Robust rendez-vous planning using the scenario approach and differential flatness

There is a growing interest in uncertainty handling in the spacecraft dynamics community. In particular, robust optimization of spacecraft maneuvers is regarded as an important challenge. This paper proposes an optimal control approach for orbital rendez-vous planning under stochastic dynamics and constraints. The method combines differential flatness theory with the scenario approach for optimization under uncertainties. By mapping state and control variables into a set of flat outputs, the enforcement of dynamics equations and boundary conditions is automatically satisfied. The rigorous foundations of the scenario approach lead to a finite-dimensional formulation of the problem which guarantees the feasibility of the solution within an arbitrary portion of the stochastic domain. The methodology is illustrated by means of two case studies involving a rendez-vous in elliptic orbit and a propellantless maneuver using differential drag, respectively.