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• Interstellar exploration is defined as bi-objective multi-vehicle problem with profits. • Mission return increases approximately linearly with mission duration. • Lower probe numbers enable more efficient routing through shorter transfers. In the past decade, the discovery of exoplanets has sparked new interests in the idea of interstellar travel and exploration. Despite various proposals for probe concepts and relevant technologies, there is a lack of extensive literature on viable exploration strategies for journeys beyond a single star system. Such exploration strategies might not only have implications on technology development strategies for achieving interstellar exploration but could also enrich existing models for galactic exploration feeding into solutions of the Fermi Paradox. This article presents optimal strategies for the exploration of a large number of near-by stars, using a dedicated, novel methodology, which sets it apart from existing literature: For the first time, the mission design problem of interstellar exploration is redefined as a bi-objective multi-vehicle open routing problem with profits. It is tackled by an adapted hybrid multi-objective genetic algorithm, which is further improved and modified according to the problem characteristics (e. g. large search space). The overall mission model assumes probes traveling on straight trajectories, utilizing flybys, and maintaining an average velocity of 10% of the speed of light. Surpassing prior research that typically relies on statistical models or restricted star data, the star models are founded on the second Gaia data release (Gaia DR2), which represents the most extensive star catalogue to the date of this study and is employed for the first time in the context of interstellar exploration. The resulting star model contains a maximum of 10,000 stars within a spherical region around Sol, covering a distance of 110 light years. It is found, that the number of explored stars J 1 scales with mission duration J 2 and probe number m according to J 1 ∼ J 2 m 0.66 , which provides an initial guidance for future interstellar mission design. Furthermore, the routes and selection of stars vary depending on the number of probes used: When conducting missions with a large number of probes, stars in close proximity to the Solar System are given more focus. On the other hand, missions with a small number of probes include more distant stars to facilitate shorter transfers along the route. Based on these findings, the following recommendations for interstellar exploration strategies can be drawn: When energy resources such as fuel reserves are scarce and the exploration mission is not limited to nearby stars, low probe numbers are more efficient. In contrast, high probe numbers enable faster exploration of nearby stars but involve less resource-efficient transfers, making them a suitable option for small, remotely propelled probe concepts. To address crowding effects in high probe number missions, swarm-based probe concepts are recommended based on the scaling law characteristics derived. [ABSTRACT FROM AUTHOR]

This work focuses on minimum-time low-thrust orbit transfers from a prescribed low Earth orbit to a specified low lunar orbit. The well-established indirect formulation of minimum-time orbit transfers is extended to a multibody dynamical framework, with initial and final orbits around two distinct primaries. To do this, different representations, useful for describing orbit dynamics, are introduced, i.e., modified equinoctial elements (MEE) and Cartesian coordinates (CC). Use of two sets of MEE, relative to either Earth or Moon, allows simple writing of the boundary conditions about the two celestial bodies, but requires the formulation of a multiple-arc trajectory optimization problem, including two legs: (a) geocentric leg and (b) selenocentric leg. In the numerical solution process, the transition between the two MEE representations uses CC, which play the role of convenient intermediate, matching variables. The multiple-arc formulation at hand leads to identifying a set of intermediate necessary conditions for optimality, at the transition between the two legs. This research proves that a closed-form solution to these intermediate conditions exists, leveraging implicit costate transformation. As a result, the parameter set for an indirect algorithm retains the reduced size of the typical set associated with a single-arc optimization problem. The indirect heuristic technique, based on the joint use of the necessary conditions and a heuristic algorithm (i.e., differential evolution in this study) is proposed as the numerical solution method, together with the definition of a layered fitness function, aimed at facilitating convergence. The minimum-time trajectory of interest is sought in a high-fidelity dynamical framework, with the use of planetary ephemeris and the inclusion of the simultaneous gravitational action of Sun, Earth, and Moon, along the entire transfer path. The numerical results unequivocally prove that the approach developed in this research is effective for determining minimum-time low-thrust Earth–Moon orbit transfers. • Earth–Moon minimum-time low-thrust orbit transfers are investigated. • Problem is formulated as a multiple-arc optimal control problem. • Costate transformations are used, related to different state representations. • Indirect heuristic algorithm with stratified objectives is employed. • Numerical results prove effectiveness of the optimization methodology. [ABSTRACT FROM AUTHOR]

The low-thrust fuel-optimal transfer problem between periodic orbits of two circular restricted three-body systems has been considered. The focus is on utilizing invariant manifolds of the respective systems. A power-limited, variable-specific impulse engine model has been employed. The system-to-system transfer problem is modeled within the framework of optimal control theory through the application of the Calculus of Variations and Pontryagin's maximum principle (PMP). Along with unknown co-states, the departure and arrival points on respective periodic orbits and manifold coast durations are chosen as design variables in the problem formulation. The solution to the associated two-point boundary value problem (TPBVP) is obtained using the shooting method. Low-thrust fuel-optimal Sun-Earth-L2 halo to Sun-Mars-L1 halo transfers are obtained. The outlined result shows a significant amount of fuel savings. Such transfer trajectories may be helpful for transferring a spacecraft or cargo mission from a near-Earth station on a periodic orbit to a similar station near Mars. • Employing a low-thrust engine model results in propellant mass saving due to their high specific impulse. • A single powered arc is required for transfers with a variable specific impulse (VSI) engine. • The system-to-system transfer problem is modeled within the framework of optimal control theory. • The goal of optimization problem is to minimize fuel consumption. • Shooting method is used to converge to the desired initial co-states of the problem. [ABSTRACT FROM AUTHOR]

Classic initial orbit determination (IOD) methods are mainly based on the hypothesis of unperturbed Keplerian motion and are inapplicable for Libration point orbits (LPOs). To this end, this paper proposes a neural network–assisted method for accurate and efficient IOD of LPOs. The proposed method consists of a long short-term memory (LSTM) neural network–based initial guess generator (IGG) combined with a second-order optimal corrector. First, the LSTM neural network is developed to compensate for the residuals between the two-body IOD solution and the true solution to generate a more accurate initial guess. Two sample forms, one in the rotating frame and the other in the inertial frame, are investigated and compared to select the better form to train the LSTM neural network. Then, a second-order optimal corrector is proposed based on the second-order state transition tensor and a two-step procedure, which takes the initial guess from the LSTM neural network and iteratively obtains a more accurate IOD solution. Finally, the proposed method is applied to solve the IOD problem in two Earth–Moon LPO scenarios: a 4:1 synodic resonant Near-rectilinear Halo orbit (NRHO) and a transfer trajectory from a lunar orbit to the 4:1 NRHO. Numerical simulations show that the estimated errors are reduced by 99% using the proposed LSTM-based IGG. Moreover, for a comparable level of accuracy, the second-order optimal corrector converges one time faster than the first-order corrector. [ABSTRACT FROM AUTHOR]

The trajectory optimization of multiple quadcopters for Mars exploration has been a challenging task due to a difficult nonconvex space formed by multiple quadcopters in the flight, the complex dynamics model, and complicated obstacle environments. We propose a distributed optimization algorithm (DiPenOpt) using direct collocation methods to solve the optimization in the nonconvex space. The DiPenOpt algorithm contains a penalty function method to transfer the nonconvex space into a convex one and an iterative optimization strategy employing initial value selection methods to enhance the algorithm's convergence rate. We design a position-tracking controller to ensure that the quadcopters can effectively follow trajectories generated by the DiPenOpt, regardless of initial position deviations and uncertainties. We compare the results of the DiPenOpt with other algorithms and find that DiPenOpt has a faster solution speed and shows superior robustness for trajectory optimization of multiple quadcopters in large and complex environments. The simulation results show that the position-tracking controller can ensure error convergence and stabilize the flight path when the quadcopter has an initial error. Practical Applications: When exploring Mars with multiple quadcopters, ensuring they move efficiently and safely is critical. Think of it like trying to coordinate several quadcopters in a maze-like environment, where every quadcopter needs its own clear path. Our research introduces a new way (DiPenOpt) to help these quadcopters find their best paths, even in complicated surroundings. Our method makes challenging path-finding problems simpler, and we have added tools to make sure quadcopters stick to their paths, even if they start off a little off-course or have uncertain disturbances. Compared to other methods, DiPenOpt is faster and better suited for situations where there are many quadcopters and obstacles. In simple terms, if we were to send a team of quadcopters to explore Mars, our method would make it easier for them to navigate and provide more reliable results, which is crucial for successful space missions. [ABSTRACT FROM AUTHOR]

Within the emerging age of lunar exploration, optimizing transfer trajectories is a fundamental measure toward achieving more economical and efficient lunar missions. This study addresses the possibility of reducing the fuel cost of two-impulse Earth–Moon transfers in a four-body model with the Earth, the Moon, and the Sun as primaries. Lawden's primer vector theory is applied within this framework to derive a set of necessary conditions for a fuel-optimal trajectory. These conditions are used to identify which trajectories from an existing database could benefit from the insertion of an additional intermediate impulse. More than 10,000 three-impulse transfers are computed with a direct numerical optimization method. These solutions contribute to enriching the database of impulsive trajectories, useful to perform trade-off analyses. While the majority of trajectories exhibit only marginal improvements, a significant breakthrough emerges for transfers featuring an initial gravity assist at the Moon. Implementing a corrective maneuver after the lunar encounter yields substantial reductions in fuel costs. [ABSTRACT FROM AUTHOR]

Space exploration presents vast prospects for scientific, industrial, and economic progress. This paper introduces the MeSat mission as a pioneering approach to Mars exploration. The MeSat aims to deepen our understanding of Martian conditions and resources by employing an optimized Earth-to-Mars trajectory, enabling a comprehensive study of the Martian atmosphere and surface. The mission comprises a cargo microsatellite hosting three 6U CubeSats and two 3U CubeSats, deployed into four separate Mars orbits to form a constellation. Each CubeSat carries distinct payloads: a THz radiometer for Martian water vapor atmospheric observation, a high-resolution surface camera, a high-tech spectrometer, and a Fourier transform spectrometer (FTS) for wind speed readings. This paper includes the majority of the key parameters; however, we focus our discussion more on two aspects of this pioneering mission: the first aspect contains the proposal of four distinct payloads for the study of Mars' atmosphere and the second aspect proposes an optimal mission design algorithm that analyzes a fuel-efficient low-thrust trajectory from Earth to Mars. Regarding the payloads, the THz radiometer requires a specific design; hence, we explain this payload in more depth; the rest of the payloads, we suggest utilizing commercially available elements for the cost-effective manufacture of a whole system. For mission trajectory optimization, the study employs a dual-step hybrid optimization algorithm (PSO-homotopy) to analyze fuel-efficient low-thrust trajectories from Earth to Mars, incorporating the ephemeris dynamics model to account for gravitational perturbations in the entire Solar System. In practical mission design, crucial factors like hyperbolic excess velocity, diverse opportunities for Earth launch and Mars rendezvous, varied propulsion systems, and time of flight (TOF) play vital roles in trajectory optimization. In summary, for the MeSat mission, we propose a comprehensive Mars environmental mission design. We consider all aspects of the mission from trajectory design to engineering detail design, since we would like to inspire future Mars missions with a complete report. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimizing minimum-time and minimum-propellant many-revolution low-thrust geocentric orbit-raising maneuvers to an arbitrary target. The proposed direct single-shooting technique utilizes the regularized h , e element set as well as analytical models for ephemeris, shadow geometry, and thrust magnitude for ease of the optimization procedure. Third body and J 2 effects are included for higher fidelity of the computed solution. The gradient information supplied through adjoint sensitivities facilitates the convergence of the numerical optimization scheme. We also propose a new automated, fast and robust initial guess generation methodology by solving a sequence of unconstrained optimization orbit-raising sub-problems. The performance of the developed algorithm is demonstrated for orbit-raising to a variety of targets: the geosynchronous equatorial orbit, the Molniya orbit, and a near-rectilinear halo orbit. • A new low-thrust trajectory algorithm is developed using adjoint sensitivities. • The sequentially generated initial guesses are fast and robust to calculate. • An end-to-end optimization formulation computes minimum-time and minimum-fuel transfers. [ABSTRACT FROM AUTHOR]

High scientific value areas on celestial bodies such as the Moon and Mars are often located in hazardous terrains. To achieve safe landing exploration, a novel planning method is proposed, which can ensure that the planned trajectory maintains a user-specified distance from obstacles, thus reducing potential collision risk induced by factors such as the body size and model uncertainties. Firstly, the basic model of the trajectory optimization problem and its convexification version is given. The obstacles are modeled as polynomial functions, based on which the "if-then" obstacle avoidance logic explicitly considering the safe distance, is described as a sum of squares constraint. This constraint formulation applies to any obstacle described by a finite number of polynomials, independent of the specific expression of the polynomials (reflecting the shape of the obstacle). Subsequently, the convexification process for the obstacle avoidance constraint is given. Finally, the sequential sum of squares programming problem for the obstacle avoidance trajectory is established, which boils down to a series of semidefinite programming problems. Simulation results show that the closest distance between the planned trajectory and obstacles strictly satisfies the specified distance constraint, and the trajectory could avoid non-convex obstacles. With the promising convergence properties of underlying convex optimization algorithms, advanced autonomous obstacle avoidance guidance schemes are expected to be formed based on the proposed trajectory planning method. • Mars/Moon landings cannot ignore unknown and hazardous surface environments. • The trajectory obtained by traditional avoidance methods is too close to obstacles. • The safe distance constraint can be described as a sum of squares constraint. • The proposed planning method applies to any obstacle described by polynomials. [ABSTRACT FROM AUTHOR]

Until recently space travel was considered a privilege of governmental astronauts, with the exception perhaps of a few billionaire space tourists, who had been accommodated on the International Space Station on some rare occasions. Nonetheless, with major space pioneers announcing plans for space tourism activities and after the successful launch in orbit of space tourism vehicles from the Virgin Galactic and Blue Origin companies, academic interest about human spaceflight for purposes of leisure and recreation has ignited. Taking into account that space tourism is in fact an unregulated activity, this paper will firstly examine whether space tourism activities fall under the scope of space law or under the scope of international air law, depending on the planned trajectory of the space tourism vehicle. Furthermore, the authors will attempt to draw conclusions concerning the legal implications of space tourism activities through a comparative analysis with the 1974 Athens Convention on the Carriage of Passengers and the Carriage of their Luggage by Sea. This international convention provides a great example on the regulation of touristic ventures, as it refers to commercial touristic activities realized within a res communis omnium , i. e., the high seas, similarly with touristic activities in space. Moreover, said Convention provides for a specialized regime for touristic activities and is of particular interest, since it has achieved stability and a desirable balance of interests between private tourism operators and passengers. In this connection, the authors will evaluate the provisions of the 1974 Athens Convention in comparison with the space treaties applicable to space tourism activities. Furthermore, suggestions will be made as to whether it would be appropriate and feasible to introduce in the space law realm certain rules of law similar to those of the 1974 Athens Convention, in order to facilitate growth in the space tourism sector, without compromising the safety of human spaceflight for space passengers. • The 1974 Athens Convention in comparison with the space treaties applicable to space tourism activities. • Legal analogy between space law and maritime law. • Legal regime governing space tourism activities. [ABSTRACT FROM AUTHOR]

Low-thrust trajectory design in the context of the three-body problem, particularly in the vicinity of liberation points, is addressed in this paper with a focus on efficiency and accuracy. The Fourier series, previously successful in approximating near-coplanar low-thrust trajectories within two-body dynamics, is applied to the challenging landscape of the three-body problem, marked by instability and nonlinearity. This paper introduces a novel approach for constructing an initial guess trajectory, that combines coast arcs from periodic orbits and intermediate trajectory arcs from other natural dynamical structures. The resulting initial guess trajectory is instrumental in generating efficient initial estimates for the coefficients of the Fourier series. The study encompasses the analysis of homoclinic and heteroclinic transfers in both two-dimensional and three-dimensional scenarios. The approximated trajectories derived from this methodology serve as invaluable starting points for high-fidelity optimization solvers, offering promise for enhancing the precision and efficiency of low-thrust transfers in cislunar space. • The shape method based on Fourier series is applied to the initial design of the transfer trajectories between periodic orbits in cislunar space. • An innovative approach to construct a continuous initial guess trajectory is introduced to derive initial guess values for the coefficients of Fourier terms. • An accurate approximation of the optimal transfer trajectory can be rapidly obtained. [ABSTRACT FROM AUTHOR]

This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses a trajectory tracking control problem for marine surface vessels (MSVs) in the presence of mismatched conditions and input saturation. Firstly, an MSV model under mismatched conditions is established to solve the problem of unreasonable modeling methods in the existing literature. Secondly, fixed‐time disturbance observers (FXDOs) are designed, where the designed FXDOs not only avoid selecting complicated parameters but also has simple structures, and the disturbance estimation errors can converge to the origin within a setting time. Thirdly, based on the FXDOs and an anti–saturation auxiliary dynamic system, a trajectory tracking control scheme in the presence of mismatched conditions and input saturation is constructed by virtue of fixed‐time integral sliding mode control (SMC), and the actual tracking error signals are uniformly fixed‐time bounded rather than finite‐time one. Fourthly, in order to decrease theoretical calculation values of the original setting time in fixed‐time control, the new setting time under three different parameter conditions is derived, and thus reducing the conservatism. Finally, the simulation results are provided to show the effectiveness and superiority of the designed tracking control scheme. [ABSTRACT FROM AUTHOR]

The presence of microbubble significantly influences the rheological properties of a jet, thereby considerably increasing the complexity of the jet instability problem. However, the instability of microbubble jets has been rarely studied, and their breakup mechanism remains obscure. The present study was focused on conducting a comprehensive analysis of bubble jet flows. A high-precision experimental system was constructed to extract the time-series signals of each cross-sectional profile along the axial direction of a jet. Glycerol solutions with three different bubble volume fractions were prepared, and the standard deviation, spectral relationship, and nonlinear dynamical behavior (i.e., autocorrelation, phase space trajectory, Poincaré section, and Lyapunov exponent) were studied. The detailed development process of small surface disturbances in space was assessed, and the influence of variations in the bubble volume fraction on the nonlinear dynamics of the jet was examined. The results demonstrate that microbubbles can significantly change the energy transfer relationship between various sections of a jet and enhance the periodicity of the signal. [ABSTRACT FROM AUTHOR]

Most mobility modeling methods are designed to solve specific tasks, leading to questions regarding their deficiency in generalizability. Inspired by the bloom of foundation models, we proposed a Trajectory Generation framework based on the Diffusion Model (TrajGDM) to capture the universal mobility pattern in a trajectory dataset by learning the trajectory generation process. The process is modeled as a step-by-step uncertainty-reducing process, in which a deep learning network with a novel training method is proposed to learn from the process. We compared the proposed trajectory generation method with six baselines on two public trajectory datasets. The results showed that the similarity between the generated and real trajectory movements measured by the Jensen-Shannon Divergence improved significantly on both datasets. Moreover, we applied zero-shot inferences on two basic trajectory tasks: trajectory prediction and trajectory reconstruction. The accuracy improved by a maximum of 25.6% on two tasks. The universal mobility pattern that is suitable for solving multiple trajectory tasks is verified, inferring the strong generalizability of our model. Finally, the study provides insights into artificial intelligence's understanding of human mobility by exploring the way the model maps the trajectory in the latent space into reality. [ABSTRACT FROM AUTHOR]

Mechanized green shoot thinning in vineyards has helped reduce labor and associated costs. However, high variability in the thinning efficiency has been observed with the current machines in non-selective thinning due to challenges faced by the operators to precisely position thinning end-effectors along the cordon trajectories. In this study, an automated green shoot thinning system is proposed for cordon-trained grapevines to enhance the precision and efficiency of mechanical thinning operation. The automated system consisted of (1) a machine vision system for estimating cordon trajectories and (2) a mechanical system to position thinning rollers along the estimated trajectories during the real-time thinning operation. The vision pipeline used a Mask R-CNN model to determine cordon profiles at different shoot growth stages and a depth image to estimate the 3D cordon trajectory. In addition, point-cloud registration estimated transformation matrices for accurately stitching adjacent cordon trajectories and generating a long map of trajectory for the thinning rollers to follow. An image processing-based calibration method was used to obtain transformation parameters that transformed the estimated trajectories from the camera coordinate space to the thinning-roller coordinate space required for trajectory following. Lab tests, conducted using simulated cordons, showed the integrated system can precisely position the thinning rollers with root mean square errors (RMSE) of 2.0 cm and 1.7 cm for vertical and lateral positions, respectively. To quantify the thinning performance of the integrated system in the field, shoot thinning efficiency (the percentage of target shoots impacted) was determined. From the field evaluation, shoot thinning efficiency of 76% and 85% were achieved for two rows of grapevines, with an overall shoot thinning efficiency of 80%. The favorable test results demonstrated that the proposed integrated system is capable of effectively automating green shoot thinning operations, which has the potential to improve shoot thinning performance in vineyards. [ABSTRACT FROM AUTHOR]

Liquid crystal diffractive sails can generate controllable tangential radiation pressures, which have advantages in the Solar Polar Imager mission (SPI). This paper proposes a composite diffractive sail design consisting of an ideal passive diffraction grating sail and liquid crystal polarization gratings (LCPGs). The main diffractive grating sail generates thrust for orbital transfer with a sun-facing attitude. An optimal 3.8-year transfer trajectory is obtained by an improved direct method. Small-area LCPGs distributed around the edge are used for three-axis attitude control. The LCPGs can continuously modulate the force and torque by controlling the applied voltage based on the electro-optical characteristic of liquid crystal materials. A control strategy, including an adaptive attitude-tracking PD controller and a control allocation method, is designed to track the attitude profile generated by the transfer trajectory. Finally, the attitude-orbit coupling dynamics are used to simulate the whole process, and the results show that orbital insertion errors are minor. • A combined diffractive solar sail model using liquid crystal polarization gratings. • Independent and controllable three-axis attitude control of diffractive solar sails. • Optimizing transfer trajectory for solar polar mission based on the proposed sail. • An adaptive attitude-tracking PD controller and a control allocation method. [ABSTRACT FROM AUTHOR]

Post-Newtonian approximations have been successful in describing various astronomical phenomena that classical Newtonian gravity could not. One such phenomenon is the precession of the periapsis of elliptical orbits. Einstein originally solved the problem in 1916 and since then others have been applying the technique to numerous complex systems. However, not much attention has been given to studying the changes in the configuration space when switching from Newtonian to post-Newtonian mechanics. Here, we compare the sizes and topologies of the configuration spaces of both these approaches and further explore the likelihood of planetary collisions in other star systems when configuration space expansion due to general relativity is taken into account. This straightforward analysis of predicted orbital precession could serve in introductory physics and astronomy courses, particularly in evaluating the likelihood of orbital collisions. [ABSTRACT FROM AUTHOR]

Currently, the visual detection of a target's shock flow field through background schlieren technology is a novel detection system. However, there are very few studies on the long-distance background schlieren imaging mechanism and its application in system design in the field of target detection. This paper proposes a design optimization method for space-based BOS detection system metrics. By establishing sensitivity evaluation models and image signal-to-noise ratio evaluation models for BOS detection systems, the influence of the different flight parameters and key parameters of BOS systems (detection spectral bands and spatial resolution) on target detection efficiency is explored. Furthermore, an optimization method based on the image signal-to-noise ratio of the BOS system and the overall metrics for specific scenarios are provided. The simulation results demonstrate that under satellite background images and speckle background images, the system metrics can detect and identify the schlieren of high-speed targets, with better applicability to disordered and complex real background images. This research contributes to advancing the development of high-speed target detection technology based on BOS. [ABSTRACT FROM AUTHOR]

The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, Linear Mapping Approximation, and state-space lumping. Despite the success of these techniques, they appear to be rather disparate, and at present, no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper, we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimizing a well-known information-theoretic quantity between the full model and its reduction, the Kullback–Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimization approaches. In addition, we derive general expressions for propensities of a reduced system that generalize those found using classical methods. We show that the Kullback–Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis–Menten enzyme system, and a genetic oscillator. [ABSTRACT FROM AUTHOR]

This article presents an approach to solve the problem of end-to-end optimization of the low-thrust interplanetary trajectory. At first, the problem of optimizing low-thrust interplanetary trajectory, which passes through the collinear libration points near the planets of departure and arrival is considered. The obtained solutions from this problem can be used as an initial guess to solve the end-to-end optimization problem, i.e., to calculate interplanetary low-thrust trajectories that satisfy the necessary optimality conditions at the match points of the heliocentric and planetocentric segments of trajectory. The minimum-fuel problem is considered. An indirect method based on the maximum principle, and the continuation method is applied to optimize interplanetary spacecraft trajectories. Numerical examples of trajectories from the Earth orbit to the orbit around the destination planet (Mars and Jupiter) are given. The possibility of a significant reduction in the required characteristic velocity is shown in comparison with the estimates obtained by using the zero-radius sphere of influence model. • End-to-end optimization, low-thrust, minimum-fuel trajectory, interplanetary transfer. • Using libration points as an initial guess to figure out the optimal match points of trajectory segments. • Analysing optimality conditions at the match points of the trajectory segments. • Comparison with conventional approach using zero-radius sphere of influence model. • End-to-end trajectory optimization significantly reduces characteristic velocity. [ABSTRACT FROM AUTHOR]

The distribution of internal defects in large-diameter steel pipes can be complicated. Due to the harsh working environments involved, the manual grinding method for correcting such defects is inaccurate, inefficient, and risky. Therefore, in this study, we designed a new internal pipe grinding robot with five degrees of freedom. The grinding trajectory was optimized, and dynamic and kinematic models of the robot were established for the internal space of a pipe with a diameter between 800 and 1,200 mm. The feasibility of the robot was verified by simulation. A trajectory optimization method that focuses on the time, energy, and impact of the trajectory of the grinding robot is proposed. The method uses modified multiobjective particle swarm optimization (MMOPSO) in the robot's trajectory planning module to obtain a Pareto solution set. The analytic hierarchy process is used with the minimum fuzzy entropy (AHP-MFE) method in the decision-making module to select the most appropriate trajectory according to the relevant working conditions. The experimental results validated the space accessibility and trajectory optimization performance. Compared with the original trajectory, operation time was shortened by 15.4%, energy consumption was reduced by 17.5%, and impact was reduced by 12.4%. The experimental error was less than 2.8%. The experimental results showed that the pipe grinding robot is safe and efficient. [ABSTRACT FROM AUTHOR]

A model for analyzing dynamic large-signal characteristics of double-barrier resonant-tunneling diodes (RTDs) is presented. The model is based on the analysis of dynamical trajectories in phase space, defined by the RTD bias and electron density in the RTD quantum well. We show that an accurate dynamic model can be reformulated in an approximate way, relying only on a directly measurable DC I–V curve and on few other RTD parameters, which could be easily estimated with simple DC calculations. We further demonstrate that a simple equivalent circuit, composed of a capacitor, inductor, and two resistors (RLRC), accurately describes the large-signal admittance of RTDs. The circuit elements can be described in terms of relaxation time, geometrical RTD capacitance, and low- and high-frequency resistors. The circuit has the very same structure as that previously derived for small-signal RTD admittance, although with deviating parameters, which are now dependent on the AC-signal amplitude. We show that the large-signal RTD relaxation time can be shorter and longer than the small-signal one. In the context of RTD oscillators, a shorter RTD relaxation time allows one to get higher output power at high frequencies. The availability of an accurate, general, but rather simple, physics-based model for analyzing large-signal RTD dynamics removes one of the major hindrances to the further development of sub-THz and THz RTD oscillators. [ABSTRACT FROM AUTHOR]

Storing and accessing memories is required to successfully perform day-to-day tasks, for example for engaging in a meaningful conversation. Previous studies in both rodents and primates have correlated hippocampal cellular activity with behavioral expression of memory. A key role has been attributed to awake hippocampal replay - a sequential reactivation of neurons representing a trajectory through space. However, it is unclear if awake replay impacts immediate future behavior, gradually creates and stabilizes long-term memories over a long period of time (hours and longer), or enables the temporary memorization of relevant events at an intermediate time scale (seconds to minutes). In this study, we aimed to address the uncertainty around the timeframe of impact of awake replay by collecting causal evidence from behaving rats. We detected and disrupted sharp wave ripples (SWRs) - signatures of putative replay events - using electrical stimulation of the ventral hippocampal commissure in rats that were trained on three different spatial memory tasks. In each task, rats were required to memorize a new set of locations in each trial or each daily session. Interestingly, the rats performed equally well with or without SWR disruptions. These data suggest that awake SWRs - and potentially replay - does not affect the immediate behavior nor the temporary memorization of relevant events at a short timescale that are required to successfully perform the spatial tasks. Based on these results, we hypothesize that the impact of awake replay on memory and behavior is long-term and cumulative over time. [ABSTRACT FROM AUTHOR]

(99942) Apophis is a potentially hazardous asteroid that will closely approach the Earth on April 13, 2029. Although the likelihood of an impact has been ruled out, this close encounter represents a unique opportunity for planetary science and defense. By investigating the physical and dynamical changes induced by this interaction, valuable insights into asteroid cohesion, strength, and internal structure can be obtained. In light of these circumstances, a fast mission to Apophis holds great scientific importance and potential for understanding potentially hazardous asteroids. To this aim, ESA proposed the mission RAMSES (Rapid Apophis Mission for SEcurity and Safety) to reach Apophis before its close encounter. In this context, the paper focuses on the reachability analysis of (99942) Apophis, examining thousands of trajectories departing from Earth and reaching the asteroid before the fly-by, using a low-thrust spacecraft. A two-layer approach combining direct sequential convex programming and an indirect method is employed for fast and reliable trajectory optimization. The results reveal multiple feasible launch windows and provide essential information for mission planning and system design. [ABSTRACT FROM AUTHOR]

Stochastic reaction networks are widely used in the modeling of stochastic systems across diverse domains such as biology, chemistry, physics, and ecology. However, the comprehension of the dynamic behaviors inherent in stochastic reaction networks is a formidable undertaking, primarily due to the exponential growth in the number of possible states or trajectories as the state space dimension increases. In this study, we introduce a knowledge distillation method based on reinforcement learning principles, aimed at compressing the dynamical knowledge encoded in stochastic reaction networks into a singular neural network construct. The trained neural network possesses the capability to accurately predict the state conditional joint probability distribution that corresponds to the given query contexts, when prompted with rate parameters, initial conditions, and time values. This obviates the need to track the dynamical process, enabling the direct estimation of normalized state and trajectory probabilities, without necessitating the integration over the complete state space. By applying our method to representative examples, we have observed a high degree of accuracy in both multimodal and high-dimensional systems. Additionally, the trained neural network can serve as a foundational model for developing efficient algorithms for parameter inference and trajectory ensemble generation. These results collectively underscore the efficacy of our approach as a universal means of distilling knowledge from stochastic reaction networks. Importantly, our methodology also spotlights the potential utility in harnessing a singular, pretrained, large-scale model to encapsulate the solution space underpinning a wide spectrum of stochastic dynamical systems. [ABSTRACT FROM AUTHOR]

Ignition on the National Ignition Facility (NIF) provides a novel opportunity to evaluate past data to identify signatures of capsule failure mechanisms. We have used new simulations of high-yield implosions as well as some from past studies in order to identify unique signatures of different ignition failure mechanisms: jetting due to the presence of voids or defects, jetting due to the capsule fill tube, interfacial mixing due to instabilities or due to plasma transport, radiative cooling due to the presence of contaminant in the hot spot, long-wavelength drive asymmetry, and preheat. Many of these failure mechanisms exhibit unique trajectories that can be distinguished through variations in experimental observables such as neutron yield, down-scattered ratio (DSR), and burn width. Our simulations include capsules using both plastic and high-density carbon ablators and span all high-yield designs considered since the beginning of the National Ignition Campaign in 2011. We observe that the variability in trajectories through the space of neutron yield, DSR, and burn width varies little across capsule design yet are unique to the failure mechanism. The experimental trajectories are most consistent with simulated preheat and jetting due to voids and defects, which are the only failure mechanisms that are indistinguishable in our analysis. This suggests that improvements to capsule compression due to improved capsule quality or reduced preheat have played a primary role in enabling high yields on NIF. Furthermore, our analysis suggests that further improvements have the potential to increase yields further. [ABSTRACT FROM AUTHOR]

The irregular satellites within the Jupiter system hold high scientific value due to their potential to contain clues about the early evolution of the solar system. This paper proposes an optimization algorithm for multiple irregular satellites flyby trajectories, which includes the powered gravity assist from Galilean moons. The algorithm is based on beam search and uses virtual trajectories to determine potential flyby targets, solving for trajectories that satisfy constraints on velocity increment, mission duration, and perijove radius. By changing the initial orbital period and optimizing the number of branches with Galilean moon gravity assist during branching, and comparing with the case without Galilean moon gravity assist, the effects of these factors on the number of irregular satellite flybys are summarized. The simulation results show that the algorithm can effectively solve for orbits that flyby multiple irregular satellites for initial orbits of different periods. The three trajectories obtained can serve as references for future missions. [ABSTRACT FROM AUTHOR]

How do words change their meaning? Although semantic evolution is driven by a variety of distinct factors, including linguistic, societal, and technological ones, we find that there is one law that holds universally across five major Indo-European languages: that semantic evolution is subdiffusive. Using an automated pipeline of diachronic distributional semantic embedding that controls for underlying symmetries, we show that words follow stochastic trajectories in meaning space with an anomalous diffusion exponent α = 0.45 ± 0.05 across languages, in contrast with diffusing particles that follow α = 1. Randomization methods indicate that preserving temporal correlations in semantic change directions is necessary to recover strongly subdiffusive behavior; however, correlations in change sizes play an important role too. We furthermore show that strong subdiffusion is a robust phenomenon under a wide variety of choices in data analysis and interpretation, such as the choice of fitting an ensemble average of displacements or averaging best-fit exponents of individual word trajectories. [ABSTRACT FROM AUTHOR]

The article proposes a criterion for the existence of sliding processes according to the frequency characteristics of the control device and the control object. It is shown that the conditions for the existence of slip are equivalent to the conditions for the absolute stability of equivalent circuits of the original systems with a variable structure. This approach is proposed by the authors as an alternative to the method of phase trajectories and state space equations used by other researchers. Frequency criteria make it possible to formulate several practical engineering provisions that are very important for the implementation of this control method in real electric drives. The main conclusions are confirmed by simulation of both processes in systems with a variable structure and in equivalent circuits. [ABSTRACT FROM AUTHOR]

This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body's middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions' extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications. [ABSTRACT FROM AUTHOR]

We calibrate the Swarm Langmuir Probe Ion Drift, Density and Effective Mass (SLIDEM) products using the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC‐1) electron density measurements. SLIDEM combines electric current measurements from the Electric Field Instrument faceplate (situated on the ram‐facing side of the satellite) with ion admittance measurements from a spherical Langmuir probe to estimate ionospheric ion density, bulk ion drift parallel to the satellite trajectory in the polar regions, and effective ion mass at low and middle latitudes. SLIDEM processing includes an eight‐parameter empirical geometry model that expresses the corrections to the effective faceplate area and spherical probe radius arising from satellite‐plasma interactions. Validation of SLIDEM density by conjunctions with COSMIC density altitude profiles reveals systematic errors, with SLIDEM underestimating corresponding COSMIC data by around 10%. Using the same conjunctions to calibrate the SLIDEM density processor, a simple one‐parameter geometry model is obtained, which significantly reduces bias in ion density. This leads to reduced bias in the ion ram speed and in the effective mass, both of which are more consistent with empirical ionospheric models. We examined three models characterizing the variation of probe effective electrode current collection areas. Faceplate geometries are statistically indistinguishable from the physical faceplate cross section. Spherical Langmuir probe radius is effectively reduced by about 10% due to satellite‐plasma interactions. We recommend updating the SLIDEM processor to use a smaller value for the spherical probe's radius. Key Points: COSMIC ionospheric electron density measurements are used to calibrate Swarm SLIDEM productsBiases in ionospheric density, effective ion mass, and ion ram speed are significantly reducedIon effective mass and ram speed estimates are consistent with predictions by empirical models [ABSTRACT FROM AUTHOR]

This paper investigates the trajectory design problem in the scenario of a multiple Sun-synchronous Orbit (SSO) space debris flyby mission from a DRO space station. At first, the characteristics of non-planar transfer from DRO to SSO in the Earth–Moon system are analyzed. The methods of large-scale ergodicity and pruning are utilized to investigate single-impulse and two-impulse DRO–Earth transfers. Using a powered lunar flyby, the two-impulse DRO–Earth transfer is able to fly by SSO debris while satisfying the requirements of the mission. After the local optimization, the optimal result of two-impulse DRO–Earth transfer and flyby is obtained. A multi-objective evolutionary algorithm is used to design the Pareto-optimal trajectories of multiple flybys. The semi-analytical optimization method is developed to provide the estimations of the transfer parameters in order to reduce the computations caused by the evolutionary algorithm. Simulations show that transferring from the 3:2 resonant DRO to a near-coplanar flyby of a SSO target debris using a powered lunar gravity assist needs a 0.47 km/s velocity increment. The mission's total velocity increment is 1.39 km/s, and the total transfer time is 2.23 years. [ABSTRACT FROM AUTHOR]

We investigate the orbital dynamics of an exosystem consisting of a solar-mass host star, a transiting body, and an Earth-size exoplanet within the framework of the generalized three-body problem. Depending on its mass, the transiting body can either be a super-Jupiter or a brown dwarf. To determine the final states of the Earth-size exoplanet, we conduct a systematic and detailed classification of the available phase space trajectories. Our classification scheme distinguishes between the bounded, escape, and collisional motions of the Earth-size exoplanet. Additionally, for cases of ordered (regular) motion, we further categorize the associated initial conditions based on the geometry of their respective trajectories. These bounded regular trajectories hold significant importance as they provide insights into the regions of phase space where the motion of the Earth-size exoplanet can be dynamically stable. Of particular interest is the identification of initial conditions that result in a bounded exomoon-like orbit of the Earth-size exoplanet around the transiting body. [ABSTRACT FROM AUTHOR]

Satellite constellation deployment is a cohesive mission where the trajectories of satellites must be planned concurrently. This paper presents an Integrated Program for Optimal Deployment of a Satellite Constellation (PODSC) consisting of m non-identical satellites in any desired arrangement in n orbital planes. The PODSC can optimize the scheduling of mission timelines, ensuring effective coordination with the trajectory of each satellite. This involves meticulous planning that considers temporal constraints and regards collision avoidance constraint. Additionally, the PODSC can select the most favorable deployment strategy, considering the trade-offs between time and fuel consumption across all possible deployment methods. The PODSC also utilizes an innovative Perturbed Multi-impulsive Inclined transfer trajectory Amalgamated with a modified Lambert targeting problem (PMIAL). The main idea of designing the mentioned maneuver is to eliminate the defects of the Lambert Targeting Problem (LTP). The LTP cannot account for space perturbations. Moreover, the LTP faces challenges when attempting to align the transfer trajectory tangentially with the final orbit in situations where there exists a substantial disparity in inclination and right ascension between the initial and final orbits. The PMIAL establishes three consecutive steps to fix the mentioned defects. Balancing the trade-off between time and achieving optimal fuel consumption will be possible by applying a hybrid IWO/PSO (The hybrid Invasive Weed Optimization/Particle Swarm Optimization) optimization algorithm in both PMIAL and PODSC. The case study will involve simulating two constellation deployment missions, with a particular focus on considering the Earth's oblateness as a notable perturbation; however, the proposed algorithms can consider any space perturbations. [ABSTRACT FROM AUTHOR]

Summary: Wind energy is a source of collision fatalities for birds and bats. To evaluate the risk that wind power development projects might pose to the conservation of protected species, it is essential to quantify the impact of collisions on the dynamics of wild populations. To address this challenge, two approaches are primarily employed: potential biological removal (PBR) and population projection analysis (PPA). PBR is a decision rule designed to calculate a sustainable fatality limit for a given population, whereas PPA relies on simulation-based modelling to forecast a population's future trajectory under various scenarios. In the context of environmental impact assessments (EIAs), we argue that PPA offers a more suitable method than PBR for evaluating population-level impacts resulting from collisions with wind turbines. Unlike PBR, PPA can be focused on a single source of disturbance, aligning with the perspective of the EIA process. By contrast, PBR necessarily adopts a population-centred perspective and is therefore only relevant when considering all sources of mortality that jointly affect a population. Furthermore, robust utilization of the PBR approach requires the definition of quantitative conservation objectives and the implementation of a comprehensive management strategy evaluation, neither of which is ever undertaken within the context of an EIA. [ABSTRACT FROM AUTHOR]

This article explores the evolution of Lorenz trajectories within attractors. Specifically, based on the characteristics of the tangents to trajectories, we derive quantitative standards for determining the spatial position of trajectory lines. The Lorenz trajectory is decomposed into four parts. This standard is objective and quantitative and is independent of the initial field of the Lorenz equation and the calculation scheme; importantly, it is designed based on the inherent dynamic characteristics of the Lorenz equation. Linear fitting of the trajectories in the left and right equilibrium point regions shows that the trajectories lie on planes, indicating the existence of linear features in the nonlinear system. This study identifies the fundamental causes of chaos in the Lorenz equation using the microscopic evolution and local characteristics of the trajectories, and indicating that the spatial position of the initial field is important for their predictability. We theoretically demonstrate that mutation is essentially self-regulation within chaotic systems. This scheme is designed according to the evolution characteristics of Lorenz trajectories, and thus has certain methodological limitations that mean it may not be applicable to other chaotic systems. However, it does depict the causes of chaos and elucidates the sensitivity of differential equations to initial values in terms of trajectory evolution. [ABSTRACT FROM AUTHOR]

With the sustained rise in satellite deployment in Low Earth Orbits, the collision risk from untracked space debris is also increasing. Often small-sized space debris (below 10 cm) are hard to track using the existing state-of-the-art methods. However, knowing such space debris' trajectory is crucial to avoid future collisions. We present a Physics Informed Neural Network (PINN)—based approach for estimation of the trajectory of space debris after a collision event between active satellite and space debris. In this work, we have simulated 8565 inelastic collision events between active satellites and space debris. To obtain the states of the active satellite, we use the TLE data of 1647 Starlink and 66 LEMUR satellites obtained from space-track.org. The velocity of space debris is initialized using our proposed velocity sampling method, and the coefficient of restitution is sampled from our proposed Gaussian mixture-based probability density function. Using the velocities of the colliding objects before the collision, we calculate the post-collision velocities and record the observations. The state (position and velocity), coefficient of restitution, and mass estimation of un-tracked space debris after an inelastic collision event along with the tracked active satellite can be posed as an optimization problem by observing the deviation of the active satellite from the trajectory. We have applied the classical optimization method, the Lagrange multiplier approach, for solving the above optimization problem and observed that its state estimation is not satisfactory as the system is under-determined. Subsequently, we have designed Deep Neural network-based methods and Physics Informed Neural Network (PINN) based methods for solving the above optimization problem. We have compared the performance of the models using root mean square error (RMSE) and interquartile range of the predictions. It has been observed that the PINN-based methods provide a better estimation performance for position, velocity, mass and coefficient of restitution of the space debris compared to other methods. [ABSTRACT FROM AUTHOR]

The ventrolateral prefrontal cortex (VLPFC) shows robust activation during the perception of faces and voices. However, little is known about what categorical features of social stimuli drive neural activity in this region. Since perception of identity and expression are critical social functions, we examined whether neural responses to naturalistic stimuli were driven by these two categorical features in the prefrontal cortex. We recorded single neurons in the VLPFC, while two male rhesus macaques (Macaca mulatta) viewed short audiovisual videos of unfamiliar conspecifics making expressions of aggressive, affiliative, and neutral valence. Of the 285 neurons responsive to the audiovisual stimuli, 111 neurons had a main effect (two-way ANOVA) of identity, expression, or their interaction in their stimulus-related firing rates; however, decoding of expression and identity using single-unit firing rates rendered poor accuracy. Interestingly, when decoding from pseudo-populations of recorded neurons, the accuracy for both expression and identity increased with population size, suggesting that the population transmitted information relevant to both variables. Principal components analysis of mean population activity across time revealed that population responses to the same identity followed similar trajectories in the response space, facilitating segregation from other identities. Our results suggest that identity is a critical feature of social stimuli that dictates the structure of population activity in the VLPFC, during the perception of vocalizations and their corresponding facial expressions. These findings enhance our understanding of the role of the VLPFC in social behavior. [ABSTRACT FROM AUTHOR]

Laser Time Transfer (LTT) has proven to be able to improve remote time transfer accuracy compared to microwave technology. The impact of satellite clock errors and atmospheric delays during LTT will be further reduced in the common-view mode. The challenge is presented as an optimization problem that is limited by satellite trajectories. This paper introduces an improved simulated annealing algorithm designed to maximize the common-view possibility among various station pairs within regional Satellite Laser Ranging (SLR) networks by optimizing satellite orbit trajectories. The study proposes a system model that integrates LTT principles with satellite visibility considerations. The simulated annealing algorithm is improved with new annealing strategies that incorporate control strategies, and modify the cooling function. Comparative simulation analyses demonstrate the effectiveness of the algorithm, resulting in a significant reduction in computation time by over 10 times. The optimized orbits exhibit common-view windows between 3.337 and 8.955 times longer than existing orbits. Further simulations are conducted to optimize the orbits, and common-view models are established for 45 pairs among 10 stations. The optimizations result in common-view times ranging from 6.183 to 60.633 min in the Asia-Pacific region and from 5.583 to 61.75 min in the Europe-to-Asia region. This can provide valuable references for designing satellite constellations. [ABSTRACT FROM AUTHOR]

Human desire to explore Mars has persisted throughout history, and especially, it is required to achieve precise and safe landings on the Martian surface. The atmospheric entry phase plays a crucial role in ensuring mission success, and active research on entry guidance methods continues. This paper presents a comparative study between the two primary types of entry guidance methods: (1) path planning-tracking and (2) predictor–corrector methods by applying them to solve two distinct Mars atmospheric entry guidance problems: (a) robotic entry and (b) human entry missions. Optimization approaches are adopted for the path planning-tracking method. After generating an optimal reference trajectory based on a mission concept-defined cost function, the receding horizon control method is employed to minimize tracking errors. In the predictor–corrector method, two parameterized entry guidance approaches are explored and analyzed. A well-known numerical predictor–corrector method that utilizes a parameterized bank angle profile for entry trajectory generation is tested to demonstrate its robustness against random dispersions. On the other hand, another predictor–corrector type guidance method that assumes a polynomial shape to shape an altitude profile over range-to-go is adopted to show its range control capability. Numerical simulations reveal the pros and cons of each type of entry guidance method, and a suitable guidance method for each Mars entry mission is identified depending on the mission concept and requirements. The analysis results provide future work. • A comparative study between path planning-tracking and predictor-corrector guidance methods. • Mars atmospheric entry problem for robotic and human landing missions. • Optimization approaches for reference trajectory generation and path tracking. • Numerical predictor-corrector based on parameterized bank angle and altitude profiles. [ABSTRACT FROM AUTHOR]

In the past, space trajectory optimisation was limited to the design of space transfers to single destinations. More recent mission concepts however present the challenge to target multiple destinations; be it for science, exploration or even exploitation. This paper focuses on space trajectories that aim to visit multiple main-belt asteroids with one single spacecraft. The trajectory design of these missions is complicated by the fact that the asteroid sequence is not known a priori, but it is the objective of the optimisation problem. Usually, these problems are tackled as global optimisation problems under the formulation of Mixed-Integer Non-Linear Programming, on which the design variables assume both continuous and discrete values. However, beyond the aim of finding the global optimum, mission designers are usually interested in providing a wide range of mission design options reflecting the multi-modality of the problem. The paper describes a multi-fidelity design pipeline that enables a consistent exploration of all feasible asteroid tours with a given set of mission boundary conditions (e.g., launch window, mission duration, Δ v). The consistency of the exploration is ensured by a deterministic search scheme which retains the n -best paths at each stage of a dynamic programming process. Bellman's principle of optimality is made applicable by transcribing the search space into a series of discretized events defined by asteroid index and fly-by epoch, as well as ensuring optimal substructure property with the choice of transfer model and design variables. The method is deployed to explore asteroid tour opportunities visiting 10 or more main belt objects and mission boundary conditions compatible with medium or discovery class missions. 79 million such trajectories are found with launch date in 2037. • A multi-fidelity pipeline is proposed to deal with the challenge of trajectories that fly-by many main belt asteroids. • A novel transcription of the mixed-integer problem allows for an efficient pruning of the search space. • A dynamic programming-based exploration is proposed, keeping the n best solutions for expansion at each unique node. • Novel mission scenarios are presented in the framework of ESA's M-class mission envelope. [ABSTRACT FROM AUTHOR]

The Reiss theory for binary homogeneous nucleation in binary vapor mixtures is critically analyzed and further developed. Based on the analysis of phase space trajectories in the supercritical zone of the phase transition, carried out within the framework of the theory of two-dimensional dynamical systems and supplemented by the flux matching condition at the boundary of the critical zone, it is shown how the theory should be modified. The proposed modification is equivalent to the earlier modifications by Langer and Stauffer, based on additional trial assumptions (ansatz) for solving the steady state equation for the non-equilibrium size distribution function, but reveals and substantiates the approximation underlying their approach. The extension of the Reiss theory to binary vapors in inert carrier (atmospheric) gases is justified. Copyright © 2023 American Association for Aerosol Research [ABSTRACT FROM AUTHOR]

Recurrence lacunarity has been recently proposed to detect dynamical state transitions over various temporal scales. In this paper, we combine suggested distribution moments and introduce multifractal recurrence lacunarity to unearth rich information of trajectories in phase space. By considering generalized moments, it provides an enhanced measurement to account for differences of black pixels in the recurrence plot at various scales. Numerical simulations have proved that the proposed method is able to differentiate varying types of time series and provide further insights of inherent features including stochastic series, chaotic maps and series contaminated interference components. In real-world applications, it performs well on quantifying the subtle structural changes of financial time series. In addition, it is intriguing to confirm that corrugation signals possess much more vivid information of heterogeneity in terms of recurrence plots than normal ones. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel distributed algorithm based on model predictive control and alternating direction multiplier method (DMPC-ADMM) for cooperative trajectory planning of quadrotor swarms. First, a receding horizon trajectory planning optimization problem is constructed, in which the differential flatness property is used to deal with the nonlinear dynamics of quadrotors while we design a relaxed form of the discrete-time control barrier function (DCBF) constraint to balance feasibility and safety. Then, we decompose the original trajectory planning problem by ADMM and solve it in a fully distributed manner with peer-to-peer communication, which induces the quadrotors within the communication range to reach a consensus on their future trajectories to enhance safety. In addition, an event-triggered mechanism is designed to reduce the communication overhead. The simulation results verify that the trajectories generated by our method are real-time, safe, and smooth. A comprehensive comparison with the centralized strategy and several other distributed strategies in terms of real-time, safety, and feasibility verifies that our method is more suitable for the trajectory planning of large-scale quadrotor swarms. [ABSTRACT FROM AUTHOR]

In this paper, an effective control and parameters identification scheme was proposed for high-precision trajectory tracking of space robotic manipulators. Our proposed control method employed a linear-extended-state-observer (LESO) based model predictive control (MPC) scheme. The feedback linearization approach was utilized to develop a model predictive controller. The optimization objective function was simplified to a standard quadratic programming (QP) problem for solution. To minimize the impact of the inaccuracy in the dynamics model, a LESO was designed to estimate the disturbance, and its convergence was demonstrated. In order to improve the accuracy of dynamic model, the physical consistency of inertial parameters was constrained using linear matrix inequality (LMI) techniques. Moreover, the dynamics parameters were estimated through semidefinite programming (SDP) techniques. To validate the effectiveness of the proposed control method, it was compared with existing controllers through simulations and experiments. The results demonstrated the superior performance of the proposed scheme, highlighting its potential for achieving high-precision trajectory tracking control in space robotic manipulators. • High-precision trajectory tracking control for space manipulator is investigated. • Feedback linearization based predictive model for MPC is established. • A LESO is designed and its convergence is proven. • A physical consistency parameters identification method is presented. • Both simulations and experiments are performed for validation. [ABSTRACT FROM AUTHOR]

For the first time in history, Parker Solar Probe touched the Sun in April 2021 when it entered the Sun's corona—humanity's first mission ever that reached the Sun—for a scientific in-situ study to unlock the mystery of our star. To reach the Sun is extremely difficult because, unlike any other space exploration destination, the Sun is the solar system's central body, around which Earth and other planets revolve. Earth orbits the Sun at a velocity of about 30 km/s, so for a spacecraft to reach the Sun from Earth the spacecraft must cancel out its velocity in the Earth orbit so it can fall to the Sun. That requires an excessively large energy higher than that required to reach any destination in the solar system, which is beyond the capability of current rockets. This paper describes how Parker Solar Probe is delivered to the Sun through a unique V7GA trajectory that enables it to attain the excessive energy through planetary gravity assists of Venus, flying by Venus seven times to ultimately come within 9.86 solar radii (R S) of the Sun. An emphasis is on in-flight trajectory control of the probe through the intricate V7GA trajectory in actual operation in an unprecedented space environment around the Sun, where unpredictable orbit perturbations plus their ripple effects on the consecutive seven Venus flybys could easily drive the flight trajectory out of control. A novel systematic 2-level control method is developed and has been applied to solve the complicated trajectory control problem in flight operation, using in-flight trajectory re-optimization to select the targets of Venus flybys as trajectory control points and then using trajectory correction maneuvers to target a Venus flyby at the control point. This method enables effective and efficient control of the intricate V7GA trajectory and has resulted in significantly better than pre-launch anticipated flight performance, saving tremendous ΔV. Four years from launch, Parker Solar Probe has completed 5 of the 7 Venus gravity-assist flybys and 12 of the 24 planned solar encounters, passing by the Sun at 13 R S in its orbit. Flight results and performance of the completed flight to date are also described. • How Parker Solar Probe was flown and touched the Sun for the first time in history. • Getting to the Sun is extremely difficult and is enabled by a unique V7GA trajectory. • A novel systematic 2-level control method for complex in-flight trajectory control. • In-flight trajectory re-optimization, trajectory correction maneuver and performance. • Flight results of 5 Venus gravity-assist flybys and record-braking solar encounters. [ABSTRACT FROM AUTHOR]

In this work, off-nominal trajectory design options for NASA's sail-based Solar Cruiser mission are examined. A novel method for constructing bounded trajectories about a periodic reference orbit is used to parameterize insertion into the target sub- L 1 halo orbit. The nominal mission plan of reaching the sub- L 1 halo orbit under purely sail power is then examined for a range of projected launch vehicle dispersions. Results indicate that cold (underburn) injections less than −0.2 m/s are incapable of arriving at the nominal sub- L 1 mission orbit. However, hot (overburn) injections are shown to be much more robust to the nominal mission plan than the low-energy trajectories. The resilience of the overburn cases compared to the underburn cases reveals that the mission would significantly benefit from additional launch vehicle hyperbolic excess energy to ensure mission requirements are satisfied. • Nominal Solar Cruiser transfer design for three deployment dates. • Novel method for bounded motion generation in ephemeris dynamics. • Effects of high and low-energy deployments on Solar Cruiser transfer. [ABSTRACT FROM AUTHOR]