Reconfiguration Of 3-Craft Coulomb Formation Based on Patched-Conic Section Trajectories

This paper investigates the non-equilibrium fixed-shape three-craft Coulomb formation reconfiguration problem. Being aware of that using the feedback control approach might result in the chattering of the charges due to the non-equilibrium nature of the system dynamics, this paper proposes a trajectory planning approach to accomplish the reconfiguration. The entire maneuver trajectories are divided into multiple phases. During each phase, only two of the three craft are charged. In this way the relative trajectory of the charged spacecraft during a certain phase is a conic section. The entire trajectories are composed of patched conics and/or straight lines. The procedures determining the three-phase maneuver strategy is developed, including a preadjusting phase and two transition phases. Numerical simulations demonstrate the effectiveness of the algorithm and the elegance of the charge histories. INTRODUCTION The concept of Coulomb formation flying (CFF) was introduced by Lyon B. King in 2001. [1] CFF utilizes the inter-spacecraft electrostatic force/forces to control the relative motion of the formation. The electric field is generated onboard by ejecting ions of a certain sign of charge using the ion engine. CFF has the following major advantages: 1. power efficient, it requires power level of only 10−3Watt; 2. clean, it does not generate the plume impingement which may cause damages to the nearby spacecraft; 3. essentially propellant-less, which may enhance the life circle of the spacecraft. On the other side, CFF poses challenges to the electromagnetic compatibility design of the spacecraft. Theoretically, CFF is suitable for the long-period, close-proximity space mission in high earth orbit or deep space. An important character of CFF is that the Coulomb forces lie only along the line-of-sight directions between spacecraft. Another challenge of CFF is that the space plasma environment shields the strength of the electrostatic force field. This effect will reduce the amount of electrostatic force acting on the neighboring charged spacecraft. The amount of shielding is characterized by the Debye length. [2] At separation distances greater than a Debye length, the intercraft Coulomb forces quickly go to zeros with exponential term. The Debye length is on the order of centimeters ∗Graduate student, Mechanical Engineering Department, University of Michigan (Ann Arbor). †Associate research fellow, Key Lab of Space Utilization, Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences. [email protected].