Abstract
In this paper, we consider controlling a spacecraft swarm in a circular low Earth orbit (LEO) via controlling its density distribution. We build on our previous research on decentralized density feedback control, which generates smooth velocity fields as a function of time and position. Performing kernel density estimation, each spacecraft compares desired density profiles with local density estimates, and invokes heat equation based feedback controller to generate the velocity commands to be tracked. Governed by Clohessy-Wiltshire equations, each spacecraft uses the velocity commands to calculate the next vehicle state and two consecutive ∆V commands to transition between states described in the local-vertical local-horizontal (LVLH) frame. The continuity of the velocity field facilitates smooth and organized behavior for spacecraft and as the numerical results illustrate, the swarm density distribution converges to the desired density distributions.
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