Stabilization of Satellite Motion Relative to a Coulomb Spacecraft Formation

Coulomb spacecraft are satellites that can actively control their electrostatic charge and thus exploit intervehicle electrostatic forces to control tight relative motion. The stabilization problem of a cluster of unequal Coulomb spacecraft is studied. Previous research has developed a nonlinear control law to stabilize the relative motion of one satellite relative to another. With only two spacecraft present, with equal mass and charging limits, Newton’s second law greatly simplified the control development. This control strategy is generalized here to stabilize the relative motion of a satellite relative to a larger cluster of Coulomb spacecraft with unequal satellite masses and individual charge saturation limits. The chief cluster motion can be either circular or elliptic. The nonlinear control methodology exploits an orbit element difference description of the satellite relative motion. Although the control is shown to stabilize the relative motion of a Coulomb satellite about any set of desired orbit element differences, convergence is shown thus far only when controlling exclusively the semimajor axis differences. Thus, this control is able to achieve bounded relative motion of the Coulomb satellite, even in the presence of saturation constraints. A simple structured control approach is numerically investigated to control the entire cluster. Numerical simulations illustrate the relative motion control behavior with the cluster chief or center of mass being on an elliptic high Earth orbit.