Collision-Avoiding Model Predictive Rendezvous Strategy to Tumbling Launcher Stages

This paper considers the situation where a small satellite shall autonomously rendezvous with a tumbling object in a circular low Earth orbit (LEO) and derives a path-based model predictive controller that uses the docking point state and position of the chaser to guide it to a safe docking autonomously. The strategy embeds collision avoidance elements and reduces the computational effort for calculating the pulses to be provided by the thrusters through opportune algebraic manipulations, a Runge-Kutta 4 propagation method using linearized state transition matrices, and implicit embedding of dynamically equivalent thrust models, leading to constant state propagation matrices. Furthermore, the inputs design optimization problem and the embedded collision avoidance scheme are modeled and explicitly crafted as convex problems, contributing positively to low computational requirements. The docking and collision avoidance capabilities of the proposed scheme are extensively tested in an environment that accounts for all the perturbations relevant to LEO frameworks, for realistic thrust schemes, and for uncertainties in the measurement. Numerical results assess which tumbling objects can be docked or not by means of the proposed schemes as a function of the tumbling rates versus the thrust capabilities and hardware uncertainty of the docker.