LOW-THRUST ORBIT TRANSFER BY COMBINING GENETIC ALGORITHM WITH REFINED Q-LAW METHOD

A new orbit transfer method is presented by combining the genetic algorithm（GA）with the refined Q-law method.Considering the energy consumption,the relative thrust efficiency is introduced as a threshold deciding whether to thrust or coast.GA is used to achieve the global time-optimal orbit transfer.The trajectory optimization problem is transformed into the constraint parameter optimization problem,thus the nonlinear two-point boundary value problem is avoided.The refined Q-law method integrated with the fuzzy logic control is adopted for the end course,the vibration is avoided and the high precision is achieved.The numerical simulation of satellite orbit transfer is implemented.Results show that the new method can achieve the time-optimal orbit transfer and the low energy consumption,thus improving the transfer precision.

Optimal aeroassisted symmetric transfer between coplanar elliptical orbits

The problem of optimal aeroassisted symmetric transfer between elliptical orbits is concerned.The complete trajectory is assumed as consisting of two impulsive velocity changes at the beginning and the end of an interior atmospheric subarc,where the vehicle is controlled via the lift coefficient and thrust.The corresponding dynamic equations are built and bounded controls are considered.For the purpose of optimization computation,the equations are normalized.In order to minimize the total fuel consumption,the geocentric radius of initial elliptical transfer orbital perigee and controls during atmospheric flight should all be optimized.It is an optimal control problem which involves additional parameter optimization.To solve the problem,a two-level optimization method denoted by ＂genetic algorithm ＋ Gauss pseudospectral method＂ is adopted：the genetic algorithm is used for parameter optimization and the Gauss pseudospectral method is used for optimal control problems.The flow chart of simulation is given.On this basis,the issue of more realistic modeling with two finite-thrust subarcs in the nonatmospheric part of the trajectory is simultaneously addressed.The orbital transfer problem is transformed to three continuous optimal control problems,and the constraints at different times are given,which are respectively solved by using the Gauss pseudospectral method.The obtained numerical results indicate that the optimal thrust control is of bangbang type.The minimum-fuel trajectory in the atmosphere consists of aeroglide,aerocruise and aeroglide.They are compared with the results of pure impulsive model,and the conclusions that a significant fuel saving will be achieved by synergetic maneuver are drawn.

Near-optimal cumulative longitude low-thrust orbit transfer

The indirect method for the continuous low-thrust near minimum cumulative longitude orbit transfer problem is addressed.The movement of the satellite is described by the Gauss equation using the modified equinoctial elements and replacing time as the system independent variable by the cumulative longitude.The maximum principle is adapted to design the optimal control in order to minimize the final cumulative longitude, and the twopoint-boundary-value problem is derived from the orbit transfer problem.The single shooting method is applied in a numerical experiment, and the simulations demonstrate that the orbit transfer mission is fulfilled and the product of the maximal thrust and the minimum cumulative longitude is near constant.

Perturbed low-thrust geostationary orbit transfer guidance via polynomial costate estimation

This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit.The Earth’s oblateness perturbation and shadow are taken into account.It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time,including high guidance optimality,robustness,and onboard computational efficiency.In this work,a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified,which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation.Based on this relationship,the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged trajectory.Five polynomial regression models are trained on the training dataset and are regarded as the costate estimators.In the transfer,the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any time.Moreover,all these computations onboard are analytical.The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality,robustness,and onboard computational efficiency.

Impulsive orbit control for spacecraft around asteroid

An impulse feedback control law to change the mean orbit elements of spacecraft around asteroid is presented. First, the mean orbit elements are transferred to the osculating orbit elements at the burning time. Then, the feedback control law based on Gauss’s perturbation equations of motion is given. And the impulse control for targeting from the higher circulation orbit to the specified periapsis is developed. Finally, the numerical simulation is performed and the simulation results show that the presented impulse control law is effective.

Midcourse correction of Earth-Moon distant retrograde orbit transfer trajectories based on high-order state transition tensors

Midcourse correction design is key to space transfers in the cislunar space.Autonomous guidance has garnered significant attention for its promise to decrease the dependence on ground control systems.This study addresses the problem of midcourse corrections for Earth-Moon transfer orbits based on high-order state transition tensors(STTs).The scenarios considered are direct Earth-Moon transfers and low-energy transfers to lunar distant retrograde orbits(DROs),where the latter involve weak stability boundary(WSB)and lunar gravity assist(LGA)techniques.Semi-analytical formulas are provided for computing the trajectory correction maneuvers(TCMs)using high-order STTs derived using the differential algebraic method.Monte Carlo simulations are performed to evaluate the effectiveness of the proposed approach.Compared with existing explicit guidance algorithms,the STT-based approach is much cheaper computationally and features fewer final position errors.These results are promising for fast and efficient orbital autonomous correction guidance approaches in the cislunar space.

Optimal impulsive rendezvous for highly elliptical orbits using linear primer vector theory

In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.

Systematic Direct Approach for Optimizing Continuous-thrust Earth-orbit Transfers

This article presents a systematic direct approach to carry out effective optimization of a wide range of continuous-thrust Earth-orbit transfers with intermediate-level thrust acceleration,including minimum-time (with a single burn arc) and mini-mum-fuel (with multiple burn arcs) transfers. With direct control parameterization,in which the control steering programs of burn arcs are interpolated through a finite number of nodes,the optimal control problem is converted into the parameter optimi-zation proble...

Direct Optimization of Low-thrust Many-revolution Earth-orbit Transfers

Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

The two-body orbital transfer problem from an elliptic parking orbit to an excess veloc-ity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. First, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse trajectory.

Cleaning space debris with a space-based laser system

High-energy pulsed laser radiation may be the most feasible means to mitigate the threat of collision of a space station or other valuable space assets with orbital debris in the size range of 1–10 cm. Under laser irradiation, part of the debris material is ablated and provides an impulse to the debris particle. Proper direction of the impulse vector either deflects the object trajectory or forces the debris on a trajectory through the upper atmosphere, where it burns up. Most research concentrates on ground-based laser systems but pays little attention to space-based laser systems.There are drawbacks of a ground-based laser system in cleaning space debris. Therefore the placement of a laser system in space is proposed and investigated. Under assumed conditions,the elimination process of space debris is analyzed. Several factors such as laser repetition frequency, relative movement between the laser and debris, and inclination of debris particles which may exercise influence to the elimination effects are discussed. A project of a space-based laser system is proposed according to the numerical results of a computer study. The proposed laser system can eliminate debris of 1–10 cm and succeed in protecting a space station.

Artificial equilibrium points and bi-impulsive maneuvers to observe 243 Ida

In the restricted three-body problem,the traditional Lagrange points L1 and L2 are the only equilibrium points near the asteroid 243 Ida.The thrust generated by a solar sail over a spacecraft enables the existence of new artificial equilibrium points,which depend on the position of the spacecraft with respect to the asteroid and the attitude of the solar sail.Such equilibrium points generate new spots to observe the body from above or below the plane of motion.Such points are very good observational locations due to their stationary condition.This work provides a preliminary analysis to observe Ida through the use of artificial equilibrium points as spots combined with transfer maneuvers between them.Such combination can be used to observe the asteroid from more different points of view in comparison to fixed ones.The analyses are made for a spacecraft equipped with a solar sail and capable of performing bi-impulsive maneuvers.The solar radiation pressure is used both to maintain the equilibrium condition and to reduce the costs of the transfers and/or to create transfers with longer duration.This is a new aspect of the present research,because it combines the continuous thrust with initial and final small impulses,which are feasible for most of the spacecraft,because the magnitudes of the impulses are very low.These combined maneuvers may reduce the transfer times of the maneuvers in most of the cases,compared with the maneuvers based only on continuous thrust.Several options involved in these transfers are shown,like to minimize the fuel spent(Dv)as a function of the transfer time or to extend the duration of the travel between the points.Extended transfer times can be useful when observations are required during the transfers.