Trajectory Planning of Spacecraft Swarm Reconfiguration Using Reachable Set-based Collision Constraints

This work presents the reachable set (RS)-based trajectory planning algorithm for spacecraft swarm reconfiguration with collision avoidance and fuel-effective consumption. To generate safe trajectories successfully for a large-scale spacecraft, an RS-based collision-avoidance constraint is first exploited in this work. By involving this constraint in the discrete convex optimization, the future collision regions among the spacecraft can be precisely monitored in advance, which can reduce the conservation of the collision-free regions. Meanwhile, a sufficient and necessary condition ensuring that any two RSs have no intersection is also provided, which simplifies the complexity of determining the collision risk between the RSs and facilitates the convexification process. Further, another collision constraint is provided to ensure that the spacecraft has no collision risk with each other at the present time. Based on the two collision constraints and sequential convex programming (SCP), an RS-based trajectory optimal algorithm is proposed for generating collision-free and fuel-effective trajectories, which not only ensures collision avoidance between the discrete time points, but also avoids unnecessary collision avoidance maneuvers. Finally, the effectiveness of the proposed method is confirmed by the numerical simulations.