Formation establishment and reconfiguration using differential elements in J2-perturbed orbits

Abstract

A practical algorithm is developed for on-board plan ning ofn-impulse fuel-optimal maneuvers for establishment and reconfiguration of spacecraft formations. The method is valid in circular and elliptic orbits and includes first-order secular h effects. The dynamics are expressed in terms of differential mean orbital elements, and relations are provided to allow the formation designer to transform these into intuitive geometric quantities for visualization and analysis. The maneuver target ing problem is formulated as an optimal control problem in both continuous and discrete time. The continuous-time formulation cannot be solved directly in an efficient manner, and the discrete time formulation, which has an analytical solution, does not directly yield the optimal thrust times. Therefore, a practi cal algorithm is designed by iteratively solving the discrete time formulation while using the continuous-time necessary conditions to refine the thrust times until they converge to the optimal values.Simulation results are shown for a variety of reconfiguration maneuvers and reference orbits, including simulations with and without navigation errors for the NASA CubeSat Proximity Operations Demonstration mission.

Simplified Maneuvering Strategies for Rendezvous in Near-Circular Earth Orbits

“…In their study [8], De Iuliis et al identified fuel-optimal low-thrust profiles capable of executing formation reconfiguration, utilizing an improved version of the well-known Legendre pseudospectral method. On the other hand, Roscoe et al [9] employed primer vector theory [10,11] to achieve impulsive orbital reconfiguration in the relative motion between two agents. Their method entails iteratively addressing the discrete fuel optimal guidance problem to match the optimal times of the continuous formulation.…”

Vision-Based CubeSat Closed-Loop Formation Control in Close Proximities

“…Another aspect of formation control of small satellites is the prescription and planning of the needed formation maneuvers at di erent situations. Planning of n-impulse fuel-optimal maneuvers for establishment and recon guration of spacecraft formations are considered for circular and elliptic orbits [6]. Collision avoidance maneuvers for a swarm of satellites in formation, which return to their original con guration after a threat has passed, is considered in [7] using biological rules of avoidance.…”

Comparison of Multiple Spacecraft Configuration Designs for Coordinated Flight Missions

“…The goal of this work is to evaluate if and how much the station keeping logic could be beneficial for coordinated flight missions characterized by a different number of spacecraft and different distance boundaries. To study and implement the station keeping logic, it can be advantageous expressing the relative motion through relative orbital elements, since the orbital elements have a slow variation over time and corrections of specific elements with theoretically no effect on the others can be obtained using impulsive control (see e.g., [25,24,23,18,3,22,12]).…”