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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.

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.

We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a “Hothouse Earth” pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be. If the threshold is crossed, the resulting trajectory would likely cause serious disruptions to ecosystems, society, and economies. Collective human action is required to steer the Earth System away from a potential threshold and stabilize it in a habitable interglacial-like state. Such action entails stewardship of the entire Earth System—biosphere, climate, and societies—and could include decarbonization of the global economy, enhancement of biosphere carbon sinks, behavioral changes, technological innovations, new governance arrangements, and transformed social values.

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.

The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

This study examines the distance that an airplane is able to fly on inclined trajectories at various angles when it starts at different altitudes. It clearly exhibits the dependence of the airplane’s performance, when it climbs or descends, on the angle of inclination of the path and on the variations in initial weight, altitude, and power available. The results are obtained by solving the airplane’s equations of motion with the airplane’s dynamic constraints. Different specific dynamic behaviors of the airplanes are shown to occur within particular ranges of the inclination angle. Two remarkable behaviors, which have not been discussed before, are exhibited, namely the existence of a “relative ceiling” in ascending trajectories and that of a “maximum gliding altitude” in descending trajectories. These are specific altitudes that delimit the ranges of altitudes from which the airplane always attains the same terminal speed and reaches the same final altitude, whatever its initial altitude. Finally, it is shown how a feasibility matrix can be constructed, with which one can rapidly determine if a considered trajectory is flyable or not. This matrix requires only a small amount of memory storage and could reside on board essentially any airplane. The results of the study are illustrated with two very different airplanes: a Cessna 182 Skylane and a Silver Fox-like small UAV.

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.

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.

This paper deals with the control of underactuated autonomous underwater vehicles (AUVs). AUVs are needed in many applications such as the exploration of oceans, scientific and military missions, etc. There are many challenges in the control of AUVs due to the complexity of the AUV model, the unmodelled dynamics, the uncertainties and the environmental disturbances. A trajectory tracking control scheme is proposed in this paper; this control scheme is designed using the sliding mode control technique in order to be robust against bounded disturbances. The control performance of an example AUV, using the proposed method, is evaluated through computer simulations. These simulation studies, which consider different reference trajectories, show that the proposed control scheme is robust under bounded disturbances.