Spacecraft Formation With J₂ Perturbation via Real-Time Probabilistic Swarm Guidance Framework

This article deals with the shape formation for a spacecraft swarm subject to J₂ perturbation. To solve this control problem, this article presents a real-time probabilistic swarm guidance framework. Its top-level strategy based on the absorbing Markov chain theory is free of target assignment and is reconfigurable, scalable, and robust to some faults. Moreover, the nonlinear drift force induced by J₂ perturbation is taken into account in the trajectory generation algorithm through the improved dynamical feasibility penalty function. Because the gradients of the improved penalty function can be derived analytically, the desired trajectory is obtained by solving an unconstrained optimization problem. Its bottom-level controller is implemented by the model-predictive control algorithm to track the desired trajectory. With limited information exchange, the spacecraft formation problem subject to J₂ perturbation is solved in real time by different levels of algorithm running simultaneously. Finally, numerical examples and experimental results illustrate the efficacy of the improved dynamical feasibility penalty function and the proposed framework.