Parallel successive convex trajectory optimization for satellite swarms using Picard iteration-based convexification

Abstract

In this paper, a parallel distributed successive convex trajectory optimization method is developed for large-scale swarms of microsatellites with limited capabilities. First, the original nonlinear satellite dynamics are convexified using Picard iteration. Second, a discretization technique based on Chebyshev polynomials is employed to convert the optimal control problem into a series of parameterized convex subproblems. Compared to traditional step-by-step discretization methods, the modified Chebyshev–Picard iteration-based discretization decouples the satellite state at each discretization point. This decoupling enables parallel computation of satellite states across all discrete points, accelerating the computational process. Third, the decoupling and filtering strategy of collision avoidance constraints is employed to support the distributed parallel optimization of trajectories for hundreds of microsatellites and to eliminate inactive collision avoidance constraints, further enhancing scalability and computational efficiency. Finally, numerical example results indicate that the proposed algorithm boosts computational efficiency by 99% and 70% compared to GPOPS and the standard successive convexification method, respectively. Moreover, it outperforms in both convergence and solution accuracy. These findings demonstrate the potential of the proposed method for real-time trajectory optimization in large-scale satellite swarms.