Multi-Sphere Method for modeling spacecraft electrostatic forces and torques

The use of electrostatic (Coulomb) actuation for formation flying is attractive because non-renewable fuel reserves are not depleted and plume impingement issues are avoided. Prior analytical electrostatic force models used for Coulomb formations assume spherical spacecraft shapes, which include mutual capacitance and induced effects. However, this framework does not capture any orientation-dependent forces or torques on generic spacecraft geometries encountered during very close operations and docking scenarios. The Multi-Sphere Method (MSM) uses a collection of finite spheres to represent a complex shape and analytically approximate the Coulomb interaction with other charged bodies. Finite element analysis software is used as a truth model to determine the optimal sphere locations and radii. The model is robust to varying system parameters such as prescribed voltages and external shape size. Using the MSM, faster-than-realtime electrostatic simulation of six degree of freedom relative spacecraft motion is feasible, which is crucial for the development of robust relative position and orientation control algorithms in local space situational awareness applications. To demonstrate this ability, the rotation of a cylindrical craft in deep space is simulated, while charge control from a neighboring spacecraft is used to de-spin the object. Using a 1 m diameter craft separated by 10 m from a 3 by 1 m cylindrical craft in deep space, a 2 deg/s initial rotation rate can be removed from the cylinder within 3 days, using electric potentials up to 30 kV. (c) 2012 COSPAR. Published by Elsevier Ltd. All rights reserved.