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• W2030860928 abstract "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." @default.
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• W2030860928 date "2015-02-01" @default.
• W2030860928 modified "2023-09-27" @default.
• W2030860928 title "Autonomous Lunar Orbit Rendezvous Guidance Based on J2-Perturbed State Transition Matrix" @default.
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• W2030860928 doi "https://doi.org/10.2514/1.g000813" @default.
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