[Paper Review] A planning tool for optimal three-dimensional formation flight maneuvers of satellites in VLEO using aerodynamic lift and drag via yaw angle deviations

Constantin Traub, Stefanos Fasoulas+1 more|arXiv (Cornell University)|Mar 15, 2022

Spacecraft Dynamics and Control37 references17 citations

TL;DR

This paper presents a novel optimal planning tool for three-dimensional satellite formation flight in Very Low Earth Orbit (VLEO) using differential aerodynamic lift and drag via yaw angle deviations. By simultaneously controlling in-plane and out-of-plane relative motion through yaw-based force modulation, the tool minimizes orbital decay during maneuvers, thereby maximizing satellite lifetime and mission sustainability while accounting for J2 perturbations, atmospheric co-rotation, and variable atmospheric density.

ABSTRACT

Differential drag is a promising option to control the relative motion of distributed satellites in the Very Low Earth Orbit regime which are not equipped with dedicated thrusting devices. A major downside of the methodology, however, is that its control authority is (mainly) limited to the in-plane relative motion control. By additionally applying differential lift, however, all three translational degrees-of-freedom become controllable. In this article, we present a tool to flexibly plan optimal three-dimensional formation flight maneuvers via differential lift and drag. In the planning process, the most significant perturbing effects in this orbital regime, namely the J2 effect and atmospheric forces, are taken into account. Moreover, varying atmospheric densities as well as the co-rotation of the atmosphere are considered. Besides its flexible and high-fidelity nature, the major assets of the proposed methodology are that the in-and out-of-plane relative motion are controlled simultaneously via deviations in the yaw angles of the respective satellites and that the planned trajectory is optimal in a sense that the overall decay during the maneuver is minimized. Thereby, the remaining lifetime of the satellites is maximized and the practicability and sustainability of the methodology significantly increased. To the best of the authors knowledge, a tool with the given capabilities has not yet been presented in literature. The resulting trajectories for three fundamentally different relevant formation flight maneuvers are presented and discussed in detail in order to indicate the vast range of applicability of the tool.

Motivation & Objective

• Address the limitation of existing differential drag methods that only control in-plane relative motion, by enabling full 3D relative motion control.
• Develop a high-fidelity, flexible planning tool that accounts for key perturbations in VLEO, including J2 effects and atmospheric forces.
• Minimize overall orbital decay during formation maneuvers to maximize satellite remaining lifetime and mission sustainability.
• Enable practical, thruster-less formation flying for small satellites by optimizing control authority via yaw angle deviations.
• Provide a foundation for future integration with on-board model predictive control and satellite design optimization.

Proposed method

• Formulate an optimal control problem using GPOPS-II to compute minimum-decay trajectories for satellite formation maneuvers.
• Model aerodynamic forces using the standard drag and lift equations, with control achieved via commanded yaw angle deviations to generate differential forces in-plane and out-of-plane.
• Incorporate time-varying atmospheric density and Earth’s atmospheric co-rotation into the orbital dynamics model.
• Use nearly-nonsingular orbital elements (Ens) to improve numerical conditioning and stability in long-duration maneuver simulations.
• Apply the Brouwer-Lyddane transformation to convert osculating elements into mean elements for robust orbit propagation.
• Simultaneously control in-plane (via differential drag) and out-of-plane (via differential lift) relative motion through yaw angle modulation, enabling full 3D maneuvering capability.

Experimental results

Research questions

• RQ1 Can yaw angle deviations enable simultaneous control of in-plane and out-of-plane relative motion in satellite formations in VLEO?
• RQ2 How does the inclusion of atmospheric co-rotation and time-varying density affect the optimality and feasibility of aerodynamic formation maneuvers?
• RQ3 To what extent can orbital decay be minimized during 3D formation flight maneuvers using differential lift and drag via yaw control?
• RQ4 How does the proposed tool compare in performance and fidelity to prior methods relying on constant atmospheric density or bang-bang control profiles?
• RQ5 What is the potential for integrating this planning tool with on-board model predictive control for real-time trajectory tracking?

Key findings

• The proposed tool enables full three-dimensional relative motion control in VLEO by using yaw angle deviations to generate both differential drag and lift forces simultaneously.
• By minimizing overall orbital decay during maneuvers, the tool maximizes the remaining satellite lifetime, significantly enhancing mission sustainability.
• The method accounts for key perturbations such as J2 effects, atmospheric co-rotation, and variable atmospheric density, improving trajectory fidelity.
• Three distinct test cases—reconfiguration, station-keeping, and collision avoidance—demonstrate the tool’s broad applicability across fundamental mission types.
• The approach outperforms prior methods by eliminating the need for thrusters, avoiding bang-bang control, and enabling smooth, optimal control profiles.
• The tool is identified as a foundational platform for future work in on-board compensation, satellite design optimization, and high-fidelity dynamic simulation validation.