The Journal of the Astronautical Sciences

, Volume 65, Issue 4, pp 377–399 | Cite as

Volume Multi-Sphere-Model Development Using Electric Field Matching

  • Gabriel Ingram
  • Joseph HughesEmail author
  • Trevor Bennett
  • Christine Reilly
  • Hanspeter Schaub


Electrostatic actuation is the process of charging two spacecraft and using the resulting Coulomb interaction to exert touchless forces and torques between the two spacecraft. For all electrostatic actuation concepts, fast and accurate models for the electrostatic force and torque are needed. The Volume Multi-Sphere Method (VMSM) seeks the optimal placement and radii of a small number of equipotential spheres to accurately model the electrostatic force and torque on a conducting space object. Prior work optimized the VMSM models by varying the radii and position of the model spheres to match the force and torque produced by a finite element truth model. This process is challenging due to finite element model errors and smoothness considerations, as well as because the force solutions are dependent on the particular probe geometry chosen. This paper investigates fitting of VMSM models to Surface-MSM (SMSM) generated electrical field data, removing modeling dependence on probe geometry while significantly increasing performance and speed. A proposed electric field matching cost function is compared to a force and torque cost function. The inclusion of a self-capacitance constraint is explored and 4 degree-of-freedom VMSM models generated using electric field matching are investigated. The resulting E-field based VMSM development framework is illustrated on a box-shaped hub with a single solar panel. Despite the complex non-symmetric spacecraft geometry, elegantly simple 2-sphere VMSM solutions provide force and torque fits within a few percent.


Electrostatics Proximity opperations Orbital debris 



This research is funded through a grant No. FA9550-15-1-0407 from the Air Force Office of Space Research.


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Copyright information

© American Astronautical Society 2018

Authors and Affiliations

  • Gabriel Ingram
    • 1
  • Joseph Hughes
    • 1
    Email author
  • Trevor Bennett
    • 1
  • Christine Reilly
    • 1
  • Hanspeter Schaub
    • 1
  1. 1.Department of Aerospace Engineering SciencesUniversity of ColoradoBoulderUSA

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