-insulator

The simulation and analysis of S-shaped waveguide bend are presented.Bend radius larger than 30 mm assures less than 0.5 dB radiation loss for a 4-μm-wide silicon-on-insulator waveguide bend with 2-μm etch depth.Intersection angle greater than 20° provides negligible crosstalk (<-30 dB) and very low insertion loss.Any reduction in bend radius and intersection angle is at the cost of the degradation of characteristics of bent waveguide and intersecting waveguide, respectively.

Enhancement of Characteristics of Antenna Arrays Employing S-Shaped Resonators

This paper illustrates a simple kind of tri-band printed G-shaped monopole antenna for Multiple-Input-Multiple-Output (MIMO) systems. The proposed antenna is used to achieve three operating frequencies, 2.45 GHz, 5.2 GHz and 8.2 GHz for wireless communications. To improve the isolation between the two radiating elements, we use left-handed materials composed of only S-shaped resonators to get negative refractive index at the three operating frequencies. When one layer of S-shaped resonators is employed, the antenna correlation, the diversity gain and the bandwidth are also enhanced. The simulated results are presented and evaluated with and without left-handed materials.

Shaping ability of thermomechanically treated files in simulated S-shaped root canals

Aim: the aim of this study was to investigate the shaping ability of thermomechanically treated files manufactured by twisting(Twisted files)and compare it to conventional rotary system (K3, Sybron Endo, Orange, CA) in S-shaped canals, including formation of ledges, zipping, elbow, outer widening, danger zone, perforation and file deformation. Materials & Methods: Forty S-Shaped canals in resin blocks were randomly divided into 2 groups of 20 each. Pre-instrumentation images of the canals were taken via a digital camera and superimposed on images taken after preparation with TF and K3 systems to apical size of 25/06 and 30/06. Canal aberrations were measured from the superimposed image at five levels using AutoCAD system. Fisher exact test and Mann Whitney test were used for analysis of the data. Results: the incidence of zipping, elbow and apical transportation was significantly lower in the TF group (P = 0.04). Generally the incidence of aberration increased when the apical size increased to 30/0.06 regardless of the file system. Significant file deformation was evident in the TF after single use (P ? 0.001). Conclusion: Under the conditions of this study, TF manufactured by new technique performed better than K3 systems when used up to size 25/06 in simulated S-shaped canals. Clinical significance: The flexibility of thermomechanically treated files is beneficial in canals with multiple curvatures;however, attention should be paid to the instrument taper and final apical size of the preparation.

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.

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.

Analysis of the generation mechanism of the S-shaped J–V curves of MoS_(2)/Si-based solar cells

Amorphous–microcrystalline MoS_(2)thin films are fabricated using the sol-gel method to produce MoS_(2)/Si-based solar cells. The generation mechanisms of the S-shaped current density–voltage(J–V) curves of the solar cells are analyzed. To improve the performance of the solar cells and address the problem of the S-shaped J–V curve, a MoS_(2)film and a p^(+) layer are introduced into the front and back interfaces of the solar cell, respectively, which leads to the formation of a p–n junction between the p-Si and the MoS_(2)film as well as ohmic contacts between the MoS_(2)film and the ITO, improving the S-shaped J–V curve. As a result of the high doping characteristics and the high work function of the p^(+) layer, a high–low junction is formed between the p;and p layers along with ohmic contacts between the p;layer and the Ag electrode. Consequently,the S-shaped J–V curve is eliminated, and a significantly higher current density is achieved at a high voltage. The device exhibits ideal p–n junction rectification characteristics and achieves a high power-conversion efficiency(CE) of 7.55%. The findings of this study may improve the application of MoS_(2)thin films in silicon-based solar cells, which are expected to be widely used in various silicon-based electronic and optical devices.

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.

An Efficient Long Short-Term Memory and Gated Recurrent Unit Based Smart Vessel Trajectory Prediction Using Automatic Identification System Data

Maritime transportation,a cornerstone of global trade,faces increasing safety challenges due to growing sea traffic volumes.This study proposes a novel approach to vessel trajectory prediction utilizing Automatic Identification System(AIS)data and advanced deep learning models,including Long Short-Term Memory(LSTM),Gated Recurrent Unit(GRU),Bidirectional LSTM(DBLSTM),Simple Recurrent Neural Network(SimpleRNN),and Kalman Filtering.The research implemented rigorous AIS data preprocessing,encompassing record deduplication,noise elimination,stationary simplification,and removal of insignificant trajectories.Models were trained using key navigational parameters:latitude,longitude,speed,and heading.Spatiotemporal aware processing through trajectory segmentation and topological data analysis(TDA)was employed to capture dynamic patterns.Validation using a three-month AIS dataset demonstrated significant improvements in prediction accuracy.The GRU model exhibited superior performance,achieving training losses of 0.0020(Mean Squared Error,MSE)and 0.0334(Mean Absolute Error,MAE),with validation losses of 0.0708(MSE)and 0.1720(MAE).The LSTM model showed comparable efficacy,with training losses of 0.0011(MSE)and 0.0258(MAE),and validation losses of 0.2290(MSE)and 0.2652(MAE).Both models demonstrated reductions in training and validation losses,measured by MAE,MSE,Average Displacement Error(ADE),and Final Displacement Error(FDE).This research underscores the potential of advanced deep learning models in enhancing maritime safety through more accurate trajectory predictions,contributing significantly to the development of robust,intelligent navigation systems for the maritime industry.

Optimal Trajectory Generation for Aircraft Engine-Off Taxi Towing System Under Stochastic Constraints

The novel aircraft engine-off taxi towing system featuring aircraft power integration has demonstrated significant advantages,including reduced energy consumption,diminished emissions,and enhanced efficiency.However,the aircraft engine-off taxi towing system lacks the consideration of attendant constraints in the trajectory generation process,which can potentially lead to ground accidents and constrain the improvement of traction speed.Addressing this challenge,the present work investigates the optimal control problem of trajectory generation for the taxiing traction system in the complex stochastic environment in the airport flight area.For the stochastic constraints,a strategy of deterministic processing is proposed to describe the stochastic constraints using random constraints.Furthermore,an adaptive pseudo-spectral method is introduced to transform the optimal control problem into a nonlinear programming problem,enabling its effective resolution.Simulation results substantiate that the generated trajectory can efficiently handle the stochastic constraints and accomplish the given task towards the time-optimization objective,thereby effectively enhancing the stability and efficiency of the taxiing traction system,ensuring the safety of the aircraft system,and improving the ground access capacity and efficiency of the airport.

Physics-Informed Neural Networks-Based Online Excavation Trajectory Planning for Unmanned Excavator

As a large-scale mining excavator,the electric shovel(ES)has been extensively employed in open-pit mines for overburden removal and mineral loading.In the development of unmanned operations for ES,dynamic excavation trajectory planning is essential,as it directly influences operational efficiency and energy consumption by guiding the dipper during excavation.However,conventional optimization-based methods for excavation trajectory planning typically start from scratch,resulting in a time-consuming process that fails to meet real-time requirements.To address this challenge,we propose an innovative online trajectory planning framework based on physics-informed neural networks(PINNOTP)that utilizes advanced data-driven techniques.The input to PINNOTP consists of onsite working conditions,including the initial state of the ES and the material surface being excavated.The output is a smooth,polynomial-based curve that serves as the reference trajectory for the dipper.To ensure smooth execution of the generated trajectory,prior domain knowledge-such as physics-based target-oriented constraints,essential system dynamics,and mechanical constraints-is explicitly incorporated into the loss function during training.A case study is presented to validate the proposed method,demonstrating that PINNOTP effectively addresses the challenges of online excavation trajectory planning.

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.