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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]

This paper presents an improved time-optimal trajectory planning algorithm leveraging the White Shark Optimizer (WSO), specifically designed for 6-degree-of-freedom (DOF) Supernumerary Robotic Limbs (SRL). This approach effectively addresses prevalent issues in trajectory planning, including low efficiency, premature convergence, and unstable operation. Beginning with an examination of the SRL’s structural peculiarities, an auxiliary joint is incorporated to rectify the coordinate offset, facilitating subsequent inverse kinematics analysis. By utilizing the WSO algorithm, we develop a timeoptimal trajectory optimization method within the joint space of the SRL. Moreover, to address the continuity challenges in the terminal movements of the SRL, we introduce a 3-5-3 piecewise polynomial trajectory planning method that integrates both 3- degree and 5-degree polynomials. Building on this foundational work, we present an optimization algorithm rooted in WSO to identify the most efficient time trajectory optimization strategy, considering multiple constraints. The effectiveness of the proposed optimization strategy is demonstrated through comprehensive co-simulation. A comparative analysis with current optimization algorithms highlights the advantages of the proposed time-optimal trajectory planning algorithm. [ABSTRACT FROM AUTHOR]

The integration of unmanned aerial vehicle (UAV) networks with intelligent reflecting surface (IRS) technology offers a promising solution to enhance wireless communication by dynamically altering signal propagation. This study addresses the challenge of maximizing system energy efficiency (EE) in IRS-assisted UAV networks. The primary objective is to optimize power allocation and IRS reflection design to achieve this goal. To tackle the optimization problem, we employ a block coordinate descent (BCD) method, decomposing it into three subproblems: phase shift optimization, power allocation, and trajectory planning. These subproblems are iteratively solved using an improved particle swarm optimization (PSO) algorithm. Simulation results demonstrate that the proposed PSO algorithm effectively plans high-quality UAV trajectories in complex environments, significantly enhancing EE. The findings suggest that the IRS-assisted UAV model outperforms traditional UAV models, offering substantial improvements in wireless communication quality and EE. [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]

This paper proposes a trajectory-optimization problem for spacecraft close proximity to a noncooperative target, aiming at the generation of a six-degree-of-freedom (DOF) trajectory with the fuel-optimal objective value and considering multiple constraints on the control magnitude, line-of-sight, and glide-slope. The line-of-sight and glide-slope constraints are coupled between translational and rotational motions. The dual quaternion is an effective method for establishing the translationally and rotationally coupled model, because it can represent the translation and rotation in an integrated manner. Therefore, in this study, the trajectory-optimization problem of spacecraft close proximity coupled with position and attitude is established using dual quaternions. Next, the close-proximity trajectory-optimization problem is converted into a nonlinear programming problem, which can be solved efficiently using well-developed algorithms such as convex optimization. However, the zero-order hold used in the discrete method of convex optimization is an equidistant dispersion, which cannot guarantee the satisfaction of constraints between discrete points. Therefore the pseudospectral convex method is proposed using nonequidistant collocation points to mitigate the problem of constraint violation between discrete points and improve the accuracy and computational efficiency of the algorithm. The proposed algorithm can be applied to tasks such as rendezvous and docking with noncooperative targets and close proximity. Finally, the effectiveness of the proposed method was validated via numerical simulation, and the results were compared with those of the existing approach, GPOPS. The results indicate that the proposed algorithm is superior to GPOPS in computational efficiency and objective values. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss a study aiming to optimize the performance of a DLR-type scramjet engine using computational fluid dynamics (CFD). For this purpose, the response surfaces technique is employed to carry out a multi-objective optimization of the strut geometry used in this engine. In the simulation, strut length and width are considered as design variables. Thrust and combustion efficiency are also constituted as objective parameters. Response surfaces are created using two methods: Kriging and nonparametric regression (NPR). The obtained results indicate a higher accuracy of the Kriging approach. The optimization results show that in the best case the amount of thrust can be increased up to 62.618 N, which is 5.6% more than the base value. Also, the combustion efficiency can be raised to a maximum value of 74.4%, which is 12.37% higher than the base value. In order to determine which design variables have a more significant effect on objective factors, sensitivity analysis has been performed. This analysis revealed that the strut width has more significant effect on the combustion efficiency, while the thrust was more dependent on the strut length. [ABSTRACT FROM AUTHOR]

Path loss is important for the unmanned aerial vehicle (UAV) placement, trajectory optimization, and power allocation in UAV-aided communications. By considering both the factors of path delay and reflection angle (RA) in the non-line-of-sight (NLoS) paths, a new machine learning-based delay–angle-joint path loss prediction method for UAV mmWave channels is proposed. The one-input back propagation based neural network (BPNN) and two-input BPNN are built to predict the path power for line-of-sight (LoS) case and NLoS case, respectively. Meanwhile, a data acquisition method is developed to obtain massive data set for training the BPNN. According to the geometric information of digital map, a calculation method for path delay and RA is also proposed to drive the BPNN. The proposed method is simulated and analyzed based on ray-tracing (RT) simulated data under a typical urban scenario at 28 GHz. The 2D relationship of power–delay for the LoS case and 3D relationship of power–delay–RA for the NLoS case are obtained through the trained BPNN, which are well consistent with the validation set of RT data and outperform the traditional methods, i.e., 3GPP model and exponential model. Moreover, it's found that the path power rapidly decreases when RA is 65 ∘ – 75 ∘ under the simulation scenario, which could be an important reference for transceiver placement and route planning to reduce the impact of NLoS paths in the UAV channel. [ABSTRACT FROM AUTHOR]

Due to the superiority of large coverage, high mobility, high-quality channels, and reusability, high altitude platforms (HAPs) can be exploited as the aerial communication means to provide users in disaster areas with long-term and stable data relay services. In this correspondence, a HAP relaying system based on clustered non-orthogonal multiple access (C-NOMA) is designed in which the HAP provides data transfer services for base station (BS) and users who cannot communicate directly. According to the system, a joint HAP flight trajectory optimization and power allocation scheme is proposed, which aims at maximizing the downlink average achievable sum rate of all users while satisfying the information causality. Since the formulated problem is non-convex, we propose an efficient iterative algorithm to derive the approximately optimal solution by alternately optimizing the HAP flight trajectory, and the transmit power of BS and HAP. The numerical simulation results demonstrate that the proposed scheme can not only effectively improve the achievable sum rate, but also significantly enhance the fairness between users compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

In this study, we investigated autonomous vessel obstacle avoidance using advanced techniques within the Guidance, Navigation, and Control (GNC) framework. We propose a Mixed Integer Linear Programming (MILP) based Guidance system for robust path planning avoiding static and dynamic obstacles. For Navigation, we suggest a multi-modal neural network for perception, demonstrating the identification of obstacle type, position, and orientation using imaging sensors. Additionally, the paper compares an error-based PID control strategy and a Model Predictive Control (MPC) scheme as well. This evaluation aids in better evaluating their performance and determining their applicability within the GNC scheme. We detail the implementation of these systems, present simulation results, and offer a performance evaluation using an experimental dataset. Our findings, analysed through qualitative discussion and quantitative performance indicators, contribute to advancements in autonomous navigation and the control strategies to achieve it. [ABSTRACT FROM AUTHOR]

In this work, a discrete maximum principle in Hamel's formalism for optimal nonholonomic motion planning is proposed, which is a discrete analogue of the usual necessary conditions for optimality obtained from the Pontryagin maximum principle. The exact Hamel integrator associated with discrete Lagrangian mechanics is adopted to derive the forced and nonholonomic integrator. A universal discrete nonholonomic optimal control framework based on moving frames is established. The optimal nonholonomic trajectory optimization for a wall-crawling mobile robot moving on a spherical tank is considered for the established framework, where the configuration space is a non-Euclidean space. The simulated results by the proposed framework accurately capture some interesting nonholonomic behaviors and geometric structures for the given mechanical model, and the feasibility and computing efficiency are verified by comparison with the open-loop control and direct parameter optimization methods. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced multi-strategy sparrow search algorithm to optimize the trajectory of a six-axis industrial robot, addressing issues of low efficiency and high vibration impact on joints during operation. Initially, the improved D-H parametric method is employed to establish both forward and inverse kinematic models of the robot. Subsequently, a 3-5-3 mixed polynomial interpolation trajectory planning approach is applied to the robot. Building upon the conventional sparrow algorithm, a two-dimensional Logistic chaotic system initializes the population. Additionally, a Levy flight strategy and nonlinear adaptive weighting are introduced to refine the discoverer position update operator, while an inverse learning strategy enhances the vigilante position update operator. These modifications boost both the local and global search capabilities of the algorithm. The improved sparrow algorithm, based on 3-5-3 hybrid polynomial trajectory planning, is then used for the time-optimal trajectory planning of the robot. This is compared with traditional sparrow search algorithm and particle swarm algorithm optimization results. The findings indicate that the proposed enhanced sparrow search algorithm outperforms both the standard sparrow algorithm and the particle swarm algorithm in terms of convergence speed and accuracy for robot trajectory optimization. This can lead to the increased work efficiency and performance of the robot. [ABSTRACT FROM AUTHOR]

Accepted by: Konstantinos Nikolopoulos We propose solving non-linear optimization problems by a trajectory method. A parameter is introduced into the optimization problem. For example, a variable in the original formulation is replaced by its squared value. The parameter is the power at which the variable is raised. For a particular value of the parameter (power of 2), the optimal solution is easily obtained. The original optimization problem is defined for another value of the parameter (power of 1). As another example, the means and standard deviations of a function based on a set of variables can be calculated. We multiply the standard deviations by a factor (the parameter) between 0 and 1. Suppose that the problem is easily solvable for zero standard deviations (factor of 0). If we 'slowly' increase the factor, the solution moves to the desired solution for a factor of 1. A trajectory connects the easily obtained solution to the desired solution. We trace the trajectory and the solution for the optimization problem is at the end of the trajectory. The procedure is applied for solving the single facility Weber location problem, and a competitive location problem with good results. [ABSTRACT FROM AUTHOR]

This article presents a trajectory design problem concerning the exploration of potentially hazardous near-Earth asteroids (PHAs) with reusable probes from cislunar space. A total of 20 probes, making round trips departing from and returning to a service space station in a lunar distant retrograde orbit, are expected to explore as many PHAs as possible by means of close flyby within a 10-year time window. The trajectory design problem was released in the 12th edition of China's Trajectory Optimization Competition on 20 August 2022, and a total of 10 sets of trajectory solutions were submitted. As the authors who proposed the competition problem, we present in this article the problem descriptions, trajectory analysis, and design, as well as an impressive trajectory solution in which a total of 105 PHAs are explored. It is concluded that taking advantage of reusable probes from cislunar space is a promising option to efficiently explore large numbers of PHAs. [ABSTRACT FROM AUTHOR]

Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on a particular aspect of the trajectory optimization, related to the optimization of a velocity along a predefined path, with the aim of minimizing power consumption. To tackle the problem, a functional formulation and minimization strategy is developed, by means of the Euler-Lagrange equation. The minimization is later performed using a neural network approach. The strategy is deemed Lagrange-Net, as it is based on the minimization of the energy functional, by the means of Lagrange's equation and neural network approximations. [ABSTRACT FROM AUTHOR]

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The research explores transition strategies of a coaxial compound helicopter transitioning to pure coaxial-rotor mode following a complete aft propeller failure. For that, a flight dynamics model is developed to predict the transition path, which is formulated as a multiphase trajectory optimization problem. Additionally, a revised aggressiveness indicator is proposed to quantify the transition difficulty. Next, the flight dynamics with and without the propeller and the accelerations at the propeller loss instant are discussed from a trim perspective. Finally, dynamic transitions are meticulously analyzed and compared using a multidimensional radar map to identify an effective strategy. Contrary to the static trim analysis, dynamic simulation results highlight the critical importance of pitch attitude control, longitudinal speed stability, and incidence instability. The potential threats include blade tip collision, significant height increase up to 300 m, and reverse longitudinal stick control regarding pitch attitude. To mitigate these risks and reduce pilot workload, we recommend gradually pitching up to enter the quasi-autorotation state. Additionally, slightly lowering the position of the propeller and maintaining a positive pitch attitude during normal flight can help improve aircraft transition stability. [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]