Robust trajectory optimization for highly constrained rendezvous and proximity operations

Rapid and reliable generation of highly constrained, optimal finite-thrust trajectories for rendezvous and proximity operations (RPOs) on an arbitrary orbit is the objective of this paper. The problem is treated in a realistic setting where non-Newtonian gravity (J₂ harmonics) and aerodynamic drag are included and the engine thrust relatively is low with finite burn times. In addition, representative RPO constraints on acquisition of dockingaxis point, approach corridor, relative velocity, and plume impingement inhibition are all imposed. Further constraints on keep-out zone for proximity trajectory and the rate of changes of the thrust vector are also enforced. The non-convex keep-out zone constraint is handled by a globally convergent successive linearization method. The resulting nonlinear optimal control problem is transformed into a sequence of second-order cone programming (SOCP) problems after using a lossless relaxation technique. A state-of-the-art primal-dual interior-point algorithm is employed to ensure the solutions to the SOCP problems.