A Pontryagin-based NMPC approach for autonomous rendez-vous proximity operations

This paper proposes a Pontryagin-based approach to Nonlinear Model Predictive Control for autonomous guidance and control in spacecraft maneuvering. The proposed approach guarantees, under suitable conditions, an explicit control law also in presence of nonlinearities. Taking advantage of the Pontryagin Minimum (or Maximum) Principle, the optimization problem solution turns into a two-points boundary value problem, whose differential equations and boundary conditions are the Karush-Kuhn-Tucker necessary conditions of optimality. Conversely to the numerical methods for nonlinear/non-convex optimization, the proposed methodology returns an explicit control law without any a-priori assumption about the input signal parametrization, achieving high performances without increasing the computational complexity of the algorithm. The proposed control algorithm is designed for the proximity operations of a rendez-vous problem which dynamics is described by the so-called Clohessy-Wiltshire equations. A modified NMPC cost function is employed in order to promote the bang-bang behavior of the input signal. This latter yields an improvement of the performances in terms of propellant consumption with respect to the classic quadratic cost indexes.