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Fuel-Optimal Formation Reconfiguration by Means of Unidirectional Low-Thrust Propulsion System

Ahmed Mahfouz, Gabriella Gaias, Florio Dalla Vedova, Holger Voos

TL;DR

This work tackles autonomous relative orbit reconfiguration for a two-satellite formation where only one deputy carries a single unidirectional low-thrust thruster. It casts the fuel-optimal trajectory problem as a convex optimization by exploiting a ROE-based linearized model and affine relaxations, enabling a QP formulation that accommodates long no-thrust periods and planned attitude slews. An MPC-like loop closes the control by re-optimizing as needed while incorporating navigation and actuator uncertainties through surrogate models. The approach demonstrates robust fuel efficiency and reliable convergence in high-fidelity simulations, outperforming a reference MPC in terminal accuracy and proving practicality for onboard implementation on Triton-X within LuxSpace’s AuFoSat framework.

Abstract

The use of electric low-thrust propulsion systems for orbit maneuvers is becoming a popular choice among satellite manufacturers due to their inherent merits over their chemical counterparts. Many designers choose to incorporate multiple of such thrusters to insure omnidirectional orbit maneuverability, while others choose to equip their satellite with only one thruster nozzle, aiming to reduce the required power, weight, and size of the orbit control system. This paper proposes guidance and control schemes to address the problem of autonomous optimal relative orbit reconfiguration for a formation of two satellites, one of which utilizes a single low-thrust throttleable nozzle. Such under-actuated orbit control system requires the controlled spacecraft to constantly slew to direct the nozzle to the desired thrust direction. These redirection attitude maneuvers are treated within the guidance layer by accommodating recurrent no-thrust periods during which slew maneuvers take place. The control loop is then closed with an MPC-like scheme. The main motivation of this article is to support the future missions of LuxSpace's flagship satellite, Triton-X. Since the proposed guidance and control schemes are meant to answer realistic market needs, they are designed to have some specific qualities that makes them attractive from the practical point of view. Namely, they require minimal computational loads, besides being able to accommodate operational time constraints, e.g. no thrusting during eclipse or during ground contact, within the guidance layer.

Fuel-Optimal Formation Reconfiguration by Means of Unidirectional Low-Thrust Propulsion System

TL;DR

This work tackles autonomous relative orbit reconfiguration for a two-satellite formation where only one deputy carries a single unidirectional low-thrust thruster. It casts the fuel-optimal trajectory problem as a convex optimization by exploiting a ROE-based linearized model and affine relaxations, enabling a QP formulation that accommodates long no-thrust periods and planned attitude slews. An MPC-like loop closes the control by re-optimizing as needed while incorporating navigation and actuator uncertainties through surrogate models. The approach demonstrates robust fuel efficiency and reliable convergence in high-fidelity simulations, outperforming a reference MPC in terminal accuracy and proving practicality for onboard implementation on Triton-X within LuxSpace’s AuFoSat framework.

Abstract

The use of electric low-thrust propulsion systems for orbit maneuvers is becoming a popular choice among satellite manufacturers due to their inherent merits over their chemical counterparts. Many designers choose to incorporate multiple of such thrusters to insure omnidirectional orbit maneuverability, while others choose to equip their satellite with only one thruster nozzle, aiming to reduce the required power, weight, and size of the orbit control system. This paper proposes guidance and control schemes to address the problem of autonomous optimal relative orbit reconfiguration for a formation of two satellites, one of which utilizes a single low-thrust throttleable nozzle. Such under-actuated orbit control system requires the controlled spacecraft to constantly slew to direct the nozzle to the desired thrust direction. These redirection attitude maneuvers are treated within the guidance layer by accommodating recurrent no-thrust periods during which slew maneuvers take place. The control loop is then closed with an MPC-like scheme. The main motivation of this article is to support the future missions of LuxSpace's flagship satellite, Triton-X. Since the proposed guidance and control schemes are meant to answer realistic market needs, they are designed to have some specific qualities that makes them attractive from the practical point of view. Namely, they require minimal computational loads, besides being able to accommodate operational time constraints, e.g. no thrusting during eclipse or during ground contact, within the guidance layer.
Paper Structure (8 sections, 14 equations, 14 figures, 3 tables, 1 algorithm)

This paper contains 8 sections, 14 equations, 14 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Dynamical model
  3. Guidance
  4. problem formulation
  5. Parameters sensitivity analysis
  6. Guidance scheme validation
  7. Closing the loop
  8. Conclusion

Figures (14)

  • Figure 1: Graphical representation of the low-thrust guidance scheme
  • Figure 2: Feasibility region comparison between the original COP (Problem \ref{['prob:original_formulation']}) and the QP problem (Problem \ref{['prob:QP_formulation']})
  • Figure 3: Sensitivity of the system to $T_{f}$ and $T_{n}$ variations
  • Figure 3: Comparison between the proposed and the reference MPCs
  • Figure 4: Optimized dimensional ROE profile
  • ...and 9 more figures