Final Trajectory Research Articles

Ballistic Missile Trajectory Design Considering Impact Angle Constraint

The current paper investigates the problem of guiding ballistic re-entry vehicles to the terminal point under the additional terminal constraint of final flight path angle. In this regard, the classical Lambert’s Problem is reformulated to include the final flight path angle constraint. The proposed solution of the modified Lambert’s problem consists of a minimum of two different trajectories starting from the same initial location and intersecting each other at a location, which is determined by applying the desired time of flight and terminal flight path angle constraints. The modified Lambert strategy strategy is shown to satisfy terminal flight path angle constraint along with the time of flight, initial and final location constraints. This scheme requires the ballistic vehicle to perform an additional stage burn during descent in-order to switch from an initial trajectory, using Lambert strategy, to a final trajectory which satisfies the final flight path angle constraint. An additional stage burn is provided such that the position and velocity of the vehicle traveling in the initial trajectory is matched with that required for it to be on the final trajectory. It is also found that the amount of propellant required for the trajectory transfer, is dependent on the total time of flight and the altitude at which the additional stage burn occurs. The optimal values of these two parameters are found using interior-point optimization technique.

A Novel Trajectory Feature-Boosting Network for Trajectory Prediction.

Trajectory prediction is an essential task in many applications, including autonomous driving, robotics, and surveillance systems. In this paper, we propose a novel trajectory prediction network, called TFBNet (trajectory feature-boosting network), that utilizes trajectory feature boosting to enhance prediction accuracy. TFBNet operates by mapping the original trajectory data to a high-dimensional space, analyzing the change rules of the trajectory in this space, and finally aggregating the trajectory goals to generate the final trajectory. Our approach presents a new perspective on trajectory prediction. We evaluate TFBNet on five real-world datasets and compare it to state-of-the-art methods. Our results demonstrate that TFBNet achieves significant improvements in the ADE (average displacement error) and FDE (final displacement error) indicators, with increases of 46% and 52%, respectively. These results validate the effectiveness of our proposed approach and its potential to improve the performance of trajectory prediction models in various applications.

Static couch non-coplanar arc selection optimization for lung SBRT treatment planning

Objective. Non-coplanar arc geometry optimizations that take advantage of beam’s eye view (BEV) geometric overlap information have been proven to reduce dose to healthy organs-at-risk (OARs). Recently, a metric called mean arc distance (MAD) has been developed that quantifies the arc geometry sampling of 4π space. The purpose of this research is to combine improved BEV overlap information with MAD to generate static couch lung stereotactic body radiotherapy (SBRT) treatment plans deliverable on a C-arm linear accelerator. Approach. An algorithm utilizing the Moller–Trumbore ray-triangle intersection method was employed to compute a cost surrogate for dose to overlapping OARs using distances interpolated onto a PDD. Cost was combined with MAD for 100 000 random combinations of arc trajectories. A pathfinding algorithm for arc selection was created, balancing the contributions of MAD and 4π cost for the final trajectory. This methodology was evaluated for 18 lung SBRT patients. Cases were also planned with arcs from a clinical treatment template protocol for dosimetric and plan quality comparison. Results were evaluated using dose constraints in the context of RTOG0915. Main results. Five of six OARs had maximum dose reductions when planned with the arc trajectory optimization algorithm. Significant maximum dose reductions were found for esophagus (7.41 ± 0.91 Gy, p = 0.00019), trachea (5.56 ± 1.55 Gy, p = 0.0025), spinal cord (2.87 ± 1.13 Gy, p = 0.039), large bronchus (3.47 ± 1.49 Gy, p = 0.0075), and aorta (3.13 ± 0.99 Gy, p = 0.012). Mean dose to contralateral lung was also significantly reduced (0.50 ± 0.06 Gy, p = 0.00019). There were two significant increases in OAR doses: mean dose to ipsilateral lung (0.40 ± 0.09, p = 0.00086) and V5Gy to ipsilateral lung (1.95 ± 0.70%, p = 0.011). Paddick conformity index increased by 0.03 ± 0.02 (p = 0.14), remaining below a limit of 1.2 for both techniques. Significance. Static couch non-coplanar optimization yielded maximum dose reductions to OARs while maintaining target conformity for lung SBRT.

Hierarchical Network-Based Tracklets Data Association for Multiple Extended Target Tracking with Intermittent Measurements.

The key issue of multiple extended target tracking is to differentiate the origins of the measurements. The association of measurements with the possible origins within the target's extent is difficult, especially for occlusions or detection blind zones, which cause intermittent measurements. To solve this problem, a hierarchical network-based tracklet data association algorithm (ET-HT) is proposed. At the low association level, a min-cost network flow model based on the divided measurement sets is built to extract the possible tracklets. At the high association level, these tracklets are further associated with the final trajectories. The association is formulated as an integral programming problem for finding the maximum a posterior probability in the network flow model based on the tracklets. Moreover, the state of the extended target is calculated using the in-coordinate interval Kalman smoother. Simulation and experimental results show the superiority of the proposed ET-HT algorithm over JPDA- and RFS-based methods when measurements are intermittently unavailable.

GRLSTM: Trajectory Similarity Computation with Graph-Based Residual LSTM

The computation of trajectory similarity is a crucial task in many spatial data analysis applications. However, existing methods have been designed primarily for trajectories in Euclidean space, which overlooks the fact that real-world trajectories are often generated on road networks. This paper addresses this gap by proposing a novel framework, called GRLSTM (Graph-based Residual LSTM). To jointly capture the properties of trajectories and road networks, the proposed framework incorporates knowledge graph embedding (KGE), graph neural network (GNN), and the residual network into the multi-layer LSTM (Residual-LSTM). Specifically, the framework constructs a point knowledge graph to study the multi-relation of points, as points may belong to both the trajectory and the road network. KGE is introduced to learn point embeddings and relation embeddings to build the point fusion graph, while GNN is used to capture the topology structure information of the point fusion graph. Finally, Residual-LSTM is used to learn the trajectory embeddings.To further enhance the accuracy and robustness of the final trajectory embeddings, we introduce two new neighbor-based point loss functions, namely, graph-based point loss function and trajectory-based point loss function. The GRLSTM is evaluated using two real-world trajectory datasets, and the experimental results demonstrate that GRLSTM outperforms all the state-of-the-art methods significantly.

ASL-SLAM: A LiDAR SLAM With Activity Semantics-Based Loop Closure

A practical back-end module with loop closure detection is very useful and important for a LiDAR simultaneous localization and mapping (SLAM) system to perform high-precision positioning and mapping tasks. However, most existing loop closure detection methods are based on images or point clouds, and these methods may produce errors when the structure or texture is similar. To overcome this problem, we propose a complete LiDAR SLAM system, including a front-end odometry module based on normal distribution transform (NDT)-LOAM and a back-end optimization module with loop closure based on activity semantics. Through the analysis and calculation of inertial measurement unit (IMU) data from SLAM platforms such as unmanned ground vehicles (UGVs), the activity semantics of turning and passing over a speed bump are detected based on the peak <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula> -axis angular velocity and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}$ </tex-math></inline-formula> -axis acceleration, respectively. Then, according to this activity semantics information and its unique and definite attributes, we establish correct loop closure detection using rough geometric detection, activity semantics matching, and point cloud rematching for validation. Finally, graph optimization theory is utilized to reduce the global cumulative error, improve the global trajectory accuracy and map consistency, and obtain the final global motion trajectory and point cloud map. We collected a dataset for evaluation, which contains indoor data, outdoor data, and indoor–outdoor integration data, and we also evaluated our method on the KITTI dataset. The experimental results for different scenes show that the addition of activity semantics can effectively help loop closure detection and improve LiDAR SLAM system performance.

Multimodal Pedestrian Trajectory Prediction Using Probabilistic Proposal Network

Forecasting multiple pedestrian trajectories is a challenging task for real-world applications, as the motion patterns of pedestrian are essentially stochastic and uncertain. Previous works have demonstrated that predicting diverse goals in advance can effectively improve the performance of pedestrian trajectory prediction. However, these methods are either unable to perform probabilistic and high-efficiency trajectory prediction, or mainly rely on the predefined template trajectories which are not high-performance and insufficient to represent the possible pedestrian behaviors. In this paper, we propose a new Probabilistic Proposal Network (PPNet) to concentrate on the generation of goals and the utilization of goal guidance. PPNet firstly generates multiple weighted goals based on the diverse latent intentions automatically obtained by unsupervised learning, and then designs the goal-conditioned Transformer networks to predict probabilistic proposals as the final trajectories. Extensive experimental results on ETH/UCY datasets and Stanford Drone Dataset indicate that PPNet achieves both state-of-the-art performance and high efficiency on pedestrian trajectory prediction.

Intraoperative electrophysiological monitoring determines the final electrode position for pallidal stimulation in dystonia patients.

Bilateral deep brain stimulation (DBS) of the globus pallidus internus (GPi) is an effective treatment for refractory dystonia. Neuroradiological target and stimulation electrode trajectory planning with intraoperative microelectrode recordings (MER) and stimulation are used. With improving neuroradiological techniques, the need for MER is in dispute mainly because of the suspected risk of hemorrhage and the impact on clinical post DBS outcome. The aim of the study is to compare the preplanned GPi electrode trajectories with final trajectories selected for electrode implantation after electrophysiological monitoring and to discuss the factors potentially responsible for differences between preplanned and final trajectories. Finally, the potential association between the final trajectory selected for electrode implantation and clinical outcome will be analyzed. Forty patients underwent bilateral GPi DBS (right-sided implants first) for refractory dystonia. The relationship between preplanned and final trajectories (MicroDrive system) was correlated with patient (gender, age, dystonia type and duration) and surgery characteristics (anesthesia type, postoperative pneumocephalus) and clinical outcome measured using CGI (Clinical Global Impression parameter). The correlation between the preplanned and final trajectories together with CGI was compared between patients 1-20 and 21-40 for the learning curve effect. The trajectory selected for definitive electrode implantation matched the preplanned trajectory in 72.5% and 70% on the right and left side respectively; 55% had bilateral definitive electrodes implanted along the preplanned trajectories. Statistical analysis did not confirm any of the studied factors as predictor of the difference between the preplanned and final trajectories. Also no association between CGI and final trajectory selected for electrode implantation in the right/left hemisphere has been proven. The percentages of final electrodes implanted along the preplanned trajectory (the correlation between anatomical planning and intraoperative electrophysiology results) did not differ between patients 1-20 and 21-40. Similarly, there were no statistically significant differences in CGI (clinical outcome) between patients 1-20 and 21-40. The final trajectory selected after electrophysiological study differed from the preplanned trajectory in a significant percentage of patients. No predictor of this difference was identified. The anatomo-electrophysiological difference was not predictive of the clinical outcome (as measured using CGI parameter).

Experimental evaluation of fracture toughness for epoxy-repaired concrete considering crack deflection angle

The fracture toughness KI+II of epoxy-repaired concrete considering possible kinked crack was mainly investigated in this research. Fracture tests with different specimen geometries and coarse aggregate volume contents were performed, and the values of KI+II were determined based on the modified two-parameter model and full-field deformations. The epoxy resin was used to repair the fractured concrete, and then retested in the same way. The final crack trajectories and strain field that around the initial notch tip were studied, and a comparison was made between KI+II and mode-I fracture toughness KI. Research results indicate that different crack paths are shown after using the epoxy resin to repair concrete and compared with the first fractured concrete, smaller horizontal strain damage region is presented under the same load value. Higher values of KI are shown for the epoxy-repaired concrete, which demonstrate that the crack resistance ability of concrete can be improved after repaired by the epoxy resin. In addition, greater values of KI+II are presented than KI for both the unrepaired and epoxy-repaired concrete.

Recovery and adjustment trajectories among Hurricane Florence survivors: Analysis utilizing nonlinear dynamic system modeling.

Self-regulation shift theory (SRST) argues that most individuals are able to successfully recover from trauma via engagement in self-regulation processes as well as the effective utilization of internal and environmental resources. However, a minority of individuals may instead experience a self-determination violation as a result of their self-regulatory capacity being overwhelmed. This self-determination violation is marked by chaotic and shifting adjustment, maladaptive regulation attempts, and, ultimately, a shift to an impaired self-state and the development of persistent psychopathology, such as posttraumatic stress disorder (PTSD). The current study utilized nonlinear dynamic system (NDS) analysis to identify adjustment trajectory dynamics among rural hurricane survivors in North Carolina (N = 131) who completed daily ecological momentary assessments (EMAs) regarding their distress (i.e., negative mood and PTSD symptoms), regulation efforts (e.g., coping), and appraisals (e.g., coping self-efficacy) over a 6-week period. Four adjustment trajectories were identified, including two largely adaptive trajectories (69.0% and 5.7%), a less stable adjustment trajectory (6.9%), and a fourth trajectory (18.4%) marked by shifting adjustment states and more frequent maladaptive regulation and negative appraisals, suggesting possible self-determination violation. Consistent with this possibility, this final trajectory was also associated with more severe PTSD symptoms relative to the other three trajectories at enrollment and 6-month follow-up. Future work should utilize NDS to model posttrauma adjustment dynamics from within a SRST framework to identify patterns of positive and negative adjustment dynamics at different time points in the trauma recovery process.

Foucault’s Adventure in Iran and His Last “Turn”

In light of the Iranian uprising of 1978–79, Foucault preferred to use the term revolt instead of revolution. In the first part of the article, we attempt to go beyond the limits of the nonspecific distinction he made between revolt and revolution by drawing on Furio Jesi’s phenomenology of revolt and showing in what sense the Iranian uprising can be considered a revolt. In the second part, the article highlights the connection between the Iranian uprising and Foucault’s later works by arguing that his adventure in Iran effectively shaped his final intellectual trajectory. By examining the tension between the transcendental and the historical in Foucault’s works, we propose to read his Iranian experience against the backdrop of such tension to better understand his different approach to the question of the transcendental in his final years.

Dual-objective intelligent vehicle lane changing trajectory planning based on polynomial optimization

With the diversification and deepening of intelligent technology research, intelligent vehicles are gradually involved in entering the transportation life. When intelligent vehicles enter the actual road driving, the success of changing lanes directly determines the rate of safety problems occurring when driving. Therefore, combining with the current background of advocating low-carbon travel, the relevant technology of intelligent vehicles is improved and supplemented in terms of trajectory planning and the degree of impact on the environment, and a trajectory optimization method is proposed that considers the traffic impact and low-carbon of the vehicle when changing lanes. The method combines a vehicle dynamics model with intelligent vehicle operating conditions, the corresponding positional relationship is used to analyze and establish the corresponding safety domain. At the same time, the quintic polynomial model in the ideal state is improved, and the hexagonal polynomial model in the longitudinal direction is established. For the lane change is difficult to get the completion time and end position of the lane change in the PSO-BP neural network to solve the problem, to get the intelligent vehicle lane change trajectory cluster a dual-objective performance evaluation function is established, optimization of evaluation results using the properties of genetic algorithms. Taking car No. 689 in the NGSIM data as an example, the established trajectory planning model and algorithm are used to solve the problem, and the final lane-changing trajectory equation is obtained. After the simulation of the obtained data, a more suitable trajectory curve is obtained when the vehicle is running in the lane change, which shows that the lane change trajectory optimization method can solve the lane change problem well. Then the study is mainly applied to the planning of trajectories required by intelligent vehicles when lane changing occurs on real roads. After knowing the parameters of the lane-changing vehicle before and after changing lanes, which can plan a safe and efficient lane change route for vehicles in real time. The two comprehensive indicators of sexuality reached a better value.

Trajectory prediction in pipeline form for intercepting hypersonic gliding vehicles based on LSTM

The interception problem of Hypersonic Gliding Vehicles (HGVs) has been an important aspect of missile defense systems. In order to provide interceptors with accurate information of target trajectory, a model based on an improved Long Short-Time Memory (LSTM) network for trajectory prediction pipeline is proposed for the interception of a skip gliding hypersonic target. Firstly, for trajectory prediction required by intercepting guidance laws, the altitude, velocity and velocity direction of the target are formulated in the form of analytic functions, consisting of linear decay terms and amplitude decay sinusoidal terms. Then, the dynamic characteristics of the model parameters are analyzed, and the target trajectory prediction pipeline is proposed with the prediction error considered. Finally, an improved LSTM network is designed to estimate parameters in a dynamically-updated manner, and estimation results are used for the calculation of the final trajectory prediction pipeline. The proposed prediction algorithm provides information on the velocity vector for midcourse guidance with the effect of prediction errors on interception taken into account. Simulation is conducted and the results show the high accuracy of the algorithm in HGVs’ trajectory prediction which is conducive to increasing the interception success rate.

Electrophoretic trajectories of non-uniformly charged particles in viscoelastic fluids: the weak surface charge limit

Electrophoretic motion of a particle carrying a weak but arbitrary non-uniform surface charge density in an Oldroyd-B fluid is analysed here in the thin electrical double layer limit. A semi-analytical generic framework, based on regular perturbation, the Lamb's general solutions and the generalized reciprocal theorem, assuming the viscoelastic effects to remain subdominant, is developed for tracing the particle's trajectory using its instantaneous translational velocity and accounting for the temporal evolution of its surface charge driven by rotation. Our results reveal that in a viscoelastic medium, non-uniformly charged particles may generally follow distinct trajectories depending on their sizes, which is in stark contrast to Newtonian fluids. By considering the multipole moments of the surface charge, we show that the particle may initially rotate until its dipole moment becomes collinear with the imposed electric field, and the nature of the surrounding medium does not alter this fundamental behaviour. However, during the course of rotation, the excess polymeric stresses within the electrical double layer and the bulk may cause the particle to migrate perpendicular to the applied field, by forcing the multipole moments of the surface charge to interact with each other. The final steady-state trajectory of the particle and its possible migration normal to the applied electric field are also largely governed by these interactions and more specifically, presence of non-zero quadrupole moments. The present framework may be helpful towards designing tools for particle separation and sorting, relevant in many biological applications.

Design and implementation of fast terminal sliding mode control with synchronization error for cable-driven parallel robots

Since the cable structure generally leads to lower stiffness, cable-driven parallel robots (CDPRs) currently face some graver control challenges, where the inevitable system uncertainty will have more significant impacts on the control accuracy of CDPRs. To improve this situation, a novel sliding mode surface and the corresponding novel approaching law are defined by investigating the multi-cable synchronization, and then a new fast terminal sliding mode control strategy with synchronization error (FTSMC-SE) is proposed in this paper. Referring to the parallel structure of CDPRs, the synchronous motion of adjacent cables is ensured to obviously improve the control accuracy. Meanwhile, by deeply analyzing the finite-time convergence characteristic of the fast terminal sliding mode control, the defined synchronization error is skillfully integrated with the sliding mode surface and its novel approaching law to achieve further improvement. The Lyapunov theory is then used to analyze the finite-time stability with the error convergence guarantee of the control system. Simulation and experimental results indicate that the more synchronized cable motion and the faster error convergence can be achieved by the proposed FTSMC-SE, which together promotes the final higher precision trajectory tracking.

Trajectory planning algorithm of manipulator based on NURBS

This paper uses the 5Dof manipulator on the YouBot developed by KUKA as a model. Combining quintic polynomial interpolation with quintic non-uniform rational B splines, a novel segmented polynomial interpolation planning technique 5-B-5 is proposed in this study. CoppeliaSim constructs the model, and MATLAB controls the model to acquire the angular displacement, angular velocity, angular acceleration, final trajectory, and joint force for every joint angle. The new optimization algorithm presented in this work is utilized to optimize the manipulator's motion trajectory. Comparing it to the classic 3-5-3 algorithm and the B spline algorithm offers advantages over the higher-order B spline interpolation without increasing the manipulator control system's operational overhead. The experiments prove that the motion trajectory inaccuracy of the manipulator is minimized, the curve is continuous and smooth, and the smoothness is improved, thereby eliminating mechanical shock and other issues.

Многошаговый алгоритм терминального наведения с интеллектуальной адаптацией к ветровым возмущениям

The paper presents a qualitatively new approach to terminal guidance at the final trajectory section for the surface-to-surface class aerial vehicles. The proposed structure of the adaptive control system for an aerial vehicle is based on the multi-step terminal guidance algorithm. Adaptive corrections to the control coefficients were calculated using the developed method for identifying the wind disturbances based on the machine learning models. The work describes technique to form an intelligent algorithm for identifying intensity and direction of the wind load acting on the aerial vehicle in flight. Options of the machine learning models used in the guidance system intelligent block were investigated; their operation results are presented; and the comparative analysis has been carried out. The adaptive guidance system operation procedure is demonstrated on a typical model of the aerial vehicle flying in the atmosphere and targeting a fixed object. Numerical simulation results are presented, and possibility of using such an algorithm and implementing the described system are demonstrated.

Formation Flying Lyapunov-Based Control Using Lorentz Forces

A formation flying control algorithm using the Lorentz force for Low Earth Orbits to achieve a trajectory with required shape and size is proposed in the paper. The Lorentz force is produced as a result of interaction between the Earth’s magnetic field and an electrically charged spacecraft. Achievement of the required trajectories represents a challenge since the control in three-dimensional space is a scalar value of the satellite’s charge. A Lyapunov-based control algorithm is developed for elimination of the initial relative drift after the launch. It also aims at reaching a required amplitudes for close relative trajectories for in-plane and out-of-plane motion. Due to the absence of full controllability, the algorithm is incapable of correcting all the parameters of the relative trajectory such as in-plane and out-of-plane phase angles. The proposed control allows to converge to the trajectory with required shape and size, though with some oscillating errors in the vicinity of the required trajectory parameters. Numerical simulation of the relative motion is used to study performance of the control algorithm for one case of one controlled satellite and two cases of five controlled satellites forming a nested ellipses and train formations. The convergence time and final trajectory accuracy are evaluated for different control parameters and orbits using Monte Carlo approach.

On the Minimum Time Tracking Control of the Active Front End Converters

This article introduces the minimum time tracking control of an active front-end (AFE) converter with excellent transient performance. Since the dynamical model of the AFE converter is a bilinear system, switching control is provided for minimum time tracking with final time-varying trajectories in this system. Due to the complexity of implementing this controller, a suboptimal closed-loop controller is proposed whose dynamic performance is very close to the minimum time tracking control. Simulation and experimental results show that the suboptimal proposed controller has excellent dynamic performance against load disturbances compared with the conventional control methods.

Disease trajectory of SLE clinical endpoints and covariates affecting disease severity and probability of response: Analysis of pooled patient-level placebo (Standard-of-Care) data to enable model-informed drug development.

Systemic lupus erythematosus (SLE) is an autoimmune disease affecting multiple organ systems. Many investigational agents have failed or shown only modest effects when added to standard of care (SoC) therapy in placebo-controlled trials, and only two therapies have been approved for SLE in the last 60 years. Clinical trial outcomes have shown discordance in drug effects between clinical endpoints. Herein, we characterized longitudinal disease activity in the SLE population and the sources of variability by developing a latent disease trajectory model for SLE component endpoints (Systemic Lupus Erythematosus Disease Activity Index [SLEDAI], Physician's Global Assessment [PGA], British Isles Lupus Assessment Group Index [BILAG]) and composite endpoints (Systemic Lupus Erythematosus Responder Index [SRI], BILAG-based Composite Lupus Assessment [BICLA], and Lupus Low Disease Activity State [LLDAS]) using patient-level historical SoC data from nine phase II and III studies. Across all endpoints, in predictions up to 52 weeks from the final disease trajectory model, the following baseline covariates were associated with a greater decrease in SLE disease activity and higher response to placebo + SoC: Hispanic ethnicity from Central/South America, absence of hypocomplementemia, recent SLE diagnosis, and high baseline disease activity score using SLEDAI and BILAG separately. No discernible differences were observed in the trajectory of response to placebo + SoC across different SoC medications (antimalarial and immunosuppressant such as mycophenolate, methotrexate, and azathioprine). Across all endpoints, disease trajectory showed no difference in Asian versus non-Asian patients, supporting Asia-inclusive global SLE drug development. These results describe the first population approach to support a model-informed drug development framework in SLE.