Shape Formation of Spacecraft Swarms via Probabilistic Swarm Guidance Algorithm Through Local Consultation

The paper deals with the shape formation of a spacecraft swarm with collision avoidance taken into account in a circular or near-circular orbit of the Earth. To solve this control problem, a probabilistic swarm guidance algorithm is proposed to reduce the complexity due to the introduction of collision avoidance and orbital dynamics. The proposed algorithm is an improvement of the traditional probabilistic swarm guidance algorithm based on the Markov chain, and the main idea of the algorithm is that each spacecraft consults the others locally. The consultation follows a series of strategies for selecting spacecraft and migration directions such that the algorithm is suitable for the shape formation problem where each subregion requires a specific number of spacecraft. Next, the algorithm includes a complete decoupling process to integrate guidance, trajectory generation and controller design problems. The paper presents how to ensure the control convergence and convergence speed via the absorbing Markov chain theory. Furthermore, the numerical examples illustrate the efficacy of the algorithm in the shape formation of two space structures.