Computationally Efficient Collision-Free Trajectory Planning of Satellite Swarms Under Unmodeled Orbital Perturbations

This paper studies the problem of collision-free trajectory planning for a satellite swarm reconfiguration under perturbations and modeling uncertainties in a low Earth orbit (LEO). Determining exact trajectory planning solutions is computationally heavy as they require solving a mixed-integer nonlinear program owing to i) nonlinear relative dynamic models of satellites, ii) fuel-optimal assignment of satellites on the final formation, and iii) nonconvex collision avoidance constraints. To address these, first, a suitable linear model for trajectory planning is identified by quantifying modeling accuracy associated with various models capturing LEO perturbations. The effects of any residual modeling errors in the path prediction are mitigated by shrinking-horizon model-predictive feedback control, which updates the control command based on the latest satellite measurements. Secondly, an optimal swarm configuration is efficiently computed by decoupling the target-assignment algorithm from the trajectory optimization problem. Based on the estimated fuel expenditure for each satellite-target pairing, the target-assignment algorithm selects a configuration with minimal fuel consumption. Lastly, to determine collision-free, fuel-optimal maneuvers, two novel trajectory planning approaches, namely, distributed and decentralized trajectory optimization, are presented. While the former iteratively searches for collision-free feasible paths to optimal terminal configuration, the latter computes a near-optimal configuration with collision-free paths.