Variable-time-domain neighboring optimal guidance and attitude control of low-thrust lunar orbit transfers

Abstract

Lunar orbit dynamics and transfers at low altitudes are subject to considerable perturbations related to the gravitational harmonics associated with the irregular lunar mass distribution. This research proposes the original combination of two techniques applied to low-thrust lunar orbit transfers, i.e. (i) the variable-time-domain neighboring optimal guidance (VTD-NOG), and (ii) a proportional-derivative attitude control algorithm based on rotation matrices (PD-RM). VTD-NOG belongs to the class of feedback implicit guidance approaches, aimed at maintaining the spacecraft sufficiently close to the reference trajectory. This is an optimal path that satisfies the second-order sufficient conditions for optimality. A fundamental original feature of VTD-NOG is the use of a normalized time scale, with the favorable consequence that the gain matrices remain finite for the entire time of flight. VTD-NOG identifies the trajectory corrections by assuming the thrust direction as the control input. Because the thrust direction is fixed with respect to the spacecraft, VTD-NOG generates the desired orientation pursued by the attitude control system. A proportional-derivative approach using rotation matrices (PD-RM) is employed in order to drive the actual spacecraft orientation toward the desired one. Reaction wheels are considered as the actuators that perform attitude control. Extensive Monte Carlo simulations are performed, in the presence of nonnominal flight conditions related to (i) lunar gravitational harmonics, (ii) gravitational pull of the Earth and the Sun as third bodies, (iii) unpredictable propulsive fluctuations, and (iv) errors on initial attitude. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and PD-RM control represents an accurate and effective methodology for guidance and control of low-thrust lunar orbit transfers.

Neighboring Optimal Guidance and Constrained Attitude Control for Accurate Orbit Injection

“…Errors on the initial velocity with Gaussian distribution, zero mean and standard deviation of 30 m/s are introduced as well. These errors are consistent with some values found in the scientific literature [13,14,20]. Moreover, errors on the initial attitude angles and rates are introduced.…”

“…In past researches VTD-NOG & CPD was successfully applied to lunar ascent [12]. Moreover, closely related G&C algorithms were adopted for low-thrust orbit transfers [13,14].…”

Optimization, guidance, and control of low-thrust transfers from the Lunar Gateway to low lunar orbit

“…The dynamics of the space vehicle is described by the state vector 𝒙 defined as 𝒙 = 𝒛 𝑇 𝑥 6 𝑥 7 𝑇 (10) where the last component is the mass ratio 𝑥 7 = 𝑚 𝑚 0 , and its governing equation is…”

“…Some have utilized the variational equations [7,8], and others used a combination of Cartesian coordinates and orbit elements in the dynamical framework of formation flying [9]. Another approach is the neighboring optimal guidance [10], which stands out for its ability to minimize the additional propellant required for correcting nonnominal flight conditions. However, the effectiveness of a neighboring optimal guidance technique relies on having a reference path in addition to all associated state and costate variables.…”

Nonlinear Earth orbit control using low-thrust propulsion

“…Schaub and Alfriend [33] used a combination of Cartesian coordinates and orbit elements in the dynamical framework of formation flying. Neighboring optimal control [34,35] represents an alternative option, with the remarkable feature of minimizing the additional propellant amount needed for correction of the nonnominal flight conditions. However, a neighboring optimal guidance technique requires an optimal reference path, together with all the related state and costate variables, in order to be appliable and effective.…”