Hierarchical Guidance for Spacecraft Proximity via Iterative State Transitions

In this article, we propose a hierarchical guidance framework for spacecraft proximity tasks subject to motion and path constraints by integrating artificial potential functions and optimization methods. The overall guidance methodology consists of two main steps: 1) iterative generation of trajectory points and 2) state transition between every consecutive pair of those points. An artificial potential function incorporating the constraints is proposed in the form of a barrier function, based on which the trajectory points are then generated by iteratively approaching the target through a quasi-Newton method. The state transition guidance, instead, is formulated as a constrained optimal control problem aiming at minimizing the energy consumption while incorporating system dynamics and motion and path constraints. We show that the latter can be turned into a convex optimization problem using the system flatness and the B-spline parameterization, thus alleviating the required computational burden. The contribution of the proposed guidance and control method consists of two aspects: 1) providing a framework to fulfill performance optimization for the conventional artificial potential function methods and 2) reducing the computational burden compared to a standard model-predictive control method. Extensive numerical simulations confirm this fact, along with showing the effectiveness of our method to guarantee safe and fast spacecraft proximity maneuvers.