结合协方差控制的卫星集群随机轨迹凸优化方法

A fast stochastic trajectory optimization method that integrates convex optimization and covariance control is proposed for addressing satellite cluster trajectory optimization under uncertainty. The trajectory optimization problem is modeled as a stochastic optimal control framework, incorporating nonlinear dynamics and non-convex constraints, where chance constraints are employed to define collision avoidance and control limitations. Following system linearization, a covariance control strategy is adopted. By utilizing variable substitution and relaxation techniques, convexification is applied to the covariance propagation equations and chance constraints, thereby transforming the original non-convex problem into a deterministic convex optimization problem involving state mean, covariance and feedback gains. Subsequently, efficient trajectory solutions are obtained through a convex optimization framework. Numerical simulation results indicate that compared to traditional deterministic open-loop trajectory optimization methods, the proposed approach significantly reduces terminal state covariance while satisfying path and control constraints. Monte Carlo simulations further confirm the probabilistic reliability—namely, the capability to satisfy chance constraints—of the method under uncertain conditions, thereby validating its applicability for rapid trajectory planning tasks involving satellite clusters.