Stochastic Trajectory Optimization for Satellite Swarm Reconfiguration via Convex Optimization

In recent years, large-scale satellite swarms, such as Starlink, OneWeb, and China’s Qianfan project, have drawn significant global attention. Trajectory optimization for satellite swarm reconfiguration is critical to space missions but presents two key challenges. First, the large number of satellites, collision avoidance constraints, and limited computational resources of microsatellites necessitate highly efficient algorithms. Second, uncertainties in real-world missions may cause deviations from planned trajectories or even collisions, requiring robust algorithms to ensure mission safety. Therefore, developing a computationally efficient and robust trajectory optimization method under uncertainty is of great importance. This paper proposes a fast stochastic trajectory optimization method for large-scale satellite swarm reconfiguration based on a convex optimization approach. First, the trajectory optimization problem is formulated as a stochastic optimal control problem with nonlinear dynamics and nonconvex constraints. Uncertainties are incorporated through chance constraints to enforce collision avoidance and control limits. Second, the original nonlinear stochastic dynamics, considering initial state uncertainties and external disturbances, are transformed into linear deterministic dynamics using first-order Taylor expansion and covariance analysis. By applying variable substitution and relaxation techniques, the covariance propagation equations and nonconvex chance constraints are convexified, converting the original covariance control problem into a deterministic convex problem. The resulting convex subproblems are then solved using convex optimization techniques. Numerical simulations demonstrate that the proposed method significantly reduces the final state covariance and exhibits strong robustness and adaptability under uncertainty. The proposed method enables the rapid generation of safe and robust trajectories for satellite swarms and holds potential applications in other aerospace domains with inherent uncertainties, such as rocket landing and spacecraft rendezvous.