Electrostatic Spacecraft Collision Avoidance Using Piecewise-Constant Charges

This paper develops a three-phase piecewise-constant spacecraft charge maneuver to achieve short-range collision avoidance with a symmetric relative trajectory. This symmetric trajectory guarantees collision avoidance, restores the original relative-motion direction, and keeps the relative kinetic energy level the same as the initial kinetic energy level. The paper first presents an analytical solution to calculate a unique symmetric trajectory when the middle phase is a circular trajectory. Next, a general symmetric-trajectory programming strategy is developed in which the middle phase can be any conic section. Four constraints are required to guarantee a symmetric collision-avoidance trajectory, and five independent variables are required to solve the problem. This leaves one degree of freedom that is used to optimize the trajectory subject to specific cost charge functions. There is a duality in the charge solution when solving for the open-loop trajectory, with one of the solutions being false. This is addressed by properly initializing and confining the region of the numerical search routine. Minimum charge criteria are determined to avoid a collision by analyzing the geometric properties of the two-body system and comparing the results from circular transitional trajectory calculations.

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