A Pontryagin-based Nonlinear Model Predictive Control for Spacecraft Rendezvous in Lunar Orbit with Obstacle Avoidance

A Nonlinear Model Predictive Control approach to spacecraft rendezvous in non-Keplerian Lunar orbits is proposed. The approach is based on the Pontryagin Minimum Principle and allows the accomplishment of minimum-propellant maneuvers. The relative motion between the chaser and the target is described by the nonlinear and unstable dynamics of the circular restricted three body-problem. The discussed methodology provides a high degree of autonomy of the control system, merging into a unique algorithm the chaser trajectory planning and control in presence of nonlinear and non-convex state constraints. In the proposed formulation, the employment of a minimum-propellant controller leads to a bang-bang behavior of the control signal. Moreover, under suitable assumptions, simplified dynamics is employed as prediction model, in order to reduce the complexity of the controller algorithm but, at the same time, without penalizing the controller tracking performance. A simulation example is provided to validate the approach. The scenario chosen for the simulation consists of the Artemis III mission where the docking of the Orion spacecraft to the Gateway station is planned.