A Model Predictive Control Technique with Guaranteed Resolvability and Required Thruster Silent Times for Small-Body Proximity Operations

The guidance and control algorithms for enabling spacecraft proximity operations about small celestial bodies are developed by using a model predictive control approach. Separate feedforward and feedback components are utilized. The feedforward, or open-loop, guid-ance is based on a pseudo way-point generation algorithm that uses a discrete linear-time-varying model of the dynamics that incorporates required thruster silent times. This leads to a convex formulation of the open-loop trajectory generation problem with control and state constraints. Particularly, the pseudo way-points are generated through the solution of a second-order cone programming problem (a subclass of semi-definite programming), and there are interior point methods to compute the global optimum with a deterministic stopping criteria and a prescribed level of accuracy. Feedback control is implemented to track the pseudo way-point trajectories in a manner that guarantees the resolvability for the open-loop problem, enabling the ability to update the guidance profile in a robust, model-predictive manner. The robust guidance and control algorithm with resolvability is demonstrated in the simulation of a spacecraft landing onto a small asteroid possessing a significant gravity field; incorporating a gravity model into the algorithm provides notable improvements in controller performance. I