Inscribed Polygon Method for Spacecraft Maneuvering Problem Arising in Single Axis Thruster Configuration

This paper addresses the guidance & control problem of a single axis thruster configured spacecraft. The relative motion dynamics has been addressed with a Linear Time Varying (LTV) model. The autonomous control algorithms are particularly challenging due to the fact that crucial geometrical and physical constraints are coupled with the translational motion of the space vehicle, resulting in a complex motion planning problem. Particularly, single axis thruster poses quadratic constraints. Hence, a distinctive feature of the proposed approach is the Inscribed Polygon Approximation (IPA) where Quadratically Constrained Quadratic Programming (QCQP) problem is converted into a Quadratic Programming (QP) problem within the Model Predictive Control (MPC) framework. The algorithm can address the three-body maneuver problem in both circular and elliptic orbits by employing Clohessy-Wiltshire (CW) and Yamanaka-Ankersen (Y-A) relative motion dynamic equations. In addition, it is aimed to trace a fuel-optimal trajectory while ensuring safety with an explicit formulation of line-of-sight (LOS) constraints. Finally, the proposed strategy is compared with directly solving the QCQP problem as well as Taylor-Series linearization method.