Jingyang Li

Analysis of Two-Segment Lunar Free-Return Trajectories

A precise and convenient procedure for designing the two-segment lunar free-return trajectory is presented in this paper. The trajectory characteristics are analyzed to support the lunar mission design associated with the higher inclination lunar approaches and safer returns from the moon. The concise procedure is established based on the matched conic model. An analytical algorithm is developed to compute the spacecraft state at the lunar sphere of influence to complete the conic matching. An iteration process is then adopted to generate favorable initial solutions that satisfy the constraints at injection, perilune, and Earth-entry interface. Orbital launch windows for departure from Earth, lunar encounter, and returns to Earth are established in the years 2024 and 2034. These years are chosen due to the moon’s inclination reaching a maximum in 2024 and it reaching a minimum in 2034 during a Metonic cycle. This novel trajectory enables greater lunar surface coverage than standard free-return trajectorie...

Generation of Multisegment Lunar Free-Return Trajectories

To support the mission and trajectory design problems associated with the Earth-to-moon trajectories for a crewed vehicle, a multisegment lunar free-return trajectory is proposed. The multisegment free return differs from hybrid profiles in that it consists of free-return sections only; however, it maintains the advantages of hybrid returns. The analysis presented here is limited to a two-segment class of trajectories. In this profile, the translunar injection puts the spacecraft onto a free-return trajectory with a high perilune altitude; then, the spacecraft performs a transfer maneuver onto a new translunar coast trajectory that has an approximate perilune altitude of 100 km. This new translunar coast trajectory is also designed as a free-return trajectory that can perform a safe return. With a finite sphere of influence model, an analytical model of the multisegment free-return trajectories is developed by the matched-conic technique. Characteristics of the injection velocity, flight time, and lunar a...

Launch window for manned Moon‐to‐Earth trajectories

Purpose – The purpose of this paper is to establish an orbital launch window for manned Moon‐to‐Earth trajectories to support Chinas manned lunar landing mission requirements of high‐latitude landing and anytime return, i.e. the capability of safely returning the crew exploration vehicle at any time from any lunar parking orbit. The launch window is a certain time interval during which the transearth injection may occur and result in a safe lunar return to the specified landing site on the surface of the Earth.Design/methodology/approach – Using the patched conic technique, an analytical design method for determining the transearth trajectories is developed with a finite sphere of influence model. An orbital launch window has been established to study the mission sensitivities to transearth trip time and energy requirements. The results presented here are limited to a single impulsive maneuver.Findings – The difference between the results of the analytical model and high‐fidelity model is compared. This ...

Autonomous Lunar Orbit Rendezvous Guidance Based on J2-Perturbed State Transition Matrix

AUTONOMOUS lunar rendezvous missions have drawn increasing interest in recent years due to the future human and robotic lunar exploration applications [1,2]. For example, the Chinese lunar exploration mission phase III, scheduled for launch in 2017, is required to perform a soft landing and autonomous rendezvous near the Moon to test the key technologies that are required for manned lunar missions [1]. The Orion crew exploration vehicle, NASA’s next-generation lunar transportation vehicle, is being designed to perform rendezvous and docking with the lunar lander in low lunar orbit [2]. In the past decade,much attention has been paid to the development of rendezvous guidance, navigation, and control algorithms (e.g., [3,4]). Typically, the initial guidance policy, based on the simple Clohessy–Wiltshire (C-W) rendezvous solutions [5], provides estimates of the impulse magnitudes and maneuver times [6]. However, modeling errors introduced by linearization and the underlying assumption of a two-body circular reference orbit result in inaccuracies of the long-term relative motion prediction and fuel requirements for maneuvers. Relative motion equations considering higher-order differential two-body gravity terms have also been analyzed by Sengupta et al. [7], Karlgard and Lutze [8], and Richardson and Mitchell [9] in recent years. Differential equation models accounting for the J2 geopotential disturbance have been developed in several studies (e.g., [10,11]). The disadvantage of the linear differential equation models is that they contain periodic coefficients and hence, in general, cannot be solved analytically. A comprehensive state transition matrix (STM) accounting for J2 was developed by Gim and Alfriend [12] (the GA-STM) for propagating the relative motion states for elliptic reference orbits. The curvilinear coordinate system was used instead of the Cartesian local-vertical-local-horizontal (LVLH) frame to minimize the linearization errors in the transformation between relative state and differential orbital elements. However, the elements of the GA-STM are complicated due to the shortand long-period effects of J2. The long-period effects of the J2 disappear and the short-period terms are considerably simplified for a mean circular orbit. With due consideration of onboard usage, this simplification is adopted in this paper to model the relative motion of vehicles with respect to a near-circular reference orbit [13]. The magnitudes of the first few nonspherical gravitational perturbation coefficients for the Moon are J2 2.03354 × 10−4, J3 8.47453 × 10−6, J4 −9.64229 × 10−6, and C22 2.24051 × 10−5 [14]. Although the lunar oblateness coefficient J2 is not as dominant as it is for the Earth, themagnitudes of the other harmonic coefficients are lower by at least one order. Hence, the use of the GA-STM captures the effects of the most significant perturbation analytically. Several studies have investigated minimum propellant rendezvous maneuvers using optimal control theory [15–18]. Fixed-time, fueloptimal rendezvous problems were investigated through the solutions for the linear boundary value problem and primer vector equations by Lion and Handelsman [16], Carter and Humi [17], and Prussing [18]. The C-W model has been adopted in these studies to obtain analytical solutions to the rendezvous equations. Although Kechichan [19] included the first-order nonspherical Earth effects in his treatment of the optimal orbital transfer problem, the method is based on numerical integration of the nonlinear equations of motion. In this paper, a precise, convenient optimization method is proposed for vehicle rendezvous guidance in a lunar orbit by using the simplified GA-STM (SGA-STM), obtained by retaining only the O e non-J2 terms and neglecting theO eJ2 terms. It is adopted for propagating the relative motion states with respect to a near-circular lunar parking reference orbit in a curvilinear coordinate system. Numerical simulations are provided to evaluate the accuracy of the relative states propagated by SGA-STM. The results show that the predicted relative states are in good agreement with the results obtained from a numerical integration approach. For onboard applications, the necessary gradients of cost and constraints are derived with linear perturbation theory, and a closed-form expression is derived for computing gradients along a general n-impulse trajectory. A concise and revealing form of optimal guidance strategy is developed to accomplish minimum-fuel, multi-impulse rendezvous. A numerical example is provided in this paper to demonstrate the performance of the optimal targeting method using a high-fidelity rendezvous simulation. Furthermore, the finite-burn thruster model available in the Satellite Tool Kit-9 (STK-9) simulation environment is employed to ascertain the validity of the impulsive-thrust approximation. Because the iterates of the optimization process are obtained without recourse to numerical integration of the equations of motion, it is believed that this methodology will be suitable for onboard control and update of guidance commands.

Autonomous Rendezvous Architecture Design for Lunar Lander

A precise and convenient targeting architecture for accomplishing the rendezvous of a lunar lander with an orbiter in a near-circular lunar parking orbit is proposed in this paper. This procedure enables a systematic design and refinement of the number of thrust impulses, their application times, and the mission duration. The simplicity and accuracy of this targeting procedure makes it well suited for onboard use during real-time control and strategy reconstruction operations. A concise and revealing form of the linearized rendezvous equations is derived based on the Clohessy–Wiltshire model, as adopted to generate feasible initial solutions to satisfy the demands of rapid mission analysis and design. A three-step iterative procedure is adopted to determine the minimum-impulse control strategies for autonomous rendezvous, involving the progress of the solution from a linear model to a nonlinear, two-body model and finally to a high-fidelity model. The two-body model is introduced as an intermediary to ena...