Abstract: This article presents a direct collocation mixed integer linear programming (DCMILP) method for energy-optimal trajectory planning of satellite formation reconfiguration. First, the formation flying problem is simplified to that of linear formulation. Second, the three-order Simpson method is extended to the formation reconfiguration problem, and the state and control variables are discretized at the nodes. Then, by means of the objective function, collision avoidance and other constraints, the formation reconfiguration problem is transformed into a problem of mixed integer linear programming so as to find a global optimal solution to this non-convex optimization problem. Finally, the three-dimension and two-dimension simulation results demonstrate that this method is able to solve the problem in a short time and that it can be used as an on-line algorithm of trajectory planning for formation reconfiguration.

Key words: formation reconfiguration, collision avoidance, direct collocation method, mixed integer linear programming, non-convex optimization