Discretization of collision avoidance constraints by expanding in cubic splines

We propose a general formulation for path-planning with collision avoidance for spacecraft. The formulation represents the spacecraft as cubes, and seeks fuel optimality for a given arrival time. We identify a general structure of the no-collision constraints where every constraint is a logical disjunction of the subconstraints. A mixed-integer-linear program is then proposed for its solution. Cubic splines are used for time-discretization of the constraints, the dynamics and the objective function