Fuel Optimization for Continuous-Thrust Orbital Rendezvous with Collision Avoidance Constraint

This paper focuses on the issue of minimum-fuel rendezvous between an active chaser satellite with continuous-thrust capability and a passive target satellite. It is first formalized as an optimal control problem subject to a collision-avoidance constraint on the path of the chaser satellite. Then, a new method for dealing with this state constraint is built by adapting to the optimal control framework a recently developed approach for solving inequality-constrained nonlinear programming problems. The resulting method implies solving a sequence of unconstrained optimal control problems, the solutions of which converge toward the solution of the original problem. Convergence of the method is proved, and its efficiency is demonstrated through numerical results obtained in the case of a rendezvous in a highly elliptical orbit.