Minimizing the Effects of Navigation Uncertainties on the Spacecraft Rendezvous Precision

Overview & Synopsis

The ability to robustly and precisely control the spacecraft relative motion will play an important role in future on-orbit inspection and on-orbit servicing missions. Model predictive control (MPC) is considered to be an effective control strategy for these types of spacecraft operations, which can easily handle mission specificconstraintswhileexplicitlyminimizingthefuelconsumption. The maneuvers plan is obtained by solving a finite horizon open- loop optimal control problem starting from the spacecraft relative state, and the optimal solution consists of a series of control actions out of which only the first one is executed. Some ideas from tube-basedMPCare used in this Note to solve the robust fixed-time spacecraft rendezvous problem for eccentric reference orbits. The purpose is to obtain a sequence of feedback policies that steers the spacecraft from an initial relative state toward an ellipsoidal set centered around a desired final state, in the presence of navigation uncertainties. This must be done while respecting the actuators saturation constraints and while pursuing a double objective: minimize the fuel cost of the mission and minimize the size of the arrival set to guarantee a good rendezvous precision. The control policies are restricted to affine disturbance feedback policies to ensure a convex formulation of the control synthesis problem. The obtained sequence of feedback policies drives the system to the guaranteed arrival set without any need for recurrent optimization.