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• 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]

• 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]

Different from the Apollo flight mode, a safer trans-lunar flight mode for the crews is preferred. The previous-arrived lunar module rendezvouses with the crew exploration vehicle at a low lunar destination orbit, and then the crews ride the lunar module to descend the lunar surface sampling destination. The lunar module, which includes the descent and ascent stages, flies from a low Earth orbit to the low lunar destination orbit with two tangential impulses. The low lunar destination orbital reachable set of the practical trans-lunar orbit limits the feasible lunar surface sampling region. Therefore, this paper addresses the low lunar destination orbital reachable set of the practical trans-lunar orbit. A retrograde semi-analytic model is proposed for rapidly computing the practical two-impulse trans-lunar orbit firstly, which refers the ephemeris table twice for more precision perilune orbital elements. The reachable set is generated using the multiple-level traversal searching approach with this retrograde semi-analytic mode. Its envelope is re-checked by the continuation theory with the high-precision orbital model. Besides, some factors that affect the reachable set are also measured. The results show that neither the Earth–Moon distance nor the trans-lunar duration affects the reachable set. However, if the trans-lunar injection inclination is smaller than the inclination of the moon's path, the reachable set becomes smaller or even reduces into an empty set. In brief, the proposed retrograde semi-analytic model for computing the reachable set provides a helpful and fast tool for selecting an applicable lunar surface sampling site for the manned lunar mission overall design. [ABSTRACT FROM AUTHOR]

Chang'e-2, Chinese second lunar probe, was inserted into a 100 km altitude low lunar orbit on October 9th, 2010, its purpose is to continuously photograph the lunar surface and possibly chosen landing sites for future lunar missions. The probe will still carry considerable amount of propellant after completing all prescribed tasks in about six months. After the successful launch of Chang'e-2, we began designing the probe's subsequent flight scenario, considering a total impulse of 1 100 m/s for takeoff from low lunar orbit and a maximum 3×10 km distance for Earth-probe telecommunication. Our first-round effort proposed a preliminary flight scenario that involves consecutive arrivals at the halo orbits around the Earth-Moon L1/L2 and Sun-Earth L1/L2 points, near-Earth asteroid flyby, Earth return, and lunar impact. The designed solution of Chang'e-2's subsequent flight scenario is a multi-segment flight trajectory that serves as a reference for making the final decision on Chang'e-2's extended mission, which is a flight to the Sun-Earth L2 point, and a possible scheme of lunar impact via Earth flyby after remaining at the Sun-Earth L2 point was also presented. The proposed flight trajectory, which possesses acceptable solution accuracy for mission analysis, is a novel design that effectively exploits the invariant manifolds in the circular restricted three-body problem and the patched-manifold-conic method. [ABSTRACT FROM AUTHOR]

The retrograde geostationary earth orbit (retro-GEO) is an Earth's orbit. It has almost the same orbital altitude with that of a GEO, but an inclination of 180°. A retro-GEO monitor-satellite gives the GEO-assets vicinity space-debris warnings per 12 h. For various reasons, the westward launch direction is not compatible or economical. Thereby the transfer from a low earth orbit (LEO) to the retro-GEO via once lunar swing-by is a priority. The monitor-satellite departures from LEO and inserts into the retro-GEO both using only one tangential maneuver, in this paper, its transfer's property is investigated. The existence of this transfer is verified firstly in the planar circular restricted three-body problem (CR3BP) model based on the Poincaré-section methodology. Then, the two-impulse values and the perilune altitudes are computed with different transfer durations in the planar CR3BP. Their dispersions are compared with different Sun azimuths in the planar bi-circular restricted four-body problem (BR4BP) model. Besides, the transfer's inclination changeable capacity via lunar swing-by and the Sun-perturbed inclination changeable capacity are investigated. The results show that the two-impulse fuel-optimal transfer has the duration of 1.76 TU (i.e., 7.65 days) with the minimum values of 4.251 km s−1 in planar CR3BP, this value has a range of 4.249–4.252 km s−1 due to different Sun azimuths in planar BR4BP. Its perilune altitude changes from 552.6 to 621.9 km. In the spatial CR3BP, if the transfer duration is more than or equal to 4.00 TU (i.e., 17.59 days), the lunar gravity assisted transfer could insert the retro-GEO with any inclination. In the spatial BR4BP, the Sun's perturbation does not affect this conclusion in most cases. [ABSTRACT FROM AUTHOR]

This paper addresses the scheduling problem arising from refueling multiple geosynchronous (GEO) satellites with multiple servicing vehicles [many-to-many (M2M) refueling]. The problem is defined by a set of potential fuel tanker locations, a homogeneous fleet of servicing vehicles with limited capacities, and a set of fuel-deficient GEO satellites with known fuel demands. The objective is to open a subset of fuel tankers, to assign GEO satellites to these tankers and to design vehicle servicing sequences, in order to minimize the total mission costs. To achieve such an economical refueling strategy, the fuel tanker location and routing decision are required to be determined simultaneously. It is shown that this problem can be formulated as a location-routing problem (LRP) which is obviously NP-hard. In order to solve it, an ant colony optimization (ACO) metaheuristic that features a special solution representation scheme is proposed. The proposed algorithm is then tested on two types of instances depending on whether the cost for opening a fuel tanker is considered or not. Numerical experiments show that both the consideration of the fuel tanker opening costs and their locations do affect the refueling schedule. Furthermore, the proposed algorithm outperforms the existing approaches in the M2M refueling mission design, and it is able to detect the optimal refueling strategy on all instances containing 85 GEO targets with 15 potential fuel tankers while previous works stopped at 15 satellites and 2 fuel tankers. • Scheduling of the multiple satellites refueling mission is presented. • Servicing vehicle routing and the fuel tanker location are considered simultaneously. • An ant colony optimization based solving methodology is proposed. • A special solution presentation scheme is applied to improve the computational burden. [ABSTRACT FROM AUTHOR]

Abstract The ninth edition of the China Trajectory Optimization Competition (CTOC9) considered the problem of navigation augmentation over a set of Chinese cities, wherein the competitors were expected to design a suitable LEO constellation to obtain the required navigation performance with the aim of minimizing overall system cost. In addition, an economical deployment strategy was also considered. The synthesis methods used by the Xi'an Satellite Control Center (XSCC) are described, along with the promising solution found by the team. Firstly, two techniques, feasible region based reduction and coverage region based reduction, are applied in sequence to narrow the search space. Then, the optimal constellation configuration is obtained through an Differential Evolution Algorithm (DE). Finally, a series of maneuver strategies are searched to inject each navigation satellite from a given initial carrying orbit to its target location. The solution obtained during the competition ranked third, and the improved one, found after the deadline, got the outstanding prize. [ABSTRACT FROM AUTHOR]

We present a study of the transfer orbits connecting landing points of irregular-shaped asteroids. The landing points do not touch the surface of the asteroids and are chosen several meters above the surface. The ant colony optimization technique is used to calculate the multiple-hopping trajectories near an arbitrary irregular asteroid. This new method has three steps which are as follows: (1) the search of the maximal clique of candidate target landing points; (2) leg optimization connecting all landing point pairs; and (3) the hopping sequence optimization. In particular this method is applied to asteroids 433 Eros and 216 Kleopatra. We impose a critical constraint on the target landing points to allow for extensive exploration of the asteroid: the relative distance between all the arrived target positions should be larger than a minimum allowed value. Ant colony optimization is applied to find the set and sequence of targets, and the differential evolution algorithm is used to solve for the hopping orbits. The minimum-velocity increment tours of hopping trajectories connecting all the landing positions are obtained by ant colony optimization. The results from different size asteroids indicate that the cost of the minimum velocity-increment tour depends on the size of the asteroids. [ABSTRACT FROM AUTHOR]