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Existing exoatmospheric guidance laws become ineffective when a thrust loss fault (like one or more engines unexpectedly shut down) occurs in a launch vehicle, which makes the nominal orbit unreachable. This paper presents a new abort orbit determination process to determine an abort orbit which the launch vehicle is able to reach. It involves solving at most two optimization problems and the abort orbit may be circular or elliptical. We will present how to transform the nonconvex optimization problems into difference of convex (DC) programming problems which can be solved by existing methods with guaranteed convergence. The main contribution of this paper lies in proposing a relaxation technique to convexify a nonconvex control constraint and the combination of the introduction of new constraints and a relaxation technique to deal with the strict terminal constraints. Validity of the relaxation technique is ensured by theoretical analysis. A unique feature of the transformation process is that the feasible sets defined by both the control constraint and the strict terminal constraints are all enlarged. This brings a critical benefit that the resulting DC programming problems can be very efficiently solved. Thus, an abort orbit determination algorithm, which is based on DC programming, can be designed to very reliably and efficiently determine an abort orbit, which will be demonstrated by numerical examples. • A new concise and practical abort-orbit determination process is proposed. • Relaxation techniques and the introduction of new constraints are properly combined. • Validity of the relaxation techniques are theoretically proved. • An abort orbit can be determined by solving at most two DC programming problems. [ABSTRACT FROM AUTHOR]

Satellite formation plays an important role in space missions such as on-orbit services and distributed space facilities. In these missions, hovering in a bounded range is one of the core tasks, but hovering technologies for the chief satellite in an elliptical orbit have been rarely investigated. Given the boundary constraints of relative motion between the chief and deputy satellites, this paper proposes two models for the design and control of hovering formation near an elliptical reference orbit through impulse: (1) the revisiting hovering formation model, which forces the deputy satellite to revisit the same relative position and maintains the formation via impulses; (2) the sequential-impulse-control hovering formation model, which uses a sequence of impulses to ensure the deputy satellite flies within the given boundary. Unlike the revisiting hovering formation model, this model does not require a fixed revisiting point, so the satellite's trajectory is more flexible. The geometrical properties, formation maintenance strategy, and impulse-control solution for both models are investigated in detail. Finally, numerical simulations are conducted to verify the advantages of the proposed methods over other conventional methods, suggesting their wide applications in practical space missions. • Two impulsive-control models are proposed for bounded hovering formation in elliptical orbit. • The proposed methods support in-plane, out-of-plane, and three-dimension hovering formations. • The in-plane and out-of-plane controls are decoupled to decrease control complexity and difficulty. • Different factors on the fuel cost are analyzed to provide a reference for practical engineering. [ABSTRACT FROM AUTHOR]

This paper proposes a method of using multiple spacecraft flying in formation in an artificially reduced halo orbit around the 2nd Lagrange point in the Sun–Earth system (SEL2) to make interferometric observations. One of the requirements for interferometric observations is to collect baseline vectors between telescopes or antennas. A shape-based approach is introduced to design a formation flight orbit that spirally spreads to satisfy this requirement. In this approach, orbits are designed on the basis of a linear theory. However, the formation orbits based on the linear theory quickly diverge because of the unstable dynamics around the SEL2. Therefore, the state-dependent Riccati equation, which allows for nonlinear control, is applied to orbit maintenance. The control system consists of two components: one for maintaining the reference orbit around the SEL2 and the other for controlling the relative position between the multiple spacecraft. The performance of the developed formation flight system is verified through a numerical simulation, confirming that the position accuracy requirement of the infrared interferometer is satisfied. It is also shown that both controls can be achieved with a low-thrust magnitude by using an electric propulsion system. • Formation flights around the Lagrange points are useful for interferometer. • An artificial halo orbit is designed with a reduced radius and a fixed shape. • Spacecraft formations are designed to collect more baseline vectors. • A nonlinear control is designed using the state-dependent Riccati equation. [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear dynamics and control problem of deorbiting an electrodynamic tethered satellite system in an inclined elliptical orbit. Considering the perturbing Lorenz forces, a set of modified equinoctial elements is employed to describe the slow-varying orbital dynamics. In addition, the fast-varying attitude dynamics of the system is incorporated into dynamic modeling by adopting an assumption of a dumbbell model. To circumvent the difficulties in computation of a real-time optimal control law for a long-term deorbiting process, a compound control scheme is proposed. A time-scale separation method is adopted to facilitate the controller design. In the scheme, a nonlinear optimal control law accounting for system constraints and nonlinear dynamics is first proposed to find an initial nominal periodic orbit without considering the variations of orbital elements. Subsequently, a closed-loop feedback control law based on energy rate is presented to track the periodic solutions for several orbits by considering the overall dynamics. Notably, the periodic solution will be re-computed after each tracking procedure to account for the slow variation in orbital elements. Comparative studies are presented to demonstrate the advantages of the proposed control law in reducing computational costs. • Orbital motion and attitude dynamics are distinguished by time-scale separation. • Nonlinear dynamics and inherent constraints of the system are accounted for. • A low-cost compound control law is proposed for long-term deorbiting maneuver. [ABSTRACT FROM AUTHOR]

This paper solves the problem of the on-line joint optimization of the target orbit and flight trajectory of a launch vehicle experiencing a thrust drop failure, and proposes state-triggered indices to improve the solving efficiency. The 'highest-height index' is triggered first to find the maximum-height circular orbit (MCO) in the orbital plane formed at the time of failure. If the orbital altitude is less than the perigee height of the prescribed target orbit, the MCO will be regarded as the optimal circular orbit to ensure safety. If not, the 'minimal orbital plane deviations index' is triggered to subsequently find the optimal elliptical orbit (OEO), where the orbital inclination and longitude of the ascending node are preferentially adjusted on the basis of the MCO. Furthermore, if the OEO is coplanar with the target orbit, a 'minimal orbital shape deviations index' is triggered to find the optimal rescue orbit, which eliminates the deviations of the perigee altitude, semi-major axis and perigee argument on the basis of the OEO. Estimation of the geocentric angle of the injection point, construction of the approximated sub-problem, and convexification processing are adopted to provide initial guesses to boost the computing. Monte Carlo simulations show that the method not only converges to the optimal or sub-optimal solution for different failure states, which avoids suspended calculations, non-convergence, and constraint violations that are common when directly solving this type of rescue problem, but also meets the basic requirements of on-line applications. • State triggered index is proposed to get optimal rescue orbit if thrust drop occurs. • Orbital altitude, plane, and shape are adjusted sequentially to ensure solvability. • Convexification and range estimation are used to get initial value and boost solving. • Simulations show the adaptability to various fault scenarios and on-line application. [ABSTRACT FROM AUTHOR]

New additional velocity vectors are introduced at the initial and final points of orbit transfer. The unit vectors' differences between the additional velocity vectors and the transfer velocity vectors are Lawden's primer vectors for the noncoplanar orbit that depends on three parameters. Also, a system of four equations with four unknowns was obtained for noncoplanar transfers. This paper shows for the first time a new notation for Lawden's primer vectors at application points of impulses for three-dimensional transfers, which depends on three constants. The geometric conditions for the noncoplanar Hohmann's transfer have been demonstrated on the basis of the result obtained. A graphical example is provided for noncoplanar Hohmann transfer, confirming the known solution. • Obtains a new notation for Lowden's primer vectors at application points of impulses. • System of four equations with four unknowns was obtained for noncoplanar transfers. • A graphical example is provided for noncoplanar Hohmann transfer. [ABSTRACT FROM AUTHOR]

In this paper optimal bi-impulse orbital transfer between coplanar and non-coplanar elliptical orbits has been considered. First, an efficient algorithm based on grid search method has been developed to find the global solution of the impulsive orbital transfer. There are three independent parameters in this algorithm: i) the angular position of the point on the initial orbit where the first impulse is applied to, ii) the angular position of the point on the final orbit where the second impulse is applied to and, iii) the argument of periapsis of the transfer orbit. The other parameters can be obtained from these three parameters in both coplanar and non-coplanar cases. The algorithm is able to obtain the global optimal solution for any arbitrary initial and final elliptical orbits. Second, the algorithm is employed to solve an extensive set of numerical examples, including coplanar and non-coplanar, co-axial and non-co-axial orbits of different shape and energy. This comprehensive set of examples allows disentangling the roles of each relevant orbital parameter in the evaluation of the optimal transfer. Finally, the numerical results are employed to achieve a very precise fitting function which is helpful onboard calculation and mission design. [ABSTRACT FROM AUTHOR]

Spectrum-Roentgen-Gamma is an international X-ray astrophysical space observatory, planned to be launched in 2019. The spacecraft will operate in the vicinity of the Lagrangian point L 2 of the Sun-Earth system. The nominal lifetime of the mission is 7 years, and it includes all-sky survey and pointed observations in the 0.1–15 keV band. The paper describes technical constraints of the mission, covering launch scenario, spacecraft structure and ground data relay network, and a design of suitable operational orbits. In addition, opportunities to achieve a suitable operational orbit are discussed, including a scenario with a lunar gravity assist and a transfer with an intermediate orbit. • Spectrum-Roentgen-Gamma is an international X-ray astrophysical space observatory. • SRG will be launched in 2019 to the vicinity of the Sun-Earth Lagrangian L2 point. • Mission technical constraints require a small-amplitude operational L2 orbit. • A lunar gravity assist allows one-impulse transfer to achieve a suitable orbit. • An intermediate orbit with a raised perigee enables to reduce orbit amplitudes. [ABSTRACT FROM AUTHOR]