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The proliferation of trajectory data in various application domains has inspired tremendous research efforts to analyze large-scale trajectory data from a variety of aspects. A fundamental ingredient of these trajectory analysis tasks and applications is distance measures for effectively determining how similar two trajectories are. We conduct a comprehensive survey of the trajectory distance measures. The trajectory distance measures are classified into four categories according to the trajectory data type and whether the temporal information is measured. In addition, the effectiveness and complexity of each distance measure are studied. The experimental study is also conducted on their effectiveness in the six different trajectory transformations.

Spacecraft need to be able to reliably slew quickly and rather than simply commanding a final angle, a trajectory calculated and known throughout a maneuver is preferred. A fully solved trajectory allows for control based off comparing current attitude to a time varying desired attitude, allowing for much better use of control effort and command over slew orientation. This manuscript introduces slew trajectories using sinusoidal functions compared to optimal trajectories using Pontryagin’s method. Use of Pontryagin’s method yields approximately 1.5% lower control effort compared to sinusoidal trajectories. Analysis of the simulated system response demonstrates that correct understanding of the effect of cross-coupling is necessary to avoid unwarranted control costs. Additionally, a combination of feedforward with proportional derivative control generates a system response with 3% reduction in control cost compared to a Feedforward with proportional integral derivative control architecture. Use of a calculated trajectory is shown to reduce control cost by five orders of magnitude and allows for raising of gains by an order of magnitude. When control gains are raised, an eight orders of magnitude lower error is achieved in the slew direction, and rather than an increase in control cost, a decrease by 11.7% is observed. This manuscript concludes that Pontryagin’s method for generating slew trajectories outperforms the use of sinusoidal trajectories and trajectory generation schemes are essential for efficient spacecraft maneuvering.

With the development of GPS-enabled devices, wireless communication and storage technologies, trajectories representing the mobility of moving objects are accumulated at an unprecedented pace. They contain a large amount of temporal and spatial semantic information. A great deal of valuable information can be obtained by mining and analyzing the trajectory dataset. Trajectory clustering is one of the simplest and most powerful methods to obtain knowledge from trajectory data, which is based on the similarity measure between trajectories. The existing similarity measurement methods cannot fully utilize the specific features of trajectory itself when measuring the distance between trajectories. In this paper, an enhanced trajectory model is proposed and a new trajectory clustering algorithm is presented based on multi-feature trajectory similarity measure, which can maximize the similarity of trajectories in the same cluster, and can be used to better serve for applications including traffic monitoring and road congestion prediction. Both the intuitive visualization presentation and the experimental results on synthetic and real trajectory datasets show that, compared to existing methods, the proposed approach improves the accuracy and efficiency of trajectory clustering.

The design of output constrained control system for unmanned aerial vehicles deployed in confined areas is an important issue in practice and not taken into account in many autopilot systems. In this study, the authors address a neural networks-based adaptive trajectory tracking control algorithm for multi-rotors systems in the presence of various uncertainties in their dynamics. Given any sufficient smooth and bounded reference trajectory input, the proposed algorithm achieves that (i) the system output (Euclidean position) tracking error converges to a neighbourhood of zero and furthermore (ii) the system output remains uniformly in a prescribed set. Instead of element-wise estimation, a norm estimation approach of unknown weight vectors is incorporated into the control system design to relieve the onboard computation burden. The convergence property of the closed-loop system subject to output constraint is analysed via a symmetric barrier Lyapunov function augmented with several quadratic terms. Simulation results are demonstrated on a quadrotor model to validate the effectiveness of the proposed algorithm.

Trajectory outlier detection is one of the fundamental data mining techniques used to analyze the trajectory data of the Global Positioning System. A comprehensive literature review of trajectory outlier detectors published between 2000 and 2022 led to a conclusion that conventional trajectory outlier detectors suffered from drawbacks, either due to the detectors themselves or the pre-processing methods for the variable-length trajectory inputs utilized by detectors. To address these issues, we proposed a feature extraction method called middle polar coordinates (MiPo). MiPo extracted tabular features from trajectory data prior to the application of conventional outlier detectors to detect trajectory outliers. By representing variable-length trajectory data as fixed-length tabular data, MiPo granted tabular outlier detectors the ability to detect trajectory outliers, which was previously impossible. Experiments with real-world datasets showed that MiPo outperformed all baseline methods with 0.99 AUC on average; however, it only required approximately 10% of the computing time of the existing industrial best. MiPo exhibited linear time and space complexity. The features extracted by MiPo may aid other trajectory data mining tasks. We believe that MiPo has the potential to revolutionize the field of trajectory outlier detection.

During the last few years the volumes of the data that synthesize trajectories have expanded to unparalleled quantities. This growth is challenging traditional trajectory analysis approaches and solutions are sought in other domains. In this work, we focus on data compression techniques with the intention to minimize the size of trajectory data, while, at the same time, minimizing the impact on the trajectory analysis methods. To this extent, we evaluate five lossy compression algorithms: Douglas-Peucker (DP), Time Ratio (TR), Speed Based (SP), Time Ratio Speed Based (TR_SP) and Speed Based Time Ratio (SP_TR). The comparison is performed using four distinct real world datasets against six different dynamically assigned thresholds. The effectiveness of the compression is evaluated using classification techniques and similarity measures. The results showed that there is a trade-off between the compression rate and the achieved quality. The is no “best algorithm” for every case and the choice of the proper compression algorithm is an application-dependent process.

A vehicle trajectory is ergodic with respect to some spatial distribution if the time spent in a region is proportional to the region's integrated density. One method of generating ergodic trajectories is projection-based trajectory optimisation, a gradient descent method that supports non-linear dynamics and balances trajectory ergodicity with control effort. In this study, the authors survey the existing literature on projection-based trajectory generation, focusing on implementation. They introduce an easy-to-use, open-source software package that generates ergodic trajectories orders of magnitude faster than previously reported. The authors’ goal is to simplify the implementation of projection-based ergodic control so it can be applied widely across disciplines.

Designing reliable trajectories for low-thrust missions faces challenges from potential Missed Thrust Events (MTEs). This paper presents an indirect method approach to generate MTE-resilient low-thrust trajectories by incorporating the Expected Thrust Fraction (ETF) model, which embeds MTE statistics into a deterministic framework. To overcome the numerical challenges associated with the indirect method, a regularized objective function with logarithmic homotopy terms is adopted in this paper, combined with shape-based reference trajectories and analytical least squares estimation techniques to ensure the robust convergence of the indirect method. The methodology is demonstrated on a fixed-time Earth-Mars rendezvous trajectory. Numerical results confirm the successful application of the ETF-informed indirect method, yielding a somewhat different optimal trajectory compared to traditional designs. This approach offers an efficient and robust tool for designing reliable low-thrust trajectories that proactively mitigate MTE risks.

Predictive models of immune protection from COVID-19 are urgently needed to identify correlates of protection to assist in the future deployment of vaccines. To address this, we analyzed the relationship between in vitro neutralization levels and the observed protection from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection using data from seven current vaccines and from convalescent cohorts. We estimated the neutralization level for 50% protection against detectable SARS-CoV-2 infection to be 20.2% of the mean convalescent level (95% confidence interval (CI) = 14.4–28.4%). The estimated neutralization level required for 50% protection from severe infection was significantly lower (3% of the mean convalescent level; 95% CI = 0.7–13%, P  = 0.0004). Modeling of the decay of the neutralization titer over the first 250 d after immunization predicts that a significant loss in protection from SARS-CoV-2 infection will occur, although protection from severe disease should be largely retained. Neutralization titers against some SARS-CoV-2 variants of concern are reduced compared with the vaccine strain, and our model predicts the relationship between neutralization and efficacy against viral variants. Here, we show that neutralization level is highly predictive of immune protection, and provide an evidence-based model of SARS-CoV-2 immune protection that will assist in developing vaccine strategies to control the future trajectory of the pandemic. Estimates of the levels of neutralizing antibodies necessary for protection against symptomatic SARS-CoV-2 or severe COVID-19 are a fraction of the mean level in convalescent serum and will be useful in guiding vaccine rollouts.

This paper focuses on the challenges of low trajectory tracking accuracy in intelligent vehicles caused by different road adhesion coefficients and vehicle speed conditions, aiming to address these challenges with an improved Model Predictive Control (MPC) algorithm. Firstly, a model encompassing vehicle dynamics featuring two degrees of freedom has been formulated, along with a corresponding model to track trajectory errors. Secondly, a Model Predictive Control (MPC) algorithm is designed with trajectory tracking accuracy and control increment as the objective functions. Additionally, incorporating a Particle Swarm Optimization (PSO) algorithm with MPC allows for the dynamic computation of the optimal prediction horizon size. Afterward, a unified simulation model is assembled, employing both CarSim and MATLAB/Simulink, to conduct dual-lane trajectory tracking simulation analysis under diverse road adhesion and vehicle speed conditions. The efficacy of the proposed control algorithms is validated through this process.