Probabilistic Collision-free Pattern Control For Large-Scale Spacecraft Swarms Around Circular Orbits

Abstract This work considers controlling large-scale spacecraft swarms to achieve complex spatial configuration. A novel distributed guidance algorithm is proposed based on Inhomogeneous Markov Chains, Probabilistic Density Guidance and Voronoi partition (IMC-PDG-Voronoi) algorithms. The physical space is partitioned into multiple bins and the density distribution of the swarm is controlled via a probabilistic approach. Then the modified Voronoi partition method is used to generate a collision-free trajectory for each agent. To apply the probabilistic control algorithm to circular Earth orbit, the periodic solution of the Clohessy-Wiltshire (C-W) equation in configuration space is transformed into a parameter space. Then a convex optimization open-loop controller with minimum fuel consumption in LVLH coordinates is designed to control the swarm to expected positions. Numerical simulations show that the algorithm can effectively guide and control large-scale spacecraft swarms to form complex configurations on circular orbits, with high precision and little cost.