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This paper seeks to examine the development of the on‐board guidance law for multi‐revolutions orbit transfer spacecraft with low‐thrust propulsion systems.

In the research, first, a set of equinoctial elements is utilized to avoid the singularities in dynamical equation of classical orbit elements. A thruster switch law is derived by analyzing the efficiency of the changing of each orbit elements. Second, by using the theory of Lyapunov feedback control, analytic expressions of thrust angles are derived. Finally, the weights of the Lyapunov function are adjusted by hybrid genetic algorithm to improve the performance of the guidance law.

First, the dynamical equations of classical orbit elements are always singularity during the orbit transfer. By using modified equinoctial elements, these singularities could be avoided. Second, the trajectory is sensitive to the weights in Lyapunov function. With reasonable weights, the key parameters under the control of the guidance law presented in this paper are very close to that of optimal trajectory.

In further research, some dynamical weights methods will be used in the control law to improve the performance index, and approach the optimal solution.

The guidance law presented in this paper could be easily used as an on‐board algorithm for the multi‐revolutions orbit transfer or stationkeeping. Furthermore, it could also be utilized as an initial design method for low‐thrust orbit transfer.

Providing a low‐thrust guidance law by combining the concept of Lyapunov feedback control with hybrid genetic algorithm. This method has a super convergence and a low‐computational cost.

The purpose of this paper is to propose strategies for satellite cluster non‐coplanar orbit transfer to reduce fuel cost of formation maintenance and orbit maneuver.

This research tries to use geometric method model to describe the relative motion of satellites in the cluster non‐coplanar orbit transfer, and genetic algorithm (GA) to optimize the proposed maneuver strategies.

Compared with the C‐W equations, the geometric method model is found to be more precise. Three strategies are proposed and optimized to maintain the relative orbit and a strategy of indefinite phase and non‐synchronous costs least fuel.

Geometric method model can be used to describe the relative motion of satellite cluster, especially on elliptical orbits considering the effects of perturbation, with a simple form and good accuracy. Fuel cost minimization is one of the most important issues in formation flight mission.

This paper provides dynamics analysis about formation non‐coplanar orbit transfer, which is involved in minor researches.

The purpose of this paper is to study the effect of J₃ perturbation of the Earth’s oblateness on satellite orbit compared with J₂ perturbation.

Based on the parametric variation method in the time domain, considering more accurate Earth potential function by considering J₃-perturbation effect, the perturbation equations about satellite’s six orbital elements (including semi-major axis, orbit inclination, right ascension of the ascending node, true anomaly, eccentricity and argument of perigee) has been deduced theoretically. The disturbance effects of J₂ and J₃ perturbations on the satellite orbit with different orbit inclinations have been studied numerically.

With the inclination increasing, the maximum of the semi-major axis increases weakly. The difference of inclination disturbed by the J₂ and J₃ perturbation is relative to orbit inclinations. J₃ perturbation has weak effect on the right ascension and argument of perigee. The critical angle of the right ascension and argument of perigee which decides the precession direction is 90° and 63.43°, respectively. The disturbance effects of J₂ and J₃ perturbations on the argument of perigee, right ascension and eccentricity are weakened when the eccentricity increases, simultaneously, the difference of J₂ and J₃ perturbations on argument of perigee, right ascension and argument of perigee decreases with eccentricity increasing, respectively.

In the future, satellites need to orbit the Earth much more precisely for a long period. The J₃ perturbation effect and the weight compared to J₂ perturbation in LEO can provide a theoretical reference for researchers who want to improve the control accuracy of satellite. On the other hand, the theoretical analysis and simulation results can help people to design the satellite orbit to avoid or diminish the disturbance effect of the Earth’s oblateness.

The J₃ perturbation equations of satellite orbit elements are deduced theoretically by using parametric variation method in this paper. Additionally, the comparison studies of J₂ perturbation and J₃ perturbation of the Earth’s oblateness on the satellite orbit with different initial conditions are presented.

The purpose of this paper is to design a solar sail heliocentric transfer orbit which can meet the requirements of control system and capture orbit, and to provide the change of angles for attitude control system.

Aiming at the problem of solar sail heliocentric transfer orbits design, this paper addresses the derivation of analytical optimal control law. The control laws can realize the combination of the control of each orbit element, but they can only give local optimal solution to meet the practical needs of mission. In order to solve this problem and meet the capture orbit and the attitude control system requirements, the modified genetic algorithm based on the analytical control law is introduced.

The algorithm addressed by this paper includes results closer to the global optimization, and also can meet the engineering constraints.

The analytical optimal control law can be applied to the future onboard sail control systems. The blending optimal algorithm is demonstrated to be suitable as a method of preliminary design for solar sail deep space exploration mission.

A blending optimal algorithm combining the analytical control law and genetic algorithm is proposed; the algorithm can search for global optimization based on the local optimal results of analytical control law.

This paper aims to investigate the problem of on-line orbit planning and guidance for an advanced upper stage.

The double impulse optimal transfer orbit is planned by the Lambert algorithm and the improved particle swarm optimization (IPSO) method, which can reduce the total velocity increment of the transfer orbit. More specially, a simplified formula is developed to obtain the working time of the main engine for two phases of flight based on the theorem of impulse. Subsequently, the true anomalies of the start position and the end position for both two phases are planned by the Newton iterative algorithm and the Kepler equation. Finally, the first phase of flight is guided by a novel iterative guidance (NIG) law based on the true anomaly update with respect to the geometrical relationship. Also, a completely analytical powered explicit guidance (APEG) law is presented to realize orbital injection for the second phase of flight.

Simulations including Monte Carlo and three typical orbit transfer missions are carried out to demonstrate the efficiency of the proposed scheme.

A novel on-line orbit planning algorithm is developed based on the Lambert problem, IPSO optimization method and Newton iterative algorithm. The NIG and APEG are presented to realize the designed transfer orbit for the first and second phases of flight. Both two guidance laws achieve higher orbit injection accuracies than traditional guidance laws.

Solid propellents can be useful for certain astronautical operations. The characteristics of these propellents are that they have a high total impulse to total rocket weight ratio, higher reliability, a tendency towards lower costs. The specific impulses are lower than for liquid propellents, about 180 to 200 seconds compared with 240 seconds.

The purpose of this paper is to develop a superconvergent trajectory optimization method for the design of low-thrust transfer trajectories from parking orbit to libration point orbits near the collinear libration points.

The optimization method is developed by merging the concept of Lyapunov feedback control law with the manifold dynamics. First, the whole transfer trajectory is divided into two segments, raising segment and coast segment. Then, the trajectories of each segment are described in different coordinate frames, and designed with Lyapunov feedback control law and the manifold dynamics, respectively. The Poincaré section is used as an effective tool to search the compatible patching point between these two segments on the manifold. Finally, the transfer trajectory is optimized using sequential quadratic programming.

In the numerical simulation, the proposed optimization method does not have any convergence problem. It is a fast and effective method for the very sensitive trajectory optimization problem.

The nonlinear constraints in the original trajectory optimization problem are satisfied by using the Lyapunov feedback control law; hence, the problem is transformed into a nonconstrained parameter optimization problem. The convergence problem of the sensitive optimization problem is solved thoroughly.

Lots of successful space missions require that the maneuvering spacecraft can reach the target spacecraft. Therefore, research on relative reachable domain (RRD) in target orbit for maneuvering spacecraft is particularly important and is currently a hot-debated topic in the field of aerospace. This paper aims at analyzing and simulating the RRD in target orbit for maneuvering spacecrafts with a single fixed-magnitude impulse and continuous thrust, respectively, to provide a basis for analyzing the feasibility of spacecraft maneuvering missions and improving the design efficiency of spacecraft maneuvering missions.

Based on the kinematics model of relative motion, RRD in target orbit for maneuvering spacecraft with a single fixed-magnitude impulse can be calculated via analyzing the relationship between orbital elements, position vector and velocity vector of spacecrafts, and relevant studies are introduced to compare simulation results for the same case and validate the method proposed in the paper. With analysis of the dynamic model of relative motion, the calculation of RRD in target orbit for maneuvering spacecraft with continuous thrust can be transformed as the solution of the optimal control problem, and example emulations are carried out to validate the method.

For the case with a single fixed-magnitude impulse, simulation results show preliminarily that the method is in agreement with the method in Ref. (Wen et al., 2016), which treats the same case and thus is plausibly correct and feasible. For the case with continuous thrust, analysis and simulation results confirm the validity of the proposed method. The methods based on relative motion in this paper can efficiently determining the RRD in target orbit for maneuvering spacecraft.

Both theoretical analyses and simulation results indicate that the method proposed in this paper is comparatively simple but efficient for determine the RRD in target orbit for maneuvering spacecraft swiftly and precisely.

The purpose of this paper is to present the obtained analytic solutions of maximal and minimal inter-satellite distances for flying-around satellite formation.

The relative motion equation is used to express the inter-satellite distance as the function of the orbital elements of two participating satellites for the flying-around satellite formation. Then by taking the derivative of the distance function with respect to the true anomaly, some possible extreme value points are obtained. According to the detailed analysis, the maximal and minimal distance solutions are found. By a reverse process, the expected initial differential orbital elements that generate the required extreme inter-satellite distances are also obtained.

The maximal and minimal distances of the flying-around formation can be analytically written as the functions of three initial orbital elements differences, i.e. the differential orbital inclination, the differential eccentricity and the differential right ascension. For the given maximal and minimal distances, there are lots of solutions of the initial differential orbital elements, which can produce the expected relative motions.

The solutions of the maximal and minimal inter-satellite distances are only accurate for the circular or near circular reference orbit. For the elliptic reference orbit, there is a need to develop new methods to find the analytic solutions.

The results here can be applied to design the factual flying-around formation with dimension requirements in mission analysis stage.

By using the solutions presented in this paper, the engineers can design the expected flying-around formation with required maximal and minimal inter-satellite distances in a very easy way.

The purpose of this paper is to study a finite‐thrust orbital transfer optimization problem via a new optimal control method‐Gauss pseudospectral method.

Based on the dynamic equations with the pseudo‐equinoctial elements as state variable, optimality condition is derived and the optimization problem is converted into nonlinear programming problem. Gauss pseudospectral method is used to avoid the two‐point boundary value problem. The dynamic equations are converted into static parameter optimization problem. The state variables and control variables are selected as optimal parameters at all collocation nodes. Two numerical examples of orbital transfer with coplanar and different planes are analyzed, respectively.

The simulation results demonstrate that Gauss pseudospectral method is not sensitive to the initial conditions of orbital transfer. They also show good robustness and control facility.

The precision and efficiency of this trajectory optimization method are demonstrated by applying it to space vehicle orbital transfer with finite thrust optimization problem.