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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]

• 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]

• 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]

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]

• 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]

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]

• 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]

Low–thrust propulsion systems of high specific impulse are advantageous in the fuel efficiency. The fuel expenditure is further reduced together with optimization techniques though fuel–optimal low–thrust trajectories result in a discontinuous bang–bang control structure that can cause numerical difficulties. The present paper introduces regularized formulations into the direct multiple shooting method of minimizing fuel expenditure for low–thrust spacecraft trajectories. Instantaneous velocity changes approximating low–thrust maneuvers are expressed by regularized variables based on the Levi–Civita or Kustaanheimo–Stiefel transformation. The new formulation removes singularities due to null thrust impulses from derivatives of an objective function and constraints. The method automatically and robustly finds fuel–efficient bang–bang control structures for multi–revolutional transfers between periodic orbits in the Earth–Moon circular restricted three–body problem. [ABSTRACT FROM AUTHOR]

• Reachable set footprint (RSF) after blackout is predicted by trajectory optimization. • Successive convex programming is used to determine RSF with intermediate states. • RSF shrinks with decreasing altitude of additional state observation during blackout. • A decision altitude exists to determine whether to update RSF with new observation. Blackout emerges in the reentry phase of reusable launch vehicles (RLV). Therein, large uncertainties exist in the telemetry signals of RLV, leading to potential safety problems. To facilitate predicting possible ranges of RLV final position when leaving blackout, this paper proposes a modified approach for computing reachable set footprint (RSF). A multi-phase trajectory optimization method is applied to simplified dynamics of RLV. Specifically, partial final boundary conditions are additionally supplemented to the first phase to exploit the intermediate state information during blackout. On this basis, RSF is predicted via solving a series of trajectory optimization problem by sequential convex programming. RSF with additional state information from different altitude are compared in numerical cases. Simulation results show that there exists a suitable range to update RSF using intermediate information. The decision altitude of updating RSF is determined for the exemplary RLV. [ABSTRACT FROM AUTHOR]

To overcome the time-consuming training caused by the sparse reward function in reinforcement learning, an efficient dense reward framework for robust low-thrust trajectory optimization is proposed. The dense reward functions are designed separately for the deterministic and considered uncertain scenarios, including state uncertainties, observation uncertainties and execution uncertainties. For the uncertainties, the dense reward function is designed to diminish the deviation with respect to the isochronous nominal state along the corresponding deterministic optimal trajectory at each step, rendering the reward function no longer sparse and suitable for complex multirevolution problems. In addition, a multistage reward function of the terminal constraints for the rendezvous missions is designed by incorporating some exponential acceleration terms, enabling significant improvement in training efficiency as the terminal errors become low. In addition, a dense reward function for the deterministic scenario is also proposed via the introduction of empirical forbidden zones and an exponential term. The effectiveness and efficiency of the proposed method is demonstrated in a simple Earth-Mars mission and a complex Earth-Venus multirevolution mission. The promising results verify the significant effect of the proposed method in speeding up the process of training an initial incapable agent to an 'expert' while guaranteeing or even improving the performance. [ABSTRACT FROM AUTHOR]

This paper proposes a shaping method via theory of functional connections (TFC) to solve the coplanar low-thrust multi-target visit problems under the J 2 perturbation. Three types of targets are considered including ground targets, space targets, and hybrid ground-space targets. The visit constraints for the ground and space targets under the linear J 2 -perturbed model are transformed into those under the two-body model with a correction term, which avoids directly solving the transfer trajectories with the J 2 effect. Then, a unified shaping method via the TFC is proposed for the three types of targets. The multi-target visit problem is transformed into a nonlinear programming problem that analytically satisfies the initial conditions and the multi-target visit constraints. Several numerical examples show that the proposed method can realize rapid optimization for the whole transfer trajectories. Furthermore, the solved trajectories are successfully applied to the initial guess estimation of the Gauss pseudospectral method for further optimization. [ABSTRACT FROM AUTHOR]

This paper studies the safe motion of a hopping rover on hazardous terrains of small bodies in the presence of initial state errors and dynamic parameter uncertainties. The collision probability is adopted to optimize the hopping trajectory. Firstly, the hazardous terrain is characterized by the least square median method, and the feasible path point zone is defined for hopping motion. Meanwhile, the hopping trajectory optimization is converted into sequence path point planning and optimal trajectory design problems based on the classical path planning algorithm. Then, considering the effects of errors and uncertainties, a performance index is derived to design a continuous hopping trajectory of sequence path points. Taking the collision probability as an index to indicate safety, local path points are optimized through path point decomposition and replacement strategy. Therefore, a collision-probability-based continuous optimal hopping trajectory can be generated to realize safe and precise motion. Finally, with the simulated hazardous terrain based on the small body 433 Eros, the effectiveness of the proposed method is verified by numerical analysis. [ABSTRACT FROM AUTHOR]

• An approximate optimization model for perturbed orbit rendezvous is obtained via a quasi-optimal thrust strategy. • A fast process to judge the low-thrust accessibility and obtain the parameters of thrust is proposed to reduce the dimensionality of the optimization model and improve the efficiency. • A fast analytical correction process is proposed to modify the solution by the numerical errors between the predicted orbit and target orbit. Trajectory optimization of low-thrust perturbed orbit rendezvous is a crucial technology for space missions in low Earth orbits, which is difficult to solve due to its initial value sensitivity, especially when the transfer trajectory has many revolutions. This paper investigated the time-fixed perturbed orbit rendezvous between low-eccentricity orbits and proposed a priori quasi-optimal thrust strategy to simplify the problem into a parametric optimization problem, which significantly reduces the complexity. The optimal trajectory is divided into three stages including transfer to a certain intermediate orbit, thrust-off drifting and transfer from intermediate orbit to the target orbit. In the two transfer stages, the spacecraft is assumed to use a parametric law of thrust. Then, the optimization model can be then obtained using very few unknowns. Finally, a differential evolution algorithm is adopted to solve the simplified optimization model and an analytical correction process is proposed to eliminate the numerical errors. Simulation results and comparisons with previous methods proved this new method's efficiency and high precision for low-eccentricity orbits. The method can be well applied to premilitary analysis and high-precision trajectory optimization of missions such as in-orbit service and active debris removal in low Earth orbits. [ABSTRACT FROM AUTHOR]

A surface geometric constraint approach is used in designing the trajectories of a solar sail. We solve the solar sail equation of motion by obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption that the cone angle is constant throughout the mission. A family of trajectory equation solutions can then be specified by defining a constraint equation that relates the radial velocity to the polar velocity of the spacecraft. The method is used to generate and analyze trajectories that are constrained on cylindrical surfaces and those that are displaced from the ecliptic plane. We apply our proposed approach to optimizing the flight time of a mission towards an asteroid with a highly inclined orbit. Lastly, we demonstrate the versatility of the approach by reproducing previous results on displaced circular orbits and orbits constrained on cylinders derived using other methods. [ABSTRACT FROM AUTHOR]

A periodic close encounter orbit is an orbit that periodically surveys a target spacecraft. The design of such orbits is important for both military and civil missions. As an example, it can be used for a preliminary mission design to better plan the repair of damaged, expensive, strategic, or extremely critical space assets. Indeed, this paper proposes an optimization approach and algorithm to reach periodic close encounter orbits through n -impulse maneuvers within the framework of Keplerian motion. The optimization is constrained to several bound requirements, such as a) distance bounds at encounter, b) total Δ v tot cost, c) single impulse cost Δ v k , d) encounter illumination angle, e) daily observation time, f) minimum perigee radius, g) maximum repetition time, h) maximum eccentricity, and i) maximum encounter time. The optimization, performed using Genetic Algorithm, has been validated by several numerical examples using the TLEs of existing satellites. The simulations showed good results and the reliability of the proposed approach via the Genetic Algorithm has been validated by a comparison with the Particle Swarm Optimization algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the energy-optimal path generating and robust trajectory tracking of satellite formation reconfiguration. First, to minimize the energy consumption during formation reconfiguration, the problem of finding optimal path and control profile is studied. This problem is solved based on the linear Hill-Clohessy-Wiltshire equations and optimal control theory. Second, considering the nonlinearities and disturbances in the dynamics of satellite relative motion, a robust control law based on an uncertainty and disturbance estimator is designed. The primary advantage of this estimator is the relaxation of the assumption on disturbances, and only frequency range is needed. The asymptotic stability of the closed-loop system formed by a robust feedback controller is analyzed. Finally, numerical simulation results are presented to validate the feasibility of the proposed reconfiguration trajectory optimization approach and control strategy. [ABSTRACT FROM AUTHOR]

For the problem of autonomous and safe landing on irregularly shaped asteroids, a real-time collision-free trajectory optimization method based on deep neural networks (DNNs) is proposed. First, in order to overcome the difficulty of solving the optimal trajectories by indirect methods caused by anti-collision path constraints and the difficulty of establishing the mapping relationship between states and initial costates by DNNs, a two-stage anti-collision trajectory optimization model is constructed, which can provide the initial costates for trajectory optimization under anti-collision constraints of each stage through the approximate analytical solution of costates. It can efficiently generate a large number of optimal trajectory samples. Second, a region division strategy is proposed for further reducing the time-consuming of DNN training. Then, the path constraints are slightly relaxed to avoid the optimal trajectories predicted by DNNs from violating the anti-collision constraints. The proposed method is applied to the scenarios of landing on asteroids 101955 Bennu and 433 Eros. The simulation results indicate that this method can estimate the initial costates efficiently and accurately, and can plan the optimal trajectories of anti-collision landing in real time. [ABSTRACT FROM AUTHOR]

• Two stage launch vehicle powered by semi-cryogenic engine for circular orbit and GTO. • Lift off mass reduction of the order of 42% for circular and 16% for GTO. • Totally eliminates the 3 stage launch vehicle with solid rocket booster stages. • Thrust throttling ranges from 33% to 100%. This paper explores in detail the design and optimization of the ascent trajectory for a two-stage liquid rocket capable of providing variable thrust. Thrust and steering profiles play an essential role in designing a launch vehicle mission. Variable thrusting or throttling requirement arises in the thrust profile of a liquid rocket due to structural, aerodynamic and mission-related constraints. The current study investigates this aspect for two-stage liquid rockets, which deliver a 500 kg payload to 500 km circular orbit and 180 × 36000 km Geostationary Transfer Orbit (GTO). As payload mass is kept constant in both cases, the lift-off mass varies. The study found that for both missions mentioned earlier, the required variation of thrust (throttling) is in the range of 100% to 33% for the first stage to achieve an optimal trajectory. For the second stage, a considerable requirement for throttling is absent. Optimal trajectory with throttling capability reduced the lift-off mass of the launch vehicle for a mission to circular orbit by 41.6% and to the GTO by 16.3% compared to the constant thrusting cases. Also, a two-stage liquid rocket using semi cryogenic engines with variable thrusting capability and stage structural factors as low as 0.1 can replace a three-stage rocket which delivers the same payload to the 500 km circular orbit. Kulasekharapattinam and Sriharikota were the launch sites considered for the circular orbit and GTO. The study did not consider spent stage impact constraints. Canonical Differential Evolution based solver is used for global optimization. Thrust profile, steering profile and lift-off mass are the outputs of the optimization strategy. [ABSTRACT FROM AUTHOR]

Gravity assist is crucial for tour exploration of Jupiter's Galilean moons. To achieve high accuracy and low cost gravity-assisted transfer trajectories, the circular, restricted, three-body problem (CR3BP) model is adopted. Since there is no analytical solution for CR3BP, the orbit propagation must be calculated by numerical integration, which requires considerable time for the design of complex Jupiter exploration missions. Artificial neural networks (ANNs) that can fully approximate complex nonlinear relationships are used to model accurate and computationally efficient maps between the orbit states before and after gravity assist. Thereafter, a new framework based on the ANN model is developed for the fast design of Jovian-moon gravity-assisted transfers, by which optimal trajectories are obtained using a genetic algorithm (GA). Finally, the accuracy and performance of the proposed method are verified by two representative test cases of the Jupiter-Europa and Jupiter-Ganymede systems. The simulation results show that using the trained ANN model can significantly improve the convergence speed of the genetic algorithm, and high-precision, optimal solutions can be obtained rapidly. [ABSTRACT FROM AUTHOR]

A constrained hypersonic reentry trajectory optimization problem is formulated and solved using a hybrid algorithm. The hypersonic reentry trajectory optimization problem is transformed into a parametric optimization problem by the control parameterization method, and the penalty function approach is used to solve path constraints and terminal constraints. To reduce the sensitivity of the initial value of the control parameterization method, the improved sparrow search algorithm is proposed as an initial value generator to obtained an excellent initial solution. The initial solution generation efficiency and global optimality are enhanced by applying the Tent chaotic sequence mapping and the golden sine update strategy. Numerical simulations of test functions demonstrate that the proposed approach has fast convergence speed and excellent accuracy when compared with other typical optimization algorithm. The results of hypersonic reentry simulations indicate that the proposed approach is effective and has good robustness. [ABSTRACT FROM AUTHOR]

• A synthetic computation procedure for transfer families using tangential velocity increments is presented. • A fast optimization method for direct transfer is constructed based on primer vector theory. • The necessary optimality conditions for a transfer utilizing powered lunar gravity assist under a minimum swing-by height constraint are deriver. • An optimization procedure for the optimal transfer utilizing powered lunar gravity assist is presented. The triangular libration points in the Earth-Moon system are considered to be potential candidates for future space missions because of their unique positions and dynamics. This paper presents a comprehensive transfer trajectory design and optimization framework for transfers from the Earth to L 4 in the Earth-Moon system, including direct transfer and transfer utilizing powered lunar gravity assist. In this framework, first, a synthetic procedure combining an initial guess, a differential correction algorithm and numerical continuation for generating tangential transfer families is illustrated. Subsequently, the optimization models for optimal transfer trajectories with the minimum velocity increment requirement are constructed. For direct transfer, the optimal direct transfer trajectory is obtained using primer vector theory. For the optimal transfer utilizing powered lunar gravity assist under a minimum swing-by height constraint, the necessary optimality conditions are found through optimal control theory, and an optimization procedure that allows for numerical convergence to the optimal solution is constructed. Numerical results indicate that the proposed transfer trajectory design and optimization framework has sufficient effectiveness to provide various transfer trajectories associated with different insertion points and fuel-optimal transfers. [ABSTRACT FROM AUTHOR]

• An algorithm for solving global optimization problems which takes inspiration from quantum mechanics is presented. • Applied to space trajectory optimization and compared with PSO and DE the algorithm shows better performance. • In the application to attitude maneuvers with the presence of constraints, it finds better solutions than PSO and DE. In this work, an algorithm for solving optimization problems is proposed, inspired by a computational method employed in Quantum Mechanics: the Diffusion Monte Carlo method, commonly used for the computation of ground states of many-particle systems. The optimization problem is re-formulated as the problem of sampling the ground state wave function of a particle subject to a potential based on the function to be minimized. The algorithm is applied to problems in space trajectory and spacecraft attitude maneuvers optimization, the first application is to the problem of transfer between circular orbits, the results obtained are compared to the results from the literature, then it is applied to the problem of rendezvous with the asteroid Pallas, and finally to the optimization of an attitude maneuver in the presence of several constraints, and the obtained results are compared to two widely used methods: Particle Swarm Optimization and Differential Evolution algorithms. The algorithm is of simple implementation, and the numerical results show better performance than the comparison methods in the considered problems. [ABSTRACT FROM AUTHOR]

• Fuel-optimal ascending trajectories from the surface of Phobos are investigated. • An ERTBP model with the irregular gravity and physical libration is established. • A trajectory maintenance strategy based on the target point method is proposed. • Some trajectories that consume less fuel and are easy to maintain are chosen. The ascending trajectory from the surface of Phobos to a resonant quasi-satellite orbit around Phobos is investigated with a newly proposed dynamical model based on the Elliptic Restricted Three-Body Problem. The proposed model incorporates the non-spherical gravity field and physical libration of Phobos as well. The trajectories from the surface of Phobos are classified into three types according to their z -componentsas short-, middle-, and long-term ascending trajectories. The total Δ V of the two-impulse ascending trajectories is optimized with the particle swarm optimization method. The total Δ V and time of flight of the optimized ascending trajectories are analyzed, and the Pareto Front is refined from the optimized solutions. A multi-impulse maintenance strategy based on the target point method is constructed to ensure that the ascender can insert into the target orbit accurately along the nominal trajectory in the real environment. The robustness of the maintenance strategy is validated by Monte-Carlo simulations in a high-fidelity model, i.e., the N-body problem with the ephemeris, Phobos' physical libration, non-spherical gravity field of Phobos, and a Gaussian uncertain perturbation. The number of the correction impulses needed is highly positively correlated with the time of flight of the trajectory. Based on the results, middle-term ascending trajectories with less time of flight on the Pareto Front are recommended. [ABSTRACT FROM AUTHOR]

The LISA Pathfinder mission was flown to test some key technologies for the in-flight detection of gravitational waves. The mechanism developed to initialise the science phase, releasing the test mass into a geodesic trajectory, produced unexpected test mass states, requiring dedicated in-flight and on-ground test campaigns. Due to the limited information available from the telemetry, the analysis of the results required a combination of experimental and analytical approaches. A dynamic model of the release mechanism, integrated by an impact model, is developed to explain the in-flight test results. The proposed interpretation of the mechanism anomalies may provide useful guidelines for the design and development of the flight units for the forthcoming LISA mission. [ABSTRACT FROM AUTHOR]

IRASSI is an astronomy mission aimed at observing stellar disks and protoplanetary regions using a constellation of five free-flying telescopes operating around the Sun-Earth/Moon L 2 point. In these regions of the cosmos, important chemical/physical phenomena can be observed in the far-infrared, which may advance our current understanding of how pre-biotic conditions in Earth-like planets are formed. The distinguishing aspect of the IRASSI interferometer, however, is its free-flying concept. Rather than relying on a fixed formation configuration and relative position control, IRASSI relies on continuously drifting baselines (e.g., inter-satellite distances) and the knowledge of these baselines during the science observations. However, not all IRASSI targets require the same formation strategy and therefore the planning of the sequence of observation tasks and of the corresponding reconfiguration and science maneuvers has been investigated. The manuscript provides thus an overview of the planning architecture devised for IRASSI, called iSCOUT, composed of different modules: 1) Target Planner Module (TPM), 2) Reconfiguration Module (ReM), 3) Collision- and invisibility Avoidance Module (CAM), 4) Baseline Pattern Module (BPM). The first module (TPM), generates an optimized sequence of targets within a specified window period, taking into account variables such as visibility of the targets at each time step, retargeting time based on the current state, target priority or number of previously observed targets of the same type. The second module, ReM, assigns positions to the telescopes based on the target sequence generated by the TPM. Each translation maneuver is optimized to achieve a specified initial formation configuration, which is both perpendicular to the target direction and three-dimensional. Parameters such as fuel use and fuel-balance as well as ΔV and ΔV-balance are used for optimizing the reconfiguration of the formation. The third module, CAM, ensures that the telescopes following the ReM trajectories do not violate relative proximity restrictions or intervisibility requirements during the reconfiguration. In such an event, the CAM computes a new path in order to avoid collisions and invisibility instances. The last module, BPM, calculates the drifting trajectories that achieve the required patterns in the so-called ' (U, V) -plane' during the science observations. (U, V) -plane projection metrics and several operational constraints are used for the optimization of the trajectories. Each module has been individually optimized and the paper describes the main outcomes thereof. Results concerning and end-to-end iSCOUT simulation for the IRASSI mission are presented and future work goals complete the paper. [ABSTRACT FROM AUTHOR]

This paper presents a propellantless spacecraft rendezvous method by using the optimal combination of aerodynamic force and Lorentz force. Aerodynamic force is provided by the rotations of the plates attached to the spacecraft, and Lorentz force is achieved by modulating spacecraft's electrostatic charge. Considering the limitation of the charging level of the spacecraft and physical constraints of the plates system, an optimal open-loop rendezvous trajectory is designed, which aims to minimize the energy consumed to actuate the hybrid system. The rotation rates of the plates and the electrostatic charge are constrained in the optimization problem, which is solved via the Gauss pseudospectral method. To track the open-loop trajectory in the presence of external perturbations, a novel adaptive nonsingular terminal sliding mode controller is designed. The stability of the closed-loop system is proved by the Lyapunov-based method. Several numerical examples are conducted to verify the validity of both the open-loop and closed-loop control strategy. [ABSTRACT FROM AUTHOR]

• Integrating economics into trajectory optimization yields more realistic missions. • Asteroid mining can be profitable using both chemical and solar-sail propulsion. • Attainable target asteroids should have Earth-like orbits. • The attainable target region is larger for solar sails than for chemical propulsion. Asteroid mining has the potential to greatly reduce the cost of in-space manufacturing, production of propellant for space transportation and consumables for crewed spacecraft, compared to launching the required resources from the Earth's deep gravity well. This paper discusses the top-level mission architecture and trajectory design for these resource-return missions, comparing high-thrust trajectories with continuous low-thrust solar-sail trajectories. The paper focuses on maximizing the economic Net Present Value, which takes the time-cost of finance into account and therefore balances the returned resource mass and mission duration. The different propulsion methods are compared in terms of maximum economic return and sets of attainable target asteroids. Results for transporting resources to geostationary orbit show that the orbital parameter hyperspace of suitable target asteroids is considerably larger for solar sails, allowing for more flexibility in selecting potential target asteroids. Also, results show that the Net Present Value that can be realized is larger when employing solar sailing instead of chemical propulsion. In addition, it is demonstrated that a higher Net Present Value can be realized when transporting volatiles to the Lunar Gateway instead of geostationary orbit. The paper provides one more step towards making commercial asteroid mining an economically viable reality by integrating trajectory design, propulsion technology and economic modelling. [ABSTRACT FROM AUTHOR]

• Minimum-time solar sail trajectories are shaped using finite Fourier series. • The control variables are the Fourier coefficients and the initial and final position. • Suitable constraints are enforced on the magnitude and direction of the solar sail thrust vector. • The proposed method is validated with three-dimensional orbit-to-orbit transfer scenarios. The heliocentric transfer of a solar sail-based spacecraft is usually studied from an optimal perspective, by looking for the control law that minimizes the total flight time. The optimal control problem can be solved either with an indirect approach, whose solution is difficult to obtain due to its sensitivity to an initial guess of the costates, or with a direct method, which requires a good estimate of a feasible (guess) trajectory. This work presents a procedure to generate an approximate optimal trajectory through a finite Fourier series. The minimum time problem is solved using a nonlinear programming solver, in which the optimization parameters are the coefficients of the Fourier series and the positions of the spacecraft along the initial and target orbits. Suitable constraints are enforced on the direction and magnitude of the sail propulsive acceleration vector in order to obtain feasible solutions. A comparison with the numerical results from an indirect approach shows that the proposed method provides a good approximation of the optimal trajectory with a small computational effort. [ABSTRACT FROM AUTHOR]

The attention to the periodic orbit in the Earth-Moon restricted three-body system continues to grow due to its special environment and locations. This research investigates the feasibility of constructing fuel-optimal single and multiple impulse transfers between unstable periodic orbits at L 1 and L 2 points. Invariant manifolds, which could provide the appropriate initial trajectories for optimization, are analyzed deeply to enable previously unknown orbit options and potentially to reduce mission cost. A global search strategy based on comparing the orbital state of the unstable and stable manifolds, incorporated with low-thrust techniques, is performed to seek a suitable matching point for maneuver application. Then the sequential quadratic programming (SQP) is adopted to further optimize the velocity increment and obtain the single/multiple impulse optimal transfers. The associated constraint gradients are derived to achieve higher accuracy and rapidity of the algorithm. To highlight the effectivity of the transfer scheme, three-dimensional low-energy transfers between different types and spatial regions of performing single and multiple impulses are explored. The total Delta-V required varies between a few meters per second and tens of meters per second, and the related flight time is about several weeks, mainly depending on the energy of periodic orbits and the invariant manifold structure. The results obtained in this paper can provide a useful reference for the selection of escape and capture site along the manifolds, maneuver magnitude and transfer time. [ABSTRACT FROM AUTHOR]

• A DNN-based method is developed to deal with low-thrust optimal orbit transfer. • The method is a combination of traditional techniques and DNNs. • The method has advantages on the computational efficiency and reliability. Initial solution guess has a significant impact on the convergence of indirect methods, especially for continuous low-thrust trajectory optimization problems. In this study, an intelligent initial solution supplying approach based on deep neural networks (DNNs) is proposed to help achieve the fast generation of optimal trajectories for low-thrust orbit transfers. Energy-optimal and fuel-optimal trajectories with three different terminal conditions are considered. Based on the training dataset obtained by an indirect method, DNNs are constructed to approximate the solutions corresponding to different flight states. Based on the trained DNNs, an intelligent trajectory optimization method named DNN-based method is developed with the help of the homotopy technique. Numerical simulations are conducted to evaluate the performance of the proposed method on success rates and time consumptions. Simulation results demonstrate that the combination of traditional techniques and the new DNN technology can achieve the fast generation of low-thrust optimal trajectories with advantages on computational efficiency and reliability. [ABSTRACT FROM AUTHOR]

This work develops an autonomous trajectory planning algorithm for 6-DOF asteroid landing. The trajectory planning problem is formulated as a nonconvex time-optimal optimization problem with two-phase free final time, while the cost is regularized by augmenting a fuel consumption penalty. The nonconvex optimization problem is solved in successive solution method, and successive convexification is used to convert the original nonconvex problem into a sequence of convex subproblems, where each subproblem is obtained by linearizing the nonconvex dynamics and state constraints and using the velocity increment to give a convex expression of the fuel consumption penalty in cost function. Specifically, in the linearization, we divide the flight time interval into two parts and normalize each part using a time dilation coefficient to solve the problem that both the final times for the two flight phases are unknown, so that the original free final time problem turns to a fixed-time problem by minimizing the sum of the two time dilation coefficients and fuel consumption penalty. Besides, trust regions and virtual control are used to increase robustness of the algorithm. A convergence analysis is presented which indicates the successive solution will recover the local optimality of the original problem. Then the validity of the proposed algorithm and effects of different factors on flight time and fuel consumption are examined by simulations of landing on an irregular asteroid. [ABSTRACT FROM AUTHOR]

• Flight vehicle with multi-combined cycle engine is researched. • Hooke-Jeeves method is introduced into PSO to accelerate convergence. • Radial basis function neural network is used to develop the guidance law. This paper researches the ascent guidance law for the vehicle with a multi-combined cycle propulsion. The guidance law comprises two parts, namely, the off-line optimal trajectories generation and online guidance. With respect to the off-line part, disturbances are discretized and incorporated into the trajectory optimization problem; subsequently, a set of trajectories is calculated to constitute a database. To quickly obtain a database that comprises a large number of trajectories, a novel ascent profile is proposed with respect to height and velocity. Based on this profile, only inequity constraints exist in the optimization model, and the original optimization problem is converted to a parameter searching problem. The optimal trajectories are calculated using a hybrid optimization method that comprises a particle swarm optimization (PSO) method and the Hooke-Jeeves (HJ) method. With respect to online guidance, the profile is updated using a radial basis function neural network (RBFNN) based on the current flight states and the database. Simulation validates the efficiency of the proposed optimization method by comparing the method with the pseudospectral method; the robustness of the guidance law is also validated using Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

• The minimum total velocity variation between elliptic orbits is calculated with three tangential impulses. • The problem is reduced to the minimization of a function of three independent variables. • The reduction of problem complexity allows the global minimum solution to be easily found. • The algorithm determines the best transfer strategy and the required number of tangential impulses. This paper introduces a mathematical model that can be used to evaluate the total velocity variation required to accomplish a given two-dimensional orbit transfer, using up to three tangential impulsive maneuvers. The problem is addressed in an optimal framework, by looking for the transfer trajectory that minimizes the total velocity variation. In particular, by exploiting the boundary nonlinear constraint equations, the total velocity variation can be calculated as a function only of the spacecraft angular position at which the impulses are applied. The small number of control variables involved in the algorithm allows the optimization problem to be solved in a simple and robust way, with a small computational effort. The algorithm is able to find the optimal transfer strategy in a generic ellipse-to-ellipse, two-dimensional, mission scenario. [ABSTRACT FROM AUTHOR]

For explorations of the far side of the Moon, it is necessary to tackle the challenge of navigation and communication as the far side is invisible to the Earth. This paper proposes a low-cost mission concept that consists of four CubeSats in an Earth-Moon L 2 (EML2) halo orbit. The mission objective is to provide real-time positioning service for lunar far-side assets, taking advantage of the visibility of EML2 halo orbits to both the Earth and lunar far side. Being miniature, CubeSats can be carried by a mother spacecraft and deployed during the mid-course. As CubeSat missions are generally constrained by limited communication, power, and propulsion capacities, this paper presents a feasibility study that takes into account the high-fidelity dynamical environment and system constraints. This paper analyzes the positioning performance in terms of accuracy, and spatial and temporal coverage. In addition, the requirement of deployment in terms of Δ v budget and thrust magnitude is also investigated. Results show that (1) a positioning accuracy of 2.7 km is achievable; and (2) several state-of-the-art propulsion systems can meet the requirement of deployment and the stationkeeping for an acceptable duration. [ABSTRACT FROM AUTHOR]

Abstract In this study, the Earth's Trojan asteroid 2010 TK 7 is selected as the rendezvous target. The multiple flyby sequence of asteroid exploration was proposed by optimizing the probe's orbit. Impulsive maneuvers and low-thrust propulsion were used respectively to design the trajectories of the multiple asteroids exploration mission. Under impulsive maneuvers, gravity assist technique was adopted to reduce fuel consumption. First a reference orbit with only 2010 TK 7 as the rendezvous target was designed. Then five asteroids near the reference orbit were selected as candidates. Finally, we obtained a multiple asteroids exploration sequence of three asteroids based on gravity assist technique and genetic algorithm, and an additional velocity impulse of 0.4 km/s was required. In the subsequent section, a sixth-degree inverse polynomial shape-based method is applied to the low-thrust trajectory design of 2010 TK 7 , and the exploration sequence under the action of low-thrust propulsion was provided. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a framework to analyze the capacity of a launch vehicle systematically. Important mission requirements and flight parameters that influence the payload capacity of a given launch vehicle configuration are identified. The response surface models (RSM; the "analyzer") for the launch capacity, coasting/burning arcs, and the velocity increment elements are developed. A series of trajectory optimization results, which are obtained with the "optimizer", are used to determine the coefficients of the models. The case study to analyze the capacity of a low Earth orbit (LEO) launch vehicle configuration is conducted to demonstrate the validity of the proposed framework. [ABSTRACT FROM AUTHOR]

Abstract This paper presents an improved understanding of the interaction of hybrid optimization method with variable low-thrust trajectory optimization requirements. To analyze fuel-optimal bang-bang control problem, a new version of homotopic algorithm, termed robust homotopic method, is investigated with the prospect of improving the efficiency and automation of the homotopic approach to achieve a high-level of robustness, and consequently enlarge its range of application. Such desired characteristics are promoted via a combination of several techniques. As an effective approach, a modified methodology of the switching detection process is presented for the bang-bang optimal-control problem. Moreover, the value of unknown costates and switching functions are mapped to new normalized intervals throughout the computational process. As a result, the optimal solution is rapidly designed to obtain the global robust-convergence to satisfy all constraints without any ambiguity. The fitting process of all iterations robustly find the unknown variables with the percent of converged solutions to maximum, and the penalty terms are quickly satisfied with predetermined high-accuracy, from the energy-optimal to the fuel-optimal solution, especially close to zero point as a critical point. Accordingly, two advanced interplanetary trajectories are optimized using two dynamic modeling approaches for the instantaneous and constant maximal thrust magnitude as a way to analyze and substantiate the robustness of the proposed algorithm. Results and performances are compared with existing solutions of the same mission problem. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the entry trajectory optimization problem of lifting type re-entry vehicle with path constraints is solved using Pigeon Inspired Optimization (PIO). Entry trajectory optimization problem involves finding the control profiles, bank angle, and angle of attack to guide the vehicle safely to the destination. The proposed approach parametrizes the bank angle to be a linear function of energy while the angle of attack is considered to be a monotonic function of Mach number. Thus, the problem of finding control profiles is transformed into three parameter search problem. The PIO algorithm is used to find the values of these parameters that minimizes the objective function. The terminal heading angle offset is minimized using traditional bank reversal logic. A new approach is proposed in which the bank angle is modulated to eliminate the oscillations observed in the altitude profile of an entry vehicle with a high lift to drag ratio (L/D). A methodology to satisfy the given load factor constraint is also proposed, as an alternative to traditional penalty factor approach used for incorporating path constraints in PIO algorithm. The proposed approach is further validated by considering sub-cases with different load factor limits and bank angle as the only control variable. The angle of attack profile obtained from the previous case is considered as the nominal profile. The proposed trajectory optimization strategy using PIO algorithm is simulated for Common Aero Vehicle with high L/D ratio (CAV-H) with different load factor constraint limits. The results show that the obtained angle of attack profile minimizes the peak heat rate experienced by the vehicle and bank angle modulation eliminates the oscillations in the altitude profile as well as makes the entry trajectory satisfy the load factor constraint. [ABSTRACT FROM AUTHOR]

This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]