Collision avoidance in low thrust rendezvous guidance using flatness and positive B-splines

Collision avoidance issue in close proximity orbital rendezvous is addressed in this paper. The arising optimal control problem is solved by means of differential flatness in order to apply algebraic geometry tools. These tools based on B-splines parametrization and positive piecewise polynomial concept provide a certification of constraints satisfaction continuously in time contrary to classical collocation techniques. The non convexity derived from the avoidance constraint is overcome by using time-varying convex approximation.