Nonlinear Earth orbit control using low-thrust propulsion

Abstract

This research is focused on the definition, analysis, and numerical testing of an effective nonlinear orbit control technique tailored to compensating orbit perturbations, as well as possible errors at orbit injection of low-and medium-altitude Earth-orbit satellites. A general, systematic approach to real-time orbit control is presented, under the assumption that the satellite of interest is equipped with a steerable and throttleable low-thrust propulsion system. Two different operational orbits are considered: (a) very-low-altitude Earth orbit and (b) mediumaltitude Earth orbit. A feedback control law based on Lyapunov stability theory is proposed and tested. Some remarkable stability properties are established analytically. Then, the overall performance of the nonlinear control at hand is investigated for cases (a) and (b), over 5 years. The effect of satellite eclipsing on available electrical power is considered as well. For mission scenario (a), suitable tolerances on the desired (nominal) conditions allow substantial savings in terms of propellant requirements.

Mars Constellation Design and Low-Thrust Deployment Using Nonlinear Orbit Control

“…Low-thrust propulsion leads to substantial propellant savings, at the price of increasing (even considerably) the time of flight. Recently, nonlinear control was proven to be an effective option for real-time feedback guidance in Earth orbit transfers, as well as for orbit maintenance [10,[16][17][18] This section is focused on low-thrust orbit dynamics, using the modified equinoctial elements to describe the dynamics of 4 carrier vehicles, modeled as point masses. Orbital motion of each carrier is mainly affected by the Martian gravitational field.…”

“…If ∶= 1 + l cos q + m sin q , the orbit (instantaneous) radius equals r = p∕ . The governing equations for the modified equinoctial elements are [17,19,20] where x 6 ≡ q and z ∶= x 1 x 2 x 3 x 4 x 5 T ≡ p l m n s T , whereas M represents the Mars gravitational parameter and…”

Optimal Q-laws via reinforcement learning with guaranteed stability

“…13 A very thorough discussion on the implications of this for trajectory design using nonlinear control can be found in Ref. 20.…”

“…This also included solar radiation pressure and third-body effects. Pontani et al 2021 20 have explored their stability in the presence of perturbations for the station-keeping and guidance problem.…”

Low-Thrust Orbit Dynamics and Periodic Trajectories in the Earth–Moon System

“…However, their convergence is strongly problem-dependent and usually requires availability of an approximate guess solution. Nonlinear orbit control [18,19] represents an alternative, very interesting approach capable of identifying a feedback control law for the thrust direction and magnitude, in relation to the instantaneous spacecraft position and velocity.…”