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Dysregulation of the CXCL12/CXCR4 axis is implicated in autoimmune, inflammatory, and oncogenic diseases, positioning CXCR4 as a pivotal therapeutic target. We evaluated optimized variants of the specific endogenous CXCR4 antagonist, EPI-X4, addressing existing challenges in stability and potency. Our structure-activity relationship study investigates the conjugation of EPI-X4 derivatives with long-chain fatty acids, enhancing serum albumin interaction and receptor affinity. Molecular dynamic simulations revealed that the lipid moieties stabilize the peptide-receptor interaction through hydrophobic contacts at the receptor's N-terminus, anchoring the lipopeptide within the CXCR4 binding pocket and maintaining essential receptor interactions. Accordingly, lipidation resulted in increased receptor affinities and antagonistic activities. Additionally, by interacting with human serum albumin lipidated EPI-X4 derivatives displayed sustained stability in human plasma and extended circulation times in vivo. Selected candidates showed significant therapeutic potential in human retinoblastoma cells in vitro and in ovo , with our lead derivative exhibiting higher efficacies compared to its non-lipidated counterpart. This study not only elucidates the optimization trajectory for EPI-X4 derivatives but also underscores the intricate interplay between stability and efficacy, crucial for delineating their translational potential in clinical applications. [Display omitted] • Lipidated derivatives of EPI-X4 exhibit increased affinity and antagonistic activity towards the CXCR4 receptor. • Lipidated EPI-X4 derivatives exhibit a half-life of >8 h in both blood and plasma. • The lipidated EPI-X4 JM#198 displays a circulation half-life of nearly 4 h in mice. • EPI-X4 JM#198 inhibits retinoblastoma tumor formation in vitro and in ovo. [ABSTRACT FROM AUTHOR]

The Lunar Gateway will represent a primary space system useful for the Artemis program, Earth–Moon transportation, and deep space exploration. It is expected to serve as a staging location and logistic outpost on the way to the lunar surface. This study focuses on low-thrust transfer dynamics, from the Near-Rectilinear Halo Orbit traveled by Gateway to a specified Low-altitude Lunar Orbit (LLO). More specifically, this research addresses two closely-related problems: (i) determination of the minimum-time low-thrust trajectory and (ii) design, implementation, and testing of a guidance and control architecture, for a space vehicle that travels from Gateway to LLO. Orbit dynamics is described in terms of modified equinoctial elements, with the inclusion of all the relevant perturbations, in the context of a high-fidelity multibody ephemeris model. The minimum-time trajectory from Gateway to a specified lunar orbit is detected through an indirect heuristic approach, which uses the analytical conditions arising in optimal control theory in conjunction with a heuristic technique. However, future missions will pursue a growing level of autonomy, and this circumstance implies the mandatory design and implementation of an efficient feedback guidance scheme, capable of compensating for nonnominal flight conditions. This research proposes nonlinear orbit control as a viable and effective option for autonomous explicit guidance of low-thrust transfers from Gateway to LLO. This approach allows defining a feedback law that enjoys quasi-global stability properties without requiring any offline reference trajectory. The overall spacecraft dynamics is modeled and simulated, including attitude control and actuation. The latter is demanded to an array of reaction wheels, arranged in a pyramidal configuration. Guidance, attitude control, and actuation are implemented in an iterative scheme. Monte Carlo simulations demonstrate that the guidance and control architecture at hand is effective in nonnominal flight conditions, i.e. with random starting point from Gateway as well as in case of temporary unavailability of the propulsion system. The numerical results also point out that only a modest propellant penalty is associated with the use of feedback guidance and control in comparison to the minimum-time optimal trajectory. • Minimum-time low-thrust orbit transfer from the Gateway to a low lunar orbit. • The optimal transfer is obtained using the indirect heuristic method. • Feedback guidance is investigated, leveraging nonlinear orbit control. • Nonlinear attitude control and actuation through reaction wheels is designed. • Numerical simulations prove effectiveness of guidance and control architecture. [ABSTRACT FROM AUTHOR]

This study investigates the potential for mitigating the non-CO 2 climate impact induced by air traffic operations at the network scale. Due to the spatiotemporal dependency of non-CO 2 climate impact, aircraft trajectory planning emerges as an operational strategy to mitigate their corresponding effects. However, trajectory planning without considering the interactions between flights is inadequate when studying the actual climate impact mitigation potential. Indeed, meeting climatically oriented aerial traffic requires a holistic view of different aspects of adopting climate-optimal trajectories. In this study, we aim to assess the network-scale effects of full 4D climate-friendly aircraft trajectories. Different indicators are employed to assess air traffic safety, manageability, cost-efficiency, and the environmental impact of optimized routes. Our findings suggest that while optimized trajectories can potentially reduce climate impact, they introduce significant challenges related to air traffic safety, complexity, and demand, especially in sectors in proximity to climate hotspots. These insights highlight the need to develop an advanced mechanism enabling a safe and efficient air traffic management system with minimal climate impact. • Climate-aware flight planning can reduce the climate impact of non-CO 2 emissions. • 4D trajectory optimization is performed for individual flights. • The effects of climate-optimal trajectories on air traffic performance are assessed. • Climate-optimal routes might increase congestion and complexity, jeopardizing safety. [ABSTRACT FROM AUTHOR]

A robust trajectory planning method for non-cooperative target rendezvous is investigated based on closed-loop uncertainty analysis. The proposed method addresses the issue that uncertainties affect the optimality of objective functions and the reliability of constraints. Considering multiple uncertainties, a stochastic optimal rendezvous model with a robustness performance index and chance constraints is presented with line-of-sight dynamics. The guidance model, angles-only navigation model and control model are derived, and uncertainty propagation equations for closed-loop GN & C system is proposed by using linear covariance analysis. The stochastic optimal rendezvous model is transformed into a robust optimal rendezvous model by using 3- σ of the random variables. The genetic algorithm is used to solve the robust trajectory planning problem, and a series of examples demonstrate that the robust maneuver solution can be significantly better than the solution corresponding to deterministic trajectory optimization problem. [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]

When legged robots perform complex tasks in unstructured environments, falls are inevitable due to unknown external disturbances. However, current research mainly focuses on the locomotion control of legged robots without falling. This paper proposes a comprehensive decision-making and control framework to address the falling over of quadruped robots. First, a capturability-based fall prediction algorithm is derived for planar single-contact and 3D multi-contact locomotion with a predefined gait sequence. For safe fall control, a novel contact-implicit trajectory optimization method is proposed to generate both state and input trajectories and contact mode sequences. Specifically, incorporating uncertainty into the system and terrain models enables mitigating the non-smoothness of contact dynamics while improving the robustness of the resulting trajectories. Furthermore, a model-free deep reinforcement learning-based approach is presented to achieve fall recovery after the robot completes a fall. Experimental results demonstrate that the proposed fall prediction algorithm accurately predicts robot falls with up to 95% accuracy approximately 395ms in advance. Compared to classical locomotion controllers, which often struggle to maintain balance under significant pushes or terrain perturbations, the presented framework can autonomously switch to the fall controller approximately 0.06s after the perturbation, effectively preventing falls or achieving recovery with a threefold reduction in touchdown impact velocity. These findings highlight the effectiveness of the proposed framework in enhancing the stability and safety of legged robots in unstructured environments. • The proposed fall prediction approach exhibits significantly enhanced reliability and flexibility. • The proposed controller can autonomously generate contact sequences, reducing damage from falls. • The designed reinforcement learning-method improves efficiency and robustness in fall recovery. [ABSTRACT FROM AUTHOR]

In this work, we address parametric non–stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation–based domain decomposition approach, we derive an optimal control problem, for which we present a convergence analysis in the case of non–stationary incompressible Navier–Stokes equations. We discretise the problem with the finite element method and we compare different model order reduction techniques: POD–Galerkin and a non–intrusive neural network procedures. We show that the classical POD–Galerkin is more robust and accurate also in transient areas, while the neural network can obtain simulations very quickly though being less precise in the presence of discontinuities in time or parameter domain. We test the proposed methodologies on two fluid dynamics benchmarks with physical parameters and time dependency: the non–stationary backward–facing step and lid–driven cavity flow. • Optimisation-based domain-decomposition algorithm for non-stationary computational fluid dynamics. • Convergence analysis for the domain-decomposition optimal control problem. • Comparison of the intrusive POD-Galerkin and a non-intrusive Neural Networks based approaches. [ABSTRACT FROM AUTHOR]

• A dynamic model for space multi-fingered system with uncertainties and disturbances is formulated. • The dynamic capture domain is designed to envelop space tumbling target for multi-fingered mechanism. • Composite controller based on model predictive control and disturbance observer is proposed. • Proposed method can handle constraints while having better interference rejection. Space debris are usually with diverse geometric shapes and no grappling points. Current capture methods lack the capability to adjust to the target shape dynamically. The capture of space debris remains a significant challenge for operational space missions. This paper presents a multi-finger envelope control strategy based on dynamic capture region in the pre-grasping phase. In the method, the proximal joints of each finger are first determined according to the target shapes. Then, an appropriate joint threshold is selected to generate a set of candidate configurations for the rest of the finger joints, and the effective multi-fingered envelope configuration that resembles the target contour is chosen from candidate finger configurations based on the Hausdorff Distance. Further, the optimal joint trajectories are obtained by minimizing the impact of multi-finger movements on the palm. Considering the model uncertainties, external disturbances and actuator saturation, a composite controller combining disturbance observer and nonlinear model predictive control (NMPC) is proposed for trajectory tracking control of multi-fingered mechanism. The simulation results show that the proposed method can rapidly find an effective envelope capture configuration and has a higher trajectory tracking performance in the presence of uncertainty compared to the Proportional Integral Differential and NMPC controllers. [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]

This work considers the trajectory optimization of a kinetic impactor spacecraft, which is sent to collide with a threatening near-Earth asteroid. It is assumed that Earth departure is done impulsively, by the upper stage of a launch vehicle, and is then followed by low-thrust electric propulsion until impact. For a given spacecraft, all of the important decision parameters, such as the date of departure, the direction of the hyperbolic departure, the thrust program, i.e. the history of the low-thrust pointing angles, and the date of impact are all chosen by the optimizer to maximize the perigee radius of the asteroid at its closest approach. Normally a trajectory optimization problem of this type would need to be described by many hundreds of decision parameters, e.g. if formulated to be solved by an optimization package (such as GPOPS) using nonlinear programming. We show that a successful and accurate optimization of the mission is possible using the heuristic method, particle swarm, and only 16 decision parameters, and present results for the deflection of 99942 Apophis at its 2029 close approach. • A particle swarm optimizer finds optimal strategies for asteroid deflection missions. • A novel method uses the system state transition matrix to increase accuracy. • The accuracy of the particle swarm solution is confirmed by using a direct transcription method. • The work shows that deflection by kinetic impact is feasible with present technology. [ABSTRACT FROM AUTHOR]

The Sun–Earth Lagrange points, L1 and L2, are excellent locations for space based observatories, due to their favorable dynamical and environmental properties. Space telescopes, however, come with an extremely high price tag, and without refueling and servicing the typical lifetime is only about ten to fifteen years. The return on investment of a space telescope could be significantly increased by developing on-orbit servicing and refueling capabilities, assuming that the servicing vehicle can be launched at a fraction of the cost of the original mission and that the lifetime of the space telescope can be significantly extended to allow for continued scientific activity. In this paper we demonstrate the feasibility of this class of servicing mission from a trajectory design perspective, using novel techniques that we have developed for quick sampling of the solution space, as well as an efficient and reliable means to obtained high-fidelity, time-optimal, end-to-end transfer trajectories. As candidates for this investigation we consider Gaia and the James Webb Space Telescope. Our trajectory design methodology is, however, general enough to be applicable to future space observatories that are designed to be serviceable in space. • The lifetime of space assets at SEL2 can be greatly extended via servicing missions. • Poincare maps are leveraged to explore the design space and obtain initial guesses. • Indirect methods are used to refine the initial guesses and design optimal transfers. [ABSTRACT FROM AUTHOR]

This paper presents a satellite constellation orbital reconfiguration method based on the intelligent multi-impulse rendezvous considering the impulse-magnitude limit. This problem is solved by two steps: the single-target rendezvous trajectory optimization and the multi-target rendezvous mission planning. For single target, the multi-impulse rendezvous problem is transformed into a Markov decision process and solved by a reinforcement learning algorithm. The rewards of the critic networks are used as estimation of fuel consumption, while the actions of the actor networks are used as initial values for further optimization. For multiple targets, an efficient Monte-Carlo tree search method is used to realize the global optimal solution of the satellite constellation reconfiguration problem. Finally, the numerical examples show that the proposed method can rapidly optimize the multi-impulse constellation reconfiguration problem. • A RL-based approach is proposed to quickly generate the rendezvous trajectory. • An improved MCTS algorithm is adopted to solve the multi-target mission planning. • The proposed approach can reduce the computation time for rendezvous problems. [ABSTRACT FROM AUTHOR]

The SpaceLiner is a futuristic concept of a suborbital space plane intended to provide ultra-fast intercontinental passenger transport, currently in pre-development at DLR-SART. Vehicles traveling at hypersonic speeds inevitably produce shock waves that are perceived at ground level as sonic booms, with associated disturbance of the overflown populations. The reduction of this disturbance, together with the decrease of the noise associated to the launch and ascent phase, is critical for a viable future operation of the SpaceLiner. The objective of this work is the redesign of the passenger stage aerodynamic shape in order to improve its atmospheric re-entry performance, in terms of a reduction of both the heat flux and the disturbance of the overflown populations. For this purpose, a MDAO methodology was developed with the tasks of (1) computing vehicle performance from a wing shape parametrization using fast estimation methods, (2) exploring the design space and (3) finding a new promising aerodynamic shape. First, a Python tool-chain was developed to compute vehicles performances from a wing shape parametrization using fast estimation methods. The tool-chain was then systematically exploited to explore the design space by means of parametric studies, whose results informed the implementation of the forthcoming optimization. Afterwards, the wing shape was optimized using a three-objective evolutionary algorithm that minimized the vehicle mass and maximized its lift-to-drag ratio and lift coefficient. Simplified trajectory optimizations were then run on the set of non-dominated solutions in order to identify the most performing configurations. Finally, multi-objective evolutionary trajectory optimizations were run for the most promising candidate along intercontinental point-to-point routes of interest. Comparisons with the previous design iteration showed a significant improvement in terms of a reduction of both reentry heat flux and population disturbance. • MDAO procedure for wing shape optimization of hypersonic passenger transport vehicle. • Conducted evolutionary multi-objective optimization for key wing performance metrics. • Trajectory optimization of pareto front vehicles to identify best compromise of metrics. • Found configurations capable of avoiding sonic booms over populated areas on various routes. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of guiding a rocket-powered vehicle to land using aerodynamic and thrust controls. The vehicle initially glides towards the landing site, flying at an unprecedentedly high angle-of-attack to decelerate, thereby reducing the propellant needed for a later retro-thrust landing. The high angle-of-attack pure aerodynamic flight leads to highly nonlinear dynamics that have not been addressed by existing powered descent guidance methods. In particular, real-time optimization of the vehicle's landing trajectory has been very challenging. In this paper, a closed-loop guidance method is proposed that optimizes a restricted 6-degrees-of-freedom (6-DoF) trajectory in real-time. To remedy the difficulty caused by the highly nonlinear dynamics, the general propellant-optimal problem is regularized with two modifications. The first is to augment the angular velocity to the performance index, removing possible singularity arcs that cause numerical difficulties. The second is to parameterize the thrust magnitude with a piecewise-constant form, reducing the number of control variables to be optimized. The regularized problem is then solved with successive convexification to update the restricted 6-DoF landing trajectory in each guidance cycle. Monte Carlo experiments with aerodynamic and thrust dispersions are conducted to examine the proposed guidance method. • A new guidance method is proposed that uses both aerodynamic and thrust controls. • The guided vehicle can fly at unprecedentedly high angle-of-attack to decelerate. • The guidance method optimizes a restricted 6-degree-of-freedom trajectory in real-time. • The guidance problem is regularized twice to address the highly nonlinear dynamics. [ABSTRACT FROM AUTHOR]

This paper focuses on the applicability of Zermelo's equation within the context of 3D commercial aircraft trajectory optimization problems. The associated optimal control problem includes two singular controls, specifically aerodynamic path angle and throttle setting, and one regular control, specifically heading angle. Using Pontryagin's maximum principle and the direct adjoining method, we show that the optimal heading angle is defined by Zermelo's equation. The significance of the presented analysis is that Zermelo's equation holds for 3D commercial aircraft flights, even in the presence of standard state-inequality constraints and a more general objective function. With the help of Zermelo's equation, the control problem is initially analyzed for a 3D time-optimal climb-phase scenario, which is solved by an indirect approach. Through the analysis of the switching function, we demonstrate the dependency of the optimal aerodynamic path angle on the optimal heading angle. Next, by tackling a 3D time-fuel-optimal free-routing flight, solved by a direct approach, we show that Zermelo's equation can help reduce the overall dimension of the associated nonlinear programming. To successfully handle the initial guess in both indirect and direct problems, it is proposed a diminutive nonlinear programming technique as a fast and robust initializer. This simple-yet-effective initializer provides sufficient information about the optimal controls and state dynamics required for initializing a direct optimization, as well as the optimal switching times and co-states required for initializing an indirect optimization. • Demonstrating the applicability of Zermelo's equation to constrained optimization of 3D aircraft flights. • Solving 3D time-optimal problem in climb phase with Zermelo's identity using an Indirect method. • Solving 3D time-fuel-optimal free-routing problem with Zermelo's identity using a new Direct transcription method. • Brief discussion on aNLP for initialization of both Indirect and Direct methods. [ABSTRACT FROM AUTHOR]

Highly distorted closed surfaces pose significant challenges for machining trajectory planning due to their intricate surface constraints and closed structures. Despite these challenges, components with such features are prevalent in industries like aerospace. This paper presents a machine learning-driven multi-objective optimization method for electrical discharge machining (EDM) trajectory planning of highly distorted closed surfaces. The method transforms the structural design of forming electrodes and trajectory planning into a multi-objective decision problem. And a discrete point trajectory planning method, guided by surface average curvature, is employed to determine the optimal position and orientation of the electrode. Additionally, an elite dataset, generated using the Monte Carlo method and Arena's Principle, is utilized to train an artificial neural network (ANN). This network predicts hyperparameters for the nonlinear optimization problem. Based on the proposed method, a multi-objective optimization model is formulated for an integral shrouded blisk, considering minimization of iteration count, axial motion, and maximization of machining surface quality. The Pareto front is utilized to obtain the optimal EDM trajectory. Experimental results demonstrate a 17.38 % reduction in the overall machining cycle duration using this trajectory, and the surface roughness and profile accuracy satisfy the design specifications, which proves the effectiveness of this method. • A machine learning-driven multi-objective optimization method for machining trajectory planning is proposed. • A discrete point trajectory planning method for EDM of highly distorted closed surfaces is deduced. • An elite dataset construction method base on the Arena's principle and Monte Carlo method is proposed. • The structural design of shaped electrodes and trajectory planning are transformed into a multi-objective decision problem. [ABSTRACT FROM AUTHOR]

Multimode spacecraft propulsion has the potential to greatly increase the maneuvering capability of spacecraft in comparison to traditional architectures. This technology combines two or more propulsive modes (e.g., chemical and electric) into a single system with a single propellant. Trajectory design techniques for spacecraft with this capability, however, are presently limited and typically require manual selection of the burn sequence. In this study, indirect optimal control formulations with automatic mode selection are developed and applied for the first time to multimode spacecraft with two modes of propulsion. Minimum-fuel transfers are solved using polar coordinates as well as using Modified Equinoctial Elements with perturbations. Propellant-constrained minimum-time problems are also solved for the first time using a penalty function approach. An interior-point constraint formulation is also provided. Sample transfers are developed for each coordinate choice and optimization objective and are compared to trajectories that use a single mode of propulsion. The results demonstrate viability of the proposed techniques and show that the multimode approach can reduce the time-of-flight in comparison to a low-thrust only trajectory while providing mass savings over high-thrust only solutions. • Indirect optimal control methods are used to solve multimode mission design problems. • Minimum-fuel and propellant-constrained minimum-time problems are solved. • The techniques extend immediately to hybrid propulsion. [ABSTRACT FROM AUTHOR]

• The infeasibility of the fuel-optimal powered landing problem is analyzed. • A maximum-thrust regulation strategy is proposed to reduce infeasibility. • A trajectory-tracking method with a disturbance compensator is proposed. • The disturbance compensator requires only the current state information. Convex optimization has great potential for onboard trajectory generation which can eliminate large state deviations and improve landing precision. In practical applications, the convex optimization problem is often infeasible under disturbances. In this paper, we analyze the reason for the infeasibility of the fuel-optimal trajectory optimization problem. The analysis result shows that the thrust saturation degrade the anti-disturbance performance and then lead to infeasibility. Based on this analysis, we improved the anti-disturbance performance of convex optimization-based guidance from two aspects: (1) a maximum-thrust regulation strategy is embedded into the original fuel-optimal problem to avoid thrust saturation; (2) a trajectory tracking method with a disturbance compensator is performed to attenuate disturbance effects and to make the initial state of each optimization cycle close to the existing feasible trajectory. Numerical simulations demonstrate that the proposed method can improve the infeasibility and can realize the high-precision landing under disturbances. [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]

This paper proposes an innovative approach for constrained rendezvous trajectory optimization (CRTO) using stochastic optimal feedback control and unscented transform (UT) uncertainty quantification. The method overcomes limitations of traditional deterministic CRTO solutions that suffer from uncontrolled terminal state error growth and severely deteriorated path constraint satisfaction when initial state uncertainty, dynamics uncertainty, and navigation uncertainty are considered. The approach involves constructing a stochastic optimal feedback control (SOFC) problem with chance constraints and introducing linear feedback control to regulate both the mean and variance of terminal state errors. UT is employed to approximately quantify the state errors and their propagation, transforming the SOFC problem into an unconstrained deterministic optimization (UDO) problem. Differential dynamic programming (DDP) is then used to solve the UDO problem. The obtained stochastic optimal solution provides a robust rendezvous trajectory and a corresponding explicit closed-loop guidance law, improving terminal accuracy and path constraint satisfaction in the presence of various considered uncertainties. The influence of different term weights in the objective function on terminal accuracy and path constraint satisfaction is also studied. The effectiveness of the proposed approach is verified through Monte Carlo simulation, demonstrating the robustness of the closed-loop control strategy. The results highlight the potential of the method in enhancing terminal accuracy and path constraint satisfaction in uncertain rendezvous scenarios. • The uncertainty-resilient rendezvous trajectory optimization algorithm provides not only a nominal trajectory but an explicit optimal state-feedback control policy. • Rendezvous trajectory uncertainty caused by initial state errors, dynamics errors, and navigation errors is propagated using an unscented transformation method. • The proposed method considers common input constraints and path constraints in space rendezvous missions. [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]

Comet Interceptor (Comet-I) was selected in June 2019 as the first ESA F-Class mission and aims to explore a pristine comet, which will visit the inner Solar System for the first time. Comet-I will hitch a ride to a Sun-Earth L2 quasi-halo orbit, as a co-passenger in ESA's M4 ARIEL's launch. At the time of writing, this is scheduled for 2029. It will then remain there awaiting the right departure conditions to leave definitively and intercept a newly discovered comet. Comet-I will be the first mission to be designed and launched without an already identified target. Given the latter, the Comet-I Target Identification Working Group is tasked with the continuous follow-up of newly discovered comets, to analyse their characteristics as virtual targets for Comet-I. The goal of the paper is to inform the decision-making process that will eventually be necessary to commit Comet-I spacecraft to its final target. Within this context, this paper presents a trajectory optimization process based on Primer Vector theory that considers intercept trajectories with multiple revolutions and multiple deep space manoeuvres (DSM). The process is applied to 21 long period comets, which were discovered since July 1, 2020 and whose characteristics are of interest for the Comet-I mission. In fact, one of the latest of these recently discovered comets, C/2023H2, is the most accessible virtual target discovered at the time of writing, with delta-V intercept costs well within Comet-I capabilities. A complete launch window analysis is thus presented for C/2023H2, which accounts not only for the most optimal delta-V intercept transfer, but also considers all launch options that satisfy all Comet-I's current boundary conditions and flyby constraints. A systematic launch window analysis is made possible by a grid search approach on which departure and fly-by dates are fixed and the remaining design variables, including the times for manoeuvres and their Δ v impulse vector, are optimized via Primer Vector theory. This allows to understand the latest possible departure date, but also the sensitivity to departure and arrival dates of key encounter characteristics such as relative fly-by speed, the solar aspect angle and the Earth distance. • A Primer Vector Theory-based trajectory optimization tool is shown, tailored for ESA's Comet Interceptor (Comet-I). • The method supports trajectories with multiple revolutions around the Sun and multiple impulses. • The method allows rapid grid search over the search space, finding the lowest cost trajectory and other notable solutions. • A novel analysis of the launch window is presented, contributing to the decision-making process of Comet-I. • A multi-manoeuvre strategy benefits Comet-I's trajectory design, lowering the delta-V cost and improving mission flexibility. [ABSTRACT FROM AUTHOR]

This study presents a novel framework of mission planning for actively removing multiple space debris in low Earth orbit. The associated problem is formulated as a multi-objective optimization problem to minimize the total velocity increments while maximizing the Hazard Criticality Index (HCI) of the candidate target debris. The main idea is based on the Random-Key (RK) encoding scheme that effectively converts a continuous search space into a discretized solution space representing the target debris and visiting sequence. With the RK encoding technique, the proposed framework can obtain the optimal solutions for target debris selection for removal, removal sequences, and other design variables for computing orbital transfer costs simultaneously in a systematic way. In order to demonstrate these favorable characteristics, the proposed framework is integrated with four well-known multi-objective Evolutionary Algorithms (EAs) to solve mission planning problems for the active removal of multiple space debris in low Earth orbit. The framework integrated with NSGA-II, compared with other EAs, shows the best performance in terms of optimality and diversity of non-dominated solutions. Moreover, the optimization results indicate that our integrated framework appropriately selects target debris with similar orbital elements and naturally employs the Right Ascension of the Ascending Node (RAAN) drift originating from J2 perturbation to shift the transfer orbit to reduce total velocity increments. The overall results show that the proposed framework is effective in the preliminary mission planning for multiple space debris removal in low Earth orbit. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative approach for generating re-entry trajectories for a reusable winged spacecraft. This approach utilizes Fourier series parametrized control profiles. The Fourier coefficients are derived through a combination of the Improved Search Space Reduction (ISSR) technique and Sequential Quadratic Programming (SQP) optimization methods, which effectively limit the maximum heat rate experienced by the spacecraft. These re-entry trajectories and control profiles are then used to train artificial neural networks, enabling the controller to provide optimal control inputs based on the spacecraft's current altitude and velocity. To validate this methodology, Hardware-in-loop (HIL) simulations are conducted, integrating the designed neural network-based controller with a Texas Instruments TI Delfino TMSF28335 controller and a real-time simulator, the OPAL-RT OP4510. The results of the HIL simulation demonstrate that the generated re-entry trajectory accurately adheres to heat rate and terminal constraints. Additionally, the Fourier series parametrization of control profiles is applied to a high lift-to-drag ratio CAV-H vehicle, showcasing the method's versatility. Furthermore, resilience of proposed method to uncertainties in aerodynamic coefficients and atmospheric density is also demonstrated. The results show that the proposed method is generic and exhibits robustness to uncertainties. [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]

• An efficient algorithm for checking the feasibility and evaluating the flight time between two neighboring resonance orbits is given. • A mixed-encoding optimization model is proposed to select the optimal resonance orbits and plan the path through them. • Transfers from the zero-inclination orbit to the polar orbit in the Jupiter system are simulated and the optimal trajectories via tens of gravity assists are analyzed. Trajectory optimization of orbit transfers via multiple gravity assists is studied to generate the time-optimal trajectory for a large-scale velocity change. The optimal trajectory is considered as a combination of transfers between different resonance orbits, and an efficient algorithm for checking the feasibility and evaluating the flight time between two neighboring resonance orbits is given. Then, a mixed-encoding optimization model is proposed to select the optimal resonance orbits and plan the path through them. The transfer from a zero-inclination orbit to a polar orbit in the Jupiter system is simulated and the optimal trajectories via tens of GAs are obtained. The results show the efficiency of the optimization process and the practicability for mission analysis and trajectory design when the third body is small and the velocity change via a single gravity assist is limited. [ABSTRACT FROM AUTHOR]

Due to the complex aerodynamic effects, the reentry trajectory optimization problem is highly nonlinear. When using sequential convex programming (SCP) methods to solve it, the iteration solution is difficult to converge. To improve this, we propose a hybrid-order soft trust region-based SCP method. We analyze the penalty effect of typical trust regions. Based on the analysis, we develop a hybrid-order soft trust region combining a small-weight first-order component and a higher-order components. To solve the subproblem reliably and effectively, we equivalently reformulate it as a second-order cone programming (SOCP) form through the relaxation technique. Combined with the line search method, we further design an SCP algorithm with guaranteed convergence under some assumptions. In the numerical simulations, the effectiveness and robustness of the proposed method have been verified using a nominal case and 200 Monte Carlo cases. [ABSTRACT FROM AUTHOR]

The fifth generation (5G) network enabled communication between devices has emerged as a state-of-the-art technology. In the era of proliferating smart devices and intelligent wireless communication networks, Reflecting Intelligent Surfaces (RIS) and Unpiloted Air Vehicles (UAV) duplet has turn out to be a trustworthy, lucrative and handy solution for various appearing real world communication issues. This article pitches into the downlink UAV communication empowered by RIS, where UAV communicates with Mobile Instruments (MI) via RIS patches installed at a tall tower. Considering the attributes like transmitted power and UAV trajectory, Deep Reinforcement Learning (DRL) based approach is recommended to maximize the overall Sum-rate. In present scenario, DRL technology has popped up as a commanding tool that allows a network to regulate itself in order to deliver optimum solution. In this article, we have proposed a novel viewpoint evolved from Deep Deterministic Policy Gradient (D-DPG) Algorithm specifically Shared Deep Deterministic Policy Gradient (SD-DPG) algorithm for downlink UAV-MI power allocation and trajectory optimization problem. Numerical outcomes manifest that our model, concerned to maximizing sum-rate, outperformed other DRL based method DD-DPG by at least 30% and D-DPG by approximately 3 folds together with optimizing power, phase-shift and UAV trajectory. [ABSTRACT FROM AUTHOR]

Building and maintaining a catalog of resident space objects involves several tasks, ranging from observations to data analysis. Once acquired, the knowledge of a space object needs to be updated following a dedicated observing schedule. Dynamics mismodeling and unknown maneuvers can alter the catalog's accuracy, resulting in uncorrelated observations originating from the same object. Starting from two independent orbits, this work presents a convex-optimization based approach to find admissible maneuvers to correlate the two orbits. In case of a feasible maneuver detection, the time profile of the maneuver is estimated, exploiting the conjugate unscented transform to map the orbits' covariance into the maneuver uncertainty. It is also shown that a careful choice of the coordinate system is pivotal to obtain the solution in one iteration, without successive convexification. • Maneuver estimation can be posed as a fuel-optimal second-order cone problem. • If a maneuver is feasible, it is detected in milliseconds. • The conjugate unscented transform transfers the state covariance into a maneuver profile. • Specific coordinates allow polynomial runtime and global convergence. • The maneuver time profile is estimated with knowledge of only the onboard propulsion system. [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]

There are complex coupling relationships between flight motion and energy management for hybrid electric fixed wing UAVs with photovoltaic/fuel cell/battery. Aiming at realizing high-energy-efficiency long endurance autonomous flight, this paper proposes a coordinated optimization method of trajectory optimization and energy management for hybrid electric UAVs. Numerical simulation and experiment are carried out. Separated by surplus demand energy except that produced by PV, this method includes an optimal energy flight trajectory optimization layer and an energy management layer. For the former, fuzzy neural network sequential convex optimization (FNNSCP) is proposed to handle the flight trajectory optimization problem for maximizing utilization solar energy. For the latter, an online energy management strategy based on convex quadratic programming MPC (CQPMPC) is proposed to realize the power allocation. Numerical simulation results show that FNNSCP reduced 2% energy requirement compared with Radau pseudo-spectral method (RPM) from flight trajectory optimization level. From energy management level, CQPMPC saves hydrogen consumption by 3.1% and 16.3% compared with nonlinear model predictive control (NMPC) and fuzzy logic state machine (FLSM), respectively. In the experiment, less hydrogen fuel is consumed by proposed method by 5.2% and 15.6% compared with NMPC and FLSM, respectively. Experimental results show that the proposed method has better energy-saving performance and excellent real time performance. It indicates that optimizing flight trajectory and improving energy management efficiency can realize the high-energy-efficiency flight of hybrid electric UAVs. This method is conducive to promoting the application of hydrogen energy in the field of UAVs. [Display omitted] • A coordinated optimization method is proposed for the high-energy-efficiency flight. • Fuzzy neural network adaptive sequential convex optimization method is proposed. • Online energy management strategy with convex quadratic programming MPC is proposed. • The proposed method is verified by simulation and energy management experiment. [ABSTRACT FROM AUTHOR]

External-cavity diode laser (ECDL) can continuously change the output wavelength by scanning its optical resonance cavity (ORC), which is a piezoelectric transducer (PZT) actuated mechanical system. However, because of the inherent hysteresis characteristic of PZT and limited system bandwidth, the dynamic response of the ORC system exhibits both the nonlinearity and vibration while high-frequency triangular wave scanning, thereby resulting in the degradation of the output wavelength performance of the ECDL. As a result, a trajectory optimization method is presented to improve the scanning characteristics of the ORC system. Firstly, the hysteresis behavior of PZT is described by the elliptic model to generate a compensation voltage for the PZT. Secondly, the cusp region of the compensation voltage is optimized by a frequency domain objective function to greatly reduce the high-order harmonic components of the compensation voltage. Finally, an optimal voltage trajectory for driving the ORC system is obtained. The experimental results demonstrate the validity of our proposed trajectory optimization method for simultaneously suppressing the nonlinearity and vibration of the ORC system within the scanning frequency of 100 Hz. • A trajectory optimization method is designed based on an ellipse model and spectrum shaping. • The method can improve the scanning characteristics of the ORC system. • A frequency domain objective function is developed to minimize the ORC system vibration. [ABSTRACT FROM AUTHOR]

Theoretical and experimental studies were performed with the goal of determining the best kind of information presented on a predictive display to provide the highest accuracy in space mission execution, taking into account the requirement for reduced propellant consumption. The following space missions were studied: docking performed in manual and teleoperator control modes and lunar landing. By using a theoretical technique, algorithms for the flight path marker in manual and teleoperator control modes were developed. For the landing mission, a technique for determining the program trajectory and its calculation in real time was proposed. The experiments performed using a ground-based simulator demonstrated the high effectiveness of a predictive display and allowed to select the best variant of information to be presented on the display. • The predictive display is a means of improving of flight safety in different space missions. • The proposed algorithm for time delay suppression improves precise tracking in a docking task performed in teleoperator mode. • The proposed law for optimizing the Lunar Lander trajectory is performed in real time and provides the economy of propellant. [ABSTRACT FROM AUTHOR]

This paper presents a distributed trajectory optimization algorithm for the reconfiguration of large-scale spacecraft formation, which uses a low thrust propulsion system to safely guide the spacecraft formation to a desired formation. Formation reconfiguration is formulated as a trajectory optimization problem with complex constraints, and the relative motion is accurately described by a nonlinear relative dynamics considering J 2 perturbation. The collision avoidance constraint is convexified into a tangent plane to ensure the accuracy of the solution. The resulting nonlinear trajectory optimization problem is solved by applying the h p -adaptive pseudospectral method to convert it into a nonlinear programming problem. In order to overcome the disadvantage of huge computation of centralized algorithm considering collision avoidance, "predicted trajectory" is introduced to transmit information between spacecraft, and the parallel computing is implemented. Finally, a numerical simulation is given to verify the computational efficiency and collision avoidance effectiveness of the proposed distributed algorithm. • Distributed trajectory optimization algorithm for massive formation reconfiguration. • The J 2 nonlinear relative dynamics is used to obtain accurate optimal trajectory. • Parallel computation is achieved by information interaction of neighbors. • Neighbor updating is proposed to reduce communication traffic. • Significantly decrease computation and achieve collision avoidance. [ABSTRACT FROM AUTHOR]

• Trajectory planning to extend the stay of stratospheric airships in an area. • Solved the problem of planning trajectories without endpoints. • Wind potential and position potential are designed for trajectory planning. • A modified rapidly exploring random tree algorithm for station-keeping is proposed. The station-keeping mission is one of the common missions of stratospheric airships. Its movement is sensitive to wind due to the large size and low airspeed of stratospheric airships. When the wind speed exceeds the maximum airspeed of the airship, the airship may fly out of the given mission region. Therefore, station-keeping trajectory planning is a new trajectory planning problem that has never existed before. A rapidly exploring random tree algorithm for station-keeping(RRT-SK) is proposed to solve the trajectory planning problem under multiple constraints of the airship, and an artificial potential field method (APF) considering wind field and relative position is designed as the objective function of the RRT-SK algorithm, both of which form the RRT-SK strategy used for the stratospheric airship station-keeping trajectory planning under multiple constraints. A multidisciplinary model is developed to simulate multiple constraints on the airship flight, including the energy model, thermal model, propulsion model, and kinematic model. The performance of the RRT-SK strategy is demonstrated in this multidisciplinary model with real wind fields. The results show that the multi-constrained station-keeping problem can be solved by the RRT-SK strategy. Compared with the conventional strategy, the RRT-SK strategy can improve the success rate of the airship's 24-h stationing flight and well cope with the impact of wind field changes and stationing area changes. Moreover, the RRT-SK strategy has better advantages in actual long-duration use. [ABSTRACT FROM AUTHOR]

Shape-based methods are commonly used in solving the low-thrust trajectory optimization problem. Designing a shape trajectory by maximizing a given performance index has been widely researched in recent years. The main contribution of this paper is to present a new pseudoequinoctial shaping method with parameter optimization to solve general low-thrust spacecraft rendezvous problems. The shaping method can solve the rendezvous problem with a large inclination difference between the initial and target orbits and greatly improve the performance index of the trajectory while meeting the thrust constraints. At the same time, the shape can provide a better feasible solution for solving the low-thrust trajectory optimization problem by direct methods. Another contribution is to introduce a general adjoint estimation for indirect methods. By linearizing the equation of motion near the proposed shape-based trajectory and constructing the Hamiltonian function, the initial guess of the adjoint variables can be obtained in a closed form. The general linearization formulations applicable to all coordinate systems are presented, and three numerical examples are given, in which the first example verifies the superiority of the proposed shape-based method, the second example tests the feasibility of the shape as the initial value for a direct method, and the last example compares the convergence rates of the initial adjoint variables generated by the proposed method under different coordinate systems for an indirect method. [ABSTRACT FROM AUTHOR]

• A tailored optimal control computational framework is developed by exploiting the sparsity pattern of the sampling-based approach. • Trajectory optimization of a benchmark re-entry problem with complex path and boundary constraints under high-dimensional uncertainties is conducted. • Robustness-optimality tradeoff is studied for different combinations of uncertainties. • A boundary arc consisting of a continuous line formed by the boundary contact points of each sampled trajectory is observed in the ensemble case. • Results are promising in terms of computational efficiency, accuracy and optimality for use in actual multi-phase mission design studies. This paper introduces a sampling-based computational framework with a pseudospectral transcription, designed to investigate performance-robustness tradeoffs for constrained re-entry flights with a non-Gaussian uncertainty propagation. Ensemble of trajectories which are generated with sparse grids with Conjugate Unscented Transformation have been integrated into the nonlinear programming via a vectorized and parallelized formulation. A cross-range maximization problem is formulated to assess the influences of uncertainties in entry interface conditions and model parametric uncertainties. A comprehensive analysis, facilitated by rapid gradient-based optimization convergence and warm-starting, highlights the significant effects of initial speed uncertainties and drag coefficient on problem feasibility, offering insights into optimal control behavior under different degrees and combinations of uncertainties. Proper scaling of controls and the objective function proves pivotal for achieving convergence. Furthermore, a novel phenomenon called "contact arcs" is discovered, composed of contact points that form an arc at the edge of the path constraint in the constrained ensemble optimal control as a counterpart to the boundary arcs in deterministic optimal control problems. Simulation results show excellent agreement with the derived optimality conditions. [ABSTRACT FROM AUTHOR]

In harsh signal environments, such as urban canyon, overpass and so on, global navigation satellite system (GNSS) navigation will be influenced by insufficient satellites, signal degradation, and bad quality which lead to the lack of redundancy and re-initialization of the ambiguities, especially for the low cost real-time kinematic (RTK) equipment. To address these issues, an velocity-constrained RTK method (V-RTK) for low-cost receiver is proposed. Instead of being initialized with the standard point positioning (SPP) result, the predicted position parameters are calculated with the velocity obtained from GNSS observation or other sensors, so that the historical filter message can be delivered to the next epoch both from the ambiguity domain and the position domain to maintain the accuracy of historical epochs. The performance of the proposed method has been assessed with two kinematic vehicular datasets collected in an urban environment, which lasts about 3 h. The results manifest that the positioning trajectory is smoother and location jumps are significantly reduced after applying the velocity constraint. And the accuracy of each dimension is improved by 10%∼40%. Besides, an in-field experiment is conducted to compare the proposed method with the PVA method, which shows a better performance in our proposed method for making full use of observations. [ABSTRACT FROM AUTHOR]

In space mission design, an important operational constraint is planned periodic coast arcs during which various mission-critical tasks such as navigation or ground communications are performed. These constraints, typically implemented as thruster duty cycles, can be characterized as discrete coast arcs enforced periodically during intervals of deterministic thrusting. A typical approach to incorporate duty cycles is by enforcing maximum thrust levels that are less than a nominal value. This work presents an embedded homotopy indirect optimization method for a smooth enforcement of discrete duty-cycle constraints for low-thrust trajectory optimization. The complexity of enforcing such discrete constraints is two-fold: (1) a precise event-detection strategy is needed to determine the beginning of deterministic thrust arcs, which must be successively updated along the trajectory and (2) a smooth modeling of the discrete coast events occurring on the order of 10s or even 100s depending on the duration of deterministic thrust arcs. Duty cycle constraints are enforced at the level of the Hamiltonian using a Composite Smooth Control (CSC) method, producing high-resolution optimal control solutions conscious of planned duty cycle coast arcs. Numerical solutions are presented for the heliocentric transfer phases of three space missions. The results are then validated against the Evolutionary Mission Trajectory Generator (EMTG), one of NASA's global trajectory optimization tools used for interplanetary mission design and capable of the explicit enforcement of periodic duty cycle coasting. The proposed indirect method is suitable for obtaining high-resolution trajectory solutions with realistically enforced thruster duty cycle, which could then be used as high-quality initial guesses in flight-fidelity mission planning tools. The proposed smooth modeling of discrete coast arcs can also be customized to enforce periodic and non-periodic thrust shutdown constraints. • Duty-cycle aware, multi-revolution, low-thrust, minimum-fuel trajectories. • A novel smooth switching function for embedding forced coast arcs. • Composite Smooth Control (CSC) is used to embed the discrete duty-cycle constraints. • Comparison with NASA's Evolutionary Mission Trajectory Generator (EMTG). • Julia programming language is used for solution of the boundary-value problems. [ABSTRACT FROM AUTHOR]

This paper investigates the trajectory design for landing on a small celestial body with a flexible lander. The flexible lander features a flexible structure that increases surface contact area and facilitates the dissipation of residual kinetic energy. Compared with rigid landing, flexible landing, which utilizes a flexible lander to execute the landing process, offers enhanced safety during the landing operation. However, the introduced nonlinear flexible force will degrade the convergence of landing trajectory optimization. To address this challenge, the homotopic approach is employed to smoothly connect the trajectory optimization problem from rigid landing to flexible landing. Then, the connection between the optimal solution of the rigid problem and the flexible problem is revealed in detail with the presented theorem. Based on this theorem, the flexible landing fuel optimal trajectory is generated by iteratively solving a sequence of convexified and discretized homotopic problems. The effectiveness of the proposed algorithm is demonstrated through 433 Eros flexible landing mission based numerical simulations. • A novel convex programming method for flexible landing trajectory design is proposed. • The proposed method is proved to converge to the optimal solution of the flexible landing problem. • The optimal thrust magnitude profile for the flexible landing problem is of bang–bang structure. [ABSTRACT FROM AUTHOR]

For the first time in spaceflight history the flight of a fully reusable launch system with rocket propulsion appears possible within the next couple of years. Apart from the implications for the orbital launch market, a fully reusable system could also enable an entirely new class of commercial point-to-point transport on Earth. Rocket propelled point-to-point systems promise the ability to transport passengers or cargo to any suitable landing site on Earth with extremely short travel times (typically less than 90 min). In this study the primary focus is on DLR-SART's SpaceLiner 7 vehicle concept with an initial comparison to Starship, currently being developed by SpaceX. The trajectories are identified using multi-objective optimization with evolutionary algorithms. These allow the identification of a solution space with regard to multiple objectives, in this case minimal overflight of populated areas and minimal peak heat flux, while still respecting other constraints (e.g. structural loads). The population disturbance is computed by using a global population density database and integrating the number of people along the flight track. Ideally, the solution space consists of a pareto-front which correlates to the most optimal solutions possible for all objectives. The mission analysis identifies various feasible trajectories around the world. Primarily, these routes are going along less populated areas such as the oceans and the polar regions. Especially the latter enable large longitudinal changes during the flight and consequently connecting distant places on Earth. The critical routes are large longitudinal crossings around the equator where land masses must be overflown. These shall be reconsidered and/or improved in the future. Comparing SpaceLiner to Starship, it is found that the mission profiles vary significantly. While SpaceLiner uses its high lift-to-drag ratio in the higher atmosphere to manoeuvre around large land masses, Starship can only follow the direct route. In contrast, Starship flies higher into space and thereby might avoid having large population disturbances on ground. Only the re-entry and landing are critical as it does not have significant cross range capability. As a design option for the next iteration of the SpaceLiner development, SpaceLiner 8, it is planned to assess the possibility of using a smaller wing to follow a similar coast through space like Starship and have a steep re-entry at the end of the flight instead of a prolonged glide. • SpaceLiner trajectory optimization using evolutionary algorithms. • Hypersonic point-to-point trajectories between major population centres on Earth. • Analysis and minimization of overflown population to avoid sonic boom disturbance. • Comparison of flight characteristics between SpaceLiner and SpaceX Starship. [ABSTRACT FROM AUTHOR]

Aiming at the perturbation of motion capability and the deviation of end effector from its desired trajectory caused by joint effectiveness partial loss failure, a fault-tolerant control strategy considering motion capability optimization is proposed to ensure that the faulty space manipulator can carry on-orbit operation tasks. Firstly, the joint effectiveness partial loss failure model is established, and the kinematic and dynamic model of the faulty manipulator is established based on the failure model. The kinematic and dynamic coupling relationship of the faulty manipulator is also analyzed. Then based on sliding mode control, the fault-tolerant control strategy that ensures the end effector trajectory tracking and base orientation deflection attenuation is designed. Meanwhile, the motion capability optimization model is designed based on the redundancy characteristic of the manipulator and combined with the fault-tolerant control system. This combined system can realize end effector trajectory tracking, base orientation deflection attenuation, and motion capability optimization at the same time. Finally, simulation experiment is carried out to verify the proposed fault-tolerant control strategy for the faulty manipulator. The result shows that the proposed fault-tolerant control strategy can realize end effector trajectory tracking, base orientation deflection attenuation, and motion capability optimization with high control accuracy, high convergence rate, and significant motion capability optimization effect. For both joint velocity partial loss and joint torque partial loss failure, the duration of convergence is less than 0.5 s, the steady-state error is less than 1 × 10 - 4 m for end effector position and less than 1 × 10 - 5 degree for base orientation deflection, and the motion capability indexes have been raised by over 40%. [ABSTRACT FROM AUTHOR]

• The mathematical model of the reachable domain of the contingency return trajectories. • Reachable domain calculation method of the contingency return trajectories based on interval analysis. • Parameter characteristic analysis of reachable domain. The investigation on reachable domain based on interval analysis is performed, which is aimed for the contingency return trajectories during the circumlunar flight stage in manned lunar landing engineering. First, the issue of contingency return trajectory, which adopts a non-coplanar maneuver during the circumlunar flight phase, is expounded upon. The mathematical model of the reachable domain of contingency return trajectories is established. Second, the contingency return trajectory is designed. An improved interval branch and bound algorithm is introduced and a reachable domain calculation method of the contingency return trajectories is proposed. Third, in numerical simulations, by comparing the reachable domain obtained by the traditional brute force method, the accuracy of the method presented in this paper is verified. It also indicates that this method has a higher calculation efficiency. Finally, numerous simulations are conducted to discuss the parameter characteristic of reachable domain by adopting this method. The study conclusions can serve as an important reference for the selection and decision of contingency return trajectory plans in the future manned lunar landing engineering. [ABSTRACT FROM AUTHOR]

After the completion of the launch mission, the soft landing recovery and reuse of the carrier rocket's first-stage can effectively control the landing area to ensure safety and significantly reduce the cost of space launch transportation. The trajectory optimization of the whole process from the first section to the landing site is significant to fuel saving. In the entire process, the first-stage needs to go through three startup ignitions of course adjustment, power deceleration, and vertical landing. For this segmented fuel optimization problem, optimizing the thrust size and direction during three sections and the switching time between each section is necessary. Optimizing the vertical landing section is essential to ensure the accuracy of landing position and speed, which greatly complicates the whole process's optimization. Therefore, the optimization process of the vertical landing is substituted by a neural network predictor, which is used to obtain the mapping relationship between the initial state of the vertical landing section and the fuel consumption of the segment. Besides, the thrust profiles of the first two startup sections are reasonably handled based on physical cognition. The combination of convex optimization and neural network successfully converted the multi-stage optimal control problem into a parameter optimization problem and solved it by a genetic algorithm. Optimization results were compared with the conventional method, which indicated its superiority. [ABSTRACT FROM AUTHOR]

Building upon the recent development of solar sailing primer vector theory and its successful applications, we propose a new formulation for indirect solar-sail trajectory optimization, which minimizes solar angle (cone angle between the sail normal and sunlight vectors) over a trajectory. The minimum solar-angle objective is introduced to address a typical demand in mission design: having the ability to design trajectories with fixed time-of-flight, which is especially crucial when the mission involves time-sensitive events, such as scientific observations with specific lighting conditions, gravity assists at specific epochs, to name a few. We derive an analytical optimal control law for minimum solar-angle sail transfers by applying Pontryagin's optimality principle. Our theoretical results illuminate that a quantity termed solar sailing primer vector characterizes the optimal solar-sail control law for both minimum-time and minimum solar-angle transfers, as is the case in Lawden's primer vector theory for conventional low-thrust transfers. We numerically demonstrate these theoretical results by applying them to asteroid rendezvous transfers for NASA's NEA Scout mission. The numerical examples also reveal the numerical advantage of using the minimum solar-angle objective over the minimum-time one for solar-sail trajectory design because of the smoother optimal control profile. Solar sailing primer vector theory provides a tool to characterize the optimal control law independent of particular state representations or solution methods, enabling mission designers to combine it with a wealth of techniques developed for low-thrust trajectory optimization. • Propose an indirect trajectory optimization formulation based on solar sail primer vector theory. • The formulation minimizes the solar angle over a transfer with fixed time-of-flight. • The formulation derives an analytical optimal control law via Pontryagin's minimum principle. • Numerical examples demonstrate the analytical results in a NASA's NEA Scout exploration scenario. [ABSTRACT FROM AUTHOR]

In this paper, Particle Swarm Optimization with energy-to-fuel continuation is proposed for initializing the co-state variables for low-thrust minimum-fuel trajectory optimization problems in the circular restricted three-body problem. Particle Swarm Optimization performs a search of the solution space by minimizing the weighted sum of squares of the two-point boundary-value problem final boundary condition residuals for the minimum-energy problem. Next, an energy-to-fuel homotopy is employed to transition the minimum-energy trajectory to a minimum-fuel trajectory, starting from the generated guess. The proposed methodology is applied to two low-thrust transfer problems in the Earth–Moon system: a transfer from a geostationary transfer orbit to an L1 halo orbit, and a transfer from an L2 halo orbit to an L1 halo orbit. The resulting minimum-fuel trajectories are validated with the literature. It is demonstrated that the methodology can successfully generate guesses for the initial co-state variables which converge to a solution for both scenarios. A strategically chosen particle swarm size is shown to improve the efficiency of the methodology. The proposed approach is of simple implementation, can be easily extended to other trajectory optimization problems, facilitates the discovery of multiple candidate trajectories, and does not require a user-provided guess, all of which are advantageous features for the preliminary phase of mission design. • Particle Swarm Optimization is proposed to guess the Lagrange co-states variables. • PSO initialization is paired with homotopy continuation for trajectory optimization. • The proposed algorithm facilitates discovery of multiple unique optimal trajectories. • Two minimum-fuel trajectory optimization problems are solved. • The effect of the particle swarm size on successful convergence is analyzed. [ABSTRACT FROM AUTHOR]

A rendezvous mission with a tumbling space object has been studied by developing a novel three-phase mission design architecture which includes model and state uncertainties by utilizing Ensemble Optimal Control and warm-start Bellman Pseudospectral Optimal Control. Ensemble optimal control problem is solved via in-house developed Stochastic-Collocation based Ensemble Pseudospectral Optimal Control Software (SC-EPOCS) by modeling the uncertainties via samples generated by Conjugate Unscented Transformation based on the initial statistical distributions. Then, a new concept called checkpoints has been introduced to decide a feasible and optimal transition trajectory from uncertainty-aware trajectories to a deterministic optimal trajectory. This is achieved by conducting a reachability analysis for all ensembles and uncertainties. As a result, two Deep Neural Networks (DNNs), one for translational and other for the rotational motion, have been trained by utilizing initial costate values that correspond to optimal trajectories, starting from the checkpoints. By deriving costate dynamics for optimal trajectories, a warm-start algorithm is developed by applying Covector Mapping Theorem. Finally, Bellman Pseudospectral Optimal Control is applied in a Caratheodory- Π sense by recursively solving an optimal control problem, subjected to state estimation errors. Results prove the feasibility, robustness, and optimality of the approach. • A novel robust trajectory optimization framework for rendezvous is proposed. • A robust trajectory database is generated via Conjugate Unscented Transformation. • Two Deep Neural Networks are trained for optimal transition trajectories. • Framework has demonstrated optimality, safety, robustness, and flexibility. [ABSTRACT FROM AUTHOR]

• Multi-target Active Debris Removal missions are necessary to reduce the proliferation of debris. • Using of simulated annealing optimization groups debris in an efficient way for removal missions. • Proposed missions have an average delta-V budget of 2.41 km/s and an average duration of 1 years. The proliferation of debris in Low Earth Orbit raises increasing challenges about the sustainability of the space environment. The current international recommendations to deorbit satellites at the end of their life are not sufficient to ensure this sustainability. To accelerate the process, it would be necessary to remove hazardous debris and thus de-congest the high-risk orbits. However, active debris removal missions are very expensive, and still in their early stages. One way to reduce its costs is to remove several pieces of debris per removal mission, which corresponds to a global optimization problem, with the objective of optimizing the number of debris removed while minimizing the cost in mission time and in propellant. In our study, the trajectory optimization is performed using a simulated annealing algorithm. The tool classifies the targets in groups gathered by similarities of orbital parameters, with the objective for each mission not to exceed a total Δ V = 4 km/s for a mission time lower than 3 years. To achieve this, a weighting is made between out-of-plane maneuvers, costly in propellant, and the use of the orbital parameter Ω drift, costly in time, to allow the spacecraft to pass from one debris to another. A criterion is set up to determine from which threshold it is more interesting to carry out a maneuver on Ω rather than to let the gravitational drift act. As a result, applied on the 50 most hazardous debris established by the International Astronautical Federation, we obtain a classification of the 50 pieces of debris into 11 optimal groups, with an average Δ V of 3.05 km/s and an average mission time of 1.5 years, which corresponds to the imposed criteria and validates the feasibility of such ADR missions. [ABSTRACT FROM AUTHOR]

• A generic non-linear post-capture detumble trajectory optimization formulation capable of including joint, base, and end-effector wrench limits. • A quaternion-based linearization of free-floating multibody system for trajectory tracking and stabilization. • A Lyapunov-based Region of Attraction analysis of the tracking controller. Recent increase in space debris combined with the increase in the number of satellites launched has created an increased risk of collisions. The effects of the increased risk can be seen in the form of an increased number of near misses in recent years. The use of robotic manipulators has been suggested for Active Debris Removal (ADR) to reduce the risk of potential future collisions that generate more debris in the orbits around Earth. Compared to other ADR methods, robotic manipulators provide increased versatility as they can be reused for On-Orbit Servicing as well as On-Orbit Assembly missions. A robotic ADR operation consists of three phases: Approach, Capture, and Detumble. This paper provides a method for performing feedback-based stabilization of post-capture detumble trajectories of the chaser-debris system. The approach presented here uses Time-Varying Linear Quadratic Regulator (TVLQR) for stabilization along the detumble trajectory. The contributions of this paper are as follows: A quaternion-based linearization method for multibody systems with a free-floating base, TVLQR for stabilizing the optimal detumble trajectory, and a probabilistic Region of Attraction analysis of the resulting closed-loop system. The estimated Region of Attraction could serve as the goal for the capture controller thus allowing for controller composition through ADR phases while guaranteeing stability and successful detumble. [ABSTRACT FROM AUTHOR]