Multiple spacecraft formation reconfiguration planning with nonconvex collision avoidance constraints

A convexification method originating from second order cone programming is applied to multiple satellites formation reconfiguration problems with concave collision avoidance constraints. Geometric relative orbit elements are introduced to straightforward depict formation configurations. Algorithm consists of external convexification iterations and the Gauss pseudospectral method is presented for coping with nonconvex transfer trajectories planning. Numerical examples are implemented for validating the proposed approach, and contrast simulations separately with spherical and rectangular approximations of concave inequality constraints are carried out, results indicate a manifestly improvement in energy optimization with the algorithm presented here.